Assessment of Temperature based equations for ETo estimation by FAO Penman-Monteith Method for Betwa Basin, Central India

Assessment of Temperature based equations for ETo estimation by FAO Penman-Monteith Method for Betwa Basin, Central India Reetesh Kumar Pyasi, and Ashish Pandey Abstract Feasibility of temperature based methods namely Blaney-Criddle and Hargreaves equations has been examined using Penman-Monteith as reference method for the estimation of ETo for the Betwa Basin located in Central India. Further, Effect of various climatological parameters (mean temp., min temp., max temp., relative humidity, wind speed) on ETo has been studied. Regression analysis between weather variables with ETo was carried out. Trend and magnitude of ETo estimated by all three methods were evaluated using Mann-Kendall test and Theil-Sen s slope estimator and spatial distribution of ETo by all the three methods were studied. Results revealed that Hargreaves equation underestimated ETo, and Blaney- Criddle method performed better than Hargreaves. Keywords Mann Kendall test, Rainfall, Reference evapotranspiration, Regression, Weather parameters. W I. INTRODUCTION ATER is a finite natural resource and its per capita, availability in India is decreasing day by day. Irrigation alone uses more than 80% of water available in India. Therefore, its efficient utilization is important. The knowledge of the exact amount of water required by different crops in a given set of climatological condition of a region is vital in planning and effective management of irrigation scheme, irrigation scheduling (Chakraborty et al. 201). Evapotranspiration (ETo) is the simultaneous process of transfer of water to atmosphere by transpiration and evaporation from a cropped area. It is necessary to estimate ETo for allocating amount of irrigation water for particular area. The FAO Penman-Monteith (P-M) method is recommended as the sole standard method (Allen et al. 1998). It has two important advantages. First, it can be used in a greater variety of environment and climate scenarios without any local calibrations. Second, it is a well-documented method that has been validated using lysimeters under a wide range of climate conditions. This method required large number of meteorological parameters for its application, i.e. air temperatures, relative humidity, wind speed and solar radiation (Darshana et al. 201). This limits its application in many regions of developing country like India. Other methods of estimating ETo are classified as temperature- based, radiation based, pan evaporation based and mass transfer based equation. Reetesh Kumar Pyasi, Graduate Student, Department of Water Resources Development and Management IIT Roorkee-27 7 (India) Ashish Pandey, Associate Professor, Department of Water Resources Development and Management IIT Roorkee-27 7 (India).Email:- ashisfwt@gmail.com Numerous studies have been conducted in the past for comparison and evaluation of various ETo estimation (Trajkovic and Kolakovic 2009). Paudel and Pandey (201) suggested that Pan Evaporation with Orang coefficient yielded closer value than that of FAO- pan coefficient. Tabari et al. (2011) compared 1 reference evapotranspiration methods against PMF- model under humid climate conditions of Iran and found that among temperature based equation Blaney-Criddle (B-C) method yield better estimates than others. Several researchers analyzed trend with various methods. Yu et al. (2002) observed increasing trend in ETo at south Taiwan, using 8 years of data (190 1997). Cohen et al. (2002) found 7% increase of ET pan in the central coastal plains of Israel in years (19-1998). Bandyopadhyay et al. (2009) reported maximum decrease in ETo was 0.0 mm/day/year all over India during 1971 2002. Two temperature based equation namely B-C and Hargreaves equation were evaluated with the P-M estimates as all required data were available. ETo of the region changes after time and in-turn it will affect irrigation water requirement and water resource planning. Therefore, trend of reference evapotranspiration were also investigated with Mann-Kendall (M-K) test and Sen s Slope Estimator. II. MATERIAL AND METHODS A. Study area The study was conducted for Betwa Basin (area=,00 km 2 ) located in central India which lies between 77 10 E and 80 20 E (longitude) and 22 and 2 0 N (latitude). The climate of the Betwa basin is moderate, mostly dry except during the southwest monsoon (Chaube et al. 2011). The average annual rainfall is 1,18 mm. The daily mean temperature ranges from a maximum of 2. C to a minimum of 8.1 C. The daily mean relative humidity varies from a minimum of 18 % (April and May) to a maximum of 90 % (August). B. Data Acquisition Various metrological parameters like maximum temperature, minimum temperature, rainfall, wind speed, relative humidity and sunshine hour have been collected for 29 years on monthly basis. Indian Meteorological Department is having 18 meteorological stations inthe study area. All data was averaged over each month in order to get monthly values of each meteorological variable. Missing observations in the time series of various data were substituted with the corresponding long-term mean. Methodology Estimation of ETo 77

The factors affecting ETo are the climatic parameters. Consequently, it may be considered as a complex climatic parameter and can be computed from weather data (Xu et al. 200). CROPWAT 8.0 Software was employed for determining monthly ETo and input parameters were monthly minimum and maximum temperature, wind speed, sunshine hour and relative humidity dataof 1 meteorological stations of the basin. FAO recommended P-M method was used in this study; because this takes into account the most significant variables, so that the influence of each of them can be analyzed (Espadafor et al. 2011). Original FAO P-M method to estimate ETo derived by Allen et al. (1998) is: 900 08 ( Rn G) U 2( es ea ) ET T 27 O (1 0.U 2)...(1) where, ETo = Reference evapotranspiration [mmday -1 ]; Rn = Net radiation at the crop surface [MJ m- 2 day -1 ]; G = Soil heat flux density [MJ m -2 day]; T = Daily air temperature at 2 m height; U = Wind speed at 2 m height [m sec -l ]; e s = Saturation vapour pressure [kpa]; e a = Actual vapour pressure [kpa]; e s -e a = Saturation vapour pressure deficit [kpa]; = Slope of vapour pressure curve [kpa C -1 ]; γ = Psychrometric constant (kpa C -1 ). Temperature based equation are as follows: Blaney-Criddle method: ET O 0. p( T 17.8) ETo = Reference evapotranspiration, mm of water per day (mean value over the month); p = Monthly per cent of total day time hours of the year; T = Mean monthly temperature in C (average of daily maximum and minimum values). Hargreaves equation: When data is scarce, ETo can be estimated with reasonable satisfactory results, using Hargreaves alternative equation, expressed as follows (Allen et al. 1998): 0. ET 0.002 ( T 17.8) ( T T ) R O MEAN MAX MIN a...(2) Where, ETo(mm/day) and Ra is the extra-terrestrial solar radiation (mm/day). C. Mann-Kendall test and Theil-Sen s Slope Estimator The MK test has been extensively used to determine trends in similar hydrologic studies previously (Aziz and Burn 200; Patra et al. 2012;). Before employing MK test, time series were checked for autocorrelation or persistence and trend free pre whitening procedure suggested by Yue et al. (2002) was applied if, persistence exists in any time series. To identify whether a trend exists, the magnitude of a trend can also be estimated by a slope estimator β (Sen 198). A positive value of β indicates an upward trend (increasing values with time or any other independent variable), whereas a negative value of β indicates a downward trend (Chakraborty et al. 201). III. RESULTS AND DISCUSSION A. Comparison of Three ETo Methods Estimates In this study, ETo were computed using P-M, Hargreaves equation and B-C method. Monthly average of ET O by all three methods for 29 years is presented in Table I. For Betwa basin B-C method gave much better results than Hargreaves equation when compared with FAO recommended P-M equation. Especially underestimation of ETo by Hargreaves equation was found for Betwa basin while B-C method gave promising results for almost all months. Ali and Shui (2009) also found that FAO P-M successively followed by B-C method during comparison of five ETo estimation methods. Fig. 1 (a and b) shows coefficient of determination and linear regression lines of monthly estimates of ETo with P-M method. Coefficient of determination (r 2 =0.9) of the B-C equation with the P-M equation was found significantly higher than that of Hargreaves equation (r 2 = 0.2). This proves poor performance of Hargreaves equation in comparison to B-C method. B. Spatial distribution of ETo To represent the spatial distribution of ETo Inverse square distance method has been applied. Ray and Dhadwal (2000) used this method to interpolate reference ETo values. Using P-M method values of ETo varies from 19 mm to 2117 mm for Hamirpur and Basoda stations respectively (Fig. 2.a). Using B-C method values of ETo varies from1927 mm to 20 mm in Begamganj station and Basoda stations respectively. (Fig. 2.b). B-C showed lesser spatial variation in the region than other two method. Hargreaves method gave significantly lower values for ETo in all the stations. Fig. 2(c) shows variation by Using Hargreaves method ETo varies from 12 mm to 170 mm in Jhansi and Bhopal stations respectively. C. Comparison of Methods by trend analysis results Annual trend of ETo were compared in the study area. It has been found that although all equations showed decreasing trend but B-C Method does not show significant trend as compared to other two equations. By this method only Hamirpur station showed significant decreasing trend (0.19 mm/year). Trend of annual ETo by P-M revealed that decreasing trends varies from 0.0mm per year to 0.2mm per year for Bhopal and Hamirpur station respectively. Hargreaves equation shows no trend in the annual ETo for the Bhopal station and a decreasing trend of 0.mm/year was observed for Shivpuri station (Table II). Month TABLE I COMPARISON OF ETO WITH THREE METHODS (MM/DAY) Penman-Monteith method Hargreaves method Blaney-Criddle Method January.92.1.0 February.19.81.1 March.2.0.7 April.21.8.0 May 7.0.80 7. June 7.20.2 7.0 July.8.0.72 August.2.20.2 September.98..8 October.9.2.9 November.10.. December.2.10.1 78

ETo (mm/month) Blaney-Criddle method 20 200 10 a R² = 0.90 100 100 10 200 20 ETo (mm/month) P-M method Fig. 1 Regression line and coefficient of determination between (a) H-R and P-M method (b) B-C method with P-M method D. Statistical analysis of weather parameter with ETo The preliminary analysis of statistical parameters (mean, standard deviation, skewness, and kurtosis) of all data series were computed for 198-2012 series (Table III). Correlation of ETo (estimated by FAO recommended P-M method) with other weather parameter was also studied. E. Regression analysis of weather parameters For analysis of the impact of weather parameters on ETo, linear regression analysis was performed on major meteorological variables and ETo (using P-M method). Linear regression lines were plotted between mean monthly values of weather parameters and ETo over the whole basin. It has been found that maximum temperature has good correlation (R 2 =0.7) with ETo however minimum temperature has much stronger correlation (R 2 =0.9) with ETO (Figs. a and b). Strong correlation between ETo and mean temperature justifies better estimates of B-C method against Hargreaves equation for the basin (Fig. c). To study correlation of relative humidity (RH) with ETo, mean annual values of relative humidity for 29 years were plotted against ETo, and it was found that ETo shows a decreasing trend and very good correlation (R² = 0.79) with RH (Fig. d). ETo (mm/month) Hargreaes equation 200 10 100 b R² = 0.2 0 100 10 200 20 ETo(mm/month) P-M method Trend of Weather Variables Table IV shows the trend analysis of maximum, minimum temperature and relative humidity in terms of Z statistics and Q value. Significant decreasing trends of maximum temperature have been found and only August month shows significant decreasing trends of maximum temperature. Decreasing trend of minimum temperature at 1% and 0.1% significance level were observed in July and August while increasing trends of minimum temperature were detected in October, November and December. April, June and July shows increasing trend of relative humidity at 1%, % and 10% significance level. Estimation of Magnitude of trends in maximum temperature, minimum temperature and relative humidity by Theil-Sen s estimator for all the months revealed that downward maximum temperature slope was 0.17 C in March and upward minimum temperature slope was highest in November (0.1 C). Upward relative humidity slope was maximum in April (1.10%). IV. SUMMARY AND CONCLUSIONS 1) Comparison of two temperature based methods with P- M showed that B-C method performed better. 2) B-C method showed negligible trend as compared to that of P-M equation when detected with M-K test and Sen s slope estimator. ) In case of limited data source (only temperature) B-C method can be used to get reasonable estimates of the ETo for short time period. ) TMAX and TMIN were positively correlated with ETo but RH have negative correlation with ETo despite high coefficient of determination. Both trend and correlation analysis of these weather parameters justified the decreasing trend of reference evapotranspiration in the Betwa basin. TABLE II COMPARISON OF TREND RESULTS OF ETO BY ALL THREE METHODS Stations Penman-Monteith equation Hargreaves equation Blaney-Criddle method Z Values Sig. Sen's Slope (β) Z Values Sig. Sen's Slope (β) Z Values Sig. Sen's Slope (β) Banda -2.1 * -0.1-2.9 ** -0.08-1. -0.02 Basoda -.7 *** -0.2 -.88 *** -0.18-0. -0.01 Begamganj -2. * -0.21-2.2 * -0.18-0.98-0.0 Bersia -2.10 * -0.12-1.2-0.10 0.0 0.02 Bhopal -0.8-0.0 0.11 0.00.0 *** 0.07 Chanderi -0.8-0.21 1.0 0.08 0.0 0.00 Chhatarpur -2. * -0.17-1. -0.08-1.0-0.0 Hamirpur -. *** -0.2 -.1 ** -0.1 -.0 *** -0.19 Jalon -2.1 * -0.1 -. *** -0. -1. -0.0 Jhasi -2.7 ** -0.18 -.72 *** -0.2-1. -0.0 Khurai -1.97 * -0.12-2.0 * -0.11 0.11 0.00 Khurwai -1.71 + -0.10 -.10 ** -0.17 0.2 0.01 Mungawali -2. * -0.1-2.79 ** -0.20-0.08 0.00 Shivpuri -1.99 * -0.1 -.7 *** -0. -0.92-0.0 Sironj -2.19 * -0.1 -.8 *** -0.19-0.1-0.01 Tikamgadh -1.97 * -0.1-1.1-0.09-0.0-0.01 ( *** if trend at=0.001 level significance, ** if trend at =0.01 level significance, * if trend at=0.0 level significance + if trend at 0.1 level significnace) 79

TABLE III STATISTICAL ANALYSIS OF WEATHER VARIABLES Duration Parameter Skewness Mean Standard Kurtosis Deviation 198-2012 Min. 0.1 20.9 o C 0.7 0.81 temp. 198-2012 Max. 0.7 1.0 o C 0. 1.87 temp. 198-2012 Wind 0.1 222.88 0. -0.98 speed km/day 198-2012 Rainfall.1 918.8 22.1 1. 198-2012 Relative humidity mm -0.1 7.72%. -0.71 TABLE IV TREND RESULTS OF WEATHER VARIABLES Weather Parameters Maximum Temperature Minimum Temperature RelativeHumidity Time series Test Z Sig. Q Test Z Sig. Q Test Z Sig. Q January -2.8 ** -0.12 0.0 0.01 0. 0.17 February -2.1 * -0.1-0. -0.0 0.92 0. March -2.87 ** -0.17-0.8-0.0 1.7 0. April -2.9 ** -0.11-1.11-0.0 2.8 ** 1.10 May -0.2-0.02 0.2 0.0 1.2 0. June 0.21 0.01-0.81-0.0 2.12 * 0.72 July 1. 0.0 -.02 ** -0.08 1.80 + 0.9 August 2.01 * 0.0 -.8 *** -0.08 0.90 0.0 September 0. 0.01-1.7-0.0 0.1 0.18 October 1.0 0.0 1.9 + 0.0 0. 0.22 November 0.09 0.00 2.2 * 0.1 0. 0.2 December -0.1-0.02 2.2 * 0.10-0.8-0.21 ( *** if trend at=0.001 level significance, ** if trend at =.01 level significance, * if trend at=0.0 level significance + if trend at 0.1 level significnace) (a) (b) (c) Fig. 2 Spatial distribution of reference evapotranspiration with three methods (a) Hargreaves equation, (b) Penman-Monteith equation, (c) Blaney-Criddle equation 80

a. 7... 8 7.... y = 0.18x - 0.11 R² = 0.7 7. b. 7...... y = 0.17x + 2.2 R² = 0.9 7. c. 7..... y = 0.1x + 1. R² = 0.9 ETo (mm/year) 220 2200 210 2100 200 2000 190 y = -12.8x + 29. R² = 0.79 d.. 20 0 0 0 Maximum temprature ( C) 1 2 Minimum Temprature ( C) 10 20 0 0 Mean Temperature ( C) 1900 Relative Humidity (%) Fig. Regression line and coefficient of determination REFERENCES [1] Ali, M. H., and Shui, L. T. (2009). "Potential evapotranspiration model for Muda irrigation project, Malaysia." Water resources management, 2(1), 7-9. [2] Allen, R. G., Pereira, L., Raes, D., and Smith, M. (1998). "FAO Irrigation and drainage paper No.." Rome: Food and Agriculture Organization of the United Nations, 2-0. [] Aziz, O. I., and Burn, D. H. (200). "Trends and variability in the hydrological regime of the Mackenzie River Basin." Journal of Hydrology, 19(1), 282-29. [] Bandyopadhyay, A., Bhadra, A., Raghuwanshi, N., and Singh, R. (2009). "Temporal trends in estimates of reference evapotranspiration over India." Journal of Hydrologic Engineering, 1(), 08-1. [] Chakraborty, S., Mishra, S., Pandey, R., and Chaube, U. (201). "Longterm Changes of Irrigation Water Requirement in the Context of Climatic Variability." ISH Journal of Hydraulic Engineering, 19(), 27-2. [] Chaube U.C., Suryavanshi S., Nurzaman L. and Pandey A (2011) "Synthesis offlow series of tributaries in Upper Betwa basin. "International Journal of Environmental Sciences 1(7):9 7 [7] Cohen, S., Ianetz, A., and Stanhill, G. (2002). "Evaporative climate changes at Bet Dagan, Israel, 19 1998." Agricultural and Forest Meteorology, 111(2), 8-91. [8] Darshana, Pandey, A., and Pandey, R. (201) "Analysing trends in reference evapotranspiration and weather variables in the Tons River Basin in Central India." Stochastic Environmental Research and Risk Assessment, 27 (): 107 121. [9] Espadafor, M., Lorite, I., Gavilán, P., and Berengena, J. (2011). "An analysis of the tendency of reference evapotranspiration estimates and other climate variables during the last years in Southern Spain." Agricultural Water Management, 98(), 10-101. [10] Patra, J. P., Mishra, A., Singh, R., and Raghuwanshi, N. (2012). "Detecting rainfall trends in twentieth century (1871 200) over Orissa State, India." Climatic change, 111(-), 801-817. [11] Paudel, H.D.; and Pandey A;(201)"Comprative study of ETo estimation methods for the water balance estimation-a case study of Sikta irrigation project,nepal"journal of Indian Water Resources Society,Vol,No.. [12] Ray, S. and Dadhwal, V. (2001). Estimation of crop evapotranspiration of irrigation command area using remote sensing and GIS, Agricultural Water Management, 9(): 29-29. [1] Sen, P.K. (198). Estimates of the regression coefficient based on Kendall s tau. Journal of the American stastitics association,, 179 89. [1] Tabari, H., Marofi, S., Aeini, A., Talaee, P. H., and Mohammadi, K. (2011). "Trend analysis of reference evapotranspiration in the western half of Iran." Agricultural and Forest Meteorology, 11(2), 128-1. [1] Trajkovic, S., and Kolakovic, S. (2009). "Evaluation of reference evapotranspiration equations under humid conditions." Water resources management, 2(1), 07-07 [1] Xu, C.Y., Gong, L., Jiang, T., Chen, D., and Singh, V. (200). "Analysis of spatial distribution and temporal trend of reference evapotranspiration and pan evaporation in Changjiang (Yangtze River) catchment." Journal of Hydrology, 27(1), 81-9. [17] Yu, P.S., Yang, T. C., and Chou, C. C. (2002). "Effects of climate change on evapotranspiration from paddy fields in southern Taiwan." Climatic Change, (1-2), 1-179. [18] Yue, S., Pilon, P., Phinney, B., &Cavadias, G. (2002). The influence of autocorrelation on the ability to detect trend in hydrological series. Hydrological Processes, 1(9), 1807-1829. 81