Short-term system scale demand forecasting for a modernized irrigation system using real-time flow data and numerical weather predictions

Transcription

1 Title Short-term system scale demand forecasting for a modernized irrigation system using real-time flow data and numerical weather predictions Kushan Chanaka Perera Submitted in total fulfilment of the requirements of the degree of Doctor of Philosophy December, 2015 Department of Infrastructure Engineering The University of Melbourne Produced on archival quality paper

2 Summary

3 Summary Summary Significant travel times and variations in irrigation demand in response to weather variations and other factors make short-term system scale irrigation distribution operation decisions challenging. Currently, major irrigation system modernization projects are being implemented to address these operational issues and state-of-art automation technologies have been developed to fully automate the irrigation distribution systems. These systems assist to plan smooth irrigation distribution operation in turn and increase delivery efficiency as well as improve level of service. A remaining challenge is that while the system automates water control in the distribution canals, bulk delivery of water to the command area still needs to be planned, as it is subject to substantial travel time delays. Short-term irrigation demand forecasting has the potential to assist in system operation, but has often been constrained by limited information on both current demand levels and likely future weather. This research aims to capitalize on the opportunity presented by detailed real-time flow data now available from fully automated open channel delivery systems and short-term weather forecasts derived from improved numerical weather prediction (NWP) systems to develop and evaluate a method to make real-time probabilistic short-term system scale irrigation demand forecasts. These forecasts are developed in and applied to a command area with four main irrigation channels in the Central Goulburn Irrigation District (CGID), Northern Victoria, Australia, which was been modernized and automated as part of the Northern Victorian Irrigation Renewal Program (NVIRP) in The thesis builds on four modelling experiments that are linked to each other and results in development of a reliable short-term system scale irrigation demand forecasting system. The first experiment compares hourly reference evapotranspiration (ET O) equations for use in estimating daily ET O. The second develops and evaluates a method to forecast short-term daily ET O using the Australian operational NWP system. The predictive performance is evaluated against observation data from 40 automatic weather stations across the Australian continent. The third experiment develops a deterministic model to forecast short-term system scale irrigation demand for a command area, coupling the real-time irrigation flow data and observed precipitation and ET O. The fourth experiment links all three previous experiments to develop ensemble forecasts of short-term system scale irrigation demand for a command area, including estimating forecast uncertainty. The estimation performance of daily ET O calculated using the FAO Penman-Monteith (FAO- PM) and the standardized ASCE Penman-Monteith (ASCE-PM) hourly ET O equations was compared against daily ET O calculated using the corresponding daily ET O equation. It examines the variations in daily ET O estimates, in terms of different methods of estimating clear-sky-radiation, different methods of aggregating hourly ET O into daily ET O and the impact of seasonality and climate type. The average ratio between daily ET O calculated using the hourly and daily equations for i

4 Summary the FAO-PM and ASCE-PM versions were 0.95 and 1.00, respectively. It was concluded that the best agreement for the FAO-PM version was found in temperate climates and for winter, spring and autumn; whereas the ASCE-PM version best agrees in tropical and arid climates during summer. Daily ET O was forecast using outputs from the Bureau of Meteorology's operational NWP forecasts derived from the Australian Community Climate and Earth System Simulator - Global (ACCESS-G). Daily ET O forecasts for lead times up to nine days were compared against observed daily ET O. NWP forecast daily ET O was better than using the long-term monthly mean ET O for up to six lead days and the average MSSS for ET O forecasts across all stations varied between 66% and 12% for lead times of one to six days. The forecast performance for daily ET O was highest in autumn for tropical climates and lowest in spring for temperate climates. The results show that the largest source of forecast error for daily ET O was incoming solar radiation, followed by air temperature, dew point temperature and wind speed for all lead times. To forecast irrigation demand at a command area scale, I developed a multivariate time series (ARMAX) model which was applied to aggregated service points flows (ID CG i, ASP) and off take regulator flows (ID CG i, OTR). It was fitted to four irrigation channels plus the sum of the four channels in the CGID. These command area specific ARMAX models forecast 1-5 days lead time daily ID CG i, ASP and ID CG i, OTR using the real-time flow data and observed meteorological data. During evaluation, the NSE for ID CG i, ASP and ID CG i, OTR across five command ranged between 0.78 and These models generated skillful forecasts (MSSS 0.5 and ACC 0.6) of ID CG i, ASP and ID CG i, OTR for all five lead days. Finally, I developed a method for real-time ensemble forecasting of irrigation demand applicable under operational conditions and applied it to irrigation command areas of various sizes for lead times of 1-5 days. The ensemble forecasts are based on a deterministic time series model coupled with ensemble representations of past flow, precipitation and ET O, and forecast precipitation and ET O. NSE values for evaluation periods ranged between 0.96 (one lead day, whole study area) and 0.42 (five lead days, smallest command area). Rank histograms and other ensemble verification scores indicated that the ensemble spread is generally a reliable representation of the forecast uncertainty for short lead times but underestimates the uncertainty for longer lead times. The deterministic and real-time probabilistic irrigation demand forecasts derived from this research were better than almost all the previous studies I am aware of. The proposed model is applicable to different temporal and spatial scales and reflects short-term dynamic changes in the irrigation demand resulting from the various pressures and opportunities that farmers face. These real-time probabilistic irrigation demand forecasts could support decision making by the system operators and mitigate the risk associated with their irrigation distribution decisions. ii

5 Declaration Declaration This is to certify that: i. The thesis includes only my original work towards the PhD, ii. Due acknowledgement has been made in the text to all other material or work used, iii. The thesis is fewer than words in length, exclusive of tables, maps, bibliographies and appendices Kushan Chanaka Perera December, 2015 iii

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7 Preface Preface This thesis presents the research carried out during my PhD candidature ( ) in the Department of Infrastructure Engineering, The University of Melbourne. All the numerical modelling experiments were conducted using the high-level language called MATLAB. The observed irrigation flow data used in this thesis, including the regulators and meter outlets gauged were provided by Goulburn-Murray Water (GMW). The climate data, including the hourly observed weather data and numerical weather prediction (NWP) model outputs were provided by the Bureau of Meteorology, Australia. This thesis comprises only my original work towards the PhD and the material included here has not been submitted for any other qualification. It contains published work and/or work prepared for publication; all of them have been co-authored. The bibliographical details of the work and where it appears in the thesis are outlined below. Chapter 4 has previously been published as: Perera, K. C., Western, A. W., Nawarathna, B., George, B., 2015, Comparison of hourly and daily reference crop evapotranspiration equations across seasons and climate zones in Australia, Agriculture Water Management, Volume 148, Page Chapter 5 has previously been published as: Perera, K. C., Western, A. W., Nawarathna, B., George, B., 2014., Forecasting daily reference evapotranspiration for Australia using numerical weather prediction outputs, Agricultural and Forest Meteorology, Volume 194, Page , and Perera, K. C., Western, A. W., Nawarathna, B., George, B., Forecasting Daily Reference Evapotranspiration for Shepparton, Victoria, Australia using Numerical Weather Prediction outputs, MODSIM 2013, 20 th International Congress on Modelling and Simulation, Modelling and Simulation Society of Australia and New Zealand, December 2013, and Page The actual content of the chapter is from the Agricultural and Forest Meteorology paper. Chapter 6 has previously been published as: Perera, K. C., Western, A. W., George, B., Nawarathna, B., 2015., Multivariate time series modelling of short-term system scale irrigation demand, Journal of Hydrology, Volume 531, Part 3, Page Chapter 7 is adapted from a paper in press in Water Resources Research title as Ensemble forecasting of short-term system scale irrigation demands using real- time flow data and numerical weather predictions. v

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9 Acknowledgement Acknowledgement First and foremost I want to thank my principal supervisor, Prof Andrew Western for his generosity of intelligence, endless guidance and support throughout the candidature. I am privileged to have had the opportunity to carry out my PhD research project under Andrew. His expertise in the field of Water Resource and constructive comments helped me to conquer difficult obstacles during the candidature. I also wish to express profound respect to my co-supervisors Dr Bandara Nawarathna and Dr Biju George for their constructive suggestions and guidance in improving this research. This work would not have been possible without the interest of the Goulburn-Murray Water (GMW) and the Bureau of Meteorology, Australia, who provided the data free of charge for research purposes. I wish to express my sincerer gratitude to Goulburn-Murray Water, Australia for providing irrigation flow data and the Bureau of Meteorology, Australia for providing NWP forecasts derived from ACCESS-G. I gratefully acknowledge Dr Mark Baily, Mr Mick Doherty and Mr John Weber, Goulburn-Murray Water, Australia and Dr Alan Seed and Dr Shaun Cooper, the Bureau of Meteorology, Australia for their enthusiastic support, especially in providing and explaining the data used. I am indebted to all staff and colleagues in the Department of Infrastructure Engineering, the University of Melbourne. I owe special gratitude to the chair of my advisory committee, Prof Hector Malano for his constructive and insightful suggestions on the PhD research project and the financial support offered through tutorial and other research opportunities during my tenure. I would also like to thank Dr Dongryeol Ryu, Dr Chun-Hsu Su, Dr Murray Peel, Dr Justin Costello, Dr Tim Peterson, and Ms Pauline Woolcock and all colleagues in the water group of the Department of Infrastructure Engineering, who helped me in various ways and means. I gratefully acknowledge support from the University of Melbourne in the form of the Australian Post-Graduate Award and also the Department in Infrastructure Engineering, Melbourne School of Engineering for travel sponsorships. I am deeply grateful to my parents, Mr Ranjith L Perera and Mrs Nanda S Gunarathna as well as my grandparents for teaching me the value of education. They sacrificed the best times of their lives for my education. I would not have come this far without their support and I sincerely dedicate this thesis to them. I extend deep gratitude to my wife, Nadeesha Hemachandra, and daughter Anuki Ayansa for their love, support, patience and understanding during the course of the PhD candidature. Finally, I would like to thank all the people whom I might have missed mentioning, but who helped me during my PhD sojourn. vii

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11 Table of content Table of Content Summary... i Declaration... iii Preface... v Acknowledgement... vii Table of Content... ix List of Figures... xv List of Tables... xix Chapter 1 Background, context & problem statement Introduction Statement of the problem Research questions Research objectives Thesis structure... 9 Chapter 2 Short-term system scale irrigation demand forecasting modelling frameworks Introduction Theoretical background of irrigation demand Crop water requirement (CWR) Biophysical irrigation water requirement Behavioural factors Irrigation demand Early irrigation demand modeling Irrigation demand forecasting models Process-based irrigation forecasting modeling frameworks ix

12 Table of content Data-driven irrigation demand forecasting modeling frameworks Knowledge gaps and research gaps Chapter 3 Conceptual framework and study area Introduction Conceptual framework Justification of the research questions Study areas and data Central Goulburn Irrigation District (CGID) Data sources Irrigation flow data Numerical weather predictions Observed climatic data from automatic weather stations Chapter 4 Comparison of hourly and daily reference crop evapotranspiration equations across seasons and climate zones in Australia Abstract Introduction Materials Study area Climate data Methodology Data processing ET O equations FAO-PM equation ASCE standardized PM equation Calculating ET O Assessing the agreement x

13 Table of content 4.5 Results and discussion Impact of R so calculation method Comparison of hourly and daily models Seasonal impact for the ET O, soh vs. ET O, daily values Comparison of 24 hour and day-time aggregations Comparison of hourly ET O equations Climatological impacts on the relationship between ET O, soh vs. ET O, daily Summary and conclusion Chapter 5 Forecasting daily reference evapotranspiration for Australia using numerical weather prediction outputs Abstract Introduction Materials Study Sites Data sources Weather forecast from ACCESS numerical weather prediction systems Observed climatic data from automatic weather stations Methodology Data pre-processing Calculating ET O Assessing forecast accuracy Results Forecast performance for weather variables Air temperature Dew point temperature Wind speed Radiation xi

14 Table of content Summary Forecasting performance for ET O Seasonality in ET O forecast performance Spatial analysis Impact of weather variable forecasts on daily ET O forecasts Discussion Summary and conclusions Chapter 6 Multivariate time series modelling of short-term system scale irrigation demand Abstract Introduction Methodology ARMAX model structure Exogenous variables Data transformation Parameter estimation Evaluation methods Cross validation Study area and data Study area Data sources and pre-processing Irrigation flow data Exogenous variables Results Time series characteristics Irrigation flows Exogenous variables xii

15 Table of content Model calibration Objective functions Weather station selection Calibration Model evaluation Discussion Summary and conclusion Supplementary materials Chapter 7 Ensemble forecasting of short-term system scale irrigation demands using real-time flow data and numerical weather predictions Abstract Introduction Study area and data Study area Data sources and pre-processing Irrigation flow data Observed climate data Weather forecasts Methodology Deterministic model and its calibration Deterministic model structure Deterministic model calibration Ensemble generation Real-time flow data Observed weather variables Precipitation Reference evapotranspiration (ET O) Forecast weather variables xiii

16 Table of content Evaluation methods Results Precipitation and ET O forecast uncertainties Ensemble demand forecasts for the model calibration period Real-time forecasting with numerical weather prediction outputs Discussion Conclusion Supplementary materials Chapter 8 Summary and conclusion Conclusive summary Key advances Integrating biophysical, behaviour and supply factors Multivariate time Series approach Improvement on irrigation demand forecasting Uncertainties in irrigation demand forecasts Limitations and further research Key contributions made by the thesis Recommendations Conclusion Bibliography xiv

17 List of figures List of Figures Figure 2.1 A Schematic diagram representing irrigation demand resulting from biophysical, behavioural and supply factors at the system scale Figure 3.1 Conceptual framework Figure 3.2 Study area - Central Goulburn channel 1, 2, 3, and 4 [Perera et al., 2015a] Figure 3.3 Spatial resolution of ACCESS models [BoM, 2010] Figure 4.1 Locations of the automatic weather stations fall under Köppen climate map [Peel et al., 2007] Figure 4.2 Calculated daily ET O as indicated by (a) ET O, soh, FAO and ET O, daily, FAO using R so simple, (b) ET O, soh, ASCE and ET O, daily, ASCE using R so complex, (c) ET O, soh, FAO and ET O, daily, FAO using R so simple, (d) ET O, soh, ASCE and ET O, daily, ASCE using R so complex for Shepparton irrigation areas, Victoria Figure 4.3 Annual and seasonal performance between ET O, soh and ET O, daily for FAO-PM and ASCE-PM versions as indicated by (a) RMSD, (b) ratio (ET O, soh / ET O, daily ), (c) regression slope and (d) R 2 for 40 AWS locations. Each box shows the lower (25 th ), middle (50 th ) and upper (75 th ) quartile and the bottom and top whiskers represent the 5 th and 95 th percentiles Figure 4.4 (a) Hourly ET O (b) Hourly energy (c) Bulk resistance and (d) Aerodynamic resistance for a warm day in the summer and a cold day in winter, calculated using hourly FAO-PM and ASCE- PM ET O equations at Shepparton airport AWS, Victoria Figure 4.5 Box plots for all AWS as indicated by the daily ratio between ET O, soh and ET O, daily (a) FAO-PM and (b) ASCE-PM equations. Each box shows the lower (25 th ), middle (50 th ) and upper (75 th ) quartile and the bottom and top whiskers represent the 5 th and 95 th percentiles Figure 4.6 Summary of mean and standard deviation for sub-climate zones of the daily ET O between the daily and hourly ET O FAO-PM and ASCE-PM equations Figure 5.1 Seasonal variation of ET O in Shepparton irrigation area Figure 5.2 Forecast performance for forecasted vs. observed daily maximum air temperature as indicated by (a) RMSE, (b) R 2, (c) ACC and (d) MSSS and forecasted vs. observed daily minimum air temperature as indicated by (e) RMSE, (f) R 2, (g) ACC and (h) MSSS for 40 AWS locations 78 xv

18 List of figures Figure 5.3 Forecast performance as indicated by (a) RMSE, (b) R 2, (c) ACC and (d) MSSS of forecasted vs. observed daily mean dew point temperature for 40 AWS locations Figure 5.4 Forecast performance as indicated by (a) RMSE, (b) R 2, (c) ACC and (d) MSSS of forecasted vs. observed daily mean wind speed for 40 AWS locations Figure 5.5 Forecast performance as indicated by (a) RMSE, (b) R 2, (c) ACC and (d) MSSS of forecasted vs. observed daily incoming solar radiation for 40 AWS locations Figure 5.6 Daily ET O forecasted (NWP forecasts driven from ACCESS-G) vs. observed at the Shepparton airport: (a) One lead day, (b) Three lead days, (c) Five lead days and (d) Seven lead days Figure 5.7 Forecast performance as indicated by (a) RMSE, (b) R 2, (c) ACC and (d) MSSS of forecasted vs. observed daily ET O for 40 AWS locations Figure 5.8 Average forecast performance across all 40 stations as indicated by (a) RMSE, (b) R 2, (c) ACC and (d) MSSS of forecasted vs. observed daily ET O Figure 5.9 Forecast performance as indicated by MSSS for nine Köppen climate classifications Figure 5.10 Average MSSS of estimated and forecasted daily ET O by swapping observed variable one at a time Figure 5.11 Forecast and measurement uncertainties for (a) Maximum temperature, (b) Mean dew point temperature, (c) Wind speed and (d) Incoming solar radiation for 40 AWS locations Figure 5.12 Accuracy of R S estimation as indicated by (a) Time series and (b) Scatter plot between satellite data driven R S and ground based observed R S for at Mildura Airport Figure 5.13 Average improvement gained in MSSS values during the bias correction for daily ET O forecast AWS locations Figure 6.1 Schematic diagram for a simple soil water bucket model Figure 6.2 Annual and seasonal variation of ID CG 1234, ASP for the study area. Each box plot represents the lower (25 th ), middle (50 th ) and upper (75 th ) percentile and the bottom and top whiskers represent 5 th and 95 th percentiles respectively xvi

19 List of figures Figure 6.3 Sample ACF and PACF for ID CG 1234, ASP for study area as indicated by transformation method Figure 6.4 CCF between daily ID CG1234, ASP and 8 potential exogenous variables using the data transformation method. A positive time lag indicates the exogenous variable leading flow. Data for T max, T mean, R s, wind speed and dew point temperature are for Shepparton airport (81125). The rainfall is the mean of Tatura Sustainable Agency (81049), Tatura Thiess (81114) and Murchison (81035) sites, which was the combination producing the highest cross-correlation at lag 1. The optimal parameter values (γ and S max ) for the WSD were taken from the optimized model Figure 6.5 Calibration performance for Daily ID CGi, ASP forecast vs. observed for CG 1, 2, 3, 4 and the study area: (a) One lead day, (b) Three lead days and (c) Five lead days for the calibration period 2006/ / Figure 6.6 Daily ID CGi, ASP forecast vs. observed for CG 1, 2, 3, 4 and the study area for lead time one, three, and five days Figure 6.7 Daily ID CGi, ASP forecast vs. observed for CG 1, 2, 3, 4 and the study area: (a) One, (b) Three and (c) Five lead days respectively Figure 6.8 Scatter plots between model residual vs, observed ID CG i, ASP and the respective residual histograms for lead times of one, three, and five for CG 1 (top row) and CG 1234 (bottom row) command areas Figure 6.9 Seasonal predictive performance for command area CG 1234 as indicated by (a) RMSE, (b) NSE, (c) ACC and (d) MSSS of forecasted vs. observed daily irrigation demand Figure 6.10 Scatter plots, (a) Number of service outlets vs. NSE (b) Standard deviation of demands vs. NSE for the evaluation period Figure 7.1 The schematic diagram of the ensemble forecast approach Figure 7.2 Time series plot (91 days) of observed daily precipitation vs. post process ensemble precipitation forecast and respective rank histograms (551 days) for lead times of one, three and five days Figure 7.3 The scatter plot (551 days) between the deterministic daily ET O forecast and forecast error, time series plot (241 days) of observed daily ET O vs. ensemble daily ET O forecast with spread between 10 th and 90 th percentile and respective rank histograms (551 days) for lead times of one, three and five days xvii

20 List of figures Figure 7.4 Time series plot of observed vs. ensemble daily ID CG 1234, ASP forecasts with the ensemble spread between 10 th and 90 th percentile for lead times of one, three and five days for irrigation year (274 days - validation scenario one in the Table 7.5) Figure 7.5 Rank histograms for observed and ensemble daily ID CG 1234, ASP forecasts for lead times of one, three and five days for irrigation years to (274 days - validation scenario one in the Table 7.5) Figure 7.6 Time series plot of observed vs. ensemble daily ID CG 1234, ASP forecasts with the ensemble spread between 10 th and 90 th percentile for lead times of one, three and five days for irrigation year to (275 days) Figure 7.7 Rank histograms for observed and ensemble daily ID CG 1234, ASP forecasts for lead times of one, three and five days during irrigation year to (275 days) Figure 7.8 Rank histograms (A) Excluding irrigation flow uncertainties (B) Excluding observed weather uncertainties and (C) Including irrigation flow and observed and forecast weather uncertainties, for observed and ensemble daily ID CG 1234, ASP forecasts for lead times of 1, 3 and 5 days during the evaluation period to (275 days) xviii

21 List of tables List of Tables Table 2.1 Summary of process-based irrigation demand forecast models Table 2.2 Summary of data-driven irrigation demand forecast models Table 3.1 Characteristics of CG 1-4 channels Table 3.2 Type of NWP models and resolution in Australia [BoM, 2010] Table 4.1 Characteristics of automatic weather stations (sorted as per Köppen climate zone) Table 4.2 Description of Köppen climate symbols and defining criteria for the climate zone in the study [Peel et al., 2007] Table 4.3 Measurement range and accuracy of climate variables from AWS [BoM, undated-b] 47 Table 4.4 Values for C n and C d Table 4.5 Summary of statistical indices for daily ET O calculated using R so simple and complex procedure Table 4.6 Statistical indicators corresponds to daily ET O calculated between the hourly and daily ET O equations of FAO-PM and ASCE-PM versions for 40 AWS stations Table 4.7 Summary of statistical indices for daily ET O calculated based on day light hour and sumof-hour using hourly ET O equations for winter Table 4.8 Statistical indicators of the daily ET O calculated using the FAO-PM and ASCE-PM hourly ET O equations Table 5.1 Statistical indices of forecast vs. observed ET O for all AWS stations Table 6.1 Characteristics of automatic weather stations and rain gauges Table 6.2 Model performance for different objective functions for calibration period from 2006/07 to 2010/ Table 6.3 Best performing precipitation combinations for each command area Table 6.4 Parameters range and average calibration performance for six split calibration scenarios for four channels and study area for ID CGi, ASP xix

22 List of tables Table 6.5 Average statistical indicators for all six evaluation periods related to the ID CG i, ASP for four channels and study area Table 6.6 ARMAX model error characteristics ID CG i, ASP during evaluation period 2011/ Table 6.7 Parameters and calibration performance for six split calibration scenarios related to the ID CG i, ASP for four channels and study area Table 6.8 Evaluation performance for six split evaluation scenarios related to the ID CG i, ASP for four channels and study Table 7.1 Perturbation methods for ET O related weather variables (daily mean temperatures ensembles T mean, ens, daily mean dew point temperatures ensembles Dewpt mean, ens, daily mean wind speed ensembles Wndspd mean, ens and daily solar radiation ensembles Srad ens) Table 7.2 Statistical indicators related to prediction performance for ensemble precipitation and ET O forecasts for study area between to and to (551 days). The range shown in brackets is the 5 th -95 th confidence interval from the bootstrapping analysis Table 7.3 Average forecast performance for ensemble daily ID CG i, ASP forecasts related to the 2 cross validation scenarios for 4 channels and study area during the last year of calibration periods ( (274 days) or (275 days)). The range shown in brackets is the 5 th -95 th from the bootstrapping Table 7.4 Average forecast performance for ensemble daily ID CG i, ASP forecasts related to the 2 cross validation scenarios for 4 channels and study area during the evaluation periods ( (274 days) or (275 days)). The range shown in brackets is the 5 th -95 th from the bootstrapping Table 7.5 Forecast performance for ensemble daily ID CG i, ASP forecasts related to the 2 cross validation scenarios for 4 channels and study area during the calibration periods ( (274 days) or (275 days)). The range shown in brackets is the 5 th - 95 th from the bootstrapping Table 7.6 Forecast performance for ensemble daily ID CG i, ASP forecasts related to the 2 cross evaluation scenarios for 4 channels and study area during the evaluation periods ( (274 days) or (275 days)). The range shown in brackets is the 5 th - 95 th from the bootstrapping xx

23 Chapter 1 Introduction Chapter 1 Background, context & problem statement 1

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25 Chapter 1 Introduction 1.1 Introduction The world s population has doubled since the late 1970 s and exceeded seven billion people during the year 2011 [FAO-UN, 2012]. Although, the population growth rate is slowing, increases in population are likely to continue until the end of the 21 st century, due to declining mortality rates, prolonged life expectancy and age structures [FAO-UN, 2013]. To meet the growing demand for food, the world s agricultural production has grown on average between 2-4% per year. According to the Food and Agricultural Organization - FAO, about 12% of the global land surface or more than 1.5 billion hectares, are used for crop production at present. The scope for further expansion of agricultural lands is limited, because the remaining lands with potential for agriculture are forested, protected for environmental reasons, or employed for urban settlements. Furthermore, there are few available fresh water resources to support expansion of agriculture. The pressure for further expansion of the agricultural lands can be reduced to some extend by increasing the productivity of existing agricultural land. Globally, most agriculture is rain-fed and climate variability substantially limits productivity [FAO-UN, 2012; FAO-UN, 2013]. Climate change also has the potential to increase climate variability and limit the productivity of rain-fed agriculture [Lebel, 2007]. Where agricultural production is water limited, irrigated agriculture has significantly boosted productivity for millennia, with major increases since the 1970 s [Cech, 2009]. Irrigation currently consumes about 70% of global fresh water withdrawals, compared to 20% for industry and 10% for domestic use [FAO-UN, 2012; Khan and Abbas, 2007]. Fresh water withdrawal has tripled over the last fifty years [Rasmussen, 2011]. The water use efficiency of most irrigation systems across the world is currently far below the potential. Over the last few decades, substantial efforts have been made to enhance land water use efficiency using three types of interventions; rehabilitation, modernization and process improvement [Renault, 1999]. The first two require radical improvement in the physical infrastructure and large capital investment compared with process improvement methods. Irrigation demand forecasting is one process improvement that could be used to improve system operation efficiency. Irrigation demand can be forecast for a paddock, distribution system or irrigation district and for a range of lead times varying from a few hours to a whole irrigation season or year. Short-term irrigation demand forecasts at the field scale facilitate irrigation scheduling [Ejieji and Gowing, 2000; Gowing and Ejieji, 2001; Graham and Harris, 2003; Rao et al., 1988; Rao et al., 1992; Rhenals and Bras, 1981] and hence minimize runoff and percolation losses while maintaining production [English et al., 2002]. Macro scale or system scale predictions assist in minimizing system loses, while ensuring timely water availability [Alfonso et al., 2011; Pulido-Calvo et al., 3

26 Chapter 1 Introduction 2003; Ticlavilca et al., 2011]. From the system operators perceptive, long term system scale irrigation demand forecasts are worthwhile for strategic decisions such as yearly irrigation allocation, channel modernization requirements, to mitigate the risks of over-extraction of ground water and to assist in making long term water savings. Short-term prediction principally supports operational decisions such as routine irrigation release decisions, catering to short-term irrigation demand fluctuations and bulk transfers subject to storage and capacity constraints in the irrigation system and thereby assists to manage, and operate irrigation systems smoothly. Research on methods to forecast short-term system scale irrigation demand is therefore a key scientific question of critical importance for system operators as well as for other stake holders in the system such as regulators, policy makers, farming communities and governments. This thesis aims to develop and evaluate a short-term system scale irrigation demand forecasting methodology that can capitalise on improvements in irrigation infrastructure, particularly flow measurement, and on improvements in weather forecasting from modern Numerical Weather Prediction (NWP) systems. 1.2 Statement of the problem Short-term system scale irrigation distribution decisions are complicated by operational challenges resulting from travel time, farmer and system operator behaviour and spatial/temporal variations and uncertainties of irrigation water consumption [Alfonso et al., 2011; CSIRO-BoM, 2007; Miller et al., 2009; Ticlavilca et al., 2011; Zaman et al., 2009]. By and large, travel time between when irrigation water is released from the source until actual delivery to the agricultural fields has a significant impact on irrigation system operations and level of service [Ticlavilca et al., 2011]. The existence of significant travel time limits the ability of irrigation system operators to react to short-term irrigation demand fluctuations arising from variations in weather, including very hot periods and rainfall events, and from various pressures and opportunities that farmers face. Modern irrigation system automation technologies have been recently developed to address a range of issues related to low irrigation water availability, prescribed environmental flows, low delivery efficiency and poor level of service, an example of which has been implemented in northern Victoria, Australia [NVIRP, 2010c]. These systems can deliver water with very short lead times, due to their fully automated distribution network [NVIRP, 2010a]. A remaining challenge is that, while the system automates water control in the distribution canals, bulk delivery of water to the command area still needs to be planned as it is subject to substantial travel time delays. Short-term irrigation demand forecasting has the potential to assist in system operation, but has often been constrained by limited information on both current demand levels and likely future weather. The short-term system scale irrigation demand is very challenging to forecast because of its dynamic and nonlinear nature, which results from complex interactions between biophysical (cropsoil-climate interaction), behavioral (farmer and system operator attitudes that influence 4

27 Chapter 1 Introduction management decisions) and supply (supply source, seasonal allocation, permanent entitlement) factors [Zaman et al., 2007]. Depending on the degree of data availability, two distinct modelling architectures have been used to forecast irrigation demand; process-based (conceptual) and datadriven (statistical) [Alfonso et al., 2011; Pulido-Calvo and Gutierrez-Estrada, 2009]. The processbased forecast models use the biophysical processes associated with the irrigation demand and overlook the behaviour factors. The data-driven models used available data to map the irrigation demand pattern and the biophysical processes remain ill-defined. Numerous process-based or biophysical irrigation demand forecast models have been developed over the last few decades, aimed at meeting farmer and/or operator needs based on the crop/water/soil interaction [George et al., 2003; George et al., 2000; Rao et al., 1988], profit/yield optimization (economic aspects) [Prasad et al., 2006; Smout, 2005; Umamahesh and Raju, 2002] and seasonal irrigation allocation [Paul et al., 2000; Rao et al., 1990]. These models have often been limited to field scale due to extensive input data requirements relating to both field characteristics (crops and soils) and recent irrigation history. The main objective of those models was to forecast the biophysical irrigation demand, and to assist in making future irrigation decisions (field scale) based on the biophysical irrigation demand, often using publically available short-term weather forecasts [Azhar and Perera, 2011; Cai et al., 2011; Gowing and Ejieji, 2001; Rogers and Elliott, 1989; Wang and Cai, 2009; Wilks and Wolfe, 1998]. A few irrigation demand forecast models have attempted to combine biophysical, behaviour and supply factors; however none forecast short-term system scale volumetric irrigation demand in the face of stochastic weather forecasts. The practical application of the biophysically based models at system scale is limited for various reasons. To upscale field scale models to the system scale is most often limited by lack of data and/or the expense of data acquisition at the system scale [Ticlavilca et al., 2011]. In addition it has been found that irrigation field data over several irrigation seasons does not reflect changes in irrigation demand patterns over a long period of time, due to the influence of many pressures and opportunities that farmers face beyond the purely biophysical water requirements, such as changing water policy, continued development of water markets, drought, and changing technology [Zaman et al., 2005; Zaman et al., 2006]. In general, most system scale biophysical models have rationalized the intra-system spatial variability based on hypothesises that inputs were spatially homogeneous. Data-driven models have mostly been aimed at system scale. A few system scale data-driven models have been successfully developed in Europe [Pulido-Calvo and Gutierrez-Estrada, 2009; Pulido-Calvo et al., 2007; Pulido-Calvo et al., 2003] and the USA [Alfonso et al., 2011; Ticlavilca et al., 2011] and their applicability elsewhere limited for various reasons. These models have solely relied on the historical demand patterns (system flow data) and statistical (time series), artificial intelligence techniques (artificial or computational neural networks (ANNs or CNNs)) or other 5

28 Chapter 1 Introduction machine learning techniques, which have been used to map the input-output pattern. The maximum lead time of these models have been limited to two lead days since beyond their predictive performances significantly declined. A few models have combined reference evapotranspiration (ET O) forecasts derived from computational models [Alfonso et al., 2011; Ticlavilca et al., 2011], and other models have not integrated weather forecast information into system-wide irrigation demand forecasts. Short-term system scale irrigation demand forecasts are too subject for uncertainties. These result from measurement, estimation and forecast uncertainties in inputs, parameters and model structure. A few models have studied irrigation demand forecast uncertainties with respect to parameter uncertainties [Alfonso et al., 2011; Ticlavilca et al., 2011] and model structural uncertainties [Alfonso et al., 2011; Pulido-Calvo and Gutierrez-Estrada, 2009; Pulido-Calvo et al., 2007; Pulido-Calvo et al., 2003; Ticlavilca et al., 2011]. In general, very few studies have been conducted to derive reliable probabilistic irrigation demand forecasts at either system scale or field scale. In fact, no studies I am aware of have combined observed and forecast uncertainties of precipitation and ET O with the measurement ucertainties of antecedent flows to derive stochastic volumetric irrigation demand forecasts at system scale. However, ensemble techniques are commonly used in other fields of the water resource engineering to represent uncertainty. In the context of forecasting; ensemble forecasting techniques have been used extensively in forecasting stream flow [Barrett et al., 2008], short-term urban water demand [Hutton and Kapelan, 2015] and floods [Alvarez-Garreton et al., 2014; Cloke and Pappenberger, 2009; Li et al., 2014a; Schaake, 2006]. These studies all showed that irrespective of the modeling architecture or uncertainty evaluation methods, lack of consistent, real-time, and good quality data across the system continued to challenge the irrigation demand forecast model development, and limit predictive performances. This thesis aims to take advantage of new opportunities for short-term system scale irrigation demand forecasting presented by improved data availability. Automated delivery systems and improved weather forecasts and observations continue to bridge the gaps in data availability at system scale. Channel automation uses state-of-art irrigation system automation technologies to automate the flow of water from the storage to the farmlands. These fully automated delivery systems record and transmit greatly improved real-time high quality irrigation flow data at meter outlets and regulators across the system. The spatial and temporal resolution and forecast accuracy for mesoscale assimilation and forecast NWP systems have also been improved significantly, and skilful NWP system driven short-term weather forecasts are now available with lead times up to ten days. Weather observation data from meteorological radars, satellites, and automatic weather stations (AWS), is also available in real-time. These all data provide an opportunity to understand 6

29 Chapter 1 Introduction biophysical, behavior and supply factors at system scale and provides new insights about farmer s and system operators behaviour with respect to irrigation decision marking, their spatial/temporal variation and uncertainties. These real-time, consistent and high quality system wide data encapsulates wide range of biophysical and farmer behavior information influencing the system wide volumetric irrigation demand. In an operational context, these wide a range of information are often better represented by data-driven models than the process-based models. Despite a few data-driven statistical time series models having been developed, mostly limited to univariate approaches [Pulido-Calvo and Gutierrez-Estrada, 2009; Pulido-Calvo et al., 2007; Pulido-Calvo et al., 2003], multivariate time series approaches to generating real-time short-term system scale irrigation demand forecasts remains poorly researched. A multivariate approach provides an opportunity to capture multiple influences from biophysical processes, farmer and operator behaviours and supply factors. Furthermore, ensemble forecasting techniques can be comprehensive combined with multivariate time series model structure to represent input and parameter uncertainties. This provides an opportunity to apply ensemble forecasting techniques to generate stochastic irrigation demand forecasts. This thesis capitalises on the opportunity presented by real-time, consistent, good quality data available across irrigation distribution systems to develop an irrigation demand forecast model, which aims to predict probabilistic short-term system scale irrigation demands for lead time approximately up to a week. The multivariate time series approach integrates system-wide biophysical processes such as precipitation and ET O and farmer behaviour embedded in the antecedent irrigation flow data. The ensemble forecasting provides an opportunity to combine input uncertainties arising from measurement, estimation and forecast uncertainties, while generating probabilistic short-term system scale irrigation demands forecasts. This thesis provides novel understanding about system scale irrigation demand prediction and associated uncertainties and with the objective of assisting system operators to mitigate the risk associated with their routine irrigation distribution decisions. 1.3 Research questions The following research questions are addressed in this thesis: 1. What is the difference between using either hourly or daily ET O equations (and data) to estimate daily ET O under Australian conditions? 2. How well can daily ET O be forecasted for various lead times using numerical weather prediction outputs across Australia? 7

30 Chapter 1 Introduction 3. How well can daily irrigation demand be modelled, and then forecast, using real-time data on recent irrigation demand and observed daily precipitation and ET O? 4. How well can an ensemble forecast of short-term system scale irrigation demands represent forecast uncertainty? 1.4 Research objectives The overall objective for this research is to conduct modelling experiments to develop a shortterm system scale irrigation demand forecast model. This broader objective is broken down into sub objectives that are reflected in the research questions above and they provide greater understanding of ET O estimation and forecasting as well as irrigation demand forecasting and associated uncertainties. The first two research questions are necessary to construct reliable inputs to the forecasts and the last two research questions aim to generate ensemble forecasting for command area specific irrigation demands for lead time up to five days. The evapotranspiration forecasting research is conducted across Australia, while the focus for the irrigation demand forecasts is on the Central Goulburn Irrigation District (CGID), in the Goulburn-Murray irrigation region, Northern Victoria, Australia. The specific sub objectives of this research are as follows: To investigate the best hourly ET O equation that can be used to estimate daily ET O utilising the hourly weather data observed from AWSs and daily incoming solar radiation product derived from satellite imagery; To develop a method to forecast short-term daily ET O at AWS locations, capitalising on the more consistent numerical weather predictions now available from the operational NWP models in Australia and observed daily ET O estimated using hourly weather data observed from AWSs and daily incoming solar radiation product derived from satellite imagery; To develop a deterministic model to forecast short-term system scale irrigation demand for a command area, coupling human behaviour (as embodied in recent irrigation demands), daily ET O and precipitation, that capitalises on the real-time irrigation flow data recorded at service outlets and regulators and observed weather data available from AWSs and satellite imagery; and To develop ensemble forecasts of short-term system scale irrigation demand for a command area that accurately represents forecast uncertainty. These ensemble forecasts are based on the measurement errors of real-time irrigation flow data recorded at service outlets and regulators, forecast errors included in the numerical weather predictions and measurement and estimation error included in the observed data available from AWS and satellite imagery. 8

31 Chapter 1 Introduction 1.5 Thesis structure The thesis is a combination of journal papers (Chapters 4 to 7) and supporting chapters. It consists of eight chapters with Chapter 1 being this introduction to the problem and thesis. Chapter 2 reviews the relevant literature, providing some theoretical background for irrigation demand estimation and forecasting, an overview of prevailing irrigation demand forecast models and identifies the relevant knowledge gaps. Chapter 3 discusses the development of the conceptual methodology for this research, the study area and data sources. Chapter 4 provides a comparison of estimates of daily ET O calculated using the Food and Agricultural Organization Penman-Monteith (FAO-PM) and the standardized American Society Civil Engineers Penman-Monteith (ASCE-PM) hourly ET O equations, against the daily ET O calculated using the corresponding daily ET O equations at various sites over the Australian continent. This chapter describes in a detailed manner the agreement between the estimation methods, including details of estimating clear-sky-radiation, different methods of aggregating hourly ET O into daily ET O and the impact of seasonality and climate type on the estimates. Chapter 5 describes and evaluates a proposed method to forecast daily ET O with lead times up to nine days using outputs from the Australian Bureau of Meteorology's (BoM) operational NWP forecasts derived from the Australian Community Climate and Earth System Simulator - Global model (ACCESS-G). The study area for this chapter is similar to Chapter 4 and the chapter evaluates forecasting performance for daily ET O as well as ET O related weather variables, (daily maximum and minimum of air and dew point temperatures, mean daily wind speed and daily incoming solar radiation. Chapter 6 describes the development of a deterministic multivariate time series model to forecast daily irrigation demand for lead times up to five days and the model application for the four irrigation channels in the CGID, Northern Victoria, Australia, under ideal conditions (using observed weather data as a substitute for forecasts). Chapter 7 discusses ensemble forecasting of short-term system scale irrigation demands in a fully operational manner. It uses real-time flow and weather data together with numerical weather predictions. This chapter translates the deterministic irrigation demand forecasts into a probabilistic irrigation demand forecasts using estimates of the measurement, estimation and prediction uncertainties of the inputs for the multivariate time series model. Chapter 8 provides a summary of this work, drawing out the major conclusions, and provides recommendations for further research. The structure of this thesis follows the University of Melbourne s Thesis with Publication format. As a result, some redundancies and repetition exist in the results chapters (Journal Papers), especially in the description of the literature and area of study. 9

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33 Chapter 2 Literature review Chapter 2 Short-term system scale irrigation demand forecasting modelling frameworks 11

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35 Chapter 2 Literature review 2.1 Introduction This Chapter aims to review the literature relevant to short-term system scale irrigation demand forecast modelling and then identifies relevant research gaps for this research. Short-term here refers to lead times of between one hour and two weeks. The spatial scale of interest varies between a field and a system where could be a command area, irrigation network, district or project. While the focus is on short-term and system scale, other scales (e.g. field (micro) scale irrigation demand forecast models) are also considered where they are of relevance to the problem at hand. This Chapter begins by talking briefly about the theoretical background of crop water requirement and irrigation demand estimation. Subsequently, it outlines the early development of irrigation demand models in general and then it reviews current irrigation demand forecast models. Current demand forecast models are considered in two groups: (1) Process-based; and (2) Datadriven. These differ in terms of the modelling architecture adopted to represent the complex interactions between biophysical processes and farmer/operator behaviour. To conclude, it discusses knowledge gaps in the field short-term system scale irrigation demand forecasting. 2.2 Theoretical background of irrigation demand Crop water requirement (CWR) The crop water requirement (CWR) is determined by two biophysical processes; Transpiration (T) and Evaporation (E), cumulatively called Evapotranspiration (ET) and it is the amount of water needed to compensate for ET [Allen et al., 1998]. The CWR or crop-et depends on crop type, stage and management and is also influenced by weather conditions and environmental aspects. Crop-ET can be measured using lysimeters [Liu et al., 2002; López-Urrea et al., 2006], or eddy covariance [Ding et al., 2010; Li et al., 2008]. It can also be estimated using several methods including various empirical formulas [Allen et al., 1998; Priestley and Taylor, 1972] or remote sensing information [Bausch, 1995; Ray and Dadhwal, 2001]. Many articles have been published discussing the advantages and disadvantages of these various methods and comprehensive reviews are provided in [Farahani et al., 2007; Kumar et al., 2012; McMahon et al., 2012; Shuttleworth, 2008]. While detailed review of these methods and measurement techniques is beyond the scope of this thesis, here I briefly explain the most commonly used method for estimating crop-et. In this method, the conceptual approach is used to estimate crop-et using reference evapotranspiration (ET O) combined with a crop coefficient (K c), where ET O is the crop-et that would occur from a reference surface and K c is the ratio between actual crop ET and ET O [Jensen, 1968] (Eq. (2.1)). ET O depends on the reference surface and weather conditions, and K c depends on the crop type and 13

36 Chapter 2 Literature review growth stage and this separation avoids mixing the meteorological and plant specific effects when considering crop specific ET. ET C = K C ET O (2.1) Based on this concept, numerous guidelines and methods have been developed to estimate each of ET O and K c. These include the Food and Agricultural Organization s (FAO) Irrigation and Drainage Paper no. 24 [Doorenbos and Pruitt, 1977], FAO Irrigation and Drainage Paper no. 56 [Allen et al., 1998], and the American Society of Civil Engineer (ASCE) Task committee final report [Walter et al., 2005]. The latter two methods are based on a hypothetical reference crop not subject to water stress, with an assumed crop height of 0.12 m, an albedo of 0.23 and a fixed surface resistance of 70 sm -1 [Allen et al., 1998]. These relationships underpin estimates of the biophysical aspects of CWR Biophysical irrigation water requirement In irrigation, the CWR is supplied by a combination of precipitation and irrigation water. The theoretical biophysical irrigation water requirement is the difference between crop water requirement and effective precipitation (Eq. (2.2)). The system scale biophysical irrigation water requirement can be quantified using three fundamental techniques; crop monitoring, soil monitoring, and the water balance technique [George et al., 2000]. In crop monitoring, biophysical irrigation quantity and timing are based on state variables of measured leaf water potential [Stegman, 1975; Turner, 1988] or canopy temperature [Jackson et al., 1977; Wanjura et al., 1995]. With this technique, crops often suffer moisture stress due to lead times in irrigation distribution systems. An alternative is to consider the soil moisture deficit, which can be determined by soil moisture sensor networks at each paddock [Cardenas-Lailhacar et al., 2008; McCready and Dukes, 2011]. This costly and/or labour-intensive and time-consuming technique is not economically viable at the system scale. In the soil water balance technique, biophysical irrigation quantity is estimated using soil water budgeting for the root zone and soil moisture deficit is the state variable that is estimated [Foroud, 1992; Rao, 1987; Rowse et al., 1983]. The soil water balance technique has often been used for biophysical irrigation demand estimation models [Feddes et al., 1974; Rowse et al., 1983] as it shows distinct advantages at the system level in terms of applicability, cost and time effectiveness, compared with in-field measurements. In practice the biophysical irrigation water requirement may exceed the theoretical amount when deep percolation [Rice et al., 1986] or runoff occurs during or following irrigation, where there is non-uniform water application, where there are losses to evaporation during irrigation or where additional water is required to leach salts [Ayars et al., 2012; Rhoades et al., 1973; Troiano et al., 14

37 Chapter 2 Literature review 1993]. All except the leaching requirement can be viewed as arising from inefficiencies in irrigation techniques. At the system scale, conveyance efficiency also needs to be accounted and system scale biophysical irrigation demand is calculated by incorporating irrigation and conveyance efficiencies with the net crop water requirement, as shown in equations Eqs. (2.2)-(2.5). CWR for a given crop "i" over a time period of T can be calculated as; CWR i = T t=0 (K C it ET Ot P effectivet ) (2.2) System scale net irrigation water requirements for "n" number of crops can be calculated as; n Net Irrigation Water Requirements = i=1 CWR i S i (2.3) Irrigation Requirement = Net Irrigation Water Requirements Irrigation efficincy (2.4) Irrigation Demand = Net Irrigation Water Requirements Irrigation efficincy Conveyance efficincy (2.5) where; CWR i is the crop water requirement of the given crop i during the growth period t, K C it is the crop coefficient of the given crop i during the growth stage t and where T is the final growth stage, ET O t is the reference ET during the growth stage t, P is the effective precipitation effectivet during the growth stage t, S i is the area cultivated with the crop i Behavioural factors Apart from the biophysical irrigation water requirement, there is an obvious influence from farmer behaviour to the actual irrigation demand. A number of studies focussed on farmer behaviour have attempted to quantify correlations between farmer behaviour and irrigation demand [Austin et al., 1998a; Austin et al., 1998b; Freebairn, 2003; Ortega et al., 2005; Richards et al., 2008]. Initially, the behaviour of several Scottish farmers was modelled and it was found that farmers who used computers to access information and to track their progress were likely to make a larger profit than those who relied on less structured forms of information [Austin et al., 1998a; Austin et al., 1998b]. Such findings were validated in Australia [Richards et al., 2008]. Furthermore, 100% of perennial pasture producers in south-eastern Australia confirmed that short-term weather forecasts were used for farm management decisions [Austen et al., 2002]. A significant number of scholars have suggested that while farmer behaviour with respect to their environmental conscience was explicit, profit maximization was their primary motivation rather than the environmental considerations [Austin et al., 1998a; Austin et al., 1998b; Freebairn, 2003; Ortega et al., 2005]. 15

38 Chapter 2 Literature review All of the above studies showed that models based purely on crop-et or the soil water balance method have reduced performance because they fail to account for differences between individual farmers in their irrigation management. This motivated research on behaviour factors. Subsequently, key factors affecting irrigation demand have been divided into biophysical and behavioural factors. Behavioural factors are influenced by individual farmer preferences and factors such as farm type, farm investment, permanent water entitlement, trading behaviour and water prices, and ordering behaviour [Zaman et al., 2006]. Zaman et al., [2008] categorised farmer behaviour strategies into two groups: activeness and risk-return preferences. Activeness was defined as the effort made by a farmer to obtain and utilise information for farm related decisions and risk-return preference was defined as the tendency of a farmer to avoid situations which involve risk or income volatility. Then the behavioural factors were modelled by finding a compromise between two conflicting objectives which were maximizing gross margins and minimizing risk of crop water-stress [Zaman et al., 2008a]. These insights relating to behavioural factors were integrated with an economic model and a biophysical water allocation model to evaluate the impacts of temporary water trading and physical water transfers [Zaman et al., 2007; Zaman et al., 2008b; Zaman et al., 2009]. While their results suggested that behavioural factors were more important for annual cropping systems, there is an over-arching requirement to integrate farmer behaviour with biophysical irrigation demand when estimating or forecasting irrigation demand Irrigation demand As described in the previous sections, irrigation demand depends on three principal interacting factors: (1) biophysical (crop-soil-climate interactions), (2) behavioural factors (farmer and supply authority attitudes) and (3) supply (water availability). Different irrigation demand modelling frameworks place different emphases on each of these factors. Figure 2.1 shows a schematic diagram of irrigation demand estimation at the system scale, with the influence from each of the principal factors on each step of the computations colour-coded. Most irrigation demand estimation and forecast models have been developed by combining biophysical and supply factors with the aim of guiding irrigation scheduling [Foroud, 1992; George et al., 2000]; optimising single [Rao et al., 1988] or multiple crop [Prasad et al., 2006; Smout, 2005; Teixeira and Mari ñ o, 2002; Umamahesh and Raju, 2002] yield; guiding water allocation [Rao et al., 1988]; or representing crop/soil/climate interactions [Rao, 1987]. 16

39 Chapter 2 Literature review Biophysical factors Supply factors Behavioral factors Spatial crop mix Spatial crop water requirement (CWR) Net irrigation requirement (NIR) Irrigation requirement (IR) Irrigation demand (ID) Irrigation release requirement (IRR) Effective precipitation Irrigation efficiency Conveyance efficiency Farmer behaviors Legend Biophysical factors Behavioral factors Supply factors Figure 2.1 A Schematic diagram representing irrigation demand resulting from biophysical, behavioural and supply factors at the system scale. 2.3 Early irrigation demand modeling The early irrigation demand models were motivated by the two overall purposes: irrigation scheduling; and yield optimization. The irrigation scheduling models aim to efficiently meet the CWR, whereas yield optimization models aim to maximize the profit or yield. Irrigation scheduling models were typically process-based, developed and tested using field data collected for specific crops and they aimed to quantify weekly crop water requirement using the weekly actual crop-et and soil moisture content. These models did not consider the dynamic nature of biophysical processes such as precipitation, crop-et and root growth within the week [Rao, 1987; Rhenals and Bras, 1981]. Subsequent developments included the addition of root growth models and daily precipitation, while remaining focussed on weekly irrigation demands [Hajilal et al., 1998; Rao et al., 1988]. They did not consider the weekly variation of the actual crop-et because it had a small effect on weekly irrigation schedules [Rhenals and Bras, 1981]. These models generated reliable weekly or biweekly irrigation demand sequences for specific crops, under uniform biophysical environments across the system. Spatial variation in weather and distribution losses resulted in increased in scatter between simulated and actual soil moisture at the field scale [Hajilal et al., 1998]. The reliability of these daily/weekly irrigation demand estimates varied according to the crop/soil/climate interactions as well as spatial and temporal variation in these factors. The yield reduction depended on the level and duration of stress and the growth stage because insufficient 17

40 Chapter 2 Literature review irrigation at some growth stage can reduce yield more than another stage. Farmer uptake of the irrigation demand estimation models was very slow during the 1990 s as models were not user friendly and there was no graphical user interface [Feddes et al., 1974; Foroud, 1992; George et al., 2000; Mujumdar and Teegavarapu, 1998; Rao et al., 1988; Rowse et al., 1983; Smith, 1992]. Further advances involved combining irrigation demand estimation models with profit or yield optimization. Most of these optimization models aimed to optimize production from irrigation under limited seasonal water allocations for either single [Rao et al., 1988] or multiple crops [Paul et al., 2000; Prasad et al., 2006; Rao et al., 1990; Smout, 2005; Sunantara and Ramirez, 1997; Teixeira and Mari ñ o, 2002] in multiple season scenarios for a given year. The main drawback of these optimization models was that short-term variations in biophysical and supply factors were not accounted for. 2.4 Irrigation demand forecasting models The above discussion has considered irrigation demand modelling in general. I now turn to irrigation demand forecasting models in particular, focussed on short-term forecasting. These models aim to forecast system scale irrigation demand for up to a week ahead using historical or real-time information. The applicability of these models for a given system depends on the spatial and temporal scale, stakeholder perceptions (water, profit and yield optimization), data availability and lead time. The prevailing irrigation demand forecast models can be categorised into processbased (conceptual) or data-driven (statistical) models, depending on the modelling architecture [Alfonso et al., 2011; Pulido-Calvo and Gutierrez-Estrada, 2009]. The next two sections discuss these two modelling approaches separately in terms of data requirements, spatial and temporal scale, advantages and disadvantages, and limitations on the applicability of specific techniques to decide which approach would be more suitable for this research Process-based irrigation forecasting modeling frameworks Process-based irrigation demand forecasting models have been developed based on the biophysical processes relating to the soil-water balance equation. These models are built on detailed understanding and representation of individual biophysical processes. Process-based models have often used weather forecasts to predict the supplemental irrigation requirements for various climate conditions. This approach has been complemented by the introduction of short-term probabilistic weather forecasts. Initially, daily weather forecasts were used for daily irrigation decisions to reduce the cost of irrigation by reducing the irrigation in the face of forecast precipitation [Allen and Lambert, 1971-a; Allen and Lambert, 1971-b] and subsequently it was found that it was only necessary to consider forecasts of larger precipitation events ( cm) to increase the profit 18

41 Chapter 2 Literature review [Rogers and Elliott, 1989]. Since then, the forecast performance for short-term weather forecasts has gradually improved over the time. A few models have used these improved short-term weather forecasts to predict short-term daily irrigation decisions [Wilks and Wolfe, 1998] as well as weekly irrigation requirements [Bras, 1981; Rao et al., 1992; Rhenals and Bras, 1981]. The results have demonstrated that using weather forecasts can help avoid excessive soil moisture and in turn reduce the irrigation water consumption. Farmer behaviour is potentially influenced by use of short-term weather forecasts for their irrigation decisions. As a result, the impact of weather forecasts to farmer behaviour has been examined [Austen et al., 2002; Bergez and Garcia, 2010; Berrisford et al., 2009; Ingram et al., 2002; Maheshwari et al., 2003]. These studies showed that farmers had a strong interest in receiving seasonal as well as short-term precipitation forecasts [Ingram et al., 2002], but they felt that threemonth seasonal climate outlooks and seven days weather forecasts needed to be more accurate and reliable to be useful in irrigation decision making [Austen et al., 2002]. Therefore, farmers only considered weather forecasts in situations where ignoring the forecast presented a greater risk, such as where the consequences were difficult to recover from (e.g. hot days.) [Bergez and Garcia, 2010]. These findings all suggested that farmer decision-making behaviour partially depended on the weather forecast. A few studies on some farms suggested that irrigation decisions were definitely taking place as a structured management process, but others it was intuitive and subjective, based on plant appearance [Maheshwari et al., 2003; Martin-Clouaire and Rellier, 2009]. More recent studies have also found that the factors or triggers used by farmers for irrigation decision making such as irrigation order placement or rejection are not widely understood [Berrisford et al., 2009]. Nevertheless, some process-based irrigation demand forecast models incorporating farmer behaviour have been developed at system scale. These models have combined farmer behaviour and short-term weather forecasts to derive sequences of optimal irrigation decisions rather than to make volumetric irrigation demand forecasts [Cai et al., 2011; Wang and Cai, 2009]. It was further revealed that farmer response to water stress was late due to either unreliable or unavailability weather forecasts and ignorance of real-time soil moisture conditions. By and large, these studies have all concluded that short-term weather forecasts were useful for optimal irrigation decision-making for field or system scale [Cai et al., 2011; Gowing and Ejieji, 2001; Wang and Cai, 2009; Wilks and Wolfe, 1998], but short-term system scale irrigation demand forecast performance was greatly influenced by the uncertainties in forecast variables (especially precipitation) and differences in farmer behaviour. The reliability of these irrigation demand forecasts has mainly been constrained by the prediction uncertainties associate with the relevant biophysical processes. These relatively higher number of observed as well as forecast biophysical processes lead to curse of dimensionality' arises while dealing with larger number of model inputs 19

42 Chapter 2 Literature review [Ejieji and Gowing, 2000; Wilks and Wolfe, 1998]. A few models have been developed minimized the dimensionality problem by limiting stochastically represented factors, only to precipitation [Ejieji and Gowing, 2000] as it is fundamentally important to forecast irrigation demand [Azhar and Perera, 2011]. Table 2.1 shows a range of process-based irrigation demand forecast models and the factors that they account for. In summary, process-based irrigation demand forecast models broadly depend on past, present and future information about the biophysical processes associated with irrigation. They recognize some of the biophysical processes that drive seasonal scale irrigation demand patterns. However, it is clear that short-term irrigation demand fluctuation cannot be forecast only using the biophysical and supply factors as farmer and operator behaviour is also has a significant influence. Overall, the reliability of process-based irrigation demand forecasts is dependent on data availability, the degree of integration of biophysical processes, temporal and spatial scale, and climate. The influence of spatial variability can potentially be addressed by considering distributed modelling; but a practical limitation is the lack of typically available spatial data to specify all the model parameters spatially. Table 2.1 Summary of process-based irrigation demand forecast models No. & Source Input BPF 1 BEHF 2 SUPF 3 Output Crop C 4 TS 5 SS [Allen and Lambert, 1971-a; Allen and Lambert, 1971-b] 02. [Rogers and Elliott, 1989] 03. [Wilks and Wolfe, 1998] 04. [Gowing and Ejieji, 2001] 05. [Bergez and Garcia, 2010] 06. [Wang and Cai, 2009] Precip. 7 Fcst 8 Daily IS 9 Flue-cured Tobacco H 10 1 D 12 FL 13 Precip. 7 Fcst 8 Daily IS 9 Sorghum A 11 1 D 12 FL 13 Weather Fcst 8 Daily Irrigation Decisions Lettuce H 10 2 D 12 FL 13 Weather Fcst 8 Daily IS 9 Potato H 10 7 D 12 FL 13 Weather Fcst 8 Daily IS 9 Corn A 11 1 D 12 FL 13 Weather Fcst D IS 9 Corn A 11 7 D 12 FL [Cai et al., 2011] Weather Fcst D IS 9 Corn A 11 7 D 12 FL 13 1 Biophysical factors, 2 Behavior factors, 3 Supply factors, 4 Climate, 5 Temporal scale, 6 Spatial scale, 7 Precipitation, 8 Forecast, 9 Irrigation schedules, 10 Humid, 11 Arid, 12 Days, and 13 Farm land 20

43 Chapter 2 Literature review Data-driven irrigation demand forecasting modeling frameworks In the field of irrigation demand forecasting, a number of data-driven models have been developed usually at the system scale. They have typically been trained to represent the relationship between various system wide influential factors and irrigation demand, with little detailed consideration of the internal structure with respect to the biophysical processes [Alfonso et al., 2011]. Data-driven models can be categorized into time series and machine learning models, depending on the model structure used to represent the input-output patterns. The first generation data-driven models were mostly developed as univariate time series models [Pulido-Calvo and Gutierrez- Estrada, 2009; Pulido-Calvo et al., 2007; Pulido-Calvo et al., 2003] for arid-zone agriculture and precipitation was not considered. These univariate models are not applicable for supplemental irrigated agriculture and cannot integrate information about other biophysical factors (e.g. crop-et, precipitation, and temperature) due to structural constraints. Consequently, more sophisticated datadriven models have been developed. Innovations in the fields of nonlinear pattern recognition and system control theories have led to gains in the capability to map the intricate interactions from input to output of complex non-linear processes. This motivated development of data-driven models based on machine learning techniques such as artificial or computational neural networks (ANNs or CNNs) and support or relevance vector machines (SVM or RVM). These techniques have been used as an alternatives to time series models, because they had the potential to provide better forecasting performance than traditional approaches such as auto-regression and multiple-regressions for nonlinear systems [Thirumalaiah and Deo, 2000]. These computational techniques have been successfully used for various forecasting applications within the water resource management; including flood forecasting [Nayak et al., 2005], stream flow forecasting [Cameron et al., 2002; Kasiviswanathan and Sudheer, 2013; Nayak et al., 2012; Pulido-Calvo and Portela, 2007], precipitation forecasting [French et al., 1992; Kuligowski and Barros, 1998], and ET O forecasting [Chauhan and Shrivastava, 2009; Tian and Martinez, 2012b], etc. The first few machine learning models were developed and compared with the forecast performances with univariate time series models [Pulido-Calvo et al., 2003] and linear multiple regressions models [Pulido-Calvo et al., 2007]. The machine learning models used one or more input variable such as maximum or mean temperature, precipitation, relative humidity, wind speed and previous irrigation flows and trained the respective neural network (ANN or CNN) with optimization algorithms such as extended-delta-bar-delta, Levenberg-Marquardt or Genetic [Pulido- Calvo and Gutierrez-Estrada, 2009; Pulido-Calvo et al., 2007; Pulido-Calvo et al., 2003]. They forecasted one-day lead time irrigation demands for several irrigation districts located in southern Spain. Forecast performances for artificial intelligence models were higher than univariate time 21

44 Chapter 2 Literature review series or regression approaches [Pulido-Calvo and Gutierrez-Estrada, 2009; Pulido-Calvo et al., 2007; Pulido-Calvo et al., 2003]. However, the one day lead time irrigation demand forecasts were very close to the immediate past flows due to the high auto-correlation between consecutive observed flows [Pulido-Calvo and Gutierrez-Estrada, 2009]. Another issue is that these CNN models were systematically over fitted and the forecast performance declined significantly during validation. These all highlighted the fact that irrigation demand forecasts were highly dependent on the immediate past irrigation flows rather than representations of variations in biophysical conditions for Mediterranean or arid climates. The next generation of the data-driven models used Bayesian machine learning techniques such as relevant vector machines (RVM) or support vector machines (SVM), which are able to control, derive predictive confidence and avoid over-fitting and thus improve generalizability. Two studies have used multivariate relevance vector machine (MVRVM) models to forecast diversion volumes for three irrigation canals in the Sevier river basin, Utah, USA for lead times of one hour to two days [Alfonso et al., 2011; Ticlavilca et al., 2011]. These models used one or more input variables including mean temperature, ET, or previous irrigation flows. Bootstrap analysis was used to derive parameter distributions which were then converted to a probabilistic irrigation demand forecast accounting for parameter uncertainty [Alfonso et al., 2011; Ticlavilca et al., 2011]. The predictive performances were compared against ANNs trained with the Levenberg-Marquardt algorithm [Ticlavilca et al., 2011] and multi-layer perceptron models. The results showed similar predictive performance for the MVRVM and ANN models; however, the bootstrap analysis demonstrated that the MVRVM models were more robust than ANN models [Ticlavilca et al., 2011]. Moreover, the results indicated immediate past inflows and variations in PET were equally important in forecasting the short-term irrigation demand. The key characteristics for the most relevant data-driven irrigation demand forecast models are provided in Table 2.2. In summary, data-driven models have been developed to forecast system scale irrigation demands for lead times up to two days or less for arid and Mediterranean climates. Which are mostly depending on the behaviour factors quantified using antecedent irrigation flows and secondary consider the biophysical processes such as crop-et, ET O and temperature. These models were problem-oriented and rely extensively on system-wide data availability. The machine learning models showed higher forecast performances than process-based models. The other distinctive advantage is that data-driven models only use available information to provide the same (or similar) results, to those generated using complete (or near complete) set of variables by processbased models [Alfonso et al., 2011]. An advantage of data-driven models is that they can handle a very large range of data without pre-processing as the machine learning techniques are not based on particular functional forms for the relationship between independent variables and dependent 22

45 Chapter 2 Literature review variables, unlike structured statistical polynomial approaches. The heuristic nature of selecting the machine learning technique, the input data set and splitting dataset between calibration and validation periods led to frequent recalibrations. Therefore, by and large, data-driven models are generally referred to as black-boxes where the complex interaction between irrigation demand and causal factors remains ill defined. Table 2.2 Summary of data-driven irrigation demand forecast models No. & Source Input BPF 1 BEHF 2 SUPF 3 Output Crop C 4 TS 5 SS [Pulido-Calvo ID 7, CD 8, Daily IS 9 Various M 11 1 D 13 DIS 15 et al., 2003] Crop data 02. [Pulido-Calvo ID 7, CD 8 Daily IS 9 Various M 11 1 D 13 DIS 15 and Portela, 2007] 03. [Pulido-Calvo ID 7, CD 8, Daily DF 10 Various M 11 1 D 13 DIS 15 and Gutierrez- Crop data Estrada, 2009] 04. [Ticlavilca et ID 7, Hourly / NA A 12 H 14 / DIS 15 al., 2011] Temperature Daily DF 10 2 D [Alfonso et al., ID 7, CD 8, Daily IS 9 Corn A 12 2 D 13 DIS ] Crop data 1 Biophysical factors, 2 Behavior factors, 3 Supply factors, 4 Climate, 5 Temporal scale, 6 7 Spatial scale, Irrigation demands - recent past, 8 Climate data - recent past, 9 Irrigation schedules, 10 Demand forecast, 11 Mediterranean, 12 Arid, 13 Days, 14 Hours and 15 Irrigation district 2.5 Knowledge gaps and research gaps The literature review shows that there are a wide variety of knowledge gaps in the field of irrigation demand forecasting. These include; 1. Almost all previous studies have adopted a "horses for courses" approach focused on the local operational challenges and based on the data availability. Consequently, the choice of model architecture, which could be adopted for a given context, is also not clear. 2. Process-based models have focused on the biophysical process associated with irrigation demand, while data-drive models have relied extensively on consistent input-output data sets but have not adequately included biophysical factors. There is an opportunity to include the strengths of both modelling architectures to a single irrigation demand forecasting model. 3. Most process-based models are field scale and they have been developed or extended for the system scale 4. The majority of previous studies have used the maximum or mean daily temperature as the most influential forcing variable, but precipitation and crop-et remain underexplored as atmospheric forcing variables. 23

46 Chapter 2 Literature review 5. Farmer behaviour in the face of probabilistic weather forecast is poorly exploited and the literature overlooks the influence of the precipitation and crop-et forecasts for system scale irrigation demand forecasting. 6. The conclusions drawn from overseas studies of system wide precipitation and crop-et estimation and forecasting may not be fully applicable in the Australian context because of the different climate, soil, crop types, agricultural practices and, farmer attitudes etc. 7. The maximum lead time for the system scale studies were limited to two days 8. It is well recognised that the irrigation demand forecasts are subject to uncertainties and these have not been quantified in the most previous studies. While a few studies consider parameter uncertainties, there exists a significant knowledge gap in integrating input, parameter and structural errors into irrigation demand forecasts. 9. Most field scale models have considered probabilistic weather forecasts (especially precipitation), but no system scale studies have examined the output uncertainties resulting from observations, estimates or prediction uncertainties of other inputs such as past irrigation flows, crop-et, and temperature. 10. Short-term system scale impacts resulting from various pressures and opportunities farmers face in terms of long-term adaption in the face of climate change phenomena, water policy, continue development and opportunities in the context of water markets as well as changes in seasonal weather patterns, regular extreme weather events (floods or droughts), land use or technological innovations (modernization, automation) etc are not understood. The availability of data associated with irrigation demand estimation and forecasting has been increasing over time. As a result, fine scale consistent irrigation flow data are now available from the SCADA (supervisory control and data acquisition) systems and more reliable forecasts are now available from NWP systems. Weather observation networks include meteorological radars, satellites and automatic weather stations-aws. These consistent real-time system scale data present an opportunity to improve forecasts and is the focus of this thesis. From the literature review, the key influences relevant to forecasts are biophysical, behaviour and supply factors. This thesis aims to link biophysical and supply processes used in process-based models into a data-driven model, which are quite able to capture behavior factors. 24

47 Chapter 3 Conceptual framework and study area Chapter 3 Conceptual framework and study area 25

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49 Chapter 3 Conceptual framework and study area 3.1 Introduction This Chapter commences by summarizing the choice of method and then the conceptual framework for this PhD research project is proposed. This conceptual framework consists of four inter-related stand along tasks, those are directly link to the research questions provided in Chapter 1. Next it provides a comprehensive justification of the research questions in terms of each task. This research has two main components: an examination of ET O forecasts; and development and evaluation of a probabilistic irrigation demand modelling framework applicable at the system scale for lead times up to five days. The first component uses data from across Australia while the second component is focussed on the Central Goulburn Irrigation District (CGID). The last sections of this Chapter describe: 1) the CGID; 2) irrigation data from the CGID; 3) Numerical Weather Prediction (NWP) data used for both components; and 4) weather observation data used for both components. These descriptions supplement the relatively brief descriptions provide in Chapters 4-7. To avoid the repetition, a detailed description about the Australian Continent is provided in Chapter 4 and 5, rather than here. 3.2 Conceptual framework Based on the literature review and the knowledge gaps highlighted in the previous Chapter, the most promising methodology for this thesis would: (1) be able to fully integrate system wide observed and forecast factors related to the biophysical, behavioural and supply influences; (2) be able to couple the key characterics of process-based and data-driven models; and (3) be able to generate real-time probabilistic system scale irrigation demand forecasts (i.e. forecasts with known uncertainty). The choice of method with respect to each of these points led to the research questions and objectives already outlined in the Introduction Chapter and discussed in more detail below. It is well established that crop-et and precipitation are the key biophysical and supply factors influencing irrigation demand, respectively. The behavioral factors cannot be quantified directly; however, they are imbedded in the irrigation flow data (along with the supply and biophysical demand). Therefore, the proposed framework for this thesis is to integrate observed and forecast information relating to crop-et and precipitation together with the historical flow. The observed and forecast values for precipitation are available from AWS stations and NWP models respectively and statistical techniques can be used to combine these with the irrigation flow data, which encapsulates the behavioral and other influences. The main requirements are: 1. A model relating precipitation, evapotranspiration, farmer behavior and irrigation demand, 27

50 Chapter 3 Conceptual framework and study area 2. Observed and forecast information on the inputs to the model, including precipitation, evapotranspiration and past demands; and 3. Methods to estimate the uncertainty of 1 and 2. In this thesis, I have adopted some methods from the literature and developed new methods. Figure 3.1 shows the overall structure of the research described in this thesis. Observed weather data from AWS NWP weather forecasts from ACCESS-G Task 1 Estimate observed daily ET O using hourly weather data Task 2 Forecast daily ET O using NWP weather predictions Observed precipitation Daily ET O estimates Irrigation flow data Daily ET O forecast Precipitation forecast Task 3 Develop irrigation demand forecast model Task 4 Ensemble forecasting of irrigation demand forecasts System boundary - Automated irrigation system Real-time probabilistic irrigation demand forecasts Figure 3.1 Conceptual framework 3.3 Justification of the research questions Considering the biophysical and supply factors first, there are weather observations and forecasts that can be used. Research exits characterizing the reliability of precipitation forecasts and downscaling them from the models to stations (e.g. [Robertson et al., 2013]). The first significant gap relates to evapotranspiration. Observed and forecast values for system wide crop-et cannot be directly calculated as it is crop dependent and typically estimated in a two-step process involving calculation of ET O and then adjustment using a crop coefficient that is crop type and growth stage dependent [Jensen, 1968]. Since, only limited real-time information about the crop mix is available at system scale it would be difficult to base forecasts on crop-et. As an alternative, ET O can be used instead of crop specific ET estimates to characterize the temporal fluctuations in crop-et. Therefore, this thesis uses ET O to represent the key biophysical factor; crop-et and observed and forecast information is integrated. 28

51 Chapter 3 Conceptual framework and study area Observed daily ET O can be measured or estimated using various methods as reviewed in section When it comes to estimation, the daily FAO-PM equation has been recommended as a standard method for computing daily ET O [Allen et al., 1989], but only a few studies have been conducted to compare hourly ET O equations at daily or sub-daily time scales [Irmak et al., 2005; Itenfisu et al., 2003; Temesgen et al., 2005]. The overseas studies related to the performance of hourly ET O equations at daily time scales may not be relevant to Australia because of the different climate. To address this concern, the first research question and task one of the conceptual framework (Figure 3.1) aims to quantitatively compare estimates of daily ET O calculated using the FAO-PM and ASCE-PM hourly ET O equations, against the daily ET O calculated using the corresponding daily ET O equation over the Australian continent. Chapter 4 of this thesis provides the details of this comparison for 40 locations (automatic weather stations), across 23 agricultural irrigation areas from nine diverse climate types. Conclusions are drawn regarding the best agreement between the hourly and daily ET O equations at daily scale. There is also a potential to forecast ET O using NWP forecasts to capture the influence of upcoming weather on irrigation demand. It is unclear how well NWP models can forecast ET O as there has only been a small number of studies in certain geographical areas such the United States of America, Europe, China and Chile and they have focussed on relatively short lead times [Arca et al., 2003; Cai et al., 2007; Silva et al., 2010]. Also forecast performance varies with NWP model, lead time, location and climate. To address this concern, the second research question and the task two of the conceptual framework (Figure 3.1) aims to quantify the forecasting performance for daily ET O for lead times up to nine days using the Australian Bureau of Meteorology's (BoM) operational NWP forecasts derived from the Australian Community Climate and Earth System Simulator - Global model (ACCESS-G). Chapter 5 evaluates the forecasting performance for ET O related weather variables (daily maximum and minimum of air and dew point temperatures, mean daily wind speed and daily incoming solar radiation) and forecasted ET O for lead times of 1 to 9 days for the 40 locations used in Chapter 4 against the observed weather variables and calculated ET O. Together these two chapters enable the model inputs to be satisfactorily obtained. The remainder of the thesis addresses forecasting of irrigation demand itself, starting with developing a model of irrigation demand. The literature review suggested that any model should capture both the biophysical, supply and behavioural influences on irrigation demand. Moreover, the proposed model structure should have provision to include input and parameter uncertainties in order to derive probabilistic irrigation demand forecasts. Most importantly, the proposed model structure should be suitable for real-time operation and real-time irrigation demand forecasts. In principle, data-driven models are able to integrate these factors and they have the advantage of not requiring detail data regarding crop patterns and management across the irrigation area. Suitable 29

52 Chapter 3 Conceptual framework and study area candidates include neural network and other artificial intelligence models and (typically linear) multivariate time series models. To this end, the multivariate time series models can capture the linear interactions and auto and cross correlations between time series variables. With careful data pre-processing they can also deal with systematic influences such as seasonality and the literature has shown that they tend to be more robust than neural network models because they are more parsimonious. Multivariate time series models have been widely used in the fields of engineering, science, medicine and finance, among others. The third research question and task three of the conceptual framework (Figure 3.1) addresses the question of finding a suitable multivariate time series model to forecast daily irrigation demand using real-time irrigation demand and observed weather data. Ideally the forecasts should have at least five days lead time, given the four day travel time for water delivery to the study area (described later). Chapter 6 describes the model development and evaluates its performance. Given that short-term system scale irrigation demand forecasts are subject to uncertainty, resulting from input, parameter and model structural uncertainties, the fourth and final research question and task four of the conceptual framework (Figure 3.1) addresses the uncertainties in irrigation demand forecasts. Specifically it develops and evaluates ensemble forecasting of shortterm system scale irrigation demand in Chapter Study areas and data Central Goulburn Irrigation District (CGID) The study area is located in the Goulburn-Murray Irrigation District (GMID), Northern Victoria, Australia, which is often referred as the Food Bowl of Australia. Agriculture is dominated by irrigated dairy, pome and stone fruit production, with other agricultural activities related to sheep for wool, beef and dairy cattle [RDV, accessed 26 Sep 2014]. During the millennium drought ( ) [van Dijk et al., 2013], the GMID system confronted severe water shortages, which resulted in cutbacks in irrigation allocations, (urban) water restrictions and reductions in environmental flows [NVIRP, 2010a]. Consequently, the Victorian Government formulated a longterm plan for water called Our Water Our Future. On 20 December 2007, a state owned enterprise for irrigation modernisation in Northern Victoria was established to plan, design and deliver the Northern Victorian Irrigation Renewal Program (NVIRP). NVIRP aimed to modernise the GMID systems, which cover 65,000 km 2. Under NVIRP Stage one, 58,500 km 2 of command area was modernised by installing automatic regulator gates, meter outlets and targeted channel lining. 30

53 Chapter 3 Conceptual framework and study area Figure 3.2 Study area - Central Goulburn channel 1, 2, 3, and 4 [Perera et al., 2015a] The main source of water supply for the study area is Lake Eildon, which releases water into the Goulburn River, to meet irrigation and environmental demands. Goulburn Weir raises the level of the Goulburn River and diverts irrigation water by gravity to the Stuart Murray, Cattanach and the East Goulburn Main Canals (Figure 3.2). The Stuart Murray Canal supplies water to the CGID 31

54 Chapter 3 Conceptual framework and study area using six gravity irrigation channels namely CG 1, 2, 3, 4, 5 and 6, with excess water diverted to Waranga Basin. The operation of these channels with respect to outlet and intermediate regulators and supply points is automated and controlled by a SCADA system called Total Channel Control TM (TCC TM ). The TCC system belongs to Goulburn-Murray Water (GMW). TCC TM is a fully automatic open channel delivery system, which is (1) close to on-demand supply to customers, (2) automates supply outlet flows as ordered and (3) has the ability to interface with on-farm automation equipment [Luscombe et al., 2004]. The system was developed by Rubicon Systems Australia (Rubicon) in partnership with the University of Melbourne and tested under the project Total channel control system pilot on CG 2 channel, Tatura with the collaboration with the Department of Sustainability and Environment (DSE), GMW and Rubicon [Luscombe et al., 2004]. The spatial characteristics of the four study area channels vary in terms of command area, crop type, soil type and degree of automation. CG 1, 2, 3 and 4 were the first four modernized channels in the CGID and the degree of automated was higher than CG 5 and 6. Therefore, the proposed framework was applied to these channels (Figure 3.2) and the characteristics for each channel are given in Table 3.1. CG 1, 2, 3 and 4 supply km 2 of irrigated agricultural area in total. The irrigation year runs from the 15 August through to the 15 May the following year and this study uses six years of system flow data for the period 15 August 2006 to 15 May It included real-time regulator flow data recorded at the four off-take regulators of CG 1-4 (Figure 3.2) and 1016 supply points. The study area is approximately 110 m above Australian height datum (AHD) and the climate is temperate with a hot summer (T hot 22) but without a dry season (Köppen climate type Cfa) [Peel et al., 2007]. Irrigation water takes on average four days to travel from Lake Eildon to farms supplied by CG 1-4. Further specific details of the system and its behaviour are presented in the chapter 6 and 7. Table 3.1 Characteristics of CG 1-4 channels Channel Length (km) Area Service points Regulators Degree of (km 2 ) (Nos.) (Nos.) Mod. 2 (%) L 1-1 L 1-2 L 1-3 Total Mod. 2 Unm. 3 Total Mod. 2 Unm. 3 Total SP 4 V 5 CG CG CG CG CG Level of distribution (L-1- backbone, L-2 - primary and L-2- secondary), 2 Modernised, 3 Unmodernised, 4 Service points, and 5 Volume through automated service points 32

55 Chapter 3 Conceptual framework and study area Data sources Irrigation flow data The irrigation water flow data related to the regulators and service points were collected from the operational SCADA system called Total Channel Control TM (TCC TM ) that belongs to GMW. During TCC TM system implementation, the manual flow control structures in channels and outdated flow meters at farms were replaced with new solar-powered channel control gates and water meters, which communicate with the control software through a radio network and deliver smart control for irrigation water distribution. As a result, manual drop bar regulators have been replaced with automated regulation structures called Flume Gates and Dethridge wheel meter points have been replaced with accurate electronic meters, capable of supplying water to farms according to requested flow rate and times [Walsh and Preece, 2009]. The TCC system is underpinned by a relational database that processes thousands of water transactions per day, stores real-time flow and water level data coming from the SCADA network and generates real-time system flow information [Walsh and Preece, 2009]. The flow data recorded at the off-take regulators for CG 1-4 (Figure 3.2) and the 1016 supply points were collected for a period of six years staring from 15 August 2006 to 15 May The off take regulator flow data and aggregated service point delivery data were converted to a daily time step. Regulators record times of flow rate change time (time resolution is seconds) and associated flow rates, which are accurate to ± 2.5% for 95% confident interval [Rubicon, 2014], under laboratory test conditions. The offtake regulator flow change time series were aggregated to a daily time step. The SCADA system records the start and end timings and flow rates of irrigation order deliveries, the service point regulators deliver uniform flow within ± 5% more than 90% of the time [NVIRP, 2010b]. Service point flows were aggregated to a daily time step and then aggregated across all the service points for the individual channel and the study area as a whole. For the small number of manual service points still existing, the irrigation order data was assumed to represent the actual volume of water taken on the day. This aggregation assumes that the travel time along the local channel or study area is significantly less than a day. These aggregated service point flows and off take regulator flows are referred to as ID CGi, ASP and ID CGi, OTR respectively. Here ASP denotes the Aggregated Service Points, OTR denotes the Off Take Regulator and i provides spatial aggregation area (where i=1, 2, 3, 4 or 1234). 33

56 Chapter 3 Conceptual framework and study area Numerical weather predictions The Australian Bureau of Meteorology s previous NWP systems (GASP, LAPs, TXLAPS and MESOLAPS) were formally replaced by new operational ACCESS (Australian Community Climate and Earth System Simulator) NWP systems on 17 August The ACCESS systems are non-hydrostatic, hybrid vertical level structure, mesoscale assimilation & forecast systems developed and tested by the earth system modeling programme of the Centre for Australian Weather and Climate Research (CAWCR). These systems are based on the UK Met Office Unified Model/Variational Assimilation (UM/VAR) system and use a four-dimensional variation data assimilation scheme (4DVAR), which results in significantly more extensive use of observations compared with the previous NWP systems such as GASP and LAPS [BoM, 2010]. The initial ACCESS system rollout has been designated the Australian Parallel Suite 0 (APS0). The domains and resolutions of the each NWP ACCESS model are given in Figure 3.3 and Table 3.2 respectively. The temporal lead time and spatial resolutions for ACCESS systems vary hours and 5-80 km respectively (Table 3.2). The forecast performance of ACCESS systems for meteorological variables such as precipitation and mean sea level pressure has been investigated thoroughly [BoM, 2010; BoM, 2012] and the forecasts have been extensively used for weather and short-term stream flow forecasting [Pagano et al., 2010; Shrestha et al., 2013; Shrestha et al., 2012]. These studies have shown that numerical weather predictions from ACCESS-C and ACCESS-A, with spatial resolutions of 5 and 10 km respectively, were relatively free from bias and that the coarser ACCESS systems had widespread systematic biases due to topography, evaporative cooling effect and land use etc. Furthermore, in hydrological applications NWP outputs from the ACCESS system are most often averaged up to daily and/or catchment scale as the forecast performance at the native resolution of the ACCESS systems (e.g. 5 km, hourly) and station observations appeared to have nearly no skill. All these results suggest that downscaling and bias adjustment is necessary at least for the ACCESS-R and ACCESS-G system outputs before use in modeling. Selecting an ACCESS system for this research is a trade-off between various factors such as forecast performance, forecast horizon, spatial resolution, and downscaling requirements including bias adjustment, since forecasting uncertainties are greater for higher spatial resolution models and longer lead times. From the real-time irrigation decision making perspective, better decisions can be made when more near future information are available. Given that the issues related to travel time, this research aims to forecast irrigation demand for lead times of at least four days. Therefore, the ACCESS-G system was selected since it has a lead time of 240 hours, in contrast to the next highest resolution model, which has a lead time of only 72 hours. 34

57 Chapter 3 Conceptual framework and study area Table 3.2 Type of NWP models and resolution in Australia [BoM, 2010] NWP System Domain Type SR 1 1 Spatial resolution, 2 Temporal resolution, 3 Assimilation, and 4 Forecast ACCESS-G is run twice a day, providing forecasts starting at a.m. and p.m. local time (i.e and 1200 UTC). The outputs from these runs are available at p.m. and 3.50 a.m. (the next day), respectively [BoM, 2010]. The NWP outputs from ACCESS-G corresponding to the a.m. local time run for the period of two years starting from 17 August 2010 to 01 August 2012 were used for this research. Then, nine mid-night to mid-night daily ET O forecast values and nine 9.00 a.m. to 9.00 a.m. daily precipitation forecast values were constructed using the three hourly NWP forecast outputs of precipitation, air temperature, dew point temperature, wind speed and incoming solar radiation. The four grid points surrounding the station were linearly interpolated to the AWS location. For some coastal sites included in Chapter 4 and 5, some of the grid points were over the sea and the preliminary evaluation found better results when all four points were included, rather than land-only points. Therefore, for all sites, ACCESS-G outputs were downscale by interpolation from the four neighbouring grid points combined with bias and variance correction regardless of the locations of grid points. (km) TR 2 (Hours) Duration ( Hours ) Runs (UTC) ACCESS - G Global Assim. 3 + Fcst , 12 ACCESS - R Regional Assim. 3 + Fcst , 12 ACCESS - T Tropical Assim. 3 + Fcst , 12 ACCESS - A Australia Assim. 3 + Fcst , 12 ACCESS - C Brisbane Fcst , 06, Perth Fcst. 4 12, 18 Adelaide Fcst. 4 VICTAS Fcst. 4 Sydney Fcst. 4 ACCESS - TC TropicalCyclone Assim. 3 + Fcst , 12 Figure 3.3 Spatial resolution of ACCESS models [BoM, 2010] 35

58 Chapter 3 Conceptual framework and study area Observed climatic data from automatic weather stations The Australian Bureau of Meteorology (BoM) is tasked with maintaining a network of weather observations across the Australian Continent and it provides weather and climate data with various reporting frequencies including annual, monthly, daily, three hourly, hourly, half hourly, and 6-minutes [BoM, undated-a]. Observed weather data were collected from 40 AWSs across Australia given that the analyses in Chapters 4 and 5 extend to the Continental scale. The commencement date of these AWSs varies between 1989 and 2009 and determines the period of available data. Longer data periods are desirable for climatological calculation and hence, hourly weather data recorded until 05 March 2013 were collected irrespective of commencement date. For the modelling experiments in Chapters 6 and 7, climate data were collected from two AWSs and three rain gauge sites located in the vicinity of the study area. These two AWSs were included in the 40 used in Chapters 4 and 5. The data used from the AWSs for ET O calculation included wet and dry bulb temperature, and wind speed. Relative humidity was calculated based on measured dry and wet bulb air temperature and wind speed, corrected to 2 m elevation. The screen height for temperature measurements was 1.2 m and wind speed was measured at 10 m [BoM, 1997]. Recorded hourly wind speed was mostly an average over the ten minutes prior to the observation time. Solar or shortwave radiation can be measured using ground-based pyranometers or estimated from space-based satellite imagery. Pyranometers require frequent calibration due to changing sensitivity with time and exposure to radiation, which is expensive and time consuming. Therefore, the Bureau's AWSs are not equipped with pyranometers. For this research, the Bureau's daily incoming solar radiation product derived from satellite imagery from the Geostationary Meteorological Satellites GMS-4, GMS-5, and MTSAT-1R, MTSAT-2 of the Japanese Meteorological Agency, and the USA's National Oceanic & Atmospheric Administration GOES-9 satellite was used [Weymouth and Le Marshall, 2001]. This product is tuned with the measured daily solar radiation from the ground-based data collected using pyranometers placed in nine monitoring sites throughout Australia. 36

59 Chapter 4 Daily ET O estimates Chapter 4 Comparison of hourly and daily reference crop evapotranspiration equations across seasons and climate zones in Australia Published as Perera, K. C., Western, A. W., Nawarathna, B., George, B., 2015, Comparison of hourly and daily reference crop evapotranspiration equations across seasons and climate zones in Australia, Agriculture Water Management, Volume 148, and Page

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61 Chapter 4 Daily ET O estimates 4.1 Abstract Estimates from the FAO Penman-Monteith (FAO-PM) and the standardized ASCE Penman- Monteith (ASCE-PM) hourly and daily reference evapotranspiration (ET O) equations were compared at daily scale, based on the hourly climate data collected from 40 geographically and climatologically diverse Automatic Weather Stations (AWS) across the Australian continent. These locations represent 23 agricultural irrigation areas in tropical, arid and temperate climates. The aims of this paper are to: compare the effects of different methods of estimating Clear-sky-radiation (R so); compare sum-of-hourly and daily ET O; compare the results of aggregation of hourly ET O over 24 hours compared with daylight hours; and examine the impact of seasonality and climate type. At selected AWS locations, the hourly ET O was calculated using the hourly FAO-PM and the ASCE- PM equations and then summed to derive daily ET O (reported as ET O, soh). This was compared against the daily ET O values, calculated using the corresponding daily equation (reported as ET O, daily). Using R so calculated following the complex approach improves the agreement between ET O, soh and ET O, daily of both hourly equations, compared with the simple approach. Better agreement between ET O, soh and ET O, daily estimates for the FAO-PM and ASCE-PM were found, when the hourly values are aggregated over 24 hours rather than over daylight hours. The average ratio between ET O, soh and ET O, daily for the FAO-PM and ASCE-PM equations is 0.95 and 1.00 respectively. The range of the former is and that of the latter is There was very strong correlation between the two hourly equations at the daily time step: on average 0.997, with a range of The results imply that the ASCE-PM hourly equation s daily ET O values are higher than those of FAO- PM, which can be explained by the difference in the treatment of surface resistances. Better agreements between ET O, soh and ET O, daily values for winter, spring and autumn were found for the FAO-PM version, while during summer, the ASCE-PM version showed better agreement. The best agreement between the hourly and daily results for the FAO-PM version was found in temperate climates and the ASCE-PM version showed best agreement in the tropical and arid climates. 4.2 Introduction During the 20 th century, the rate of fresh water consumption has increased at more than twice the rate of population growth, [UN-Water, 2006]. It is anticipated that in 2025 there will be 50% and 18% growth in fresh water withdrawals in developing and developed countries, respectively [UNEP, 2007]. At present, agricultural irrigation consumes 70% of the world s fresh water withdrawals. Therefore, more efficient irrigation water use is essential. Irrigation water requirement depends mainly on evapotranspiration (ET). Quantification of ET assists in carrying out tasks such as water allocation, water resource management and planning, water and energy balance estimation, yield estimation and irrigation scheduling. However, direct measurement of ET is difficult and costly, 39

62 Chapter 4 Daily ET O estimates given that it is a vapour transfer process affected by dynamic factors such as weather parameters, crop characteristics and management and environmental aspects [Allen et al., 1998]. Jensen, [1968] introduced a conceptual approach to estimate crop-et using reference evapotranspiration (ET O) and a crop coefficient (K c), where ET O is crop-et from the reference surface and K c is the ratio between actual crop ET and ET O. Based on this concept, the Food and Agricultural Organization s (FAO) Irrigation and Drainage Paper no. 24 provided guidelines to calculate ET O based for a reference crop of 8 to 15 cm tall green grass. They also provided a range of K c for various crops [Doorenbos and Pruitt, 1977]. They recommended four methods to calculate ET O, namely, Blaney-Criddle, FAO-24 Radiation, modified Penman, and pan evaporation, depending on data availability. The modified Penman was the preferred method of the four recommended methods, but it has frequently overestimated ET O (by up to 20%) in low evaporative conditions, with the over-estimation of ET O differing with locality [Allen et al., 1998]. Subsequently, FAO Irrigation and Drainage Paper no. 56 (FAO-56) was published along with hourly and daily FAO Penman-Monteith (FAO-PM) ET O equations. These are based on a 12 cm high hypothetical reference crop and updated K c values are supplied [Allen et al., 1998]. The daily FAO-PM equation was recommended as the sole standard method for computing daily ET O and numerous studies were conducted to evaluate its performance against other ET O equations as well as against measured ET O [Allen et al., 1989; Amatya et al., 1995; Chen, 2005; Chiew et al., 1995; George et al., 2002; Jensen et al., 1990]. However, only a handful of studies have been conducted to evaluate the FAO-PM hourly ET O equation and its performance at daily and sub-daily time scales [Irmak et al., 2005; Itenfisu et al., 2003; Temesgen et al., 2005]. In 1999, the Evapotranspiration in Irrigation and Hydrology Committee of the American Society of Civil Engineers (ASCE) endeavoured to standardize ET O calculations, and updated the hourly and daily ET O equations provided in the FAO-56 [Walter et al., 2005]. As an alternative to FAO-PM hourly and daily ET O equations, the ASCE committee proposed a standardized Penman- Monteith equation to calculate both hourly and daily ET O. The standardized Penman-Monteith (ASCE-PM) ET O equation is based on two different reference surfaces, a short crop (similar to clipped grass) and a tall crop (similar to full - cover alfalfa). During the standardization process, the ASCE committee used two constants, namely the numerator - C n (as an alternative to 900 in the FAO-PM) and the denominator - C d (as an alternative to 0.34 in the FAO-PM). Values of C n and C d vary according to the reference surface and time step. The FAO-PM and ASCE-PM ET O equations for daily time step are identical. However, for a short crop, the ASCE-PM hourly equation C n values use surface resistances of 50 sm 1 and 200 sm 1 during the day-time and night-time respectively, compared with the uniform surface resistance of 70 sm 1 throughout 24 hour period for the FAO- PM hourly equations. This is due to the fact that several studies have shown that the uniform surface 40

63 Chapter 4 Daily ET O estimates resistance assumption of 70 ms -1 (standard height of 0.12 m) of the FAO-PM hourly version results in day-time hourly ET O estimates being more than the actual field observations and vice-versa for night-time conditions [Allen, 1996; Allen et al., 2006; Irmak et al., 2005; Ventura et al., 1999; Walter et al., 2005]. As part of the ASCE standardization process, Itenfisu, [2003] estimates from hourly (aggregated to daily) and daily ET O equations for grass and alfalfa reference surfaces across 49 locations in the United State of America (USA) using ASCE-PM were compared with various other ET O equations including the FAO-PM. Results showed that the ratio between the sum-of-hourly and daily ET O values for the FAO-PM version ranged from 0.90 to 1.04 and from 0.94 to 1.07 for the ASCE-PM version. In terms of agreement between hourly and daily versions, it was found that the ASCE-PM ET O equations agreed better than the FAO-PM equations. The study did not examine possible causes of differences between the two versions that were found in terms of location, especially advective and non-advective environments. Irmak et al., [2005] stated that the differences were partially due to the constant daily ratio between soil heat flux density and net radiation at the crop surface [Irmak et al., 2005]. They recommended the ASCE hourly ET O equation, as opposed to the FAO-PM version, when hourly climate data is available; due to the fact that neither daily equation reflects diurnal changes in wind speed, air temperature, or vapour pressure deficit. Similar conclusions were drawn by Gavilán et al., [2008] for semi-arid climate conditions in Andalusia, Southern Spain[Gavilán et al., 2008]. They found that hourly ET O calculated using the ASCE-PM version was 4% higher on average compared with the FAO-PM version. However, daily ET O calculated using the ASCE-PM hourly equation was higher than the ASCE daily ET O equation, and the differences between these two estimates were not dependent on the wind speed or the magnitude of the ET O values. Studies comparing ET O estimates with measurements have also been conducted. Berengena and Gavilan, [2005] found that hourly ET O calculated using the ASCE-PM and FAO-PM versions underestimated measured hourly ET O by 2% and 3% respectively, in Cordoba, Spain [Berengena and Gavilan, 2005]. Contrasting conclusions were derived by Lopez Urrea and López, [2006] after evaluating measured and calculated hourly ET O under the semiarid conditions in Albacete, Spain [Lopez Urrea and López, 2006]. They revealed that on an average calculated hourly ET O using the FAO-PM version was similar to the measured hourly ET O, but on average the ASCE-PM version was 4% higher. This result was supported by Suleiman and Hoogenboom, [2009] using 15-minutes climate data for eleven representative and well-distributed sites throughout the state of Georgia, USA [Suleiman and Hoogenboom, 2009]. They stated that more consistent results were found between hourly and daily FAO-PM ET O equations in humid climates, and that the hourly ET O calculated using ASCE-PM were higher than those of FAO-PM during the day and vice-versa during 41

64 Chapter 4 Daily ET O estimates the night, which results from the treatment of surface resistance as 50 sm 1 during the day and 200 sm 1 during the night, respectively. In contrast, Yildirim, [2004] calculated daily ET O using 12- minute interval meteorological data for the GAP project, Turkey and found that the FAO-PM hourly equation underestimated daily ET O by 2 mm day -1 [Yildirim, 2004]. These results all suggest inconsistencies between daily ET O calculated using the hourly equation (ASCE-PM or FAO-PM) and the respective daily equation as well as between daily ET O calculated using the two hourly equations. Previous studies conducted to evaluate the agreement between daily ET O calculated using hourly and daily equations in the USA and Europe have drawn conflicting conclusions. Therefore, on the global scale, we are unable to distinguish a version (ASCE-PM or FAO-PM), which provides the best agreement between the hourly and daily ET O equation at daily scale. The degree of agreement respect to ASCE-PM or FAO-PM equations were highly influenced by the locality and the degree of diurnal change. On the other hand, the hourly ET O equations have often been used to calculate daily ET O due to the sub-daily reporting frequency of expanded AWS networks and subdaily temporal scales for numerical weather prediction models and irrigation scheduling tools. For these reasons, it is important to distinguish the agreement between daily ET O calculated using the hourly and daily equation and to understand whether the degree of agreement is geographically consistent or location dependent. Furthermore, no studies have compared hourly and daily based estimates of ET O by season to identify whether systematic differences between the methods are seasonally dependent. This paper aims to quantify the estimation performance of daily ET O calculated using the FAO-PM and ASCE-PM hourly ET O equations, against the daily ET O calculated using the corresponding daily ET O equation over the Australian continent. We calculated daily ET O using the hourly equations for 40 locations (automatic weather stations), across 23 agricultural irrigation areas from nine diverse climate zones and assessed the agreement with the daily ET O calculated using the corresponding daily equation. We also evaluated the temporal, spatial and climatological variation of agreement between the methods. Further, we investigated the possible causes of differences between the methods. 4.3 Materials Study area This paper uses the same study area and climate stations as the study of ET O forecasting by [Perera et al., 2014].The study area covers a wide range of irrigation areas as well as climates across 42

65 Chapter 4 Daily ET O estimates the Australian continent. These irrigation areas fall between latitudes 15 and 39 south and longitudes 116 and 153 east. Twenty three (23) irrigation districts were included for the evaluation, based on regions where higher densities of irrigation pixels occur on the 2005/06 Australian land use map [ABARES, 2010]. We selected 40 Automatic Weather Stations (AWS) in these irrigation districts and collected a highquality and complete hourly climate data set, which is important since the quality of climate data influences the agreement between the two daily ET O estimation approaches, and completeness of the climate data impacts the reliability of evaluations of agreement. Generally, the instrument enclosure area (16 m x 16 m) of these AWSs is in the middle of a 30 m x 30 m buffer area, which is level, free from buildings or trees and aligned in the true North - South direction [BoM, 1997; BoM, 2014]. The majority of these buffer areas are mostly covered by short grass, but a few are partly covered. The short grass or natural vegetation with in the instrument enclosure area is maintained to a height of no more than 50 mm and buffer area around the enclosure is maintained to a height of no more than 500 mm [BoM, 1997; BoM, 2014]. Figure 4.1 shows the 40 AWSs in these irrigation districts together with the Köppen climate zones. Table 4.1 provides the characteristic of these AWSs, which are sorted according to the Köppen climate classification (Table 4.2). The stations fall in three main climates, namely tropical, arid and temperate, and nine sub-climates [Peel et al., 2007]. The elevation of these stations ranges from 4 m to 871 m Australian Height Datum (AHD). Mean annual precipitation and average daily mean temperature ranges from 400 mm to 2400 mm and from 0 C to 36 C, respectively. Long-term mean monthly ET O varies from 1 mm day -1 during midwinter (July) for the southern stations to 12 mm day -1 during mid-summer (January). 43

66 Chapter 4 Daily ET O estimates Table 4.1 Characteristics of automatic weather stations (sorted as per Köppen climate zone) No. AWS No. Name State Latitude ( ) Longitude ( ) El. 1 (m) Climate Zone Nos. Days Irrigation Area Townsville Airport QLD -19º14'54" 146º45'58" 4.3 Aw 2067 Burdekin-Haughton Woolshed Airport QLD -19º25'00" 146º32'11" Aw 1753 Burdekin-Haughton Kununurra Airport WA -15º46'53" 128º42'36" 44.0 BSh 1954 Ord Emerald QLD -23º34'10" 148º10'32" BSh 2026 Nogoa-Mackenzie Loxton research Centre SA -34º26'20" 140º35'52" 30.1 BSk 1873 Golden Heights Yanco AG Institute NSW -34º37'20" 146º25'57" BSk 1939 Murrumbidgee Deniliquin Airport NSW -35º33'27" 144º56'45" 94.0 BSk 1939 Murray Griffith Airport NSW -34º14'55" 146º04'10" BSk 1936 Murrumbidgee Mildura Airport VIC -34º14'09" 142º05'12" 50.0 BSk 2009 Sunrays Charlton VIC -36º17'05" 143º20'03" BSk 714 Pyramid Boort Renmark Airport SA -34º11'54" 140º40'36" 31.5 BWk 522 Renmark University of QLD QLD -27º32'37" 152º20'15" 89.0 Cfa 1968 Logan River Kingaroy Airport QLD -26º34'25" 151º50'23" Cfa 1955 Logan River Oakey Airport QLD -27º24'12" 151º44'29" Cfa 2043 Logan River Dalby Airport QLD -27º09'38" 151º15'48" Cfa 2075 Condamine Warwick QLD -28º12'22" 152º06'01" Cfa 1910 Logan River Toowoomba Airport QLD -27º32'33" 151º54'48" Cfa 1973 Logan River Narrabri Airport NSW -30º18'55" 149º49'49" Cfa 1845 Namoi Gunnedah Airport NSW -30º57'13" 150º14'58" Cfa 1930 Namoi Temora Airport NSW -34º25'45" 147º30'40" Cfa 1892 Murray 44

67 Chapter 4 Daily ET O estimates No. AWS No. Name State Latitude ( ) Longitude ( ) El. 1 (m) Climate Zone Nos. Days Irrigation Area Kyabram VIC -36º20'06" 145º03'50" Cfa 1982 Central-Goulburn Tatura Sustainable Institute VIC -36º26'16" 145º16'02" Cfa 853 Central-Goulburn Yarrawonga VIC -36º01'46" 146º01'50" Cfa 1956 Shepparton Shepparton Airport VIC -36º25'44" 145º23'41" Cfa 2046 Shepparton Applethorpe QLD -28º37'18" 151º57'12" Cfb 1855 Condamine Bendigo Airport VIC -36º44'22" 144º19'36" Cfb 1945 Central-Goulburn East sale Airport VIC -38º06'56" 147º07'56" 4.6 Cfb 1600 West Gippsland Bairnsdale Airport VIC -37º52'54" 147º34'01" 49.4 Cfb 1934 Shepparton Morwell Airport VIC -38º12'34" 146º28'29" 55.7 Cfb 2084 West Gippsland Mount Moornapa VIC -37º44'53" 147º08'34" Cfb 2053 West Gippsland Colac VIC -38º14'00" 143º47'33" Cfb 1949 Gippsland Collie east WA -33º21'39" 116º10'18" Csa 1919 South West Dwellingup WA -32º42'37" 116º03'34" Csb 1042 South West Bridgetown WA -33º56'55" 116º07'52" Csb 1830 South West Nuriootpa SA -34º28'34" 139º00'20" Csb 448 South East Mount Gambier Airport SA -37º44'50" 140º46'26" 63.0 Csb 1950 South East Coonawarra SA -37º17'26" 140º49'31" 57.0 Csb 1494 South East Casterton VIC -37º34'59" 141º20'02" Csb 1863 South East Dartmoor VIC -37º55'20" 141º15'41" 51.0 Csb 1354 South East Ayr DPI Centre QLD -19º37'01" 147º22'33" 17.0 Cwa 608 Burdekin-Haughton 1 Elevation, NSW-New South Wales, QLD-Queensland, SA-South Australia, VIC-Victoria, WA-Western Australia 45

68 Chapter 4 Daily ET O estimates Figure 4.1 Locations of the automatic weather stations fall under Köppen climate map [Peel et al., 2007] Table 4.2 Description of Köppen climate symbols and defining criteria for the climate zone in the study [Peel et al., 2007] 1 st 2 nd 3 rd Description A Tropical w - Savannah B Arid W - Desert S - Steppe h - Hot k - Cold C Temperate s - Dry Summer w - Dry Winter f - Without dry season a - Hot Summer b - Warm Summer 46

69 Chapter 4 Daily ET O estimates Climate data The Australian Bureau of Meteorology (BoM) maintains the network of AWSs across the Australian Continent and provides climate data with various reporting frequencies including monthly, daily and sub-daily scales [BoM, undated-a]. The purpose of the AWS is classified according to the observation program and 40 selected stations are classified as synoptic (seasonal, climatological, aeronautical and upper air etc.). These synoptic AWSs measure climate data in compliance with world meteorological standards [WMO, 2010]. Commencement dates for the AWSs used here vary between 1989 and 2009 and this determines the data availability. We used a six year study period from 01 January 2007 to 31 December Five out of the 40 AWSs commenced operation after 01 January 2007 but were included nevertheless since there were no alternates within those irrigation districts. We obtained hourly temperature, dew point temperature, relative humidity and wind speed recorded at the AWSs. Relative humidity was based on measured dry and wet bulb air temperature and wind speed, with a correction for station elevation. The screen height for temperature measurements was 1.2 m and wind speed was measured at 10 m [BoM, 1997]. Recorded hourly wind speed was mostly an average over the ten minutes prior to the observation time. Solar or shortwave radiation can be measured using ground-based pyranometers or estimated from space-based satellite imagery. Pyranometers require frequent calibration due to changing sensitivity with time and exposure to radiation, which is expensive and time consuming. Therefore, the Bureau's AWSs are not equipped with pyranometers. For this study, the Bureau's daily incoming solar radiation product derived from satellite imagery was used [Weymouth and Le Marshall, 2001]. This product is tuned with the measured daily solar radiation from the ground-based data collected using pyranometers placed in nine monitoring sites throughout Australia. The measurement range and accuracy of these observed weather variables were given in Table 4.3. Figure 5.12 of the Chapter 5 provides a comparison of satellite and ground-based measurements. Table 4.3 Measurement range and accuracy of climate variables from AWS [BoM, undated-b] Sensor Range Accuracy Unit Air Pressure 750 to hpa Air temperature -25 to C Wet bulb temperature -25 to C Relative Humidity 2 to % Wind Speed 2 to knot Wind Direction 0 to degree Rainfall 0 to % mm 47

70 Chapter 4 Daily ET O estimates It is important to note that the measurement conditions for the operational climate data from the AWSs do not reflect the reference conditions for ET O calculation, which is often the case. Key differences are that soil moisture may be restricting evapotranspiration, the temperature and humidity measurements are at less than 2 m height (rather than 2 m) and the wind measurements are at 10 m (which we corrected to the ET O standard 2 m). It is unlikely that the differences in measurement conditions significantly influence the agreement between hourly and daily ET O calculations, as the same data is used irrespective of the time step. The effect of using disaggregated rather than measured hourly radiation is examined later. 4.4 Methodology Data processing Automatic weather stations nominally provide continuous measured weather data; however, there were times within the study period when hourly weather data were missing due to various reasons. In those instances, the entire day was removed from the data set. Table 4.1 provides the number of evaluated days for each AWS and the percentage of missing data. We assessed approximately 180 station-years of data or on average 1,727 AWS-days per location, ranging between 448 and 2,084 AWS-days respectively. The mean hourly air temperature was computed using two consecutive hourly readings and the mean daily air temperature was taken as the average of daily maximum and minimum air temperature rather than the mean of the hourly air temperatures for a given day. This was to avoid underestimation of daily ET O due to the non-linear relationship between the saturation vapour pressure and temperature [Allen et al., 1998]. The mean hourly or daily dew point temperature was calculated by taking the average over the given period of time. BoM uses four types of anemometers, mounted 10 m above the ground level to measure the wind speed and record hourly wind speed, mostly an average over the ten minutes prior to the observation time [BoM, 1997; Huysing and Warne, 1993]. Then, the mean hourly or daily wind speed at the standard height of 2 meters was calculated by taking the average over the given period of time and converting to 2 m height by multiplying by a factor derived from Eq. (4.1), in line with the wind profile relationship provided in FAO-56. The starting threshold for these anemometers is 2 knot or 1.03 m s -1. Across the 40 stations, on average, recorded wind speed exceeded the starting threshold % of the time. Therefore, a specific threshold correction method was not applied as impact from very low wind speed values for the agreement between hourly and daily ET O values is minor. Wind speed measurements below the threshold were entered as zero. 48

71 Chapter 4 Daily ET O estimates u 2 = u z 4.87 ln(67.8z 5.42) (4.1) where; u 2 is wind speed at 2 m above ground surface (ms -1 ), u z is measured wind speed at z m above ground surface (ms -1 ), z is height of measurement above ground surface (m). The Bureau does not have sub-daily incoming solar radiation products for the stations studied. Hourly incoming solar radiation values were calculated using daily values and a daily to hourly incoming solar radiation disaggregation method, which assumed a temporal pattern consistent with a clear-sky day due to the fact that there is no way to determine various circumstances such as intermittent heavy\light clouds or continuous light clouds from the daily totals [Duffie and Beckman, 2006]. The incoming solar radiation disaggregation method (described in more detail in section 4.4.5) provided robust results as shown below. This may reflect a high number of clear-sky days, as found by [Duffie and Beckman, 2006] ETO equations All daily ET O calculations were made according to the guidelines provided in FAO-56 [Allen et al., 1998] or the ASCE Task committee final report [Walter et al., 2005], as appropriate. Both of these estimate daily ET O for a 12 cm high hypothetical grass surface reference crop [Allen et al., 1998]. Eq. (4.2) denotes the FAO-PM and ASCE-PM hourly and daily ET O equations. ET 0 = (R n G)+γ C n T+273 u 2 (e s e a ) +γ(1+c d u 2 ) (4.2) where; ET O is the daily or hourly reference crop evapotranspiration (mm day -1 or mm hour -1 ), Δ is the slope of the saturation vapor pressure versus air temperature curve (k Pa C -1 ), R n is the daily or hourly net radiation at the crop surface (MJ m -2 day -1 or MJ m -2 hour -1 ), G is the daily or hourly ground heat flux density at the soil surface (MJ m -2 day -1 or MJ m -2 hour -1 ), T is the mean daily or hourly air temperature at 1.5 to 2.5 m height ( C), U 2 is the mean daily or hourly wind speed at 2 m height (m s 1 ), e s is the saturation vapor pressure (kpa), e a is the actual vapor pressure (kpa), γ is the psychometric constant (kpa C 1 ), and is a coefficient (m 2 mm MJ 1 ) converting energy flux to water flux FAO-PM equation The FAO appointed a panel of experts and researchers in 1990 to revise and update the FAO crop water requirement guidelines. The panel adopted the Penman-Monteith (PM) combination method to estimate the ET O of a 12 cm high hypothetical grass surface. The equations use a surface resistance of 70 sm -1 ; an albedo or canopy reflection coefficient of 0.23, and Stefan-Boltzmann 49

72 Chapter 4 Daily ET O estimates constant of MJ K -4 m -2 day -1. The corresponding values for C n and C d of the FAO-PM hourly and daily equations are provided in Table 4.4. FAO-56 provides three methods to estimate the actual vapor pressure (e a) depending on climate data availability. No preference is expressed and the choice leads to slight differences in e a values. We calculated e a for hourly and daily periods using the average relative humidity and the saturated vapour pressure for the given period. FAO-56 guidelines also provide the equations to estimate clear-sky solar radiation (R so) with or without calibrated values of the fraction of extra-terrestrial radiation reaching the earth on clear-sky days. They recommended a complex procedure to obtain more accurate R so by considering the turbidity and vapor effect and using Beer s law ASCE standardized PM equation In 1999, the American Society of Civil Engineers appointed a task committee to standardize the prevailing ET O equations and crop coefficients. They derived a standardized ET O equation for two reference surfaces; a short crop of 0.12 m tall grass and a tall crop of 0.5 m tall rougher crop surface like alfalfa. Only the short crop is considered in this study. The ASCE-PM equations use different surface resistances depending on the reference surface (short/tall), temporal scale (daily/hourly) and time of calculation (day/night) (Table 4.4). Further, the committee updated equations related to the estimation of clear-sky solar radiation (R so) by modifying some of the constants when calculating the clearness index for direct beam radiation (K B) and the corresponding index for diffuse beam radiation (K D). Moreover, the committee recommended an order of preference to estimate actual vapor pressure (e a) depending on climate data availability and to avoid differences in e a values. We followed the same method (used for the FAO-56 version) to calculate e a for hourly and daily periods, to maintain consistency during the comparison. During the standardization, six equations related to the three time steps and two reference surfaces were reduced to a single equation (Eq. (4.2)) using two constants, C n and C d, the values of which are shown in the Table 4.4. Table 4.4 Values for C n and C d Version Time step C n C d r s (m s 1 ) Units for ET O Short reference (0.12 m high) Units for R n and G FAO-PM Daily mm day -1 MJ m -2 day -1 Hourly ( day & night times) mm hour -1 MJ m -2 hour -1 ASCE-PM Daily mm day -1 MJ m -2 day -1 Hourly ( daytime) mm hour -1 MJ m -2 hour -1 Hourly ( night-time) mm hour -1 MJ m -2 hour -1 50

73 Chapter 4 Daily ET O estimates Calculating ETO Four daily ET O values for a given day were calculated using hourly and daily ET O equations of FAO-PM and ASCE-PM. The daily ET O calculated using the hourly equations was based on the basis of sum-of-hourly ET O (SOH) for a 24 hour period and two daily ET O estimates were reported as ET O, soh, FAO and ET O, soh, ASCE respectively. The two daily ET O estimates calculated using the daily equations were reported as ET O, daily, FAO and ET O, daily, ASCE respectively. The FAO-PM and ASCE-PM equations use the same procedure to compute hourly and daily R n, G, u 2, e s and e a. The latter three parameters were calculated as described in section R n is significantly larger than G and the calculation procedure for hourly and daily G for both the FAO-PM and ASCE-PM equations are identical and depend on R n (Eqs. ( 4.3)-(4.5)). G daily = 0 (4.3) G hourly (daytime) = 0.1 R n (4.4) G hourly (nighttime) = 0.5 R n (4.5) Hourly or daily R n was calculated as the difference between the incoming net shortwave radiation(r ns) and the outgoing net longwave radiation (R nl) [Allen et al., 1998]. Hourly or daily R ns was calculated using the incoming shortwave solar radiation (R s) and an albedo of Daily R s was taken as the Bureau daily R s products. Hourly R s was calculated by disaggregating daily R s into hourly R s using the ratio of hourly total to daily total R s for each hour, r t, which was calculated using Eqs. (4.6)-(4.8), as suggested by [Collares-Pereira and Rabl, 1979]. Although, this method performs best for clear-sky days as daily R s values do not reflect intermittent cloudiness or turbidity, many studies have evaluated the performance of the disaggregation method using pyranometers and found that it provides accurate hourly R s across climates and seasons [Ahmad and Tiwari, 2008; Benseman and Cook, 1969; Collares-Pereira and Rabl, 1979; Kumar et al., 2009; Singh et al., 1997]. r t = π 24 (a + b cos ω) cos ω cos ω s sin ω s πω s 180 cos ω s (4.6) a = sin(ω s 60) (4.7) b = sin(ω s 60) (4.8) where; ω and ω s are hourly angle and sunset angle in degrees Daily R nl was estimated from the daily maximum and minimum air temperature and relative shortwave radiation, calculated using the collected daily R s and calculated clear-sky solar radiation (R so) (Eq. (4.9)). 51

74 Chapter 4 Daily ET O estimates R nl,daily = σ. [ T max,k 4 +T min,k 4 2 ]. ( e a ). (1.35 R s Rso 0.35) (4.9) where; R nl, daily is the daily net outgoing longwave radiation (MJ m -2 day -1 ), σ is the Stefan- Boltzmann constant ( MJ K -4 m -2 day -1 ), T max,k and T min,k are maximum and minimum absolute temperature during the 24-hour period (K= C ), R s/r so is the relative shortwave radiation(limited to 1) Hourly R nl was estimated from the mean hourly air temperature and relative shortwave radiation, calculated using the hourly R s and hourly R so (Eq. (4.10)). R nl,hourly = σ. T 4 hr,k. ( e a ). (1.35 R s 0.35) (4.10) Rso where; R nl, hourly is the hourly net outgoing longwave radiation (MJ m -2 hour -1 ), σ is the Stefan- Boltzmann constant ( MJ K -4 m -2 hour -1 ), T hr,k mean absolute temperature during the hourly period (K= C ), R s/r so is the relative shortwave radiation(limited to 1) R so was calculated using both the simple and the complex approaches described in FAO- 56 [Allen et al., 1998] and the ASCE task committee final report [Walter et al., 2005]. The daily ET O resulting from these two approaches were compared given that calculated hourly and daily R s/r so depends on the R so calculation method. First, we calculated R so as a function of station elevation and extra-terrestrial radiation using Eq. (4.11) and this approach is identical for the FAO- PM and ASCE-PM versions. Secondly, R so was calculated using complex approach (Eq. (4.12)), which is more accurate [Allen et al., 1998; Walter et al., 2005] and considers sun angle, water vapour and turbidity effects. The calculation procedure for the complex approach is identical for FAO-PM and ASCE-PM versions, but constants used during the calculation of the clearness index for direct beam radiation (K B) and the corresponding index for diffuse beam radiation (K D) are different. R so = ( z)r a (4.11) R so = (K B + K D )R a (4.12) where; z is the station elevation above the sea level, R a is the extra-terrestrial radiation (MJ m -2 day -1 ), K B is the clearness index for direct beam radiation and K D is the corresponding index for diffuse beam radiation. We also calculated daily ET O during the day light hours using the hourly equations. These two daily ET O estimates were reported as ET O, dlh, FAO and ET O, dlh, ASCE respectively. The day light period varies with the latitude of AWS and Julian day of the year. First, the sunrise and sunset angles were calculated for each station and day of year. Secondly, the day light period was taken as the 52

75 Chapter 4 Daily ET O estimates time period between sunrise and sunset. Then, the calculated hourly ET O was filtered according to the day light hours and summed to derive daily ET O, dlh for each version Assessing the agreement The FAO-PM and ASCE-PM hourly ET O equations are intended to apply on an hourly basis rather than a sum-of-hour basis for daily time step. However, in principle, daily ET O calculated using the hourly ET O equation and sum-of-hour basis should be equal to that calculated using the respective daily ET O equation. Scatter between the two daily ET O estimations reflects a fundamental difference, where former method focusses on diurnal changes and the latter method focuses on average conditions for a given day. The statistical indices used to quantify the agreement between different equations were the root mean squared difference (RMSD) (Eq. (4.13)), the coefficient of determination (R 2 ) (Eq. (4.14)), the slope and intercept of the linear regression line and the ratio between daily ET O values. The slope and intercept of the linear regression line between ET O, soh and ET O, daily for each version are indicators of systematic bias. The daily ET O calculated using the hourly ET O equations were taken as dependent variable and daily ET O calculated using the corresponding daily ET O equation was taken as the explanatory variable. As a result, the daily ET O calculated using the daily ET O equation became the benchmark, which can be justified as follows. (1) The daily ET O equations are recognized as the standard method of computing daily ET O [Allen et al., 1998]. (2) Under the standard conditions, daily ET O values calculated using both daily ET O equations are identical [Walter et al., 2005]. (3) Practically, daily ET O is a presumed value that is very difficult to measure under the defined context. The ratio of the daily ET O from the sum-of-hourly equation and the daily ET O was calculated for each day and averaged. RMSD = ( n i=1 (ET o,soh,x ET o,daily,x ) n R 2 = 1 i=1 (ET o,soh,x ET o,soh,x n ) ) n (ET o,daily,x ET ) 2 i=1 o,daily,x (4.13) (4.14) In Eqs. (4.13)-(4.14), the over bar indicates the mean of the corresponding variable. 4.5 Results and discussion Our comparison mainly focuses on the over/underestimation of daily ET O,soh compared with the corresponding ET O,daily and probable causes of difference between the daily ET O,soh values estimated from the hourly ET O equation of ASCE-PM and FAO-PM, since the two daily ET O equations are identical. This section is structured into six subsections which address: different methods of estimating R so; a comparison of sum-of-hourly and daily ET O; a comparison of 53

76 Chapter 4 Daily ET O estimates aggregation of hourly ET O over 24 hours compared with daylight hours; the impact of seasonality; and the impact of climate type. These comparisons enable the probable causes for the difference between two hourly ET O values to be investigated. Due to the sheer volume of results generated from 69,088 AWS-days at 40 AWS locations, it is not practical to demonstrate these graphically for individual stations. Therefore, to maintain consistency, only the results related to the AWS at Shepparton Airport (81125) in the Shepparton irrigation region are shown graphically, where necessary and plots and tables summarizing performance across all stations are included in each section Impact of Rso calculation method As mentioned above, R so can be calculated either using the simple or the complex method. Although, FAO-56 and the ASCE Task committee final report mentioned that the complex method is more accurate, it was not practical to verify this with measured R so for the 40 AWS locations in this study. Therefore, this section investigated which R so estimation method provide the best agreement between ET O, soh and ET O, daily rather than comparing estimated R so with measured R so. Figure 4.2 shows four plots of ET O, daily against ET O, soh for all combinations of FAO-PM and ASCE- PM, with the simple and complex R so methods at Shepparton, Victoria. Table 4.5 summarizes the statistical indicators across all 40 AWS locations. For both FAO-PM and ASCE-PM, the best agreement between ET O, soh and ET O, daily was obtained, when R so was estimated using the complex approach. In both versions, the R so complex approach provided slightly lower RMSD and marginally higher R 2 values. When R so was calculated using the complex approach, the mean of the daily ratio (ET O, soh / ET O, daily) reduced by 0.19 and for FAO-PM and ASCE-PM versions respectively, compared with the simple method. Both the regression slope and intercept also reduced when moving from the simple to the complex method. Figure 4.2 Calculated daily ET O as indicated by (a) ET O, soh, FAO and ET O, daily, FAO using R so simple, (b) ET O, soh, ASCE and ET O, daily, ASCE using R so complex, (c) ET O, soh, FAO and ET O, daily, FAO using R so simple, (d) ET O, soh, ASCE and ET O, daily, ASCE using R so complex for Shepparton irrigation areas, Victoria. 54

77 Chapter 4 Daily ET O estimates Table 4.5 Summary of statistical indices for daily ET O calculated using R so simple and complex procedure Statistics R so simple R so complex FAO-PM Hourly & Daily Equations ASCE PM Hourly & Daily Equations Mean Max. Min. Mean Max. Min. RMSD Daily Ratio Regression Slope Regression Intercept R RMSD Daily Ratio Regression Slope Regression Intercept R The complex R so calculation method results in lower ET O than the simple method for both versions because it increases net outgoing longwave radiation, thus reducing net all-wave radiation and ET O estimates. The impact is greater on the hourly estimates. Both the hourly and daily R so values calculated using the complex methods from FAO-56 were slightly higher than those using the ASCE task committee final report. These results all show that daily ET O calculated using the R so complex approach provided a relatively higher agreement between ET O, soh and ET O, daily for both the versions compared to R so complex approach. This further suggests that the representation of air-turbidity, vapour pressure effect and sun angle on R so influence the agreement between ET O, soh and ET O, daily estimated values irrespective of the version Comparison of hourly and daily models Table 4.6 shows the statistical indicators for the comparison between ET O, soh and ET O, daily for the FAO-PM and ASCE-PM versions. The RMSD between the ET O, soh, FAO and ET O, daily, FAO ranges between and mm day -1 between locations, whereas those for the ASCE-PM version range between and mm day -1. At the majority of locations, RMSD values for ASCE- PM were 10% greater than FAO-PM. The exceptions are Woolshed (QLD) and Warwick (NSW). FAO-PM showed smaller systematic differences between ET O, soh and ET O, daily than the ASCE-PM version. On average the ratio between ET O, soh and ET O, daily of the FAO-PM was 0.95 (ranging between 0.90 and 0.98) and that for the ASCE-PM versions was 1.00 (ranging between 0.96 and 1.04). That is across sites the FAO-PM hourly equation shows a consistent underestimation of daily 55

78 Chapter 4 Daily ET O estimates ET O, whereas the ASCE-PM hourly equation did not. The greatest contributor to the difference is the diurnal variation in surface resistance (50 sm 1 and 200 sm 1 ) for the hourly ASCE-PM equation compared with the constant value of surface resistance (70 sm 1 ) used for the FAO-PM hourly equation. Comparatively higher variability for daily ratio (ET O, soh / ET O, daily) was observed for the ASCE-PM version than the FAO-PM version, where, the standard deviation (calculated between days of each site) for the ASCE-PM version was always higher than that of the FAO-PM. The better agreement between values of ET O, soh, ASCE and ET O, daily, ASCE for ASCE-PM than FAO-PM is also evident in the regression line slopes and intercepts (Table 4.6). In general intercepts are slightly positive and slopes are slightly less than one, suggesting that, the ET O, soh tends to exceed ET O, daily at relatively low daily ET O values. The lower slopes and intercepts for the FAO-PM indicate larger deviation from the 1:1 line at large ET O values, compared with the ASCE-PM version. The R 2 of both versions exceeds 98% for most sites and the correlation between ET O, soh and ET O, daily values was slightly higher for the FAO-PM version than for the ASCE-PM version (Table 4.6). The mean R 2 between ET O, soh, FAO and ET O, daily, FAO was 98.3% (ranging from 96.4 to 99.1%) whereas for ASCE- PM it was 98.1% (ranging from 98.9% to 95.7%). The lowest R 2 was obtained for Kununurra Airport (NT) in both the versions. This is the closest location to the equator, has a tropical climate, and is subjected to large diurnal changes. One potential factor that might influence the difference between the hourly and daily based methods is the fact that we disaggregated global radiation rather than using measured hourly radiation, due to lack of data. The radiation disaggregation method (daily into hourly) doesn t account for diurnal changes in cloudiness or turbidity. The measured hourly R S is available for a few stations and we undertook a preliminary evaluation (not presented) using the limited available data to determine the impact on the agreement between ET O, soh and ET O, daily from the disaggregation. The pairwise correlation coefficients between disaggregation hourly R S and measured hourly R S were more than across climates and seasons at Mildura (VIC) and Townsville (QLD). At Mildura the radiation data corresponds in part with the study period. When hourly observed radiation was used the correlation reduced from to , the slope changed from to and the mean ratio reduced from to , compared with using disaggregated radiation for the FAO method. Similar changes were observed for the ASCE method. This suggests that the use of disaggregated radiation had a minimal impact on the difference between ET O, soh and ET O, daily. 56

79 Chapter 4 Daily ET O estimates Table 4.6 Statistical indicators corresponds to daily ET O calculated between the hourly and daily ET O equations of FAO-PM and ASCE-PM versions for 40 AWS stations AWS ID Site FAO-PM Version ASCE-PM Version RMSD Ratio Slope Incp. 1 R 2 RMSD Ratio Slope Incp. 1 R Townsville Woolshed Kununurra Emerald Yanco Deniliquin Griffith Mildura Charlton Loxton Renmark Gatton Kingaroy Oakey Dalby Warwick Toowoomba Narrabri Gunnedah Temora Kyabram Tatura Yarrawonga Shepparton Applethorpe Bendigo East sale Bairnsdale Morwell Mount moornapa Colac Collie east Dwellingup Bridgetown Nuriootpa Mt. Gambier Coonawarra Casterton Dartmoor Ayr Incp. 1 Intercept 57

80 Chapter 4 Daily ET O estimates Another possible explanation for the difference between hourly and daily estimates is the treatment of ground heat flux. The hourly methods do not assume a zero ground heat flux on average over the day, while the daily methods do assume zero ground heat flux. We examined the possibility of using the aggregated hourly heat flux in the calculating the net energy availability in the daily equations. Doing this resulted in greater discrepancies between the hourly and daily based estimates because it tended to decrease the ET O (due to positive average hourly G) on days with high ET O and decrease it on days with low ET O. Overall the approach (FAO or ASCE) with the best agreement between the ET O, soh and ET O, daily depends on which statistics are considered. In terms of RMSD and R 2, the FAO-PM version showed best agreement, whereas the ASCE-PM worked better if we use ratio and linear regression as the indicators Seasonal impact for the ETO, soh vs. ETO, daily values This section investigates, how the agreement between the ET O, soh and ET O, daily values changes seasonally (summer, autumn, winter and spring). The statistical indicators were calculated according to the calendar months of each season in the southern hemisphere (i.e. summer: Dec-Feb, autumn: Mar-May, winter: Jun-Aug, & spring: Sep-Nov). Figure 4.3 shows the annual and seasonal box plots for various statistical indices for the 40 AWS locations. Seasonal RMSD values reduced from summer through spring and autumn to winter for both FAO-PM and ASCE-PM, in line with overall seasonal ET O variation. The ASCE-PM version shows higher median RMSD and spread for all four seasons. Figure 4.3 (b) and (c) show the daily ratio (ET O, soh / ET O, daily) and slope of the best fit regression line. In both cases, the ASCE-PM version showed a higher median and spread for all the four seasons. The mean daily ratio indicates that FAO-PM hourly ET O equation resulted in lower estimates than the daily ET O with the exception of winter and the ASCE-PM hourly ET O equation resulted in higher estimates than the daily ET O with the exception of summer. Both hourly ET O equations tend to exceed the daily ET O equation during the winter (0.04% and 8.7% respectively) and are slightly less than the daily estimates during the summer (7.5% and 3.0% respectively). During autumn and spring, the ASCE-PM hourly equation exceeds the daily ET O equation by 3.20% and 0.06% respectively, but the FAO-PM hourly equation underestimates it by 2.7% and 5.1 % respectively. The seasonal regression slope for both the version was better than that for the annual data for summer and spring and worse for winter and autumn. R 2 values were also higher for summer than winter, probably reflecting greater ET O and greater temporal variance in ET O in summer compared with winter. R 2 values were more than 0.96 in all seasons except winter. 58

81 Chapter 4 Daily ET O estimates The statistical indicators demonstrate that the correspondence between hourly and daily estimates changes with time of year. The seasonal differences in comparison are no doubt driven by the seasonal difference in magnitude of input variables such as air and dew point temperature, short wave radiation and wind speed. Higher daily ET O values led to greater RMSD and lower ratios between ET O, soh and ET O, daily. One of the reasons for the seasonal difference in sum-of-hourly ET O compared with daily ET O relates to night-time ET O. During winter night-time ET O was very small or negative and effectively did not contribute to daily ET O, whereas in summer night-time ET O was significant. Considering all these statistical indicators, the agreement between ET O, soh and ET O, daily values were better for the FAO-PM version during winter, spring and autumn, but during summer, the ASCE-PM version showed better agreement. Figure 4.3 Annual and seasonal performance between ET O, soh and ET O, daily for FAO-PM and ASCE-PM versions as indicated by (a) RMSD, (b) ratio (ET O, soh / ET O, daily ), (c) regression slope and (d) R 2 for 40 AWS locations. Each box shows the lower (25 th ), middle (50 th ) and upper (75 th ) quartile and the bottom and top whiskers represent the 5 th and 95 th percentiles Comparison of 24 hour and day-time aggregations The ASCE-PM hourly equation exceeded the daily ET O equation, with the exception of summer and the FAO-PM hourly equation exceeds daily ET O during winter. Neither the FAO-56 paper not the ASCE Task committee final report provide guidelines for the use of hourly equations at daily time steps, especially their application at night, but they do provide guidance on the use of hourly data (meteorological data averaged over a 24 hourly period) for the daily equations. Although, in principle daily ET O calculated using the hourly equation is equal to sum-of-hourly ET O over a period of 24 hours, one can rationalize the sum-of-hours basis only for the daylight hours. This could be justified by the facts that photosynthesis is inactive and net radiation is negative at night-time, suggesting zero ET O at night. A few authors, [McMahon et al., 2012; Stigter, 1980; Van Niel et al., 2011] provide the starting point for this argument and it has not been either fully rejected or fully accepted in the literature. This argument is stronger for winter than for the other seasons, 59

82 Chapter 4 Daily ET O estimates given the low number of daylight hours and dew point temperatures often exceeding night-time air temperatures resulting in zero or negative estimates of hourly ET O, which lead to reduce the sum-ofhourly ET O over a given day in winter. To examine the impact of night-time ET O, we tested the above argument for winter, and Table 4.7 provides the summary of statistical indicators during winter for daily ET O calculated using the sum-of-hourly ET O for 24 hour periods (ET O, soh) and daylight hour periods (ET O, dlh) compared against the daily ET O calculated using the daily equation (ET O, daily). Many, if not most, of the ET O, dlh values were lower than ET O, soh over 24 hours. When compared with the ET O, daily values, all performance indicators were in favor of the sum-of-hour over 24 hour period. The ET O, dlh values increased the RMSD values for both FAO-PM and ASCE-PM. The mean daily ratio for the FAO- PM version indicated that SOH basis over 24 hour period exceeded daily ET O (1.004) whereas the same was underestimated (0.982) during daylight-hours. For the ASCE-PM version, the daylighthour basis further enlarged the ratio from to The regression slope and R 2 values for both the versions decreased from SOH basis over 24 hour period to the daylight-hour basis. All the statistical indices indicate that better agreement is achieved between hourly and daily ET O estimates when the hourly values are aggregated over 24 hours rather than over daylight hours. Table 4.7 Summary of statistical indices for daily ET O calculated based on day light hour and sumof-hour using hourly ET O equations for winter Version Statistics SOH - 24 Hours SOH - DLH Hours Mean Max. Min. Mean Max. Min. RMSD Daily Ratio FAO-PM Regression Slope Regression R RMSD Daily Ratio ASCE-PM Regression Slope Regression R Comparison of hourly ETO equations The main difference between the FAO-PM and ASCE-PM hourly equations is the surface resistance (r s), where the former is based on an r s of 70 sm 1 for all times while the latter is based on 60

83 Chapter 4 Daily ET O estimates an r s of 50 sm 1 for the day-time and 200 sm 1 for the night-time. The diurnal variation of hourly ET O, energy, bulk and aerodynamic resistances for the two hourly equations for hot and cold days is shown in Figure 4.4, and the respective statistical indicators are given in Table 4.8. The correlation between the daily ET O calculated using FAO-PM and ASCE-PM hourly ET O equations (ET O, soh, FAO and ET O, soh, ASCE) was 0.99 on average. Moreover, the RMSD between ET O, soh, FAO and ET O, soh, ASCE was very small, compared with the RMSD between ET O, soh and ET O, daily of the respective versions. The mean daily ratio between the ET O, soh, FAO and ET O, soh, ASCE values was always less than one (i.e. ASCE-PM hourly ET O > FAO-PM hourly ET O). This was mainly due to the difference in r s, since the hourly energy term and bulk surface resistance terms remained almost the same for both versions for all hourly periods (Figure 4.4). Therefore, for the ASCE-PM version, the higher hourly ET O during the day-time outweighed the lower hourly ET O during the night, resulting in higher overall daily ET O. This was reflected in the regression slope and intercept for all 40 locations. Figure 4.4 (a) Hourly ET O (b) Hourly energy (c) Bulk resistance and (d) Aerodynamic resistance for a warm day in the summer and a cold day in winter, calculated using hourly FAO-PM and ASCE- PM ET O equations at Shepparton airport AWS, Victoria. 61

84 Chapter 4 Daily ET O estimates Table 4.8 Statistical indicators of the daily ET O calculated using the FAO-PM and ASCE-PM hourly ET O equations AWS ID Site Köppen region Number of Observations RMSD Avg. Ratio Slope Intercept R Townsville Aw Woolshed Aw Kununurra BSh Emerald BSh Yanco BSk Deniliquin BSk Griffith BSk Mildura BSk Charlton BSk Loxton. BSk Renmark BWk Gatton Cfa Kingaroy Cfa Oakey Cfa Dalby Cfa Warwick Cfa Toowoomba Cfa Narrabri Cfa Gunnedah Cfa Temora Cfa Kyabram Cfa Tatura Cfa Yarrawonga Cfa Shepparton Cfa Applethorpe Cfb Bendigo Cfb East sale Cfb Bairnsdale Cfb Morwell Cfb Mount moornapa Cfb Colac Cfb Collie east Csa Dwellingup Csb Bridgetown Csb Nuriootpa Csb Mt. Gambier Csb Coonawarra Csb Casterton Csb Dartmoor Csb Ayr Cwa

85 Chapter 4 Daily ET O estimates Climatological impacts on the relationship between ETO, soh vs. ETO, daily The agreement between daily ET O values calculated using the hourly and daily ET O equations depended on the location and it was not consistent spatially (Table 4.6). Therefore, this section breaks the comparison down by the nine climate Köppen zones represented by the stations. The most important measure of agreement between two daily ET O values is the mean daily ratio as this reflects both the over/under-estimation and scatter in the ET O, soh values, relative to ET O, daily. Figure 4.5 shows box plots of the daily mean ratio for each location. Figure 4.6 shows the mean and standard deviation for each Köppen climate zone. For all climates, the best agreement between ET O, soh and ET O, daily in terms of ratio was found under ASCE-PM equations. The highest underestimation for daily ET O calculated using the hourly FAO-PM equation was found in arid climates followed by tropical and temperate climates, whereas for the ASCE-PM version, daily ET O calculated using the hourly equation was overestimated and followed the same order. The box plots show that the ratios were positively skewed for most climates, with the exception being BSh and Cwa climates. The variance for the ratio between ET O, soh and ET O, soh was higher for the ASCE-PM equations than for the FAO-PM equations for all climates and there is greater variation within a climate zone than between the zones. Within the temperate climate, for both the versions, the highest variability and the maximum daily ratio (averaged over the study period) were found in the Csb sub-climate, which has a dry and warm summer. Particularly, daily ET O calculated using hourly FAO-PM equation found to be overestimated for two AWSs under the temperate climate (Figure 4.5). On the other hand, the mean and standard deviation of the daily ratio was lowest for both versions under the BSh climate zone (Emerald Airport-QLD). Notably, in BSh and BWk climate zones both the hourly ET O equations resulted in lower estimates of ET O than the daily ET O. In the tropical climate, the best agreement between the ET O, soh and ET O, daily values were found for the ASCE-PM version, whereas on average mean daily ratio was 1.00 and the variability was moderate. In the temperate climates without a dry season, the FAO-PM hourly ET O equation underestimated daily ET O by 3.9%; where else the ASCE-PM hourly ET O equation overestimated daily ET O by 2.35%. In the Arid climate both the hourly ET O equation underestimated the daily ET O by 4.9% and 0.5% respectively. Therefore, the best agreement between the ET O, soh, FAO and ET O, daily, FAO values was found in the temperate climate, whereas agreement between ET O, soh, ASCE and ET O, daily, ASCE values was best in tropical and arid climates. 63

86 Chapter 4 Daily ET O estimates Figure 4.5 Box plots for all AWS as indicated by the daily ratio between ET O, soh and ET O, daily (a) FAO-PM and (b) ASCE-PM equations. Each box shows the lower (25 th ), middle (50 th ) and upper (75 th ) quartile and the bottom and top whiskers represent the 5 th and 95 th percentiles. Figure 4.6 Summary of mean and standard deviation for sub-climate zones of the daily ET O between the daily and hourly ET O FAO-PM and ASCE-PM equations 4.6 Summary and conclusion In this paper, two major ET O models, namely the FAO-PM and standardized ASCE-PM, were comprehensively compared at hourly and daily time steps using hourly weather data from 40 AWS locations representing diverse climates across Australia. The sum-of-hour based daily ET O calculated using the hourly equation was compared to the respective daily ET O from the daily equation. The results were quantified using the RMSD, daily ratio between the ET O, soh and ET O, daily, slope/intercept of the best fit linear regression line, and coefficient of determination - R 2. The difference between daily ET O calculated using the hourly and daily ET O equations have previously been considered with respect to certain geographical areas only. In fact, this is the first study to compare such differences between two daily ET O estimations at a continental scale on a broader spectrum of factors, which included seasonality, climate type, different methods of estimating R so and different aggregation methods (sum-of-hourly and daylight hours). The results showed that the range for the ratio between ET O, soh and ET O, daily was narrower than most previous studies, probably reflecting the quality of the data set and the moderately large study period. Here, 64

87 Chapter 4 Daily ET O estimates the range of ratio for FAO-PM and ASCE-PM versions were and respectively, compared with 0.90 to 1.04 (FAO-PM) and 0.94 to 1.07 (ASCE-PM) for [Itenfisu et al., 2003] study and (ASCE-PM) for [Irmak et al., 2005] study. Our results were similar to the studies of [Gavilán et al., 2008], who found that hourly ET O calculated using the ASCE-PM version was higher than the FAO-PM version and resulted higher daily ET O estimates. Overall, the daily ET O from the hourly ASCE-PM equation exceeded the corresponding daily equation by 5%, whereas for FAO- PM the hourly exceed the daily equation by 2-3% in previous studies [Berengena and Gavilan, 2005; Gavilán et al., 2008]. Our results for the averaged RMSD for FAO-PM and ASCE-PM versions were 0.26 mm day -1 and 0.28 mm day -1 were better than similar studies in Turkey using 12-minutes intervals meteorological data [Silva et al., 2010]. The best agreement between ET O, soh and ET O, daily estimates for summer was found in the ASCE-PM version which corresponds closely to similar studies conducted in the USA and Europe [Irmak et al., 2005; Itenfisu et al., 2003; Lopez Urrea and López, 2006]. In this study we found that the R so calculated using the complex approach improved the agreement between ET O, soh and ET O, daily for both versions, compared with R so calculated using the simple approach. The average ratios between the ET O, soh and ET O, daily in the FAO-PM and ASCE- PM versions were 0.95 and 1.00 respectively, and the range was for the FAO-PM version and in the ASCE-PM version. The RMSD difference between the ET O, soh and ET O, daily for FAO-PM and ASCE-PM versions was on average 0.26 mm day -1 and 0.28 mm day -1 respectively and suggesting that daily ET O calculated using hourly and daily ET O equations agreed more closely for FAO-PM. However, other statistical indices such as the average daily ratio and the regression slope showed closer agreement between the ASCE-PM equations. During the winter, spring and autumn, the best agreement between the hourly and daily versions was found for FAO-PM, whereas in the summer, the ASCE-PM version had closer agreement. Since both the hourly versions exceeded the daily ET O during the winter, the daily ET O was calculated on a daylight-hour basis and compared with the daily ET O calculated using the sumof-hour basis over a 24 hour period. The performance indicators favor aggregating over 24 hours. There was a very good correlation between both the hourly equations at daily time step, on average with a range of The average ratio and range between the ET O, soh, FAO and ET O, soh, ASCE were 0.97 and respectively. The ASCE-PM s lower r s during the daytime increases the hourly ET O and vice versa during the night, the day time changes exceed the night-time changes, resulting in a higher overall estimate of ET O. The best agreement between the hourly and daily result for the FAO-PM version was found in the temperate climate and the ASCE-PM version showed the best agreement in the tropical and arid climates. 65

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89 Chapter 5 Daily ET O forecasts Chapter 5 Forecasting daily reference evapotranspiration for Australia using numerical weather prediction outputs Published as Perera, K. C., Western, A. W., Nawarathna, B., George, B., 2014., Forecasting daily reference evapotranspiration for Australia using numerical weather prediction outputs, Agricultural and Forest Meteorology, Volume 194, Page

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91 Chapter 5 Daily ET O forecasts 5.1 Abstract Farmers and irrigation system operators make real-time irrigation decisions based on a range of factors including short-term weather forecasts of rainfall and temperature. The simplest and oldest statistical method for forecasting daily ET O is to use the long-term monthly mean ET O based on historical observations. Forecasts of reference crop evapotranspiration (ET O) can be calculated from Numerical Weather Prediction (NWP) outputs and ET O has the advantage of being more directly relevant to crop water requirements than temperature. This paper evaluates forecasts of ET O made using the Bureau of Meteorology's operational NWP forecasts derived from the Australian Community Climate and Earth System Simulator - Global (ACCESS-G). The forecast performance for ET O was quantified using the root mean squared error (RMSE), coefficient of determination (R 2 ), anomaly correlation coefficient (ACC) and mean square skill score (MSSS). Daily ET O forecasts for lead times up to nine days were compared against ET O calculated using hourly observations from the 40 automatic weather stations across Australia. It was found that using NWP forecast daily ET O was better than using the long-term monthly mean ET O for lead times up to six days, beyond which the long-term monthly mean was better. The average MSSS for ET O forecasts across all stations varied between 66% and 12 % for lead times of one to six days, respectively. Further, it was found that forecast performance for daily ET O was highest in autumn for tropical climates and lowest in spring for temperate climates. Errors in incoming solar radiation were the most important source of ET O forecast error, followed by air temperature, dew point temperature and wind speed, for all lead times. Also, it was found that the forecast performances for incoming solar radiation and mean wind speed were relatively poor compared with the air and dew point temperatures. 5.2 Introduction Evapotranspiration (ET) and precipitation predictions play a fundamental role in basin scale real-time water resources management decisions by quantifying the prospective spatial and temporal changes of hydrological, agricultural, ecological and climatological processes. These real-time decisions frequently rely on agricultural irrigation water demand predictions, since agriculture is often the dominant water user, consuming 70% of world s fresh water withdrawals [UN-Water, 2006; UNEP, 2007]. Real-time irrigation decisions are generally coupled with crop-et rather than precipitation, because precipitation in most agricultural irrigation areas is fairly low. Crop water use can be estimated by multiplying reference evapotranspiration (ET O) with the crop coefficient (K c), where K c is expressed as the ratio between crop-et and ET O [Jensen, 1968]. Given that ET O varies with the weather, forecasts of ET O are valuable in real-time irrigation decisions. ET O forecasting procedures can be categorised into direct and indirect methods, 69

92 Chapter 5 Daily ET O forecasts depending on the methodology used and the input data. In the direct methods, current and historical data is used to forecast ET O either using time series methods or using artificial or computational neural networks (ANNs or CNNs). In the indirect method, weather variables needed to calculate ET O are forecasted (often by numerical weather prediction (NWP) models) and then empirical or analytical models such as the Hargraves [Hargreaves and Samani, 1985], Penman [Penman, 1948], or Penman-Monteith [Allen et al., 1998] models are applied to forecast ET O. The simplest and oldest statistical method for forecasting daily ET O is to use the long-term monthly mean ET O based on historical observations. More advanced time series models, such as autoregressive moving average (ARMA) or autoregressive integrated moving average (ARIMA) models have also been used to forecast monthly, weekly or daily ET O [Landeras et al., 2009; Marino et al., 1993; Mohan and Arumugam, 1995; Raghuwanshi and Wallender, 1999] and it has been found that forecast monthly, weekly or daily ET O was better than using corresponding long-term averages. Nonlinear system theoretical models such as artificial or computational neural networks (ANNs or CNNs) are an alternative to time series models and [Thirumalaiah and Deo, 2000] stated that they are superior in forecasting than traditional approaches such as auto-regression and multipleregressions. ANNs have been utilized to forecast numerous hydrological processes including shortterm river runoff [Abrahart and See, 2002; Cameron et al., 2002; Pulido-Calvo and Portela, 2007; Thirumalaiah, 1998] and biophysical factors such as precipitation [French et al., 1992; Kuligowski and Barros, 1998] and temperature [Hayati and Mohebi, 2008]. In the context of ET O, CNNs or ANNs were initially used to estimate monthly [Tahir, 1998] and daily [Kumar et al., 2002] ET O using historical observations. Then, ANN models were used to forecast one month ahead, monthly ET O for the southeast Europe [Trajkovic et al., 2003; Trajkovic et al., 2005] and for the Mahanadi reservoir project area, India [Chauhan and Shrivastava, 2009] as well as one week ahead, weekly ET O for northern Spain [Landeras et al., 2009]. These studies found that both monthly and weekly ET O forecasts were better than respective historical averages as well as ET O forecasts derived from time series models. These studies all intended to forecast weekly or monthly ET O and more recently the focus has turned to forecasting daily ET O. By the beginning of the 21 st century, the forecasting performance of mesoscale NWP models had improved significantly and this encouraged the use of indirect methods to forecast daily ET O. Consequently, Duce et al., [1999] forecasted ET O hours ahead, for six locations in California, United States. They used 20 km grid resolution hourly NWP forecasts derived from the Mesocale Atmospheric Simulation (MAS) and found that ET O forecast under-predicted observed ET O by 2 to 10 %. Cai et al., [2007] developed an analytical method to translate publically available weather forecasts in China into weather variables needed to calculate ET O and forecast one day ahead daily ET O. The results for the Willmot index of agreement and coefficient of determination were above 70

93 Chapter 5 Daily ET O forecasts 0.96 and 0.91 respectively, for all stations. Subsequently, publically available weather forecasts in China have been coupled with an ANN technique using least-squares support vector machines (LSSVMs) to forecast daily ET O [Guo et al., 2011], resulting in successful daily ET O forecasts for lead times up to one day, where the root mean square error and mean absolute error were less than 0.5 and 0.4 mm day -1 respectively. Some studies have attempted to forecast ET O using coarse-scale NWP model or Global Climate Model (GCM) output together with downscaling techniques. Tian and Martinez, [2012 a, b] conducted a study in the southeaster United States, to firstly forecast daily ET O up to 5 days in advance for at a grid resolution of 2.5 x 2.5 and secondly to compare the performance of two downscaling methods (natural analog and constructed analog) to produce both probabilistic and deterministic downscaled daily ET O forecasts at points. NWP forecasts for air temperature, relative humidity and wind speed from the National Centers for Environmental Prediction s (NCEP s) Global Forecast System (GFS) reforecast dataset and, in the absence of GFS reforecast for incoming solar radiation, observed solar radiation from the NCEP-U.S. Department of Energy (DOE) Reanalysis 2 dataset (R2) were used. This work found that most daily ET O forecasts were skilful up to five lead days and after applying downscaling techniques skilful deterministic results were limited to three days lead times [Tian and Martinez, 2012a; Tian and Martinez, 2012b]. Similarly, Ishak et al., [2010] used the MM5 mesoscale model (developed by National Centre for Atmospheric Research) to downscale European Centre for Medium Range Weather Forecasts (ECMWF) Re- Analysis (ERA-40) data to produce hourly weather variables needed to calculate ET O in the Brue catchment, southwest England. They found that forecast daily ET O was over-predicted by 27% - 46%. The numerical weather forecasts, derived from MM5 were utilised not only to forecast daily ET O, but also to estimate the daily ET O. Silva et al., [2010] also used MM5 outputs and estimated daily ET O, in the Maipo basin in Chile [Silva et al., 2010]. They found that daily ET O based on MOS (model output statistics) corrected weather variables reduced the root-mean-squared-error by 10-20% compared to the raw MM5 model output. Similarly, Er-Raki et al., [2010] evaluated the weather forecast data collected from the ALADIN (Aire Limitée, Adaptation Dynamique,développement InterNational) NWP model as an alternative to ground based observations to calculate daily ET O in Tensift basin (central of Morocco) and the Yaqui Valley (Northwest Mexico). These results all suggest that potential for forecast ET O using NWP forecasts and that the uncertainties of these ET O forecasts will decline as the performance of the NWP models increases or systematic errors are removed from the forecast weather variables. Moreover, reliable ET O forecast reduce costs and provide ET O data in a more timely fashion by eliminating or reducing the number of automated weather networks that are currently needed to provide near-real time ET O data 71

94 Chapter 5 Daily ET O forecasts for irrigation scheduling purposes [Duce et al., 2000]. However, quantification of ET O forecast performance using outputs from NWP models has been limited to a small number of studies in certain geographical areas such United States, Europe, China and Chile and to relatively short lead times [Arca et al., 2003; Cai et al., 2007; Silva et al., 2010] and forecast performance varies depending on NWP model, lead time, location and climate. In addition, seasonal variations in performance have not been assessed. This paper aims to quantify the forecasting performance for daily ET O with lead times up to nine days using the Australian Bureau of Meteorology's (BoM) operational NWP forecasts derived from the Australian Community Climate and Earth System Simulator - Global model (ACCESS-G). We forecasted ET O for lead times of 1-9 days for 40 locations (automatic weather stations), across 23 agricultural irrigation areas from nine diverse climates zones and assessed the accuracy against daily ET O calculated using the observed weather variables recorded at the corresponding automatic weather station (AWS). We also evaluated the temporal and spatial variation of daily ET O forecast performances. Further, we quantified the forecasting performance for ET O related weather variables, (daily maximum and minimum of air and dew point temperatures, mean daily wind speed and daily incoming solar radiation) and investigated the sensitivity of ET O forecasts to errors in each weather variable to determine which weather variable contributed most to the ET O forecast errors. 5.3 Materials Study Sites The study area covers a wide range of irrigation areas as well as various climates across the Australian Continent. The locations of those stations fall between latitudes 15 and 39 south and longitudes 116 and 153 east. We included 23 agricultural irrigation districts in the assessment, based on the 2005/06 Australian land use map [ABARES, 2010]. Figure 4.1 shows the locations of 40 Automatic Weather Stations (AWS) in these irrigation districts together with the Köppen climate zones. The stations fall in three main climates, tropical, arid and temperate, and nine sub-climates [Peel et al., 2007]. Table 4.1 provides the characteristic of these AWSs, which are sorted according to the Köppen climate classification (Table 4.2). The elevation of these stations ranges from 4 m to 871 m in reference to Australian Height Datum (AHD) and precipitation and mean annual temperature ranges from 400 mm to 2400 mm and from 0 C to 36 C, respectively. Long-term monthly mean ET O varies from 1 mm day -1 during mid-winter (July) for the southern stations to 12 mm day -1 during mid-summer (January). 72

95 Chapter 5 Daily ET O forecasts Data sources Weather forecast from ACCESS numerical weather prediction systems The weather variables needed to forecast daily ET O were collected from the BoM's operational NWP forecasts generated using ACCESS-G. The ACCESS systems are non-hydrostatic, hybrid vertical level structure, mesoscale assimilation and forecast systems developed and tested by the Earth System Modeling program of the Centre for Australian Weather and Climate Research (CAWCR). These systems are based on the UK Met Office Unified Model/Variational Assimilation (UM/VAR) system [BoM, 2010; BoM, 2012; Met Office UK., 2011]. It uses a four-dimensional variational data assimilation scheme (4DVAR), which results in extensive use of observations compared with the Bureau's previous NWP systems such as GASP and LAPS [BoM, 2010]. The trial implementations for global, regional and tropical ACCESS NWP models were implemented by the Operational Development Subsection of National Meteorological & Oceanographic Centre in September The BoM s previous NWP systems (GASP, LAPs, TXLAPS and MESOLAPS) were formally replaced by the ACCESS system, including mesoscale Australian ACCESS NWP model on 17 August The forecast performance of the ACCESS systems for meteorological variables such as precipitation and mean sea level pressure has been investigated thoroughly [BoM, 2010] and the outputs have been used extensively for short-term stream flow forecasting [Pagano et al., 2010; Shrestha et al., 2013; Shrestha et al., 2012]. The temporal (lead time) and spatial resolutions for ACCESS systems vary from +1 to +240 hours and 5 to 80 km, respectively. There is a trade-off between forecast horizon, resolution and accuracy for short-term irrigation decision making. Better decisions can be made when more near future information is available. Therefore, we selected the ACCESS-G system, which has the largest lead time (+240 hrs.) and the largest grid cells (80 km). The next higher resolution model has a lead time of only 72 hours. ACCESS-G is run twice a day providing forecasts starting at a.m. and p.m. local time (i.e. 00:00 and 12:00 UTC). The outputs from these runs are available at p.m. and 3.50 a.m. (the next day), respectively [BoM, 2010]. We used the a.m. local time run and constructed nine mid-night to mid-night daily ET O forecasts using the three hourly NWP forecast outputs of air temperature, dew point temperature, wind speed and incoming solar radiation from 17 August 2010 to 01 August The four grid points surrounding the station were linearly interpolated to the AWS location. For some sites, some of the grid points were over the sea. We undertook a preliminary evaluation (not presented) of using either land-only points or all four points and found better results when all four points were included. Therefore all results presented include NWP grid point over the sea in some coastal locations. 73

96 Chapter 5 Daily ET O forecasts Observed climatic data from automatic weather stations The Australian Bureau of Meteorology is missioned to maintain the network of AWSs across the Australian continent and provides climate data with various reporting frequencies including monthly, daily, and hourly [BoM, undated-a; BoM, undated-b]. Commencement dates for these AWSs varies between 1989 and 2009 and determines the data availability. Longer data periods are desirable for climatological calculation and hence, we collected all hourly data available to 05 March Weather variables used from the AWS were dry bulb and wet bulb air temperature and wind speed. Air temperature measurements were at 1.2 m above the ground level and wind speed was at 10 m. Recorded hourly wind speed was mostly an average over the ten minutes prior to observation time. Recorded hourly dew point temperature was derived theoretically from dry- and wet-bulb temperatures, with a correction made for the site's elevation [BoM, undated-a]. The measurement range and the accuracy of observed weather variables are given in T The BoM's AWSs are not equipped with pyranometers to measure solar radiation, so the BoM's daily incoming solar radiation product derived from satellite imagery was used [BoM, undated-c]. This product is derived using a physical model developed at the Bureau of Meteorology Research Centre [Weymouth and Le Marshall, 2001]. The uncertainty for the observed incoming solar radiation estimates from satellite is estimated in the section (5.6.). 5.4 Methodology Data pre-processing ET O integrates the effect of air temperature, dew point temperature, wind speed and solar radiation over a given period of time at a given location. Any bias in forecasts of these variables would result in systematic errors in forecast ET O; therefore, it is important that weather variable forecasts have similar statistical characteristics to the observed data. As a minimum, the forecast weather variables should have the same mean and variability as the observations. Given that the large cell sizes in ACCESS-G mean that local effects of topography and other factors can cause biases. The biases in the mean and variance of each forecast weather variable were corrected before calculating ET O by matching the mean and variance of the NWP forecasts for each weather variable with the observations, treating each lead time separately, for the whole period of overlapping data Calculating ETO All daily ET O calculations were made according to the guidelines provided by the United Nations Food and Agricultural Organization Irrigation and Drainage Paper No. 56 (FAO 56), which estimates daily ET O for a 12 cm high hypothetical reference crop [Allen et al., 1998]. This method 74

97 Chapter 5 Daily ET O forecasts has been recommended as the standard method of computing daily ET O [Allen et al., 1998] and numerous studies have demonstrated the superior performances of the FAO-PM equations compared with other ET O equations [Allen et al., 1989; Amatya et al., 1995; Chen, 2005; Chiew et al., 1995; George et al., 2002; Jensen et al., 1990]. The FAO Penman-Monteith (FAO-PM) daily ET O equations [Allen et al., 1998] is: ET 0 = (R n G)+γ 900 T+273 u 2 (e s e a ) +γ(1+0.34u 2 ) (5.1) where ET O is the daily reference crop evapotranspiration (mm day -1 ), is the slope of saturation vapor pressure versus air temperature curve (k Pa C -1 ), R n is the net radiation at the crop surface (MJ m -2 day -1 for daily), G is the ground heat flux density at the soil surface (MJ m 2 day 1 for daily), T is the mean daily air temperature at 1.5 to 2.5 m height ( C), U 2 is the mean daily wind speed at 2 m height (m s 1 ), e s is the saturation vapor pressure (kpa), e a is the actual vapor pressure (kpa), is the psychometric constant (kpa C 1 ), and is a coefficient converting MJ m -2 day -1 to mm day -1 of water. Daily mean air temperature was taken as the average of daily maximum and minimum air temperature rather than mean of the hourly air temperatures for a given day. This is recommended to avoid the underestimation of daily ET O occurring due to the non-linear relationship between the saturation vapour pressure and temperature [Allen et al., 1998]. Daily mean dew-point temperature and wind speed were taken as mean of hourly data for a given day. All daily net radiations (forecast and observed) were calculated as the difference between the incoming net shortwave radiation and the outgoing net longwave radiation [Allen et al., 1998]. Incoming net shortwave radiation was calculated using the incoming shortwave solar radiation and an albedo of 0.23 [Allen et al., 1998]. Outgoing net longwave radiation was estimated from the daily maximum and minimum air temperature and relative shortwave radiation, calculated using the collected incoming shortwave solar radiation and calculated clear-sky radiation following [Allen et al., 1998] Assessing forecast accuracy The overall quality of NWP weather or ET O forecasts depends mainly on six attributes: accuracy, reliability, sharpness, skill, resolution and uncertainty and no single verification measure provides complete information about the quality of forecasts [Stanski et al., 1989]. In reality, the last two attributes are not relevant for evaluating forecasts of air and dew point temperature, wind speed, solar radiation or daily ET O, because resolution relates to distinguishing between snow, rain, and hail etc., while uncertainty refers to precipitation event occurrence. Therefore, here the forecast performance of both the NWP weather variables and daily ET O were quantified using accuracy, reliability, sharpness and skill. Accuracy is the level of agreement between the forecast and actual 75

98 Chapter 5 Daily ET O forecasts as represented by observations and it was measured using the root mean squared error (RMSE). The coefficient of determination (R 2 ) was used to measure agreement between the forecast and observed values and provides insight into the reliability. The anomaly correlation coefficient (ACC) provided a measure of the sharpness of forecasts or the tendency to forecast extreme values. It measures correlation between the anomalies of the forecast and observed weather variables from the corresponding long-term monthly mean [Miyakoda et al., 1972]. Note that all anomalies in this paper refer to the daily data relative to the respective long-term monthly mean. The mean square skill score (MSSS) was used to quantify forecast skill since it is a measure of the relative accuracy to the monthly climatology. In past studies, these statistical indices have been used extensively to quantify the forecast performance of daily ET O [Alexandris and Kerkides, 2003; Cai et al., 2007; Liu et al., 1998; Pereira, 2004; Stöckle et al., 2004]. We utilized these statistical indices to evaluate the forecast performance for each lead time for the forecast weather variables (daily maximum and minimum temperature, daily mean dew point temperature, daily mean wind speed and daily incoming solar radiation) and for the daily ET O. These statistical indices are calculated as follows. The root mean squared error, RMSE is: RMSE = (P i O i ) 2 n (5.2) Coefficient of determination (R 2 ) is: R 2 = [ (P i P )(O i O )] 2 (P i P ) 2 (O i O ) 2 (5.3) The Anomaly Correlation Coefficient (ACC) [Miyakoda et al., 1972] is: ACC = (P i C )(O i C ) [ (P i C ) 2 (O i C ) 2 ] 1 2 (5.4) The Mean Square Skill Score (MSSS) [Murphy, 1988] is: [1 (1 n) MSSS = 1 ]2 (P i O i ) 2 (5.5) (C O i ) 2 In Eqs. (5.2)-(5.5), O i and P i are the i th observed and predicted and values respectively, n is the number of observations and C is the climatological or long-term mean monthly observation. O and P are mean of O i and P i for the period of verification. 5.5 Results Daily ET O varies with latitude and the day of year. The peak and nadir of daily ET O occur during mid-summer (January in the southern hemisphere) and mid-winter (July), respectively. The highest absolute variability in daily ET O was observed in summer, followed by spring, and autumn and was lowest in winter. This robust seasonality is mainly due to variability in solar radiation as a result of latitude, with most of the study sites being between 23 and 38 south. Figure 5.1 illustrates 76

99 Chapter 5 Daily ET O forecasts the long-term observed mean monthly ET O and variability of daily ET O for the Shepparton AWS (36º 25' 44" S, 145º 23' 41" E), where long-term monthly mean ET O varies from 1.12 mm day -1 during mid-winter (July) to 7.30 mm day -1 during mid-summer (January). The mid-summer daily ET O varies between 5 to 10 mm for 95% of the data, suggesting that long-term monthly mean ET O is not sufficiently accurate for real-time irrigation decisions. Figure 5.1 Seasonal variation of ET O in Shepparton irrigation area This variability in ET O is mainly due to variability in weather; specifically air temperature, dew point temperature, wind speed and solar radiation. Because the forecasting accuracy of daily ET O is directly related to the forecast accuracy of and sensitivity to these variables [Duce et al., 1999; Duce et al., 2000; George et al., 1985], we first report the forecast performance for these variables at the study sites. Then we report the ET O forecast performance for lead times of 1-9 days, including both temporal and spatial aspects for ET O. Finally, the sensitivity of daily ET O forecasts to each weather forecast variable is presented Forecast performance for weather variables Air temperature Daily maximum air temperature (T max) and minimum air temperature (T min) were required to calculate saturation vapour pressure as well as net long wave radiation. The respective statistical indices are shown in Figure 5.2. The forecast performance for T max and T min declines with increasing lead time for all locations, as expected. The RMSE for T max and T min approximately doubles as the lead time increases from 1-9 days. On average, RMSE values of T max ranged between 1.2 and 4.6 C and between 1.1 and 3.6 C for T min. The smaller range in RMSE for T min with lead time was observed at all locations, except Ayr, QLD (station 40). Most often, RMSE for T max was higher than for T min, with the exception of three AWSs located around Townsville, on the north-eastern coast of 77

100 Chapter 5 Daily ET O forecasts Queensland. The best R 2 values were found at the same three AWSs. The R 2 for T max and T min was more than 0.94 and 0.86 respectively for all lead times and all stations. As noted for the RMSE, the R 2 range for T min was higher than T max and the highest variability with lead time for both cases were found in Csb climate zone. The ACC for T max ranged between 0.95 and 0.28, whereas for T min they ranged between 0.93 and The MSSS for T max ranged between 0.90 and and MSSS values for T min ranged between 0.83 and For most lead times, the locations of the highest and lowest ACC and MSSS values for T max/t min coincided. Comparatively strong linear relationships between the temporal pattern of the forecast and observed anomalies for T max and T min were found in BSk and Csb climates. MSSS for T max was higher than for T min for Csb, but this reversed for Aw and BSh climates. T max and T min forecasts derived from ACCESS-G were on average better than climatology for lead times up to 7 days. These results all suggest that forecast performance for T max was relatively higher than T min and ACCESS-G s ability to forecast air temperature for Csb and BSk climates is higher than other climates in the study. Figure 5.2 Forecast performance for forecasted vs. observed daily maximum air temperature as indicated by (a) RMSE, (b) R 2, (c) ACC and (d) MSSS and forecasted vs. observed daily minimum air temperature as indicated by (e) RMSE, (f) R 2, (g) ACC and (h) MSSS for 40 AWS locations Dew point temperature The actual vapour pressure used in calculating ET O is calculated using dew point temperature averaged over the 24 hour period, rather than using wet-bulb/dry-bulb temperature or relative humidity [Allen et al., 1998; Walter et al., 2005]. The forecast performance for daily mean dew point (Dewpt mean) is shown in Figure 5.3. The RMSE for Dewpt mean increases with lead time for all locations and ranged between 0.8 and 4.0 C. The RMSE values for arid climates were comparatively lower than that for tropical or temperate climates. The R 2 for Dewpt mean was greater 78

101 Chapter 5 Daily ET O forecasts than 0.77 for all lead times. Like the RMSE, R 2 was better for arid climates. The ACC values for Dewpt mean ranged between 0.95 and 0.27 and MSSS ranged between 0.90 and Comparatively weaker ACC and MSSS values were found under BSk and Csb climates. In general, Dewpt mean forecasts derived from ACCESS-G were better than climatology up to five days lead time. The synoptic-scale forecast skill (ACC 0.6) for Dewpt mean was typically limited to four lead days. These results all suggest that dew point temperature forecast performance was relatively lower than air temperature forecast performances. ACCESS-G s forecast performance for dew point temperature was lowest within Csb and BSk climate regions. Figure 5.3 Forecast performance as indicated by (a) RMSE, (b) R 2, (c) ACC and (d) MSSS of forecasted vs. observed daily mean dew point temperature for 40 AWS locations Wind speed The statistical indices related to the forecast performance for daily mean wind speed (WSpd mean) are shown in Figure 5.4. On average, RMSE values for WSpd mean ranged between 0.64 and 2.60 km hour -1. Relatively higher RMSE values for WSpd mean were found under the BSk and Csb climates. On average, R 2 values for WSpd mean ranged between 0.64 and The ACC and MSSS values for WSpd mean ranged between 0.83 and 0.01 and 0.62 and respectively. Lower ACC and MSSS values suggest a weak linear relationship between the temporal pattern of the forecast and observed anomalies for WSpd mean. Moreover, there were six locations, where climatological WSpd mean was better than those derived from ACCESS-G for all lead times. The forecast performance for WSpd mean declines faster than T max, T min or Dewpt mean with increasing lead time. Also, the variability of statistical indices was higher than those for T max, T min or Dewpt mean as wind speed is the most dynamic weather variable considered. Nevertheless, WSpd mean forecast by ACCESS-G was better than climatology up to four days lead time. All these results suggest that wind speed forecast performance was the lowest of all the weather variables considered. 79

102 Chapter 5 Daily ET O forecasts Figure 5.4 Forecast performance as indicated by (a) RMSE, (b) R 2, (c) ACC and (d) MSSS of forecasted vs. observed daily mean wind speed for 40 AWS locations Radiation The forecast performance for daily incoming solar radiation ( R S) is shown in Figure 5.5. Additional caution is required in evaluating R S as the comparison is against the Bureau of Meteorology's satellite imagery derived R S product. RMSE values for R S ranged between 2.8 and 7.4 MJ m -2 day -1. The ACC and MSSS values for R S ranged between 0.83 and 0.11 and 0.63 and The AWSs located in the tropics have relatively better RMSE and R 2 and poorer ACC and MSSS. This is related to the fact that they have the lowest variability for all lead times due to the lower seasonality. Climatology provided a better forecast than ACCESS-G for R S within the tropics particularly at Kununurra, WA (station 03), which is the closest location to the equator. In all sites, ACC and MSSS values for R S were better than for wind speed, but poorer than for T max, T min or Dewpt mean. Generally, R S forecasts derived from ACCESS-G were better than climatology up to four lead days. Figure 5.5 Forecast performance as indicated by (a) RMSE, (b) R 2, (c) ACC and (d) MSSS of forecasted vs. observed daily incoming solar radiation for 40 AWS locations Summary Forecast performance for air temperature was highest followed by Dewpt mean, R S and finally WSpd mean, for all lead times. It was not possible to distinguish a location or climate zone that corresponded to highest and lowest forecast performances for all four weather variables; however, bias correction was particularly important for sites where some surrounding NWP grid cells occurred 80

103 Chapter 5 Daily ET O forecasts over the sea, for example the three AWSs located around Townsville, QLD. While sea effects induced greater bias, as noted earlier, preliminary analysis showed that it was better to include the sea points rather than exclude them. Further, overall forecast performance for weather variables showed that ACCESS-G was able to generate higher quality forecasts of ET O related variables in temperate rather than tropical or arid climates. Overall, NWP forecasts for all four weather variables were better than climatology for lead times of 3-7 days, depending on the variable and they should provide useful information for ET O Forecasting performance for ETO We evaluated 1-9 day lead time forecast daily ET O against "observed" ET O calculated using the observed hourly weather data and daily R S. Figure 5.6 shows example scatter and anomaly scatter plots of forecast vs. observed daily ET O values for lead times of one, three, five and seven days at Shepparton Airport, Victoria. The increase in scatter between forecast and observed daily ET O values with lead time results from the declining forecast performance for the weather variables, as discussed previously. To quantify the daily ET O forecast performance throughout Australia, the statistical performance indices were calculated for the 40 AWS locations (Table 5.1 and Figure 5.7). Forecast performance for ET O gradually declines with increasing lead time, similar to the weather variables. The regression slopes and intercepts behaved identically for all 40 locations, where regression slope declined and regression intercept increased as the lead time increased. For most locations (85 %), ET O was slightly over-predicted for all lead times (Figure 5.6, top left panel) and gradually decreased the over-prediction as the lead time increased. For the remaining sites, the forecast ET O was under-predicted compared to the observations for all lead times. On average, the regression intercept was more than zero, suggesting that for small daily ET O, the forecast very slightly over-predicted ET O whereas at the relatively high daily ET O values forecast under-predicted ET O for longer lead times. This was not the case for one day lead time, where regression intercept was less than zero at more than half of the sites. Except for outliers (define as outside the range, for values are beyond q3/ q1 ± 1.5(q3 q1),where q1 and q3 are the 25 th and 75 th percentiles) the ratio between forecast and observed daily ET O values ranged between 0.97 and 1.27 for all sites and for all lead time. Averaged over all sites, the ratio of forecast daily ET O to observed ET O was greater than one and the over-prediction increased from 4% to 12 % as lead times increased. This was mainly related to days with quite low observed ET O. The RMSE approximately doubled, as the lead time increased; with the exception of three AWSs located around Townsville, QLD. RMSE values were on average 0.73 and 1.43 mm day -1 for 1 and 9 day lead times, respectively. The lowest and highest RMSE were observed at Woolshed Airport, QLD (station 02) and Kununurra Airport, WA (station 03). The correlation 81

104 Chapter 5 Daily ET O forecasts between forecast and observed ET O ranged between 0.91 (one day lead time) and 0.01 (nine day lead time), and the highest and lowest R 2 values were found at Dwellingup, WA (station 33) and Kununurra Airport, WA (station 03), respectively. The ACC ranged from 0.91 to 0.22 and the highest and lowest values were found in Nuriootpa, SA (station 35) and Ayr, QLD (station 40), respectively. Variability in ACC values between sites was approximately equal for all lead times and average ACC values decreased linearly with increasing lead time. Thus, forecast and observed daily ET O anomalies were consistent throughout Australia. The MSSS progressively declined from 1-9 lead days, ranging from 0.78 to -1. On average MSSS values over all stations ranged between 0.66 (one day lead time) and (nine day lead time) and it typically becomes negative after six days lead time. Locations with the highest and lowest MSSS values varied with lead time, but overall MSSS values were highest at Nuriootpa, SA (station 35) and lowest at Kununurra Airport, WA (station 03). Figure 5.6 Daily ET O forecasted (NWP forecasts driven from ACCESS-G) vs. observed at the Shepparton airport: (a) One lead day, (b) Three lead days, (c) Five lead days and (d) Seven lead days Figure 5.7 Forecast performance as indicated by (a) RMSE, (b) R 2, (c) ACC and (d) MSSS of forecasted vs. observed daily ET O for 40 AWS locations 82

105 Chapter 5 Daily ET O forecasts Table 5.1 Statistical indices of forecast vs. observed ET O for all AWS stations No AWS No. AWS Name Lead Time 1 Day 5 Day 9 Day RMSE R 2 ACC MSSS RMSE R 2 ACC MSSS RMSE R 2 ACC MSSS Townsville Airport Woolshed Airport Kununurra Airport Emerald Loxton research Centre Yanco AG Institute Deniliquin Airport Griffith Airport Mildura Airport Charlton Renmark Airport University of QLD Kingaroy Airport Oakey Airport Dalby Airport Warwick Toowoomba Airport Narrabri Airport Gunnedah Airport Temora Airport

106 Chapter 5 Daily ET O forecasts No AWS No. AWS Name Lead Time 1 Day 5 Day 9 Day RMSE R 2 ACC MSSS RMSE R 2 ACC MSSS RMSE R 2 ACC MSSS Kyabram Tatura Sustainable Inst Yarrawonga Shepparton Airport Applethorpe Bendigo Airport East sale Airport Bairnsdale Airport Morwell Airport Mount Moornapa Colac Collie east Dwellingup Bridgetown Nuriootpa Mount Gambier Airport Coonawarra Casterton Dartmoor Ayr DPI Centre

107 Chapter 5 Daily ET O forecasts The declining forecast performance of the ET O forecast is directly due to the declining forecast performance for the input weather variables [Duce et al., 1999; George et al., 1985]. Furthermore, daily ET O forecasts were over-predicted due to the overall effect of the weather variables being overpredicted as discussed above (i.e. the negative effect of over-predicted Dewpt was outweighed by positive effect of all other weather variables being over-predicted). The forecast daily ET O was better than climatology up to six days lead time Seasonality in ETO forecast performance Irrigation areas of our interest have different irrigation seasons depending on the crop type, location and rainy season, etc. For example irrigation seasons in southern Australia (SA, VIC) are different from northern Australia (QLD). Therefore, seasonal evaluation of ET O forecast performance ET O is useful. This section investigates the forecasting performance for daily ET O during the Austral summer (DJF), autumn (MAM), winter (JJA) and spring (SON). Figure 5.8 shows the average seasonal and annual performance indicators for all lead times. Figure 5.8 Average forecast performance across all 40 stations as indicated by (a) RMSE, (b) R 2, (c) ACC and (d) MSSS of forecasted vs. observed daily ET O. The RMSE values for winter and autumn were approximately half or less than those of summer for all lead times. The seasonal RMSE falls from highest to lowest; in the order summer, spring, autumn, winter and the latter three RMSE values were less than the annual values. This pattern relates to the proportionality between RMSE and the overall magnitude of seasonal ET O. The seasonal R 2 values were less than the annual values due to lower overall variability and the highest and lowest values were found during autumn and summer, respectively for all lead times. In general ACC values for summer and autumn were higher than annual values, while corresponding values for winter and spring were less than annual for all lead times. The highest MSSSs for first five days lead times were found in autumn followed by winter, summer and spring. For longer lead times, the highest values were in winter. Moreover, MSSS values for autumn and winter were higher than annual values. All seasonal MSSS values become negative after seven days lead time, with the exception of winter. There are bigger seasonal differences between RMSE and R 2 than between 85

108 Chapter 5 Daily ET O forecasts ACC and MSSS as the seasonality has already been removed from ACC and MSSS. The four performance indicators do not provide consistent results, although the forecast performance for daily ET O is generally higher during autumn in terms of ACC and MSSS. The next best forecast performance was found during winter followed by summer and spring Spatial analysis Forecast performance for daily ET O varied spatially as forecast performance for weather variables partly depends on the climate. Therefore, spatial forecast performances for daily ET O were quantified. The statistical indices calculated earlier were divided into nine Köppen climate zones. When comparing the four statistical indices, the most important measure of forecast performance is the MSSS as this reflects both the bias and scatter in the forecast, relative to monthly climatology. Figure 5.9 shows the MSSSs grouped by each climate zone for various lead times. In all climates, forecast performances decreased and variability in MSSS increased with lead time. MSSS values for Aw was more than zero for all lead times, but other climates MSSE values fell below zero between five and nine days lead time. Overall there appears to be little difference in performance between climate zones, except for long lead times (seven days) where the degradation in performance is greatest in the temperate climates. The lowest and highest RMSE values were found in BSh and Aw climates respectively (not shown). A similar pattern was observed in the R 2 values, where the highest and the lowest were found in BSh and Aw climates respectively. ACC values changed marginally from one climate to other with the exception of Cwa. Overall there is little dependence of forecast performance on climate zone and forecast performance varies significantly within the zones. In some zones there are only one or two AWS locations and performance cannot be generalized for the zone. Figure 5.9 Forecast performance as indicated by MSSS for nine Köppen climate classifications 86

109 Chapter 5 Daily ET O forecasts Impact of weather variable forecasts on daily ETO forecasts In this section, four daily ET O forecasts were made by replacing one forecast weather variable (air temperature, dew point temperature, incoming solar radiation, daily mean wind speed) with the equivalent observation. This approach effectively removes the forecast error for each variable in turn and makes it possible to assess the sensitivity of the ET O forecast to errors in the weather forecast for that variable. Statistical indices were computed using these forecasts. All four performance indices showed essentially identical improvements, hence only MSSS is shown in Figure All ET O forecasts show some improvement when each weather variable is replace by the observations; however, the differences for wind speed are marginal. The important point here for interpretation is that the larger the improvement (or sensitivity) gained by using corresponding observed weather variable, the more important forecast errors in that variable are in terms of forecast errors in ET O. The greatest improvement was seen by substituting observed incoming solar radiation followed by air temperature, dew point temperature and wind speed for all lead time. Improvements increased with lead time because the errors in forecast weather variables increase with lead time. These results suggest that most of the forecast decline with lead time relates to radiation and temperature and also that improvement in incoming solar radiation forecasts followed by temperature forecasts would lead to the greatest gains in ET O forecasts. This would provide daily ET O forecasts that are better than climatology up to nine days lead time, depending on the scale of improvement. Figure 5.10 Average MSSS of estimated and forecasted daily ET O by swapping observed variable one at a time 87

110 Chapter 5 Daily ET O forecasts 5.6 Discussion This study assessed the forecasting performance of daily ET O using the NWP forecasts derived from ACCESS-G across the Australian Continent. Many, if not most short-term hydrological or agricultural forecasting models need reliable ET O forecasts. It is not always possible to forecast ET O or weather variables (those needed to calculate ET O) from historical data or in situ weather measurements. One alternative is to collect weather forecasts from NWP models, like ACCESS-G and apply those for forecasting applications. However, only few assessments of ET O forecasting based on NWP weather forecasts have been made. This study helps to understand the potential of using NWP weather forecasts to forecast the daily ET O with lead times up to nine days. Weather variables selected for this study were air temperature (T), dew point temperature (Dewpt), wind speed (WSpd) and incoming short wave solar radiation (R S). It is important to consider the effects of measurement errors on our results, as they contribute to degradation in the assessment statistics. Figure 5.11 shows the forecast uncertainties (95% confidence intervals) calculated from the histogram of residuals between forecasts and observed against the measurement error (uncertainties in observation) for all 40 sites and lead times. The increase in the variance of forecast uncertainties with the lead time is clear. For all weather variables, the measurement errors were significantly less than the corresponding forecast uncertainties for all lead times. This suggests that effects of measurement error on the forecast evaluation were small. Figure 5.11 Forecast and measurement uncertainties for (a) Maximum temperature, (b) Mean dew point temperature, (c) Wind speed and (d) Incoming solar radiation for 40 AWS locations The relative difference between the measurement error and forecast error was highest for T followed by Dewpt, R S, and then WSpd. In all cases except WSpd the measurement error is small compared with the forecast error. Also forecast ET O was insensitive to error in WSpd. Therefore, our results are not significantly affected by the measurement error. The descending order for the relative difference between the measurement error and forecast error is almost the same as the conclusion drawn while analysing the impact of errors in weather variable forecasts on daily ET O forecasts, where, the improvement in R S forecasts would lead to the greatest gains in ET O forecasts. 88

111 Chapter 5 Daily ET O forecasts The swapping of T and R s comes about due to different sensitivities in ET O to T and R s. This relates to the fact that R S is the key driver of ET O, because it supplies most of the energy for evapotranspiration. However, R S was the only weather variable, that was indirectly estimated from satellite imagery rather than being measured on the ground. Therefore, the accuracy of satellite imagery driven R S was evaluated against the R S observed using the ground-based pyranometers. The Bureau has only a limited number of ground based solar observed site across Australia and Mildura Airport (station 09) is one of those. Data was not available for the study period, so a comparison was made over a different period. Figure 5.12 shows the satellite derived R S and ground observed R S for the period of 01 Jan 2013 to 31 May 2013 and a scatter plot. The R 2 and RMSE between the two R S values were 0.99 and 1.7 MJm -2, respectively. Therefore, satellite derived R S acted as a very good alternative for ground based R S and errors in satellite derived R s had little impact on the results. Figure 5.12 Accuracy of R S estimation as indicated by (a) Time series and (b) Scatter plot between satellite data driven R S and ground based observed R S for at Mildura Airport Systematic bias in NWP weather forecasts can also influence the ET O forecasts. Therefore, the increase in the forecast performance from bias correction of each forecast variables was evaluated. The statistical indices RMSE and R 2 were used to quantify improvement, as these reflect prediction error and goodness of fit in the forecast, relative to observed values. The improvements for the RMSE and R 2 were calculated by subtracting the values before bias correction from the corresponding values after bias correction for each variable for all lead time. It was found that systematic bias correction substantially improved the forecast performance for all weather variables except R S, which was marginal. The marginal improvement for R S was due to the strong seasonality. The improvements gain during bias correction for the minimum temperature and mean dew point temperature were greater than other variables. It may be due to the evaporative cooling and greater thermal inertia associated with irrigation accounts for some of the bias in ACCESS-G forecasts, given that the weather stations are in or near irrigation areas and irrigation is not included in ACCESS-G. Bias correction of the weather variables improved the forecast performance for daily ET O. This was quantified using MSSS, as this reflects both anomalies between forecast and observed daily 89

112 Chapter 5 Daily ET O forecasts ET O, relative to monthly climatology and is shown in Figure Improvement for MSSS values were on average 8.3 % and 2.0% for one and nine day lead times, respectively. Figure 5.13 Average improvement gained in MSSS values during the bias correction for daily ET O forecast AWS locations NWP models output have previously been used as a data source to forecast as well as to estimate daily ET O. In the forecasting context, this is the first study to forecast daily ET O up to 9 days lead time using the NWP model output. The results showed that the forecasting performance for daily ET O was higher than most of the previous studies, probably reflecting the steady improvement in NWP over time. The results were substantively better than daily ET O forecasts using coarse-scale NWP or GCM model output. Here over-prediction for one day ahead daily ET O was 4% on average compared with 27-46% [Ishak et al., 2010]. Our results were similar to finer-scale (20km gird) NWP models like MAS [Duce et al., 1999] and the study of [Cai et al., 2007]. Overall the forecast performance for daily ET O using ACCESS-G output was higher than previous studies. From an estimation prospective, NWP derived ET O forecasts have been used as an alternative to observations, when in situ measurements for weather variables are not available or sparse. The statistical indices (R 2 and RMSE) corresponding to one day ahead daily ET O derived using NWP model ACCESS-G as a daily ET O estimations were better 0.25 and 0.16 mmday -1 respect to R 2 and RMSE than similar studies in Chile using MM5 [Silva et al., 2010] and in Morocco and Mexico using ALADIN [Er-Raki et al., 2010].We further extended this idea and evaluated one day ahead daily ET O as an alternative to weekly or month ET O estimation. It was found that the RMSE and R 2 for weekly ET O estimates were 2.36 mm week -1 and 0.96 respectively. For monthly ET O estimates RMSE and R 2 were 7.03 mm month -1 and This suggested that one day ahead daily ET O forecast could be used as very good estimation for daily to monthly ET O across Australian continent. From the irrigation prospective, the simplest and widely-used daily ET O forecast is the longterm monthly mean ET O based on historical observations. The result showed that daily ET O 90

113 Chapter 5 Daily ET O forecasts forecasted using ACCESS-G data was better than long term monthly mean up to six days led time. Moreover, up to four days lead time, the RMSE was less than 1 mm day -1 on average which is small. 5.7 Summary and conclusions Short-term ET O forecasts would be useful in making short-term real-time irrigation decisions. There is an opportunity to forecast daily ET O from NWP systems like ACCESS-G. This paper quantifies the forecast performance for ET O using weather variables from the Bureau of Meteorology's operational NWP forecasts derived from ACCESS-G for 40 sites in irrigation areas across the Australian Continent. Daily ET O was forecast for lead times up to nine days and evaluated against "observed" ET O calculated using observed weather data from 40 automatic weather stations across Australia. The results showed that ACCESS-G is capable of generating skilful forecasts (MSSS 0.5[Murphy, 1988] and ACC 0.6 [Miyakoda et al., 1972]) of daily minimum and maximum screen level air temperature, daily average dew point temperature and 10 m wind speed, and daily solar radiation (against a satellite based comparator) up to three days ahead and that for lead times up to seven days ACCESS-G s NWP forecasts are better than using the monthly mean climatology. Moreover, daily ET O forecasts calculated using NWP weather variable forecasts were better than the long-term monthly mean ET O for lead times up to six days, after which the long-term monthly mean ET O provided a better forecast. ET O forecast performance varies temporally and spatially. In terms of seasonality, it was found that forecast performance for daily ET O was highest during the autumn, and then decreased in turn for winter, summer and spring. Spatially, forecast performance was largely independent of climate type, although the decline in performance with lead time was larger for temperate climate zones. Furthermore, it was found that the largest source of error between forecast and observed ET O was the forecasting performance of incoming solar radiation, followed by air temperature, dew point temperature and wind speed for all lead time. This agrees with the forecast performance of the input weather variables where radiation (along with wind speed) actually showed the lowest skill. It would be valuable to investigate the potential of improving on the ACCESS-G ET O forecasts by using the mesoscale NWP model ACCESS-R (spatial resolution ~ 37.5 km, forecast horizon +72 hours) for the first three days. From a practical perspective, farmers and irrigation system operators could gain useful information on daily ET O forecasts computed using NWP forecasts derived from ACCESS- G for lead times of up to six days. 91

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115 Chapter 6 Deterministic irrigation demand forecasts Chapter 6 Multivariate time series modelling of shortterm system scale irrigation demand Published as Perera, K. C., Western, A. W., George, B., Nawarathna, B., 2015., Multivariate time series modelling of short-term system scale irrigation demand, Journal of Hydrology, Volume 531, Part 3, Page

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117 Chapter 6 Deterministic irrigation demand forecasts 6.1 Abstract Travel time limits the ability of irrigation system operators to react to short-term irrigation demand fluctuations that result from variations in weather, including very hot periods and rainfall events, as well as the various other pressures and opportunities that farmers face. Short-term systemwide irrigation demand forecasts can assist in system operation. Here we developed a multivariate time series (ARMAX) model to forecast irrigation demands with respect to aggregated service points flows (ID CG i, ASP) and off take regulator flows (ID CG i, OTR) based across five command areas, which included area covered under four irrigation channels and the study area. These command area specific ARMAX models forecast 1-5 days ahead daily ID CG i, ASP and ID CG i, OTR using the real-time flow data recorded at the service points and the uppermost regulators and observed meteorological data collected from automatic weather stations. The model efficiency and the predictive performance were quantified using the root mean squared error (RMSE), Nash-Sutcliffe model efficiency coefficient (NSE), anomaly correlation coefficient (ACC) and mean square skill score (MSSS). During the evaluation period, NSE for ID CG i, ASP and ID CG i, OTR across five command areas were ranged These models were capable of generating skilful forecasts (MSSS 0.5 and ACC 0.6) of ID CG i, ASP and ID CG i, OTR for all five lead days and ID CG i, ASP and ID CG i, OTR forecasts were better than using the long term monthly mean irrigation demand. Overall these predictive performance from the ARMAX time series models were higher than almost all the previous studies we are aware. Further, ID CG i, ASP and ID CG i, OTR forecasts have improved the operators' ability to react for near future irrigation demand fluctuations as the developed ARMAX time series models were self-adaptive to reflect the short-term changes in the irrigation demand with respect to various pressures and opportunities that farmers' face, such as changing water policy, continued development of water markets, drought and changing technology. 6.2 Introduction Travel time between the source (reservoir) and irrigated fields leads to significant challenges for irrigation system operators in terms of reacting to short-term irrigation demand fluctuations arising from variations in weather including very hot periods and rainfall events, as well as the various other pressures and opportunities that farmers face. Modern irrigation system automation technologies have recently been developed with the aim of improving delivery efficiency and level of service, an example of which has been implemented in northern Victoria, Australia [GMWater, 2010]. These systems can deliver water with very short lead times due to their fully automated distribution network [NVIRP, 2010a]. They also deliver a step change in the amount of real-time data available through monitoring and telemetry of all regulators within the system. A remaining challenge is that while the system automates water control in the distribution canals, bulk delivery 95

118 Chapter 6 Deterministic irrigation demand forecasts of water to the command area still needs to be planned as it is subject to substantial travel time delays. Short-term irrigation demand forecasting has the potential to assist in system operation but has often been constrained by limited information on both current demand levels and likely future weather. This research aims to capitalize on the opportunity presented by the large amount of consistent real-time irrigation system data now available and expanding numerical weather predictions to forecast irrigation demand. In particular, this paper develops and evaluates a time series model to forecast short-term irrigation demand based on recent irrigation demand and weather data. The dynamic and nonlinear nature of short-term irrigation demand results from complex interactions between biophysical (crop-soil-climate interaction), behavioral (farmer and system operator attitudes that influence management decisions) and supply (supply source, seasonal allocation, permanent entitlement) factors [Zaman et al., 2007], and is very challenging to forecast. Various irrigation demand forecast models have been developed to predict irrigation water demand aimed at meeting a variety of farmer and/or operator objectives including: irrigation scheduling [George et al., 2003; George et al., 2000; Rao et al., 1988]; yield/profit optimization [Prasad et al., 2006; Smout, 2005; Umamahesh and Raju, 2002]; and water allocation [Paul et al., 2000; Rao et al., 1990]. Practical application of these models at system scale is often limited by the lack of required data or the expense of data acquisition [Ticlavilca et al., 2011]. Depending on the degree of data availability, two distinct modelling architectures have been used to forecast irrigation demand; process-based (conceptual) and data-driven (statistical) [Alfonso et al., 2011; Pulido-Calvo and Gutierrez-Estrada, 2009]. Process-based models use the physical concepts associated with the irrigation demand while data-driven models are trained to map the relationship between influential factors and irrigation demand with no detailed considerations about the internal structure of the physical processes [Alfonso et al., 2011]. In an operational context with good real-time dynamic system response data available, data-driven models are often preferred as these measurements encapsulate a wide range of information about the many factors influencing the current system behavior. Most process-based models are based on the soil-water balance equation including biophysical demand and supply factors. These models forecast the irrigation demand by incorporating historical, current (real-time) or future (often from short-term weather forecasts) information on those factors at various spatial scales from paddock [Ejieji and Gowing, 2000] to system[cai et al., 2011; Wilks and Wolfe, 1998], as well as from lead times of 1-2 days [Cai et al., 2011; Wilks and Wolfe, 1998] to weeks [Ejieji and Gowing, 2000; Wang and Cai, 2009]. The reliability of these forecasts is mainly constrained by the prediction uncertainties of the influential factors and various model structural and parameter errors [Ejieji and Gowing, 2000; Wilks and 96

119 Chapter 6 Deterministic irrigation demand forecasts Wolfe, 1998]. The prediction uncertainties for inputs increase with the lead time, especially precipitation [Azhar and Perera, 2011]. Furthermore, process-based models are also usually structured to capture correlations between short-term weather forecasts and farmer behavior [Austen et al., 2002; Bergez and Garcia, 2010; Ingram et al., 2002]. These behavioural factors cannot be directly measured, unlike biophysical or supply factors. This, combined with a lack of consistent flow data often makes quantification of farmer behaviour difficult. As a consequence of the above issues, process-based models have most often been used to derive optimal irrigation decisions [Cai et al., 2011; Wang and Cai, 2009] rather than to make volumetric irrigation demand forecasts with a few exceptions (e.g.[tian and Martinez, 2014]). Existing data-driven irrigation demand forecast models have been based on a variety of statistical (time series) models as well as artificial intelligence techniques such as artificial or computational neural networks (ANNs or CNNs) or other machine learning techniques. Although, these computational models have been successful in forecasting flood discharges [Nayak et al., 2005] and stream flow [Abrahart and See, 2002; Kasiviswanathan and Sudheer, 2013; Nayak et al., 2012], in which precipitation acts as the forcing variable, the inverse relationship between precipitation and irrigation demand combined with the variety of other influences has limited the irrigation demand forecast performances of these models. Nevertheless, a few CNN models have been developed to forecast one day lead time irrigation demands for several irrigation districts locate in the southern Spain [Pulido-Calvo and Gutierrez-Estrada, 2009; Pulido-Calvo et al., 2007; Pulido-Calvo et al., 2003]. Those models didn t combine the precipitation and reference evapotranspiration (ET O) forecasts which were available from computational models [Kuligowski and Barros, 1998; Tian and Martinez, 2012b] or the Numerical Weather Forecast (NWP) models. These studies showed CNN calibration forecast performances that were higher than for univariate time series approaches, but the CNN models were systematically over fitted and the forecast performances declined significantly during validation [Pulido-Calvo and Gutierrez-Estrada, 2009]. In an alternative approach, irrigation demand has been expressed as a multivariate output using the Bayesian machine learning algorithm called multivariate relevance vector machine (MVRVM). Using MVRMV, demand volumes for irrigation channels have been forecasted in the arid Sevier river basin, Utah, USA for lead times of one hour up to two days [Ticlavilca et al., 2011] and for 4 day lead times [Alfonso et al., 2011]. These models did not consider precipitation as an input (due to the lack of precipitation in the arid climate) and instead used forcing variables such as temperature or ET O. Overall, these data-driven models are black-boxes where the complex interactions between irrigation demand and causal factors remain ill defined. The heuristic nature of selecting the artificial intelligent technique, the network design, the input data set and the calibration period have led to difficulties in model architecture, network parameters, and frequent recalibrations. 97

120 Chapter 6 Deterministic irrigation demand forecasts Data-driven statistical time series models have also been used and are mostly limited to univariate [Pulido-Calvo and Gutierrez-Estrada, 2009; Pulido-Calvo et al., 2007; Pulido-Calvo et al., 2003], as they were mainly developed for arid-zone agriculture where precipitation does not significantly influence irrigation decisions and the inter-seasonal climate variability is low. These univariate cannot be successfully applied in supplemental irrigated agriculture due to structural constraints (inability to include precipitation effects). Multivariate time series model are an alternative that can be applied to model daily irrigation demand as a multivariate output resulting from biophysical processes, farmer and operator behaviours and supply factors. These models can capture interactions between time series variables in terms of auto- and cross- correlations as well as linear (trend) and nonlinear (diurnal and seasonal) patterns, depending on the time step and model structure. Multivariate time series models have been widely used in engineering, science, medicine and finance, among other areas. ARMAX (autoregressive moving average with exogenous variable) models have been found to be very successful in forecasting short-term electricity demand [Chao- Ming et al., 2005; Hong-Tzer et al., 1996] and power output for photovoltaic systems [Li et al., 2014b], where temperature acts as the exogenous variable. In the field of water resources engineering, ARX (autoregressive with exogenous variable) and ARMAX model structures have also been used extensively to forecast short term runoff [Haltiner and Salas, 1988], stream flow [Chang et al., 2001; Dutta et al., 2012; George et al., 2011; Sun et al., 2014], and urban water demand [Zhou et al., 2002; Zhou et al., 2000] in which climate variables such as precipitation, ET O and temperature act as the exogenous variables. However, we are unaware of any multivariate time series models for forecasting short-term irrigation demand. Most of the prevailing irrigation demand forecast models have been based on 2-3 years of irrigation. This means that inter-annual variations for a given season (e.g. summer) have not been well captured. The consistent fine scale irrigation demand data available from modernized irrigation systems along with improving short-term weather forecasts is significantly improving data availability and opening new opportunities to employ data-based demand forecasts. In this paper, we develop a multivariate ARMAX model to forecast daily irrigation demand for lead times of up to five days. It is structured to capitalize on the opportunity of using real-time flow data and to enable future inclusion of weather forecast data. In this paper the model is applied to six years of data for four irrigation channels in the Central Goulburn Irrigation Area. The remainder of the paper describes the study area, the model development including input data selection, the results of calibration and cross validation, the evaluation forecast uncertainty and seasonality of forecast performance, as well as the conclusions that can be drawn. 98

121 Chapter 6 Deterministic irrigation demand forecasts 6.3 Methodology In principle, most polynomial time series model structures are suitable for representing daily irrigation demand as linear filters of corresponding inputs, as are a variety of neural networks. To select an appropriate model framework, we undertook a preliminary evaluation (not presented) that tested the potential of using ARX (autoregressive with exogenous variable), ARMAX (autoregressive moving average with exogenous variable), ARIX and ARIMAX (extends the ARX and ARMAX using an integrator for the noise), BJ (Box-Jenkins), OE (Output-Error), input-output fitting feed-forward neural networks and time series neural network such as NAR (nonlinear AR) and NARX (nonlinear ARX). In general, the neural network model performances were higher during calibration, but the predictive performance was significantly poorer than the polynomial time series models during evaluation. Out of all other polynomial models, the ARMAX model structure derived the best predictions. This is likely to be because the moving average of the white noise has a greater potential to absorb forecast errors compare with other approaches. Furthermore, adding the exogenous variable led to an improvement in the Nash-Sutcliffe model efficiency coefficient by around 0.10 (for lead time one) and 0.4 (for lead time five) compare with autoregressive moving average (ARMA). Consequently, the ARMAX model structure was selected to model the daily irrigation demand as the output of a linear filter of inputs of recent past irrigation demands and an exogenous variable series, combined with a white-noise error representation. The following section describes the ARMAX model structure, and discusses potential exogenous variables, methods to transform non-stationary to stationary data and the two step parameter estimation approach used. We also discuss the statistical indices used to evaluate the predictive performance of the forecasted irrigation demand and the cross-validation steps ARMAX model structure An autoregressive moving average model with exogenous variable (ARMAX) is used to capture the auto regressive processes and influences of external factors (notably the weather) apparent in the demand data. Forecast daily irrigation demand is a combination of past daily irrigation demands and exogenous variables and can be written as follows: ID(t) + a 1. ID(t 1) + + a na. ID(t n a ) = b 1. u(t n k ) + + b nb. u(t n k n b + 1) + c 1. e(t 1) + + c nc. e(t n c ) + e(t) (6.1) The difference equation (Eq. (6.1)) can be write in a more compact way as A(q). ID(t) = B(q). u(t n k ) + C(q). e(t) (6.2) 99

122 Chapter 6 Deterministic irrigation demand forecasts A(q) = 1 + a 1 q a na q n a (6.3) B(q) = b 1 + b 2 q b nb q n b+1 (6.4) C(q) = 1 + c 1 q c nc q n c (6.5) where, ID(t) is the daily irrigation demand at time t, u is the exogenous variable, q is the delay operator, n a is the number of time lags in the autoregressive part, n b is the number of time lags in the exogenous term, n c is the number of moving average parts, and n k is the number of input samples that occur before the input affects the output, also called the dead time in the system. e(t)... e(t n c ) is the white-noise disturbance value, which is a Gaussian process, independent and identically distributed (iid), with zero mean and variance σ 2 e. Here a time step of one day is used and n k is set to one, meaning there is one days delay in the influence of the exogenous variable Exogenous variables The range of potential exogenous variables includes many factors which directly or indirectly influence the irrigation demand. Variable selection depends on the degree of cross correlation between irrigation demand and these exogenous variables. We considered daily maximum temperature (T max), daily mean temperature (T mean), daily incoming solar radiation (R s), reference evapotranspiration (ET O), precipitation, Normalized Difference Vegetation Index (NDVI) and Leaf Area Index (LAI) as surrogates for plant water use. We also considered an index of water supply deficit based on a simple water balance model that aims to capture both plant water uses combined with the influence of rainfall. Final selection of exogenous variable is discussed at the beginning of the results section (6.5) under the perfect weather forecasts. Plant water demand is crop dependent and typically estimated in a two-step process involving calculation of ET O, which is then adjusted using a crop coefficient that is crop type and growth stage dependent [Jensen, 1968]. The limited real-time information about the crop mix meant that crop specific ET estimates were not available and hence ET O was used. All daily ET O calculations were made according to the guidelines provided by the United Nations Food and Agricultural Organization Irrigation and Drainage Paper No. 56 (FAO 56) [Allen et al., 1998]. To allow for the effects of precipitation, we estimated an index of water supply deficit (WSD) using a simple soil water bucket model (Figure 6.1) based purely on atmospheric forcing (precipitation and ET O). This provides an estimate of the soil water supply from precipitation, which is subtracted from ET O to estimate the component of crop demand that must be met from irrigation. This is essentially a command area average value. It is input as the exogenous forcing and calculated as follows. First the nominally rain-fed evapotranspiration ET t, is calculated as 100

123 Chapter 6 Deterministic irrigation demand forecasts ET t = ET 0 ( S t S max ) γ (6.6) where, ET O is the daily reference crop evapotranspiration (mm day -1 ), S t is the soil moisture storage at time t, (mm day -1 ), S max is the field capacity or plant available water storage capacity (mm), and is a parameter representing the shape of the evapotranspiration response to soil water storage. From the water balance equation, ignoring runoff and percolation S t = S t 1 + Precip t 1:t ET 0 t 1:t ( S t S max ) γ (6.7) where, Precip t-1:t is the precipitation over the day. WSD t (mm) is then calculated as WSD t = ET 0 t [1 ( S t S max ) γ ] (6.8) Figure 6.1 Schematic diagram for a simple soil water bucket model Data transformation Time series data can possess non-stationary characteristics such as a seasonal pattern and linear trends. In this case the irrigation demand data and exogenous variables were non-stationary. Data transformation techniques were applied to convert these non-stationary time series into stationary or weak-stationary (2 nd order stationary) time series as the ARMAX model provides a parsimonious description of a (weakly) stationary stochastic process in terms of the three polynomials. Linear regression analysis and various differencing operations can be used to remove linear trends and seasonality respectively. Inter-annual variation can also be removed using normalization or standardization techniques to adjust each year daily irrigation demands onto a notionally common scale. Several approaches were investigated to find the best transformation method in terms of maintaining a constant mean and variance over time for both the daily irrigation demand and the 101

124 Chapter 6 Deterministic irrigation demand forecasts exogenous variable. Linear regression techniques were not included in the data transformation methods because the trend across the year was close to zero and trend removal did not significantly improve the stationarity of the transformed daily time series. Furthermore, inter-annual normalization or standardization techniques cannot be used to remove inter-annual variability in an operational forecasting context because the annual total would need to be known ahead of time. During the preliminary investigation (not presented), one particular data transformation method provided significantly better stationarity in the transformed time series. In this method, the raw data was differenced from a seasonal index. The seasonal index was calculated as the mean of a backward moving window of 1 to 30 days. The window was applied using the day of the year with all six years included. The preliminary evaluation results showed that the mean of a given day of the year (i.e. window width of one) provided the best stationarity characteristics for the both the daily irrigation demand and the exogenous variable. The raw data time series was therefore transformed using; T Y doy,y = Y doy,y Y doy (6.9) The seasonal index is calculated as Y doy = 1 n n y=1 Y doy,y (6.10) where, doy is a given day of irrigation year, y is the irrigation year, n is the number of irrigation T years, Y doy,y is the transformed time series variable for a given day at irrigation year y, Y doy,y is the raw time series variable for a given day at irrigation year yy and Y doy is the seasonal index for a given day of irrigation year, which is the mean of the moving window (difference operator) calculated using Y doy,y Parameter estimation The relationship between daily irrigation demand and the exogenous variable is represented by the ARMAX model parameters (n a,n b,n c and associated coefficients) and those arising from the exogenous variable sub model (γ, S max). A two-level iteration process was used. The first or outer iteration addressed the order of the transfer function and sub model parameters and the second or inner iteration estimated the coefficients (a i, b i, c i). An initial approximation of the order for each transfer function (n a,n b and n c) was determined from the sample autocorrelation function (ACF), the sample partial autocorrelation (PACF), and the cross-correlation functions (CCF) [Chao-Ming et al., 2005; Hong-Tzer et al., 1996]. The most popular method for selecting the best fit orders for each transfer function out of tentative models is to search for the minimum mean square forecasting error using gradient based search techniques [Chao-Ming et al., 2005]. This method is prone to stall at local optimas and therefore a population-based optimization algorithm, a mixed integer Genetic 102

125 Chapter 6 Deterministic irrigation demand forecasts algorithm (MatLab function - gaoptimset) was used to derive efficient estimates for parameters n a,n b,n c, γ and S max was used to search for the global optima. During the second iteration step, the ARMAX coefficients (a i, b i, c i) were estimated using MatLabs prediction-error search method, which chooses between ' Gauss-Newton direction ', ' Gauss-Newton approach ', ' Levenberg- Marquardt ', and 'gradient search method depending on search performance to obtain a sufficient reduction in error is achieved. Three objective functions, namely Nash-Sutcliffe efficiency (NSE) [equivalent to sum of squared error minimisation, Akaike information criterion (AIC) and Bayesian information criterion (BIC) were considered. There is a penalty term included in the AIC and BIC aims to avoid over fitting of model for data, but not in NSE often do results over fitting. BIC applies a larger penalty for higher parameter numbers than AIC. Models were optimised on the basis of BIC but NSE and AIC statistics are provided for comparison. The estimators for the three objective functions are: NSE = 1 [1 MSE OSS ] (6.11) AIC = log MSE + 2d N (6.12) BIC = N. log MSE + d. log N (6.13) In Eqs. (6.11)-(6.13), MSE is the mean squared prediction error, OSS is the mean squared fluctuation of the observation about its mean, d is the number of parameters and N is the number of observations Evaluation methods The predictive performance of the daily irrigation demand were quantified using accuracy, reliability, sharpness and skill statistics, which represent different attributes of forecasts quality [Stanski et al., 1989]. Accuracy is the level of agreement between the forecast and actual as represented by observations and it was measured using the root mean squared error (RMSE). The Nash-Sutcliffe model efficiency coefficient (NSE) [Nash and Sutcliffe, 1970] was used to measure agreement between the forecast and observed values and provides insight into the reliability. The anomaly correlation coefficient (ACC) provided a measure of the sharpness of forecasts or the tendency to forecast extreme values. It measures correlation between the anomalies of the forecast and observed irrigation demand from the corresponding long-term monthly mean [Miyakoda et al., 1972]. Note that all anomalies in this paper refer to daily data relative to the respective long-term monthly mean. Here long term is six years due to record length limitations. The mean square skill score (MSSS) [Murphy, 1988] was used to quantify forecast skill since it is a measure of accuracy relative to the long term monthly mean irrigation demand. We utilized these statistical indices to 103

126 Chapter 6 Deterministic irrigation demand forecasts evaluate the predictive performance for each lead time for the forecasted daily irrigation demand. They are calculated as follows. RMSE = (P i O i ) 2 n (6.14) NSE = 1 (P i O i ) 2 (O i O ) 2 (6.15) ACC = MSSS = 1 (P i C )(O i C ) [ (P i C ) 2 (O i C ) 2 ] 1 2 (n n 1 (P i O i ) 2 (6.16) ) 2 (C O i ) 2 (6.17) In Eqs. (6.14)-(6.17), P i and O i are the i th predicted and observed values respectively, n is the number of observations and C is the climatological or long-term mean monthly observation. O, P, S O 2 and S P 2 are the mean and variance of P i and O i for the period of verification (POV) Cross validation To test the ability of models to predict independent data, model calibration and evaluation approaches typically split the available data into two datasets; one for calibration and the other for evaluation. Among other issues this enables over-fitting to be identified. Cross-validation is a useful version of this for model selection. Available data is split into a number of different periods and each period is omitted from the calibration in turn, with the omitted data used to evaluate the predictions. By re-calibrating the model each time independent predictions are made for the entire data record and the model with the highest predictive ability is selected [Arlot and Celisse, 2010]. A leave-one-year-out cross-validation (LOOCV) technique was applied to select the best ARMAX models in terms of forecast performance for each command area for the six years of data available. This also allowed us to assess the final model in the face of the substantial inter-annual variability present in the data (both severe drought very wet conditions are present in the data - see later) and to derive a robust set of parameters. 6.4 Study area and data Study area The study area is in the Goulburn-Murray Irrigation District (GMID), Victoria, Australia, which is often referred as the Food Bowl of Australia. Agriculture is dominated by irrigated dairy, and pome and stone fruit production, with other agricultural activities related to sheep for wool, beef and dairy cattle [RDV, accessed 26 Sep 2014]. During the millennium drought ( ) [van 104

127 Chapter 6 Deterministic irrigation demand forecasts Dijk et al., 2013], the GMID system was confronted by severe water shortages, which resulted in reductions in irrigation allocations, (urban) water restrictions and reductions in environmental flows [NVIRP, 2010a]. Consequently, the Victorian Government formulated a long-term plan for water called Our Water Our Future. On 20 December 2007, a State Owned Enterprise for Irrigation Modernisation in Northern Victoria was established to plan, design and deliver the Northern Victorian Irrigation Renewal Program (NVIRP) to modernise the GMID systems, which covers 65,000 km 2. Under NVIRP Stage one, 58,500 km 2 of command area was modernised by installing automatic regulator gates and meter outlets, and targeted channel lining. Flow monitoring data from all automated regulators and meter outlets are telemetered in real-time to a central control room. The main source of water supply for the study area is Lake Eildon, which releases water into the Goulburn River, to meet irrigation and environmental demands. Goulburn Weir raises the level of the Goulburn River and diverts irrigation water by gravity to the Stuart Murray, Cattanach and the East Goulburn Main Canals (Figure 3.2). The Stuart Murray Canal supplies water to the Central Goulburn Irrigation Area (CGIA) using six gravity irrigation channels, namely CG 1, 2, 3, 4, 5 and 6, with excess water diverted to Waranga Basin. The irrigation year is from 15 August to 15 May the following year. The spatial characteristics of these channels vary in terms of command area, crop type, soil type and degree of automation. CG 1, 2, 3 and 4 were the first four modernized channels in the CGIA and the degree of automation was also higher than for the other two channels. Therefore, this study used CG 1-4 (Figure 3.2) and the characteristics for each channel are given in Table 3.1. CG 1, 2, 3 and 4 supply km 2 of irrigated agricultural area. The study area is approximately 110 m above Australian height datum (AHD) and the climate is temperate with a hot summer (T hot 22) but without a dry season (Köppen climate type Cfa) [Peel et al., 2007]. Irrigation water takes on average four days to travel from Lake Eildon to farms supplied by CG Data sources and pre-processing Irrigation flow data The irrigation water flow data related to the regulators and service points were collected from the operational SCADA system known as Total Channel Control TM (TCC TM ) that is used by Goulburn-Murray Water (GMW). TCC TM is a fully automated open channel delivery systems, which is (1) close to on-demand supply to customers, (2) automates supply outlet flows as ordered and (3) can interface with on-farm automation equipment [Luscombe et al., 2004]. The system captures flow measurements in real-time at all regulating structures and farm supply points. We obtained the flow data recorded at four off-take regulators of CG 1-4 (Figure 3.2) and 1016 supply points from 15 August 2006 to 15 May 2012; effectively six irrigation years. 105

128 Chapter 6 Deterministic irrigation demand forecasts The off take regulator flow data and aggregated service point delivery data were converted to daily (midnight to midnight) volumes. Regulators record times of flow rate change time (time resolution is seconds) and the associated flow rates, which are accurate to ± 2.5% with a 95% confident interval [Rubicon, 2014], under laboratory test conditions. The SCADA system records the start and end timings and flow rates of irrigation order deliveries. Service point regulators deliver uniform flow within ± 5% more than 90% of the time [NVIRP, 2010b]. Service point flows measurements were aggregated to daily and then, aggregated across all service points for the individual channel and for the study area as a whole. This assumes that the travel time between along the local channel or study area is significantly less than a day. Flows for manual service points are inferred from order information while flows for automated points are from real-time data. Table 3.1 shows the percentage of delivered volume through the automated points, so the addiction uncertainty from the manual point is small. These aggregated service point flows and off take regulator flows are referred to as ID CGi, ASP and ID CGi, OTR respectively. Here ASP denotes the Aggregated Service Points, OTR denotes the Off Take Regulator and i provides spatial aggregation area (where i=1, 2, 3, 4 or 1234). The OTR data differs from the ASP data for as number of reasons including, channel seepage and evaporative losses, minor diversions for stock and domestic purposes, operational reasons (e.g. channel filling) and end of channel outflows. Models were constructed for both types of data, but we concentrate on the ASP flows here as they are most directly related to irrigation demand Exogenous variables Climate data were obtained from two automatic weather stations (AWSs) and three rain gauge sites operated by the Australian Bureau of Meteorology [BoM, undated-b] located in and around the study area (Figure 3.2).The characteristics of each weather station are given in Table 6.1. The hourly weather variables needed to estimate daily ET O were collected from AWSs (air temperature, dewpoint temperature, wind speed) and satellite imagery (solar radiation) as described in [Perera et al., 2014; Perera et al., 2015b]. Daily precipitation records were collected from all five sites as the area often witnesses patchy rainfall events. These five sites were established well before the channel automation and record start dates vary between 1883 and AWSs and rain gauges nominally provide continuous measured weather data; however, there were times within the study period when hourly/daily weather data were missing for various reasons. For missing daily precipitation, aggregated values were recorded at the end of the missing period and these were uniformly disaggregated over the missing period. For other weather variables, missing data were infilled from the other station. 106

129 Chapter 6 Deterministic irrigation demand forecasts NDVI and LAI values were derived from satellite imagery taken from Moderate Resolution Imaging Spectrometer (MODIS) images for various spatial resolutions on an Integerized Sinusoidal (IS) 10-degree grid and details could be found in We used NDVI 250 m resolution 16-day composite [Huete et al., 2002] and LAI 1000 m resolution 8- day composite [Myneni et al., 2002] from the Oak Ridge National Laboratory Distributed Active Archive Centre-DAAC [DAAC, 2012]. These were average over a 7 by 7 km square centred on the middle of the study area (i.e. at 145º18'0"E, -36º25'00"S) and values available from the DAAC have already been corrected for geometry and atmospheric effects, and filtered to retain the best index value for a given time window for each pixel [García et al., 2013]. Daily NDVI and LAI values were obtained by assuming NDVI and LAI values were constant over the 8-day and 16-day composite respectively. Table 6.1 Characteristics of automatic weather stations and rain gauges No. AWS no. Name Latitude (degrees) Longitude (degrees) El. (m) 1 Precipitation, 2 Daily temperature, 3 Dew point temperature, 4 Wind speed and 5 Solar Radiation Precip. 1 T 2, Dew 3, WS 4 & SRad Shepparton Airport -36º25'44" 145º23'41" Tatura Sustainable Institute -36º26'16" 145º16'02" Thiess Service -36º26'40" 145º13'40" Waranga Reservoir -36º30'39" 145º05'25" Murchison -36º36'53" 145º12'51" Results Time series characteristics Irrigation flows The yearly and monthly variability of ID CG1234, ASP and the corresponding observed mean for the study period of six years are shown in Figure 6.2. The ID CG1234, ASP exhibits seasonality that is mainly due to crop cycle, and the seasonal variation in ET O and precipitation. The highest absolute variability and the peak demand was during January (mid-summer in the southern hemisphere). The higher demands in April compared with February and March are at least partly due to establishing annual winter pastures. The yearly mean for ID CG1234, ASP was approximately equivalent with the exception for irrigation years 2010/11 and 2011/12 and more importantly does not show long-term trend. 2010/11 was a particularly wet summer following from extended drought conditions while 2011/12 was a more average summer but with significantly higher irrigation allocations (Figure 6.2). 107

130 Chapter 6 Deterministic irrigation demand forecasts The daily and monthly mean and variance of the ID CG1234, ASP changed over time leading to a nonstationary time series. Figure 6.3 (a) and (b) show the auto correlation function (ACF) and partial autocorrelation function (PACF) for the transformed ID CG1234, ASP time series derived using the data transformation method explained earlier. Both the ACFs of transformed time series possess the correlation characteristics of a weakly stationary time series. The ACF and PACF for the transformed time series was a mixture of exponential and damped sine waves and the transformed ID CG1234, ASP time series tails off with increased in lag days. This transformation method was preferred over the other methods of different backward moving window sizes (during preliminary study) in terms of the highest PAC values with the lag one and least numbers of lags taken to falls below significant level for 95% confidence interval. Figure 6.2 Annual and seasonal variation of ID CG 1234, ASP for the study area. Each box plot represents the lower (25 th ), middle (50 th ) and upper (75 th ) percentile and the bottom and top whiskers represent 5 th and 95 th percentiles respectively. Figure 6.3 Sample ACF and PACF for ID CG 1234, ASP for study area as indicated by transformation method 108

131 Chapter 6 Deterministic irrigation demand forecasts Exogenous variables The sample cross correlation function (CCF) was calculated between daily ID CG 1234, ASP and the eight potential exogenous variables discussed in section (Figure 6.4). The CCF varies between the eight exogenous variables. The LAI and NDVI CCFs were changed marginally with short-term ID CG 1234, ASP fluctuations as the CCF for LAI and NDVI fall repeatedly inside and outside 95 % significant levels respectively for all days. Positive correlations indicate that higher values of T max, T mean, R s, ET O and WSD are associated with higher irrigation demand and precipitation events lead to lower irrigation demand, which is all matches process-based expectations. The highest CCF value was found whilst for WSD. The highest CCF values occurred at lag 1. Therefore, the WSD was used as the exogenous variable. Figure 6.4 CCF between daily ID CG1234, ASP and 8 potential exogenous variables using the data transformation method. A positive time lag indicates the exogenous variable leading flow. Data for T max, T mean, R s, wind speed and dew point temperature are for Shepparton airport (81125). The rainfall is the mean of Tatura Sustainable Agency (81049), Tatura Thiess (81114) and Murchison (81035) sites, which was the combination producing the highest cross-correlation at lag 1. The optimal parameter values (γ and S max ) for the WSD were taken from the optimized model Model calibration The multivariate ARMAX time series model structure was calibrated using the exogenous variable WSD for the aggregated service point flows ID CG i, ASP and also for the off take regulator flows ID CGi, OTR. To forecast near future ID CG i, ASP or ID CGi, OTR, we adopted a perfect weather forecast by using the observed weather data. Finally, the predictive performance for the calibrated ARMAX time series models were evaluated up to five days lead time. Lead times longer than one day were forecast by recursively applying the one-day lead time model. 109

132 Chapter 6 Deterministic irrigation demand forecasts The effort to parameterize a separate model for each command area would reduce the prediction uncertainty and the calibrated models would represent the local conditions more than an overall conditions. Therefore, this section essentially researches numerous calibration scenarios in terms of different data transformation methods, objective functions, weather data from various stations and cross validation scenarios. The calibration results for these various scenarios were given separately and the model selection section discusses the trade-off between above factors to derive parameterized ARMAX model for each commend area. However, the conclusions derived during model calibration is identical for both ID CG i, ASP and ID CG i, OTR and this section shows results related for the ID CG i, ASP to avoid the repetition Objective functions The impact for predictive performance from the three objective functions was investigated. We used three objective functions and observed data relevant for calibration period (2006/ /11) to calibrate command areas specify ARMAX time series models. The predictive performance for the time series model was evaluated only using NSE as this reflects scatter in the forecast, relative to observed values. Table 6.2 Model performance for different objective functions for calibration period from 2006/07 to 2010/11 Parameters NSE (lead days) n a n b n c S max γ TP Nash-Sutcliffe coefficient CG CG CG CG CG Akaike information criterion CG CG CG CG CG Bayesian information criterion CG CG CG CG CG Total number of parameters 110

133 Chapter 6 Deterministic irrigation demand forecasts The 2011/12 season was used to assess predictive performance. The calculated NSEs between forecast and observed ID CG i, ASP for lead times up to five days are shown in Table 6.2. The predictive performances were relatively higher whilst using objective functions NSE and AIC than BIC for all lead time as a result of overfit due to lack (NSE) or insufficient (AIC) penalty value for increase of a parameter. NSE and AIC lead to substantially more parameters (higher order) than BIC with only a small decrease in sum of square errors (increase in NSE). This means there is a much higher risk of overfitting in NSE and AIC than BIC. Therefore we chose to use BIC as the objective function for the reaming analysis Weather station selection The predictive performances for ID CG i, ASP varied spatially as irrigation demand partly depends on the spatially distribution of the exogenous variable WSD. To this end, predictive performances with respect to the spatial distribution for ET O and precipitation were separately evaluated for each command area. Spatial differences in daily ET O were small between Tatura Institute of sustainable agency (81049) and Shepparton Airport (81125); hence the Tatura data were used for calibration and evaluation. Comparisons between rain gauge stations suggested significant differences and that selecting one or more gauge stations for each command area would be advisable. It was not possible to distinguish a single combination of mean precipitation that corresponded to highest and lowest predictive performances for all five command areas. Therefore, the best performing precipitation combination was selected for each command area (Table 6.3). Table 6.3 Best performing precipitation combinations for each command area Command area Aggregated service point flow (ID CG i, ASP) CG CG 2 Average of 81049, and CG 3 Average of 81049, and CG 4 Average of 81125, and CG 1234 Average of 81125, and Calibration As part of the cross-validation approach, the models for each channel and the whole study area were calibrated six times. Each time used five years for model fitting; with one year held out for independent testing. The overall predictive performance for ID CG i, OTR was marginally lower than ID CG i, ASP but the overall patterns (between channels and between years) of performance were similar. This might be because the regulator flow lumps the behaviour of operators and farmers. 111

134 Chapter 6 Deterministic irrigation demand forecasts This section concentrates on the ID CG i, ASP to avoid repetition. Table 6.4 provides an overall summary of the calibration outcomes and the performance for each individual calibration is in Table 6.7 (Supplementary material). In general the performance metrics were reasonably consistent between years, with the exception of the RMSE. The RMSE tends to be higher in years with more variability in daily demands (Table 6.7). The other metrics are normalised by flow variability, which leads to greater consistency between years. Figure 6.5 shows calibration results scatter plots of forecast vs. observed daily ID CG i, ASP values for 2006/7-2010/11 periods (2011/12 was validation). Lead times of one, three and five days are shown. The scatter between forecast vs. observed daily ID CG i, ASP for lead time one is directly resulted from calibration and forecasts for lead time three and five using the one day lead time model recursively over several days. The linear regression lines shown in Figure 6.5 behave similarly for all five command areas. This leads to slightly over-predict the relative small daily ID CG i, ASP forecasts and under-predict the relatively high daily ID CG i, ASP forecasts for all lead times. The scatter between forecast vs. observed daily ID CG i, ASP and the respective linear regression lines suggest that forecast performances are significantly higher for larger command areas and over/under prediction gradually increases as the lead time increased. Table 6.4 Parameters range and average calibration performance for six split calibration scenarios for four channels and study area for ID CGi, ASP Channel Parameter range Average performances for lead time 1 n a n b n c S max γ RMSE NSE ACC MSSS (L 1 -U 2 ) (L 1 -U 2 ) (L 1 -U 2 ) (LV 3 -UV 4 ) (LV 3 -UV 4 ) (ML day -1 ) CG CG CG CG CG Lower Order, 2 Upper Order, 3 Lower Value, 4 Upper Value The performance metrics tend to decline as the lead time increases from one day to five day, with RMSE approximately doubling as errors are compounded. The exception is CG 1 and 2, where the RMSE only increases modestly with lead time but the performance is relatively poor in those command areas because they are relatively small compared to the others. There is also an improvement in performance moving from CG 1 through to CG 4. This is presumably related to the larger number of service points and hence greater opportunity for averaging across irrigation events 112

135 Chapter 6 Deterministic irrigation demand forecasts at individual service points. The performance improvements are particularly evident in the relationship between the data and the 1:1 line, with significantly more smoothing (underestimation of high values, overestimation of low values) for smaller channels and longer leads times. The data clouds are also more dispersed for smaller channels and longer lead times. Figure 6.5 Calibration performance for Daily ID CGi, ASP forecast vs. observed for CG 1, 2, 3, 4 and the study area: (a) One lead day, (b) Three lead days and (c) Five lead days for the calibration period 2006/ /11 113

136 Chapter 6 Deterministic irrigation demand forecasts In terms of quantitative metrics, for the largest channel (CG 4), the NSE between forecast and observed ID CG i, ASP shows that over 90% of the daily variability in demand is predicted for one day lead time and even at five days lead time two thirds of the daily variability is predicted. For the much smaller CG 1, this falls to 55% and 29% for one and five days lead time respectively. Similarly, the highest and lowest ACC and MSSS values among channels were found at CG 4 and CG 1 respectively. The ACC and MSSS ranged from 0.95 to 0.47 and from 0.90 to 0.22 respectively. On average MSSS values over the study area ranged between 0.92 (one day lead time) and 0.57 (five day lead time). The decline in predictive performance with time occurs because of errors accumulating over time. This could be partly due to the relatively low influence of the exogenous variable, but is also due to the influence of structural errors in the model (e.g. the myriad of various management decisions) and other error sources. There are also some difference between small and large channels in terms of total number of parameters, with higher order (more parameters) being selected for the larger channels, perhaps reflecting the reduction in noise due to averaging over more supply points and hence greater ability for the calibration to extract more subtle patterns from the data Model evaluation Perhaps the more important aspect of model performance is the predictive ability for independent test periods. This was tested using the six evaluation years individually to examine whether there were any significant differences between calibration and evaluation processes. Spatially and temporal based predictions of the calibrated ARMAX models for both ID CG i, ASP and ID CG i, OTR were evaluated up to five lead days. During the evaluation period, the overall predictive performance for ID CG i, OTR was marginally lower than ID CG i, ASP as similar to the calibration period. Therefore, this section present only evaluation results related for the ID CG i, ASP to avoid the repetition. Table 6.5 provides an overall summary of the evaluation performance for each command area and Table 6.8 (Supplementary material) provides evaluation performance for each command area with respect to the independent data sets corresponding to the 6 spilt calibration scenarios for lead time one, three and five. The behavior patterns of the statistical indices were identical for calibration and evaluation periods, but the statistical indicators were higher for evaluation than calibration for most of the six spilt calibration scenarios. This is likely to be due to the relative length of the calibration and validation periods. Being five years the calibration period includes inter-annual variability, whereas the validation period does not. This leads to lower RMSE during the validation period. The marginal predictive performances between six different evaluations periods with respect to six LOOCA scenarios suggested that were only small differences between years with the 114

137 Chapter 6 Deterministic irrigation demand forecasts exception of RMSE related to irrigation year 2011/12, which was 30-50% higher than the typical RMSE. Therefore, only the evaluation results related to the LOOCA-S one is shown graphically. The results are the best in terms of NSE, but more importantly this year was chosen because it is most representation of typical years. The first four years of the study period were drought years with very low water availability compared with historical conditions was a very wet summer of the end of the drought. Figure show time series and scatter plots between daily ID CG i, ASP forecasted vs. observed for one, three and five lead days respectively for the irrigation year 2011/12. On average, RMSE values for the study area were and ML day -1 for one and five day lead times, respectively. This was 43% and 49% lesser than calibrations for one and five day lead times, respectively. The NSE were ranged between 0.96 (one day lead time) and 0.71 (five day lead time), and for CG 4 and CG 1 channels, respectively and for the study area it was ranged between 0.96 and 0.84 for one and five day lead times, respectively. This was 3% and 30% increase compared to the calibrations period for one and five day lead times, respectively. The ACC and MSSS for study area respect to one and five day lead times were ranged from 0.98 to 0.93 and from 0.96 to 0.85 respectively. As a result, The ACC values were increased 2% and 24 % and the MSSS values were increased 4% and 59% for one and five day lead times respectively. All these significantly higher predictive performance for daily ID CG i, ASP for evaluation period show the model s ability of making sufficiently accurate spatially and temporal based predictions using the calibrated ARMAX models. Table 6.5 Average statistical indicators for all six evaluation periods related to the ID CG i, ASP for four channels and study area Channel Lead time 1 Day 3 Day 5 Day RMSE NSE ACC MSSS RMSE NSE ACC MSSS RMSE NSE ACC MSSS CG CG CG CG CG

138 Chapter 6 Deterministic irrigation demand forecasts Figure 6.6 Daily ID CGi, ASP forecast vs. observed for CG 1, 2, 3, 4 and the study area for lead time one, three, and five days 116

139 Chapter 6 Deterministic irrigation demand forecasts Figure 6.7 Daily ID CGi, ASP forecast vs. observed for CG 1, 2, 3, 4 and the study area: (a) One, (b) Three and (c) Five lead days respectively 6.6 Discussion This study developed a deterministic multivariate time series model to forecast short-term daily irrigation demand at the system scale. The model was applied for an irrigated agricultural area which operates under a fully automated irrigation distribution system. The spatial and temporal 117

140 Chapter 6 Deterministic irrigation demand forecasts forecasting performance was assessed under an assumed perfect weather forecast. The spatial forecasting performance was assessed across four command areas (irrigation channels) and for the study area as a whole. Temporal forecasting performance was assessed for lead times up to five days. In the above analysis various assumptions about model residuals were made, including that the model error should be normally distributed, independent of predictors and serial correlations, and be homoscedastic. Table 6.6 shows the ARMAX model error mean, variance and skewness for ID CG i, ASP and ID CG i, OTR for each command area as well as for all times. Figure 6.8 shows the residual histograms and relationships with the observed demand for lead times of one, three, and five days for the CG 1 and CG 1234 command areas. Table 6.6 ARMAX model error characteristics ID CG i, ASP during evaluation period 2011/12 Channel µ 1 ID 4 µ 1 - Residual σ 2 σ 2 - Residual g 3 g 3 - Residual Lead time ID 4 Lead time ID 4 Lead time CG CG CG CG CG Mean, 2 standard deviation, 3 skewness, and 4 observed irrigation demand Figure 6.8 Scatter plots between model residual vs, observed ID CG i, ASP and the respective residual histograms for lead times of one, three, and five for CG 1 (top row) and CG 1234 (bottom row) command areas. 118

141 Chapter 6 Deterministic irrigation demand forecasts Figure 6.8 a shows that there is systematic over-prediction of low demands and underprediction of high demands, which increases as a proportion of the average demand as the size of command area reduces and as the lead time increased. The increase over time is due to the compounding influence across forecast time steps. These systematic biases are inherited from the high auto correlation between consecutive daily irrigation demands. The mean, standard deviation and skewness increased in absolute terms but decrease in relative terms (c.f. the mean flow) with increased command area and lead time (Table 6.6). Model residuals were slightly negatively skewed but close to normally distributed. Overall the ARMAX model residuals match the underlying statistical assumptions reasonably well. The raw irrigation demands show significant seasonality, suggesting there could also be some seasonality in the predictive performance. Therefore, we investigate the forecasting performance for daily irrigation demand during the Austral spring (SON), summer (DJF) and autumn (MAM) (the irrigation system is non-operational during winter (JJA)) (Figure 6.9). The RMSEs were highest during autumn and approximately equal for summer and spring for all lead times. The seasonal NSEs, ACCs and MSSSs for spring and autumn are approximately equal for a given lead time. The summer values were higher (better) than annual values. The four performance indicators provide consistent results, with predictive performance of the proposed time series model being better during summer compared with spring or autumn. This reflects the irrigation behavior being more in line with the weather drivers (i.e. WSD) during summer. It is likely that the low predictive performance for autumn and spring may have resulted from irrigation demand fluctuations stemming from management decisions such as irrigation to establish annual pasture in Autumn, uncertainties in the sewing date for perennial crops during spring, progressive announcements of seasonal allocations over spring, and carry over announcements in Autumn. These behavior factors were only crudely captured in the model through the autocorrelation component and initial data transformations. Figure 6.9 Seasonal predictive performance for command area CG 1234 as indicated by (a) RMSE, (b) NSE, (c) ACC and (d) MSSS of forecasted vs. observed daily irrigation demand. The predictive performance depends on the size of the number of service points (command area) and variability in the irrigation flow data (Figure 6.10). These two factors are strongly related. The increase in predictive performance with the size of command area (and also the number of 119

142 Chapter 6 Deterministic irrigation demand forecasts service outlets) is likely to be due to greater lumping of the behavior of farmers and system operators. The order of the optimal ARMAX models also increased with command area (Table 6.2), suggesting the models were able to extract more nuanced behavior (e.g. subtle patterns depending perhaps on the day of the week). Figure 6.10 Scatter plots, (a) Number of service outlets vs. NSE (b) Standard deviation of demands vs. NSE for the evaluation period We now turn to a comparison of our results to those in the literature. Our overall results showed that daily irrigation demand forecasted using time series models was skilful for lead times up to five days. In fact for the independent evaluation, NSE varied between 0.71 and 0.84 for 5 day lead times, indicating there is substantial information in the forecasts even at this relatively long lead time. The forecasting performance for daily irrigation demand was higher than most of the previous studies, probably reflecting both the integration of rainfall and potential evapotranspiration into a single variable (the WSD index) representing weather conditions and the high quality data available from the automated system. The results were substantially better than machine learning techniques applied in other studies. In this study, model efficiency (NSE) for ID CG 1234, OTR (command area 287 km 2 ) vary over for 1-5 lead days compared with for 1-2 lead days (command area 280 km 2 ) [Ticlavilca et al., 2011] and for 1-2 lead days (command area 105 km 2 ) [Alfonso et al., 2011] of the models that have been used to forecast diversion volumes for three irrigation canals in Sevier river basin, Utah, USA. These two studies use forecast weather, which may contribute to the lower predictive performances compare with our study. Moreover, NSE for ID CG 1234, ASP for 1 day lead time is 0.98, which was significantly higher than the NSE values of similar studies conducted for several irrigation districts locate in the southern Spain such as

143 Chapter 6 Deterministic irrigation demand forecasts [Pulido-Calvo and Gutierrez-Estrada, 2009], 0.95 (olive and cotton) [Pulido-Calvo et al., 2007] and 0.82 [Pulido-Calvo et al., 2003] respectively. Although, overall the predictive performance of the multivariate time series model was higher than almost all the previous studies we are aware of, irrigation demand forecasts from ARMAX models were determined more by the strong serial correlation in demand than the weak crosscorrelation with the exogenous variable. This was the one of the major reasons for the systematic bias in the irrigation demand forecasts. These issues were most pronounced during periods of rapid change and some lag was evident in the predictions of rapid changes. One way to overcome this issue might be to replace the system wide WSD with measured information on soil moisture status coming out from paddocks in the command area, although a large number of sensors would be required to account for variations in management between individual fields. It may also be possible to find alternative data transformation methods that could convert the non-stationary irrigation demand time series into a strictly stationary time series, given that the method we have adopted was not able to fully eliminate the linear and seasonal components existing in the irrigation demand as well as systematic farmer and operator responses towards water allocation and carryover announcements, winter crop establishments etc. Finally, the uncertainties associated with weather forecasts were not evaluated in this study as we used observed weather data for forecasting. This will be addressed in future work. 6.7 Summary and conclusion This paper capitalizes on an opportunity to forecast daily irrigation demands using real-time system data available from modernized irrigation systems and observed weather data available from automatic weather stations. This paper developed a multivariate time series model (ARMAX) to forecast irrigation demands with respect to aggregated service points flows (ID CG i, ASP) and off take regulator flows(id CG i, OTR) across five command areas, which included area covered under four irrigation channels and the study area. We used a data transformation technique to convert nonstationary daily irrigation demand and exogenous variables time series of into stationary or weakstationary (2 nd order stationary) time series. Eight potential exogenous variables, namely, T max, T mean, R s, ET O, precipitation, LAI, NDVI and a water supply deficit index (WSD) were evaluated as potential exogenous variables for the ARMAX model. WSD showed the highest cross correlation function value with the irrigation demand. The command area specific ARMAX models were calibrated using a genetic algorithm with the Bayesian Information Criterion (BIC) calculated from daily demands was used as the objective function. Daily irrigation demands (ID CG i, ASP and ID CG i, OTR) were forecast for lead times up to five days using the calibrated ARMAX time series model under the perfect weather forecast. The spatial 121

144 Chapter 6 Deterministic irrigation demand forecasts and temporal predictive performance were evaluated against observed data recorded 1016 service points and four off take regulators. The ARMAX model efficiency (NSE) during the evaluation period (2011/12) for ID CG i, ASP and ID CG i, OTR across five command areas ranged from 0.79 (CG 1) to 0.98 (CG 1234) and from 0.78(CG 1) to 0.96 (CG 1234), respectively for lead times of 1-5 days. Further, these developed ARMAX time series models were capable of generating skilful forecasts (MSSS 0.5 [Murphy, 1988] and ACC 0.6 [Miyakoda et al., 1972]) of ID CG i, ASP and ID CG i, OTR for all five lead days. These irrigation demand forecasts were better than using the monthly mean irrigation demand. Overall the predictive performances from the ARMAX time series models were higher than almost all the previous studies we are aware of. Generally the maximum lead times considered here are also significantly longer than previous studies. Predictive performance increased markedly with command area size and declined with long lead times. The performance was highest during summer with spring or autumn being similar to each other. Uncertainties associated with irrigation demand forecasts were not looked at in detail here as forecasts were made under the perfect weather forecasts. A future study will extend this work to examine the characterize and incorporate the impacts of uncertainty in the measured input data, model parameters, and real-time weather forecasts. This will enable short-term system scale irrigation demand forecasts derived from the developed ARMAX model to enhance the decision making ability of the system operators. 122

145 Chapter 6 Deterministic irrigation demand forecasts 6.9 Supplementary materials Table 6.7 Parameters and calibration performance for six split calibration scenarios related to the ID CG i, ASP for four channels and study area Channel Split Calibration Parameters Observed flow Lead time scenario Mean STD 1 Day 3 Days 5 Days No VY 1 n a n b n c S max γ RMSE (ML day -1 ) NSE ACC MSSS RMSE (ML day -1 ) NSE ACC MSSS RMSE (ML day -1 ) NSE ACC MSSS CG / / / / / / Average Performances CG / / / / / / Average Performances CG / / / / / / Average Performances CG / / / / / / Average Performances CG / / / / / / Average Performances Validation year 123

146 Chapter 6 Deterministic irrigation demand forecasts Table 6.8 Evaluation performance for six split evaluation scenarios related to the ID CG i, ASP for four channels and study Channel 1 Validation year Split calibration Observed flow Lead time scenario Mean STD 1 Day 3 Days 5 Days No VY 1 RMSE (ML day -1 ) NSE ACC MSSS RMSE (ML day -1 ) NSE ACC MSSS RMSE (ML day -1 ) NSE ACC MSSS CG / / / / / / Average performances CG / / / / / / Average performances CG / / / / / / Average performances CG / / / / / / Average performances CG / / / / / / Average performances

147 Chapter 7 Probabilistic daily irrigation demand forecasts Chapter 7 Ensemble forecasting of short-term system scale irrigation demands using real-time flow data and numerical weather predictions In press as Perera, K. C., Western, A. W., Robertson, D. E., George, B., Nawarathna, B., (2016)., Ensemble forecasting of short-term system scale irrigation demands using real-time flow data and numerical weather predictions, Water Resource Research. 125

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149 Chapter 7 Probabilistic daily irrigation demand forecasts 7.1 Abstract Irrigation demands fluctuate in response to weather variations and a range of irrigation management decisions, which creates challenges for water supply system operators. This paper develops a method for real-time ensemble forecasting of irrigation demand and applies it to irrigation command areas of various sizes for lead times of one to five days. The ensemble forecasts are based on a deterministic time series model coupled with ensemble representations of the various inputs to that model. Forecast inputs include past flow, precipitation, and potential evapotranspiration. These inputs are variously derived from flow observations from a modernized irrigation delivery system; short-term weather forecasts derived from numerical weather prediction models and observed weather data available from automatic weather stations. The predictive performance for the ensemble spread of irrigation demand was quantified using rank histograms, the mean continuous rank probability score (CRPS), the mean CRPS reliability, and the temporal mean of the ensemble root mean squared error (MRMSE). The mean forecast was evaluated using root mean squared error (RMSE), Nash Sutcliffe model efficiency (NSE) and bias. The NSE values for evaluation periods ranged between 0.96 (1 day lead time, whole study area) and 0.42 (5 days lead time, smallest command area). Rank histograms and comparison of MRMSE, mean CRPS, mean CRPS reliability and RMSE indicated that the ensemble spread is generally a reliable representation of the forecast uncertainty for short lead times but underestimates the uncertainty for long lead times Introduction Short-term system scale irrigation demand forecasts are extremely useful for system operators to make irrigation water distribution decisions, but they are subject to uncertainties resulting from input parameters and model structure. Parameter and structural uncertainties are inherent in models, as models try to simplify the complex reality. Input uncertainties are also important as inputs are subject to measurement, estimation or prediction uncertainties. From the irrigation demand forecasting prospective, uncertainties in the irrigation demand forecasts can result from observation, estimation or prediction uncertainties in biophysical (crop-soil-climate interaction), behavioral (farmers and system operators attitude that influencing management decisions) and supply (supply source, seasonal allocation, permanent entitlement) factors [Zaman et al., 2007]; as well as from the respective parameter uncertainties, depending on the specific models used. This research makes ensemble forecasts of irrigation demand using a multivariate time-series model of short-term (up to five days) daily irrigation demand forced by observed demands and observed and forecast weather integrating measurement errors, estimation errors, and weather forecast uncertainty. 127

150 Chapter 7 Probabilistic daily irrigation demand forecasts Past research has used sophisticated and highly complex modelling architectures such as process-based (conceptual) and data-driven (statistical) approaches [Alfonso et al., 2011; Pulido- Calvo and Gutierrez-Estrada, 2009] to derive irrigation demand forecasts. Typically, process-based approaches have been used at field scale and data-driven approaches have been used at system scale. Few of these studies have attempted to estimate irrigation demand forecast uncertainties. Studies at the system scale have mainly used data-based deterministic models to forecast irrigation demand [Pulido-Calvo and Gutierrez-Estrada, 2009; Pulido-Calvo et al., 2007; Pulido-Calvo et al., 2003]. A few of these studies have considered uncertainty, mainly focusing on parameter uncertainties. Both bootstrap methods [Ticlavilca et al., 2011] and Bayesian techniques [Alfonso et al., 2011] have been used to investigate the irrigation demand forecast uncertainties resulting from model parameters. Also, some univariate time series models based on previous irrigation flows [Pulido- Calvo and Gutierrez-Estrada, 2009; Pulido-Calvo et al., 2007; Pulido-Calvo et al., 2003] have captured the combined uncertainty from inputs and model structure by including the associated error model to represent the random error component in the irrigation demand forecasts. Many models have used short-term weather forecasts to make irrigation decisions, especially precipitation [Azhar and Perera, 2011; Cai et al., 2011; Gowing and Ejieji, 2001; Rogers and Elliott, 1989; Wang and Cai, 2009; Wilks and Wolfe, 1998], temperature [Ticlavilca et al., 2011; Wilks and Wolfe, 1998] and evapotranspiration [Alfonso et al., 2011; Tian and Martinez, 2014]. Weather forecasts have often been considered for field scale and a few studies that we are aware of have incorporated weather forecasts at the system scale [Tian and Martinez, 2014]. Field scale models have often used weather forecasts for irrigation scheduling (i.e. predict timing and its volume) and weather forecast uncertainties were manifest mainly in variations of the irrigation timing [Cai et al., 2011; Gowing and Ejieji, 2001; Wang and Cai, 2009; Wilks and Wolfe, 1998]. These models only used limited forecast information as the quality of the available weather forecast at that time was poor at longer lead times (greater than three days lead times) [Gowing and Ejieji, 2001]. This was seen as a major impediment at the time. [Alfonso et al., 2011] and [Tian and Martinez, 2014] forecasted system scale irrigation demands, combining stochastic reference evapotranspiration forecasts derived from a machine learning algorithm and currently operational Global Ensemble Forecast System (GEFS), respectively. [Ticlavilca et al., 2011] also combined daily maximum and minimum temperature with system scale irrigation demand forecasts using a machine learning algorithm. These system scale models were mainly developed for arid-zone agriculture and precipitation forecasts were not considered, as it is not important for irrigation decisions in those environments [Alfonso et al., 2011; Tian and Martinez, 2014; Ticlavilca et al., 2011]. These studies have generated system scale stochastic irrigation demand forecasts with prediction intervals. In terms of assessing 128

151 Chapter 7 Probabilistic daily irrigation demand forecasts the probabilistic forecasts, all studies provided a graphical comparison of observed time series overlain on the forecast prediction intervals without a quantitative evaluation. [Tian and Martinez, 2014] also provided relative operating characteristic (ROC) diagrams that suggested, they didn t provide any statistical analysis of the reliability or sharpness of the probabilistic forecasts. The maximum lead time for the most of these studies was two days or less and no study comprehensively integrates input uncertainties into the irrigation demand forecast uncertainties. While ensemble techniques have been used elsewhere, in hydrology [Addor et al., 2011; Li et al., 2015; Shrestha et al., 2013; Zappa et al., 2011] and hydrometeorology [Brown et al., 2010; Ebert et al., 2011; Gneiting, 2013; Robertson et al., 2013; Rossa et al., 2011], no studies we are aware of have used both stochastic precipitation and reference evapotranspiration forecasts nor have there been studies that combine uncertainties in antecedent flows and observed and forecast weather to derive stochastic volumetric irrigation demand forecasts at system scale. Ensemble techniques are commonly used to represent uncertainty in non-linear models. In the context of forecasting; ensemble forecasting is a form of Monte Carlo analysis that is used to characterize uncertainty in model outputs [Toth and Kalnay, 1993]. In principle, this technique can be applied for both input and parameter uncertainty depending on the context of the modelling. Ensemble forecasting techniques have been widely used in science, engineering, medicine and ecology, among other areas. It has been widely used in weather forecasting [Ebert, 2001; Ebert et al., 2011; Gneiting, 2013; Gneiting and Raftery, 2005] and species distribution modelling [Araújo and New, 2007; Buisson et al., 2010; Grenouillet et al., 2011; Thuiller et al., 2009] to capture errors in the initial condition and model structure. In the field of water resources engineering, ensemble forecasting techniques have also been used extensively in forecasting stream flow [Bennett et al., 2014], short-term water demand [Hutton and Kapelan, 2015] and floods [Alvarez-Garreton et al., 2014; Cloke and Pappenberger, 2009; Li et al., 2014a; Schaake, 2006; Schaake et al., 2005]. In these studies, sources of uncertainty included in forecast ensembles were uncertainty in inputs (mainly precipitation forecasts), state variable (soil moisture), and model structures through model parameters. We are unaware of any irrigation demand forecast model that has used ensemble forecasting techniques to derive stochastic irrigation demand forecasts. The structure of the multivariate time series model used here, which has auto-correlated and cross-correlated multivariate inputs, some of which are non-linearly transformed, suggests ensemble forecasting techniques to derive output uncertainties would be useful. This technique has advantages in multivariate time series models compared with the bootstrap method, which can often distort the cross correlations between multivariate inputs and outputs [Khaliq et al., 2009; Rummel et al., 2010], whereas ensemble forecasts can preserve the error covariance among input time series which is then transferred through the regression structure to the stochastic output. However, the outcomes from 129

152 Chapter 7 Probabilistic daily irrigation demand forecasts an ensemble forecasting technique is dependent on the quality of the input time series. Therefore, a good quality data set (i.e. fine scale, free from bias and complete) is important for generating reliable, unbiased output ensembles. Past impediments such as the lack of required data, the expense of data acquisition and low data quality are being reduced with the availability of irrigation flow data from fully automated irrigation distribution systems, short-term weather forecasts from numerical weather predictions (NWP) models and observed weather data from automatic weather stations. In particular, the accuracy of the weather forecasts is continuously improving and consistent real-time irrigation flow data are now available from modernized distribution systems. This provides an opportunity to apply ensemble forecasting techniques to generate stochastic irrigation demand forecasts. This paper develops ensemble irrigation demand forecasts using the irrigation distribution system in the Goulburn-Murray Irrigation District (GMID) in Northern Victoria as a case study. This system has been modernized and automated connections provide consistent real-time flow data [NVIRP, 2010a]. Previously, [Perera et al., 2015a] developed a deterministic model and assessed its performances under perfect weather forecasts i.e. using observed weather data. This paper uses that model as a basis and both brings real weather forecasts into the analysis and develops an ensemble framework to incorporate uncertainties arising from the weather forecast data as well as other inputs. In doing this we use data from the GMID and numerical weather predictions (NWP) from the Bureau of Meteorology (BOM) to develop ensemble irrigation demand forecasts. This is a relatively new and high level of data availability compared with many irrigation systems. The analysis includes input uncertainties associated with the flow measurement and weather measurements and forecasts. The remainder of the paper describes the area of study where the methodology has been applied and forecasting performance for command area driven stochastic irrigation demand forecasts and conclusions that has been drawn. This provides novel understanding about the irrigation demand prediction uncertainties like input uncertainties related to biophysical, behavioral and supply factors and in turn assists system operators to mitigate the risk associated with their routine irrigation distribution decisions. 7.3 Study area and data Study area The study area and data sources are described in detail in [Perera et al., 2015a]. The study area is located in the Central Goulburn Irrigation District (CGID), Victoria, Australia. Agriculture in the study area is dominated by irrigated dairy, pome and stone fruit production, with other agricultural activities related to sheep for wool, beef and dairy cattle [RDV, accessed 26 Sep 2014]. The main source of water supply for the CGID is from Lake Eildon, with delivery via the Goulburn 130

153 Chapter 7 Probabilistic daily irrigation demand forecasts River, Goulburn weir, and the Stuart Murray Canal. Water flows from Stuart Murray Canal to the CGID through six gravity irrigation distribution channels namely CG 1, 2, 3, 4, 5 and 6. Any excess water in the Stuart Murray Canal is diverted to Waranga Basin (Figure 3.2). The irrigation distribution system in the CGID is highly automated and a SCADA (supervisory control and data acquisition) system monitors levels and flows and controls the regulator gates and meter outlets across the district. Irrigation water takes about four days to travel from Lake Eildon to the farms in this area. The proposed ensemble forecasting methodology was applied to 287 km 2 of irrigated agricultural land supplied by CG 1, 2, 3 and 4. The characteristics for each channel are given in Table 3.1. The irrigation year starts on 15 August and continues to 15 May the following year. The study area is approximately 110 meters above the Australian height datum (AHD) and the climate is temperate with a hot summer (T hot 22 o C) but without a dry season (Köppen climate type Cfa) [Peel et al., 2007] Data sources and pre-processing Irrigation flow data The irrigation flow data related to the regulators and service points were collected from the operational SCADA (supervisory control and data acquisition) system known as Total Channel Control TM (TCC TM ) that is used by Goulburn-Murray Water (GMW). TCC TM is a fully automated open channel delivery system that captures flow measurements in real-time at all regulating structures and farm supply points. We used the flow data recorded at 1016 supply points for the period 15 August 2006 to 15 May 2012; which includes six irrigation years. The service point delivery data were aggregated to a daily time step. The SCADA system records the start and end times and flow rates of irrigation order deliveries. Service point flows were aggregated across all service points for each individual channel and the study area as a whole. This aggregation implicitly assumes that the travel time along the local channel or study area is significantly less than a day. The aggregated service point flows are denoted ID CGi, ASP. Here ASP denotes the Aggregated Service Points, and i provides spatial aggregation area (where i=1, 2, 3, 4 or 1234) Observed climate data The observed climate data were obtained from two Automatic Weather Stations (AWSs) and three daily-read rain gauge sites operated by the Australian Bureau of Meteorology (BoM) [BoM, 2005] located in and around the study area (Figure 3.2).The characteristics of each weather station are given in Table 6.1. Daily precipitation records were collected from all five sites as the area often witnesses localised patchy precipitation events. These five sites were established well before the 131

154 Chapter 7 Probabilistic daily irrigation demand forecasts channel automation and record start dates vary between 1883 and The hourly weather variables needed to estimate daily ET O were collected from the AWSs (air temperature, dewpoint temperature, wind speed) and satellite imagery (solar radiation) as described by [Perera et al., 2014; Perera et al., 2015b]. The measurement ranges and accuracies of these observed weather variables are given in Table 4.3. The AWSs and rain gauges nominally provide continuous measured weather data; however, there were times within the study period when hourly/daily weather data were missing due to various reasons. For missing daily precipitation, the aggregated value recorded at the end of missing period was uniformly disaggregated over the missing period, while other weather variables were infilled from the neighbouring AWS Weather forecasts The short-term weather forecasts relevant for the study area were collected from the Australian Bureau of Meteorology's operational NWP forecasts derived from the Australian Community Climate and Earth System Simulator (ACCESS) [BoM, 2010; BoM, 2012; Puri et al., 2013]. The ACCESS systems are non-hydrostatic, hybrid vertical level structure, mesoscale assimilation & forecast systems. They have been operational since 17 August, The temporal (lead time) and spatial resolution for different ACCESS systems vary from +1 to +240 hours and 5 to 80 km, respectively. The forecast performances for precipitation and mean sea level pressure of the ACCESS systems have been comprehensively evaluated [BoM, 2010; BoM, 2012; Puri et al., 2013] and also its outputs have been extensively used for short-term stream flow forecasting [Pagano et al., 2010; Shrestha et al., 2013; Shrestha et al., 2012]. We selected the ACCESS-G system, which has the largest lead time (+240 hrs.) and the largest grid cells (80 km) in order to derive irrigation demand forecasts for longer lead times, where the next higher resolution model has a lead time of only 72 hours. ACCESS-G is run twice a day providing forecasts starting at a.m. and p.m. local time (i.e and 1200 UTC). The outputs from these runs are available at 03:50 p.m. and 03:50 a.m. (the next day), respectively [BoM, 2010]. We used the 10:00 a.m. local time run and constructed nine mid-night to mid-night daily reference evapotranspiration (ET O) and 09:00 a.m. to 09:00 a.m. daily precipitation forecasts using the three hourly NWP forecast outputs of precipitation, air temperature, dew point temperature, wind speed and incoming solar radiation from 17 August 2010 to 01 August The four grid points surrounding the station were linearly interpolated to the AWS location and biases in the forecast ET O input variables were corrected following [Perera et al., 2014] and precipitation forecasts were post processed following [Robertson et al., 2013].The ET O forecasts have been evaluated in detail by [Perera et al., 2014], who found that the root mean squared error (RMSE) and coefficient of determination (R 2 ) values ranged over mm day 1 and for one and nine day lead times, respectively. Precipitation forecasts have R 2 values of 0.65 and 0.55 for one and three day lead times, respectively [BoM, 2010]. 132

155 Chapter 7 Probabilistic daily irrigation demand forecasts 7.4 Methodology In this paper, the multivariate time series model developed previously by [Perera et al., 2015a] is used to derive irrigation demand forecast ensembles for lead time up to five days. In principle, the ensemble forecasting approach can include all sources of uncertainties. We undertook some preliminary evaluations to decide which uncertainties to incorporate in this analysis (not presented). This involved perturbing model inputs and parameters individually and collectively and examining the output ensemble spread. It was found that including both model input and parameter uncertainty did not significantly change the ensembles compared with only including model input uncertainty. Including only parameter uncertainty led to very narrow output ensembles. Therefore, the ensemble forecast approach used here was simplified by omitting the parameter component. Figure 7.1 provides the schematic diagram of the ensemble forecast approach that has been adopted and shows the flow of input data through to ensemble irrigation demand forecasts along the time line. Steps 1-3 are about characterizing the statistical structure of each input time series, including measurement error characterisation; correction of NWP forecast bias and characterisation of NWP forecast uncertainty, followed by creation of the input ensembles for each model input. We used different perturbation methods in order to account for measurement, observation and forecast uncertainties given that the deterministic multivariate time series model is forced by observed demands and observed and forecasted weather. The selected perturbation methods are discussed in detail later in this section. We post-processed input ensembles using the Schaake Shuffle method [Clark et al., 2004] to achieve realistic cross-correlations and temporal persistence within each ensemble. Step four involves preparing past and future forcing variable (water supply deficit) and running the deterministic ARMAX models with the various input ensembles. A brief description of the deterministic model and its calibration is given in the next section (7.4.1) and further details can be found in [Perera et al., 2015a]. Step five summarizes the daily ensemble irrigation demand forecasts into a probabilistic irrigation demand forecasts. The various modelling steps above are described in more detail in the following methodology sections. The last part of the methodology describes the evaluation methods that have been used to quantify the forecast performance of ensemble irrigation demand forecast. 133

156 Chapter 7 Probabilistic daily irrigation demand forecasts Figure 7.1 The schematic diagram of the ensemble forecast approach 134

157 Chapter 7 Probabilistic daily irrigation demand forecasts Deterministic model and its calibration Deterministic model structure The model used here is a multivariate time series model, which has been previously developed to derived irrigation demand forecasts for the same study area [Perera et al., 2015a]. This time series model combines biophysical factors (weather) as the exogenous variable with behaviour factors captured through the auto-regressive process dependent on immediate past irrigation demands. The model is an autoregressive moving average model with an exogenous variable (ARMAX) (Eq. (7.1). ID(t) + a 1. ID(t 1) + + a na. ID(t n a ) = b 1. u(t n k ) + + b nb. u(t n k n b + 1) + c 1. e(t 1) + + c nc. e(t n c ) + e(t) (7.1) where, ID(t) is the daily irrigation demand at time t, u(t) is the daily exogenous variable at time t, n a is the number of past irrigation demand terms included, n b is the number of time points at which the exogenous term is specified plus 1, n c is the number of autoregressive error terms, n k is the number of input samples that occur before the input affects the output, also called the dead time in the system, ID(t)... ID(t n a ) are the previous outputs on which the current output depends, u(t n k )... u(t n k n b + 1) are the previous and delayed inputs on which the current output depends, e(t)... e(t n c ) are the white-noise disturbance values, which is modelled as an independent and identically distributed (iid) Gaussian process, with zero mean and variance σ 2 e. The exogenous variable (u) is a water supply deficit (WSD) index which reflects the effect of atmospheric forcing on irrigation demand as a combination of precipitation and ET O. The WSD is estimated using using a simple soil water bucket model with two parameters. WSD t = ET O t [1 ( S t S max ) γ ] (7.2) The storage at time t, S t, is calculated using a soil water balance, S t = min ( S t 1 + P t 1:t ET 0 t 1:t ( S t S max ) γ, S max ) (7.3) where, ET O (mm day -1 ) is the daily reference crop evapotranspiration, S t (mm) is the soil moisture storage, S max is the maximum soil moisture storage (mm), P (mm) is the precipitation. The bucket capacity (S max) and the nonlinearity (γ) of actual evapotranspiration are determined in the model fitting. WSD is essentially a command area average index aiming to represent the pattern of supplemental water that would need to be supplied through irrigation. 135

158 Chapter 7 Probabilistic daily irrigation demand forecasts Deterministic model calibration A detailed description of the model fitting and selection through cross-validation is provided in [Perera et al., 2015a]. This included developing data transformation to remove seasonality and scaling differences in the raw data set. Then, the model parameters were estimated in two steps: the first of which determined the order of each transfer function and S max and γ; and the second of which determined the lag coefficients. Model selection was guided using the Bayesian information criterion (BIC). BIC = N. log MSE + d. log N (7.4) where, MSE is the mean squared prediction error, d is the number of parameters and N is the number of observations. This is essentially a mean squared error minimisation penalised by parameter number as a measure of model complexity. The deterministic model calibration process used a leave-one-yearout cross-validation (LOOCV) technique to select the best time series models based on the BIC calibration. In the original paper [Perera et al., 2015a] six years of data were used (calibration on five years, validation on one year); however, the NWP weather forecasts from ACCESS-G are only available the and irrigation seasons due to changes in the Bureau s NWP systems. Therefore this study focusses on just two of the original models; the ones that were validated on the and irrigation seasons. Cross-validations showed that the overall patterns between command areas and years were similar. The average performances for RMSE and NSE during calibration, among six cross-validation scenarios across five command areas ranged from 2.33 ML day -1 (CG 1) to 28.5 ML day -1 (CG 1234) and from 0.55 (CG 1) to 0.93 (CG 1234) respectively, for one day lead time [Perera et al., 2015a] Ensemble generation Real-time flow data The measurement uncertainty for the irrigation flows was estimated from the manufacture s specifications and in-field audits. The measurement uncertainty for automated off take regulators and meter outlets is ± 2.5% (95% confidence) under laboratory test conditions [Rubicon, 2014]. However, under operational conditions, the Total Channel Control TM (TCC TM ) SCADA system was assessed as being able to maintain a constant rate of flow as channel level varied. Specifically, the field assessment concluded that the modernised backbone will deliver a uniform flow within ± 5% more than 90% of the time [NVIRP, 2010b]. We have interpreted these two sources of information as representing likely bounds on the in-field performance of the system and we consider 136

159 Chapter 7 Probabilistic daily irrigation demand forecasts error scenarios between these bounds. The above statements imply measurement error standard deviations (as a proportion of measured flow) of (±5.0% with 90% confidence) and (±2.5% with 95% confidence) respectively, assuming a normal distribution. A preliminary evaluation (not presented) was carried out to select the measurement uncertainty standard deviation for generating ensembles of observed flow. This evaluation considered standard deviations of , 0.025, 0.02, and The results shows the standard deviation for measurement error for and meter outlets of 0.02 (i.e. 2% of measured flow) generated reasonably reliable one day lead time forecast ensembles under calibration conditions. This measurement uncertainty is assumed to be a constant proportional error across the full range of flows. In addition, the measurement errors under laboratory conditions and supply error in the field need to be generalised across all the automated off take regulators and meter outlets as regulators record times of flow rate change and meter outlets record the start and end timings and flow rates of irrigation order deliveries. The off take regulator and aggregated service point flow ensembles were created similarly, perturbing daily irrigation flow time series with an additive percentage error. The additive error is assumed to be a white noise. The variance is adjusted for the daily aggregated service point (ID CGi, ASP) data; given that it is the sum of many individual service points with individual errors that were assumed to be independent of each other. Therefore, the irrigation flow ensembles for daily aggregated service point (ID CGi, ASP) are derived using Eqs. (7.5)-(7.6). ens ID CGi,ASP ID = ID CGi,ASP ± ξ CGi,ASP (7.5) ID ξ CGi,ASP 2 2 ~N (0, σ CGi,ASP ) and σ CGi,ASP = 0.02 ID CGi,ASP (7.6) ens Where, ID CGi,ASP is the irrigation demand ensemble for aggregated service, ID CGi,ASP is the daily ID aggregated service point, and ξ CGi,ASP is the Gaussian additive noise representing measurement 2 error with zero mean and a variance of σ CGi,ASP. The variance derives from assuming that the 99% measurement confidence interval is ±5.0 percentage of the measured flow Observed weather variables The errors in the atmospheric forcing variables for the WSD are a key component contributing to uncertainties in the irrigation demand estimation and forecasting. Estimation uncertainty for the exogenous variable WSD results from the precipitation measurement errors and the estimation errors of ET O. Given the various non-linearities in converting weather variables to ET O and WSD, a Monte Carlo method is applied to create ensembles for the WSD, where precipitation and ET O are perturbed with known error parameters. 137

160 Chapter 7 Probabilistic daily irrigation demand forecasts Precipitation, ET O and irrigation flow ensembles were post-processed using the Schaake Shuffle method [Clark et al., 2004] and historical records. During the calibration, we used a moving window of 100 days (equivalent to the number for ensembles); either centred, forward shifted or back shifted, depending on the day of the year. These three types of moving window were necessary to given that the irrigation distribution operation is inactive for three months (15 May to 15 August) of each year, meaning there is no irrigation flow data for that period. Similar moving windows were used to post-process the irrigation flow ensembles for the evaluation period, but the immediate past year s data were used because observations are unknown ahead of time in an operational forecasting context Precipitation Lognormal multiplicative error models have been widely used to generate ensembles for precipitation and to simulate rainfall error in hydrologic data assimilation [Alvarez-Garreton et al., 2014; Li et al., 2014a]. Therefore, we used a lognormal multiplicative error to create the ensembles representing measured rainfall: P ens = ξ P P obs (7.7) ξ P ~LN(μ P, σ P ) (7.8) where, P ens is the daily precipitation ensemble member, P obs is observed daily precipitation, ξ P is the multiplicative error, which follows a lognormal distribution with the mean of μ P and standard deviation of σ P. To create an unbiased rainfall ensemble, μ P is set to 1 σ P set to be 0.25 (25% error). This error represents both gauge errors and spatial variability. The assumption of the variance of the rainfall multiplier being 25% is agreed with various studies that have been investigated rain gauge representativeness errors [Barancourt et al., 1992; Ciach and Krajewski, 1999; Villarini et al., 2008] and also consistent with other recent studies [Alvarez-Garreton et al., 2014; DeChant and Moradkhani, 2012; Li et al., 2014a]. The representativeness error of rain gauges for areas of order 200 km 2 is quite variable but of this order. Perera et al., [2015a] found the performance of the ARMAX model was insensitive to choice of individual or combinations of rain gauges in the area, indicating that the modelling is likely to have relative low sensitivity to this choice. In accordance with the definition of the lognormal probability distribution model, the natural logarithm of ξ P, denoted as ξ LN P, follows a normal distribution with mean and variance given by: μ = ln(μ P ) 1 2 ln (1 + σ P μ P ) (7.9) 138

161 Chapter 7 Probabilistic daily irrigation demand forecasts σ = ln (1 + σ P μ P ) (7.10) Reference evapotranspiration (ETO) ET O was calculated based on the guidelines provided by the United Nations Food and Agricultural Organization Irrigation and Drainage Paper No. 56 (FAO 56) [Allen et al., 1998]. The daily ET O ensembles were created by perturbing observed weather variables (daily mean air temperature; daily mean dew-point temperature, daily mean wind speed and incoming shortwave solar radiation) using zero mean additive noise. The equations used to calculate the inputs to ET O are given in Table 7.1, along with the corresponding measurement accuracy [BoM, 2005] and the standard deviations used in the perturbations. Measurement accuracies were assumed to represent a three standard deviation spread [BoM, 2005] and measurement errors were assumed to be independent when calculating the perturbation standard deviations. The perturbation standard deviations account for the number of measurements contributing to each ET O input. Table 7.1 Perturbation methods for ET O related weather variables (daily mean temperatures ensembles T mean, ens, daily mean dew point temperatures ensembles Dewpt mean, ens, daily mean wind speed ensembles Wndspd mean, ens and daily solar radiation ensembles Srad ens) Input estimator T mean ens = T max+t min +ξ Temp 2 Measurement accuracy (±3σ) 0.3 ºC Perturbation standard deviation DewPt mean ens = 1 24 Dewpt 24 hr=1 hr + ξ Dewpt 0.3 ºC Wndspd mean ens = ξ Wndspd 24 hr=1 Wndspd hr 1.03 ms Srad ens = Srad + ξ Srad 1.5 MJ m Forecast weather variables To forecast irrigation demand, forecast weather is required, which has errors resulting from the NWP weather forecasts. NWP models like ACCESS usually contain both systematic biases due to the NWP model structure, site elevation, temporal and spatial resolution and interpolation techniques, together with noise [Perera et al., 2014; Shrestha et al., 2013]. In constructing irrigation demand ensembles, the NWP weather forecasts should be corrected for bias and the noise should 139

162 Chapter 7 Probabilistic daily irrigation demand forecasts also be represented. The error characteristics of the forecast precipitation are quite different to the forecast errors for ET O and hence they are treated differently here. Forecast precipitation ensembles were developed using the approach of Wang et al., [2009], which was developed for ACCESS NWP forecasts. This approach uses a simplified version of the Bayesian joint probability technique to derive forecast probability distributions for individual sites as well as for each lead time [Wang et al., 2009]. A joint probability distribution of observations and forecasts is fitted based on past forecast data. Ensemble forecasts are then generated from conditional probability distributions based on the joint probability distribution conditioned on the NWP forecast for that particular day. Space-time correlations are imposed by linking the samples from the forecast probability distributions using the Schaake shuffle [Clark et al., 2004]. Further detail of the post processing can be found in [Robertson et al., 2013]. While the [Wang et al., 2009] method could potentially also be applied to ET O forecasts, differences in the distribution characteristics meant this was unsuccessful. An alternative approach based on the analysis of [Perera et al., 2014] where ACCESS-G NWP weather forecasts were used to generate deterministic daily ET O forecasts for lead times of 1-9 days. In essence the weather variables input to ET O were first bias corrected using a regression between forecast and observed data following [Perera et al., 2014] and then used to make a deterministic ET O forecast. The errors in that deterministic forecast were then examined against observed ET O for the relevant climate station. This showed that the ET O forecast error is multiplicative. Finally, bias-free ensemble daily ET O forecasts were generated using the deterministic daily ET O forecasts and forecast error realizations based on the observed multiplicative error and then daily ET O ensemble forecasts were post-processed using the Schaake Shuffle method as above Evaluation methods The reliability of the ensemble in terms of bias and spread is the most important attribute of ensemble forecasts as it describes the capability of the ensemble spread to represent the real probabilistic uncertainty of the forecast. In this paper, the reliability of ensemble irrigation demand forecasts is quantified using the temporal mean of the ensemble root mean squared error (MRMSE), the mean continuous ranked probability score (CRPS) and one of its decomposition the mean CRPS reliability [Hersbach, 2000], which are defined in Eqs. (7.11)-(7.13) respectively. The MRMSE is derived by calculating the RMSE at each time step using all ensemble members and then averaging the RMSEs for the entire period of interest [Li et al., 2013; Li et al., 2015]. The mean CRPS and mean CRPS reliability are calculated following step provided by Brown et al., The negative orientation of these skill scores leads to 0 for a perfect spread and higher skill scores indicates that forecasts become more biased or the spread less reliable (or both). 140

163 Chapter 7 Probabilistic daily irrigation demand forecasts The rank histogram approach [Hamill, 2001] is also used to evaluate the reliability of ensemble irrigation demand forecasts. Rank histograms are generated by repeatedly finding the rank of the observation relative to values from the forecast ensemble sorted from lowest to highest. The resulting ranks are then plotted into a histogram. If the ensemble is reliable, the observations should be evenly spread across the various ensemble member ranks. Therefore, a flat rank histogram indicates a reliable ensemble spread; a U-shaped (n-shaped) histogram indicates the ensemble spread is too narrow (wide); and an asymmetric histogram is a sign of bias. Other attributes such as accuracy, sharpness and skill are also important to determine the overall quality of forecasts. Therefore, we further quantify the predictive performance of the mean ensemble daily irrigation demand forecasts through three additional statistical indices, (1) the root mean squared error (RMSE) of the ensemble mean, (2) the Nash-Sutcliffe efficiency coefficient (NS) of the ensemble mean and (3) the mean error (BIAS), which are described in Eqs. (7.14)-(7.16) respectively. We also looked at the ratio between MRMSE and RMSE. This ratio becomes one for a perfect spread, but values less than or more than one indicate ensemble forecasts spreads are under or overestimated, respectively. All forecast verification scores are normalized using the size of the respective command area to make the predictive performance indicators are independent from the size of the commend area (NSE is unaffected by this normalization). The uncertainties of all of the forecast verification scores are evaluated using the bootstrapping technique [Efron and Tibshirani, 1986] and the 5 th and 95 th confidence intervals are provided along with score. The temporal mean of the ensemble root mean squared error, MRMSE is: MRMSE = 1 T T 1 N (ID i N fcst,t ID obsv,t ) 2 t=1 i=1 CA j (7.11) The mean continuous ranked probability score (CRPS) T t=1 Mean CRPS = 1 T (F fcst,t(id) F obsv,t (ID)) 2 d ID CA j (7.12) F obsv,t (ID) = { 0 (ID < ID obsv,t) 1 (ID ID obsv,t ) (7.13) The root mean squared error, RMSE is: RMSE = 1 T IDobsv,t ) 2 CA j (7.14) T (ID i i=1 fcst,t 141

164 Chapter 7 Probabilistic daily irrigation demand forecasts Nash Sutcliffe (NS) model efficiency coefficient (NSE) is: NSE = 1 T (ID i IDobsv,t fcst,t ) 2 i=1 T (ID obsv,t ID ) 2 i=1 obssv (7.15) The the mean error (BIAS) is: BIAS = 1 T IDobsv,t ) CA j (7.16) T (ID i i=1 fcst,t i In Eqs. (7.11)-(7.16), ID fcst,t is the i th ensemble prediction at time, t, and ID obsv,t is the observed i values at t, N is the number of ensembles, T is the total number of time steps ID fcst,t is the predicted ensemble mean at t, ID obsv,t is the mean of ID obsv,t for the period of verification (POV) and CA j is the size of j th command area. 7.5 Results Precipitation and ETO forecast uncertainties The exogenous variable, WSD, acts as a weather forcing variable for irrigation demand and it is calculated using precipitation and reference evapotranspiration (ET O). The forecast and observed uncertainties in these two weather variables contribute to irrigation demand forecast uncertainties. The observation uncertainties for the weather variables are instrument and measurement network dependent, while the forecast uncertainties depend on the forecast skill of the NWP system. The observation uncertainties for weather variables were obtained from the Australian Bureau of Meteorology [BoM, 2005]. For the weather forecasts, ensemble forecasts were first constructed as outlined in section Detailed evaluations of these ensemble forecasts for the study region were then undertaken through comparisons with local observations. This section briefly evaluates the forecast performance of the precipitation and ET O ensemble forecasts derived from ACCESS-G. Table 7.2 summarizes the statistical indicators related to the forecast performance for precipitation and ET O ensemble forecasts and Figure 7.2 and Figure 7.3 summaries the results for precipitation and evapotranspiration, respectively. These stats are for the periods of to and to (551 days). The forecast performance for ensemble daily ET O and precipitation forecasts declines with increasing lead time, as expected. For precipitation forecasts, the MRMSE, mean CRPS and RMSE increase approximately 42%, 32% and 27% respectively and mean CRPS reliability remain same, as the lead time increases from one to five days. For ET O forecasts the MRMSE, mean CRPS, mean CRPS reliability and RMSE increase more than twice for lead time five days and indicated spread of ET O ensemble forecasts is poor reliable for longer lead times. The NS efficiency coefficient for mean precipitation and ET O ranged between 142

165 Chapter 7 Probabilistic daily irrigation demand forecasts 0.57 and 0.20 and between 0.77 and 0.53, respectively, for lead times of one to five days. The rank histogram and bias shows that the ensemble precipitation forecast was slightly negatively biased and that the ensemble ET O forecast was slightly positively biased and the uncertainty was underestimated for ET O. The results also suggest that the forecast performance for ET O was higher than for precipitation. Table 7.2 Statistical indicators related to prediction performance for ensemble precipitation and ET O forecasts for study area between to and to (551 days). The range shown in brackets is the 5 th -95 th confidence interval from the bootstrapping analysis. Lead time Ensemble verification score Variable Precipitation ET O 1 Day 3 Day 5 Day MRMSE mm day ( ) 1.00 ( ) Mean CRPS mm day ( ) 0.37 ( ) Mean CRPS Rel. mm day ( ) 0.02 ( ) RMSE (mean) mm day ( ) 0.72 ( ) NSE (mean) 0.51 ( ) 0.90 ( ) BIAS (mean) mm day ( ) ( ) MRMSE mm day ( ) 1.37 ( ) Mean CRPS mm day ( ) 0.48 ( ) Mean CRPS Rel. mm day ( ) 0.03 ( ) RMSE (mean) mm day ( ) 0.9 ( ) NSE (mean) 0.23 ( ) 0.84 ( ) BIAS (mean) mm day ( ) ( ) MRMSE mm day ( ) 1.67 ( ) Mean CRPS mm day ( ) 0.58 ( ) Mean CRPS Rel. mm day ( ) 0.05 ( ) RMSE (mean) mm day (4.42-7) 1.07 ( ) NSE (mean) 0.2 ( ) 0.77 ( ) BIAS (mean) mm day ( ) ( ) 143

166 Chapter 7 Probabilistic daily irrigation demand forecasts Figure 7.2 Time series plot (91 days) of observed daily precipitation vs. post process ensemble precipitation forecast and respective rank histograms (551 days) for lead times of one, three and five days. 144

167 Chapter 7 Probabilistic daily irrigation demand forecasts Figure 7.3 The scatter plot (551 days) between the deterministic daily ET O forecast and forecast error, time series plot (241 days) of observed daily ET O vs. ensemble daily ET O forecast with spread between 10 th and 90 th percentile and respective rank histograms (551 days) for lead times of one, three and five days Ensemble demand forecasts for the model calibration period The model parameters reported in [Perera et al., 2015a] are used here. The following results are based on forecasts for the and irrigation seasons. The deterministic model was calibrated to the , , and seasons plus one of or Independent validation results were obtained for each of the and irrigation seasons. Tabulated values below were obtained by calculating the calibration (or validation) metrics for each of the two seasons and then averaging these. We note that the calibration period results correspond to only one of the five years contributing to the original model fitting. 145

168 Chapter 7 Probabilistic daily irrigation demand forecasts Table 7.3 provides the average statistical indicators between two calibration scenario for ensemble daily ID CG i, ASP forecasts across all five command areas and the performance for each individual calibration scenario is in Table 7.5 (Supplementary material. These calibration periods have four years in common, with the fifth year being different between the two sets of results and the results in Table 7.3 only represent the average of those fifth year. Only the results relating to the best LOOCV calibration scenario and the full study area (i.e. LOOCV-S one for CG 1234 are shown graphically as time series (Figure 7.4) and rank histograms (Figure 7.5). The statistical indicators for the two scenarios corresponding to each command area vary significantly due to the differences in irrigation flows between years. We start by considering the ensemble mean forecast. The NSE between forecast and observed irrigation demand ranged between 0.91 (one day lead time, CG 1234) and 0.31 (five day lead time, CG 1). The highest and lowest NSE values were always found at CG 1234 and CG 1, respectively due to differences in the area irrigated and number of supply points. For five day lead times compared with one day lead times, NSE decreased by more than 40 % for small command areas (CG 1, CG 2 and CG 3) and approximately 25% for larger command areas (CG 4 and CG 1234). The bias was highest at CG 1234 and lowest at CG 1 and it is proportional to the size of the area irrigated. The bias showed that the ensemble daily demand forecasts slightly over predicted the observed flows for all command areas and mostly remains approximately same with increased in lead time. The ensemble spread can be evaluated through the MRMSE, mean CRPS, mean CRPS reliability, RMSE and the rank histograms. The difference between MRMSE and RMSE increased with the increasing command area or decreasing lead times. The mean CRPS, mean CRPS reliability and difference between these two scores increased with the increasing command area or lead times. These facts suggest that reliability of ensemble spread declines with increasing command area or lead times. The MRMSE was higher than the corresponding RMSE for all command areas and for all lead times. Across the five command areas, MRMSE, mean CRPS, mean CRPS reliability and RMSE increase on average by approximately 23 %, 53%, 8% and 73% respectively from 1 day to 5 days lead time. For most cases, these statistics and the rank histograms (Figure 7.5) show that the ensemble spread marginally overestimated the forecast error variability for the first day and then tend to be flat with increased in lead time, indicating a reliable ensemble spread. During the calibration periods, the observed daily ID CG 1234, ASP values were within the ensemble daily ID CG i, ASP forecast spread (10 th -90 th percentile) for 86%, 83% and 82% of the time with respect to lead time one, three and five days. 146

169 Chapter 7 Probabilistic daily irrigation demand forecasts Table 7.3 Average forecast performance for ensemble daily ID CG i, ASP forecasts related to the 2 cross validation scenarios for 4 channels and study area during the last year of calibration periods ( (274 days) or (275 days)). The range shown in brackets is the 5 th -95 th from the bootstrapping Lead time 1 Day Ensemble verification score Average performances for command area CG1 CG2 CG3 CG4 CG1234 MRMSE (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) Mean CRPS (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) Mean CRPS Rel (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) RMSE (mean) (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) NSE (mean) ( ) ( ) ( ) ( ) ( ) BIAS (mean) (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) 3 Day 5 Day MRMSE (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) Mean CRPS (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) Mean CRPS Rel (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) (0-0.01) RMSE (mean) (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) NSE (mean) ( ) ( ) ( ) ( ) ( ) BIAS (mean) (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) MRMSE (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) Mean CRPS (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) Mean CRPS Rel (ML day -1 Km -1 ) ( ) ( ) ( ) (0-0.01) (0-0.01) RMSE (mean) (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) NSE (mean) ( ) ( ) ( ) ( ) ( ) BIAS (mean) (ML day -1 Km -1 ) ( ) ( ) (0-0.05) ( ) ( ) 147

170 Chapter 7 Probabilistic daily irrigation demand forecasts Figure 7.4 Time series plot of observed vs. ensemble daily ID CG 1234, ASP forecasts with the ensemble spread between 10 th and 90 th percentile for lead times of one, three and five days for irrigation year (274 days - validation scenario one in the Table 7.5) Figure 7.5 Rank histograms for observed and ensemble daily ID CG 1234, ASP forecasts for lead times of one, three and five days for irrigation years to (274 days - validation scenario one in the Table 7.5) 148

171 Chapter 7 Probabilistic daily irrigation demand forecasts Real-time forecasting with numerical weather prediction outputs We now examine the results for validation conditions using a similar approach to the previous section. With the exception of the fitting of uncertainty parameters for the NWP ensembles, these demand forecasts are made under operational conditions; that is using observation data available from automatic weather stations, the SCADA network of supply points and NWP forecast data, all of which would be available at the time of making an operational forecast, and with the ARMAX model fitted to independent data. The aim is to test the forecast performance of both the ensemble mean and to assess how well the ensemble represents the forecast uncertainty. Table 7.4 provides the average statistical indicators between two evaluation scenario for ensemble daily ID CG i, ASP forecasts across all five command areas and the performance for each individual evaluation scenario is in Table 7.6 (Supplementary material). Figure 7.6 shows the time series plots of observed and ensemble daily demand forecast for evaluation year 2011/12, while Figure 7.7 shows the rank histograms and associated probabilities. The NSE values ranged between 0.97 (one day lead time, CG 4) and 0.22 (five days lead time, CG 1) and for the whole study area it ranged between 0.97 and 0.79 for one and five day lead times, respectively. The bias varied with the evaluation year, being positive for 2010/11 and negative for 2011/12. This is partly reflects the variability of irrigation flow within each year, where the highest variability occurred during year 2011/12. The ensemble spread is again examined by using MRMSE, mean CRPS, mean CRPS reliability, RMSE and rank histograms. In general all MRMSE, mean CRPS, mean CRPS reliability and RMSE decrease with increasing irrigated area reflecting the higher forecast performances for larger command areas and the spread of forecast uncertainties is not reliable for smaller command areas. The pattern between the MRMSE, mean CRPS, mean CRPS reliability and RMSE was similar to calibration period, where MRMSE is higher for all command areas and all lead times. The difference between MRMSE and RMSE increased and the difference between mean CRPS and mean CRPS reliability decreased with the increasing command area and decreasing lead times. Typically MRMSE is larger than RMSE values indicating that the ensemble spread is somewhat overestimating the forecast uncertainty at system scale, when irrigation flow among distribution channels aggregated. The average ratio MRMSE/RMSE across two validation years varies between 1.10 and 4.20 for all command areas for one day lead time. Ideally this ratio should be one and significant deviations from one indicate that the ensemble spread is unreliable. For the small command areas (CG 1 and CG 2) MRMSE/RMSE varies between 1.16 and 1.44, indicating the ensemble spread is slightly overestimated for the smaller command areas and consistently overestimated for the larger command areas. The rank histograms for the whole study area show 149

172 Chapter 7 Probabilistic daily irrigation demand forecasts that the ensemble is marginally too wide and slightly negative biased for one day lead time. This negative bias increases with lead time and forecast ensemble spreads are slightly under-dispersive for lead times of three and five days. This is consistent with the indications from mean CRPS, mean CRPS reliability and MRMSE vs RMSE; however, those statistics are likely to be more sensitive to outliers than the rank histograms. During the evaluation periods, the observed daily ID CG 1234, ASP values were within the ensemble daily ID CG i, ASP forecasts spread (10 th -90 th percentile) for 86%, 80% and 72% times for lead times of one, three and five days respectively. Overall, these results suggest that the ensemble forecasts give good estimates of forecast uncertainty and reliable probabilistic irrigation demand forecasts, particularly for the large command areas, but that the ensemble spread does not grow quickly enough with time. 150

173 Chapter 7 Probabilistic daily irrigation demand forecasts Table 7.4 Average forecast performance for ensemble daily ID CG i, ASP forecasts related to the 2 cross validation scenarios for 4 channels and study area during the evaluation periods ( (274 days) or (275 days)). The range shown in brackets is the 5 th -95 th from the bootstrapping Lead time 1 Day Ensemble verification score Average performances for command area CG1 CG2 CG3 CG4 CG1234 MRMSE (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) Mean CRPS (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) Mean CRPS Rel (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) RMSE (mean) (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) NSE (mean) ( ) ( ) ( ) ( ) ( ) BIAS (mean) (ML day -1 Km -1 ) ( ) (0-0.03) ( ) ( ) (0-0.02) 3 Day 5 Day MRMSE (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) Mean CRPS (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) Mean CRPS Rel (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) RMSE (mean) (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) NSE (mean) ( ) ( ) ( ) ( ) ( ) BIAS (mean) (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) MRMSE (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) Mean CRPS (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) Mean CRPS Rel (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) RMSE (mean) (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) NSE (mean) ( ) ( ) ( ) ( ) ( ) BIAS (mean) (ML day -1 Km -1 ) ( ) ( ) ( ) ( ) ( ) 151

174 Chapter 7 Probabilistic daily irrigation demand forecasts Figure 7.6 Time series plot of observed vs. ensemble daily ID CG 1234, ASP forecasts with the ensemble spread between 10 th and 90 th percentile for lead times of one, three and five days for irrigation year to (275 days) Figure 7.7 Rank histograms for observed and ensemble daily ID CG 1234, ASP forecasts for lead times of one, three and five days during irrigation year to (275 days). 152

175 Chapter 7 Probabilistic daily irrigation demand forecasts 7.6 Discussion The ensemble forecasting techniques used here build on those used in forecasting short runoff or stream flow [Addor et al., 2011; Bennett et al., 2014; Robertson et al., 2013; Shrestha et al., 2013; Smiatek et al., 2012]. Those studies have either used stochastic precipitation forecasts that have been post-processed or output from NWP models. While, the inputs and the techniques are similar for forecasting stream flows and irrigation demands, the dynamic responses of the systems are the opposite; with irrigation demand decreasing when precipitation increases and evapotranspiration decreases and streamflow doing the opposite. In catchments there is also likely to be more variation in antecedent conditions prior to rainfall events (antecedent moisture tends to be controlled by the application of irrigation in irrigated fields). This means that the forecast performance is not directly comparable between streamflow and irrigation demand. The forecast performance for the ensemble irrigation demand predictions were evaluated for lead times of one to five days across the four command areas plus the full study area. Both the average forecasts (ensemble means) and the uncertainty estimates (ensemble spread) performed well overall. NSEs for forecast conditions were up to 0.97 for one day lead time and larger command areas and remained above 0.69 for five day lead times, with the exception of the two smallest command areas. There were clear dependencies on lead time and command area. The area dependence relates to the amount of averaging between individual irrigation farms while the dependence on lead time relates to accumulation of forecast errors over time. From the system operators perspective, these probabilistic short-term system scale irrigation demand forecasts could assist with planning operations, particularly those operations such as transferring water from the main storage at Lake Eildon to the irrigation command areas. The ensemble approach provides a reliable estimate of forecast uncertainty that could be used to inform operational risks. The modelling also provides a quantitative link to enable operational weather forecasts to be more easily utilized in system operation decisions. From the forecasting context, this is the first study to generate probabilistic daily irrigation demand forecasts with lead times up to five days at the system scale. The results showed that the forecasting performance for ensemble daily irrigation demand forecasts were higher than most previous studies [Alfonso et al., 2011; Pulido-Calvo and Gutierrez-Estrada, 2009; Tian and Martinez, 2014; Ticlavilca et al., 2011] and the performance of the forecasted ensemble mean is marginally lower than the deterministic forecasts derived by [Perera et al., 2015a] using the same time series model. The rank histograms highlighted that the spreads were slightly over dispersive for lead time one and then change to slightly under dispersive as lead time increases. This implies the influence of other sources of uncertainty that are not being fully captured by input errors. There 153

176 Chapter 7 Probabilistic daily irrigation demand forecasts are a number of influences not explicitly included in the model. These include responses to regular (~ monthly) adjustments in yearly water allocation, changes in the price of water in the market, variations in sowing date for crops, on-farm storages and stock and domestic (non-irrigation) water leading to additional errors. These are in general model structural uncertainties, which we have not dealt with this paper. There are some subtle differences in the evolution of ensemble spread in different situations. In general, where there is a low antecedent flow, the one day lead time spread is small and it increases with antecedent flow. The low initial spread is due primarily to the multiplicative error applied to the observed flows, which has the largest influence on the lead one ARMAX outputs. The evolution of the ensemble spread over time is influenced by both the initial ensemble spread and the contributions to spread from the error component of the ARMAX model and the weather forecasts. The error structure for the observe reference evapotranspiration is complicated by its propagation from measurements through the Penman-Monteith equation. The inputs to the observed ET O calculation are assumed to have additive errors. The rainfall observation error model is multiplicative. These choices of measurement error structure reflect the nature of measurement errors for the different types of instruments involved. The ensemble evolution is influenced by the error structure in the ARMAX model itself and the weather forecasts. The ARMAX model has an additive error structure, which is justified by the forecast errors from the deterministic ARMAX model (Perera et al., [2015], Figs 8 and 9). The forecast ET O also has an additive error structure, justified by error analysis in (Perera et al., [2014], Fig 7). The rainfall forecast errors are determined by the structure of the Bayesian Joint Probability model [Robertson et al., 2013; Wang et al., 2009]. Of these, the additive errors in the ARMAX model have the greatest effect on the ensemble evolution under different conditions and they lead to rapid ensemble widening when the initial spread is small but slow widening when the initial spread is larger. As discussed in the previous paragraph, there are a variety of sources of uncertainty incorporated into the ensembles, including uncertainty in antecedent conditions (observed flow/demand, observed weather) and forecast weather uncertainty. To further understand the importance of the antecedent conditions in contributing to the ensemble variability, we undertook two additional sets of simulations. The first excluded uncertainty in the antecedent flow and the second excluded uncertainty in the antecedent weather. Figure 7.8 shows the resulting rank histograms. The top row of histograms indicates that the ensembles become biased when flow uncertainty is excluded. Comparing the middle and lower rows in Figure 7.8 shows that including the impact of antecedent weather uncertainty also leads to subtle improvements in the ensemble (less under-dispersion, slightly less bias), but the improvements are smaller than the effect of antecedent flow. These results suggest that including the antecedent conditions as a source of uncertainty is 154

177 Chapter 7 Probabilistic daily irrigation demand forecasts important and that flow is more important than past weather. The difference in influence of past flow and past weather is as expected given that the ARMAX model weights past flows more heavily than past weather. Figure 7.8 Rank histograms (A) Excluding irrigation flow uncertainties (B) Excluding observed weather uncertainties and (C) Including irrigation flow and observed and forecast weather uncertainties, for observed and ensemble daily ID CG 1234, ASP forecasts for lead times of 1, 3 and 5 days during the evaluation period to (275 days) In this paper, the input error terms are assumed to be independently and identically distributed. These assumptions are not valid in practice because the time series plots show a serial correlation of the irrigation demand forecast error. This might be due to structural errors in the model but could also be partly due to serial correlation of the ET O forecast error as the serial correlation of the precipitation error was corrected using the post-processing approach following [Robertson et al., 2013]. This serial correlation of irrigation demand forecast error is highly subjective for nonstationary time series like previous irrigation flows and accordingly, the systematic bias increased with the increase in lead time. However, in the face of higher auto-correlation between consecutive observed irrigation flows, the serial correlation of ET O forecast error is not significant. Nevertheless, ensemble forecasting scheme has provided sufficiently accurate probabilistic irrigation demand forecasts that can be useful to the system operators for their routine irrigation distribution decisions. 155