Atmospheric Research

Similar documents
What is the IPCC? Intergovernmental Panel on Climate Change

CHARACTERISTICS OF PRECIPITATION IN THE ATHENS AREA, GREECE

Forecasting Drought in Tel River Basin using Feed-forward Recursive Neural Network

Analysis of Historical Pattern of Rainfall in the Western Region of Bangladesh

Optimum Neural Network Architecture for Precipitation Prediction of Myanmar

Projected Change in Climate Under A2 Scenario in Dal Lake Catchment Area of Srinagar City in Jammu and Kashmir

Will a warmer world change Queensland s rainfall?

CLIMATE CHANGE IMPACTS ON HYDROMETEOROLOGICAL VARIABLES AT LAKE KARLA WATERSHED

Evaluation of the Version 7 TRMM Multi-Satellite Precipitation Analysis (TMPA) 3B42 product over Greece

Current and future climate of the Cook Islands. Pacific-Australia Climate Change Science and Adaptation Planning Program

SHORT COMMUNICATION EXPLORING THE RELATIONSHIP BETWEEN THE NORTH ATLANTIC OSCILLATION AND RAINFALL PATTERNS IN BARBADOS

Climatic Classification of an Industrial Area of Eastern Mediterranean (Thriassio Plain: Greece)

International Journal of Scientific and Research Publications, Volume 3, Issue 5, May ISSN

SPATIAL AND TEMPORAL DISTRIBUTION OF AIR TEMPERATURE IN ΤΗΕ NORTHERN HEMISPHERE

1 Ministry of Earth Sciences, Lodi Road, New Delhi India Meteorological Department, Lodi Road, New Delhi

Extreme Rainfall Indices for Tropical Monsoon Countries in Southeast Asia #

Medium Term Forecasting of Rainfall using Artificial Neural Networks

Current and future climate of Vanuatu. Pacific-Australia Climate Change Science and Adaptation Planning Program

Three main areas of work:

1990 Intergovernmental Panel on Climate Change Impacts Assessment

Water Balance in the Murray-Darling Basin and the recent drought as modelled with WRF

Chapter outline. Reference 12/13/2016

Atmospheric circulation patterns associated with extreme precipitation amounts in Greece

URBAN HEAT ISLAND IN SEOUL

Manfred A. Lange Energy, Environment and Water Research Center The Cyprus Institute. M. A. Lange 11/26/2008 1

Prediction of Monthly Rainfall of Nainital Region using Artificial Neural Network (ANN) and Support Vector Machine (SVM)

ColomboArts. Volume II Issue I Dynamic Trends of Intensity of Rainfall Extremes in Sri Lanka

Understanding Weather and Climate Risk. Matthew Perry Sharing an Uncertain World Conference The Geological Society, 13 July 2017

Project Name: Implementation of Drought Early-Warning System over IRAN (DESIR)

RELATION BETWEEN AIR POLLUTION EPISODES AND DISCOMFORT INDEX IN THE GREATER ATHENS AREA, GREECE

Global warming and changing temperature patterns over Mauritius

DISTRIBUTION AND DIURNAL VARIATION OF WARM-SEASON SHORT-DURATION HEAVY RAINFALL IN RELATION TO THE MCSS IN CHINA

2015: A YEAR IN REVIEW F.S. ANSLOW

Analysis of Trends and Patterns of Annual Rainfall in Australian Cities

Appendix E. OURANOS Climate Change Summary Report

Summary and Conclusions

DEPARTMENT OF EARTH & CLIMATE SCIENCES Name SAN FRANCISCO STATE UNIVERSITY Nov 29, ERTH 360 Test #2 200 pts

A RADAR-BASED CLIMATOLOGY OF HIGH PRECIPITATION EVENTS IN THE EUROPEAN ALPS:

Analysis of Relative Humidity in Iraq for the Period

Characteristics of long-duration precipitation events across the United States

Mozambique. General Climate. UNDP Climate Change Country Profiles. C. McSweeney 1, M. New 1,2 and G. Lizcano 1

CHAPTER 1: INTRODUCTION

Current Climate Trends and Implications

9th Scientific Statement. Recent Irish weather extremes and climate change Ray McGrath, Rowan Fealy and Tom Sheridan

Fire Weather Drivers, Seasonal Outlook and Climate Change. Steven McGibbony, Severe Weather Manager Victoria Region Friday 9 October 2015

Impacts of the climate change on the precipitation regime on the island of Cyprus

Optimal Artificial Neural Network Modeling of Sedimentation yield and Runoff in high flow season of Indus River at Besham Qila for Terbela Dam

Climatic Extreme Events over Iran: Observation and Future Projection

Extreme Weather Events and Climate Change

The South Eastern Australian Climate Initiative

Seasonal trends and temperature dependence of the snowfall/ precipitation day ratio in Switzerland

WINTER NIGHTTIME TEMPERATURE INVERSIONS AND THEIR RELATIONSHIP WITH THE SYNOPTIC-SCALE ATMOSPHERIC CIRCULATION

Verification of the Seasonal Forecast for the 2005/06 Winter

Association of geopotential height patterns with heavy rainfall events in Cyprus

Changes in Southern Hemisphere rainfall, circulation and weather systems

Chapter 2 Variability and Long-Term Changes in Surface Air Temperatures Over the Indian Subcontinent

Chapter 1 Climate in 2016

A STUDY ON THE INTRA-ANNUAL VARIATION AND THE SPATIAL DISTRIBUTION OF PRECIPITATION AMOUNT AND DURATION OVER GREECE ON A 10 DAY BASIS

Annex I to Target Area Assessments

DROUGHT IN MAINLAND PORTUGAL

A High Resolution Daily Gridded Rainfall Data Set ( ) for Mesoscale Meteorological Studies

Application of Text Mining for Faster Weather Forecasting

To Predict Rain Fall in Desert Area of Rajasthan Using Data Mining Techniques

Climate Change 2007: The Physical Science Basis

Phenomenological features of precipitation series in agricultural regions

DETECTION AND FORECASTING - THE CZECH EXPERIENCE

The role of teleconnections in extreme (high and low) precipitation events: The case of the Mediterranean region

Data and prognosis for renewable energy

Statistical Analysis of Long Term Temporal Trends of Precipitation and Temperature in Wainganga Sub-Basin, India

Temperature Prediction based on Artificial Neural Network and its Impact on Rice Production, Case Study: Bangladesh

Analysis of Rainfall and Other Weather Parameters under Climatic Variability of Parbhani ( )

MODELLING FROST RISK IN APPLE TREE, IRAN. Mohammad Rahimi

CONSIDERATIONS ABOUT THE INFLUENCE OF CLIMATE CHANGES AT BAIA MARE URBAN SYSTEM LEVEL. Mirela COMAN, Bogdan CIORUŢA

Atmospheric patterns for heavy rain events in the Balearic Islands

Training: Climate Change Scenarios for PEI. Training Session April Neil Comer Research Climatologist

Figure ES1 demonstrates that along the sledging

Assessment of Snow Cover Vulnerability over the Qinghai-Tibetan Plateau

TROPICAL-LIKE CYCLONES IN THE MEDITERRANEAN: IMPACTS AND COMPOSITE DAILY MEANS AND ANOMALIES OF SYNOPTIC CONDITIONS

Mesoscale and High Impact Weather in the South American Monsoon Leila M. V. Carvalho 1 and Maria A. F. Silva Dias 2 1

Long-Term Trend of Summer Rainfall at Selected Stations in the Republic of Korea

Rainfall Analysis in Mumbai using Gumbel s Extreme Value Distribution Model

ANALYSIS OF FLOODS AND DROUGHTS IN THE BAGO RIVER BASIN, MYANMAR, UNDER CLIMATE CHANGE

Future pattern of Asian drought under global warming scenario

J8.4 TRENDS OF U.S. SNOWFALL AND SNOW COVER IN A WARMING WORLD,

Comparison learning algorithms for artificial neural network model for flood forecasting, Chiang Mai, Thailand

Daily Rainfall Disaggregation Using HYETOS Model for Peninsular Malaysia

Agrometeorological activities in RHMSS

LONG RANGE FORECASTING OF LOW RAINFALL

NOTES AND CORRESPONDENCE. El Niño Southern Oscillation and North Atlantic Oscillation Control of Climate in Puerto Rico

EL NINO-SOUTHERN OSCILLATION (ENSO): RECENT EVOLUTION AND POSSIBILITIES FOR LONG RANGE FLOW FORECASTING IN THE BRAHMAPUTRA-JAMUNA RIVER

Reprinted from MONTHLY WEATHER REVIEW, Vol. 109, No. 12, December 1981 American Meteorological Society Printed in I'. S. A.

Keywords: lightning climatology; lightning flashes; Macedonia Greece.

Chiang Rai Province CC Threat overview AAS1109 Mekong ARCC

PREDICTING DROUGHT VULNERABILITY IN THE MEDITERRANEAN

Climates of NYS. Definitions. Climate Regions of NYS. Storm Tracks. Climate Controls 10/13/2011. Characteristics of NYS s Climates

Forecasting of Rain Fall in Mirzapur District, Uttar Pradesh, India Using Feed-Forward Artificial Neural Network

Definitions Weather and Climate Climates of NYS Weather Climate 2012 Characteristics of Climate Regions of NYS NYS s Climates 1.

SEASONAL AND ANNUAL TRENDS OF AUSTRALIAN MINIMUM/MAXIMUM DAILY TEMPERATURES DURING

National Wildland Significant Fire Potential Outlook

Climatic study of the surface wind field and extreme winds over the Greek seas

Transcription:

ATMOS-252; No of Pages 8 Atmospheric Research xxx (211) xxx xxx Contents lists available at SciVerse ScienceDirect Atmospheric Research journal homepage: www.elsevier.com/locate/atmos Rain intensity forecast using Artificial Neural Networks in Athens, Greece P.T. Nastos a,, K.P. Moustris b, I.K. Larissi c, A.G. Paliatsos d a Laboratory of Climatology and Atmospheric Environment, Faculty of Geology and Geoenvironment, University of Athens, Panepistimiopolis GR-15784 Athens, Greece b Department of Mechanical Engineering, Technological Education Institute of Piraeus, 25 Thivon and P. Ralli Str., GR-12244 Athens, Greece c Laboratory of Environmental Technology, Department of Electronic Computer Systems Engineering, Technological Education Institute of Piraeus, 25 Thivon and P. Ralli Str., GR-12244 Athens, Greece d General Department of Mathematics, Technological Education Institute of Piraeus, 25 Thivon and P. Ralli Str., GR-12244 Athens, Greece article info abstract Article history: Received 22 November 2 Received in revised form 27 July 211 Accepted 29 July 211 Available online xxxx Keywords: Rain intensity Artificial Neural Networks Athens Greece The forecast of extreme weather events become imperative due to the emerging climate change and possible adverse effects in humans. The objective of this study is to construct predictive models in order to forecast rain intensity (mm/day) in Athens, Greece, using Artificial Neural Networks (ANN) models. The ANNs outcomes concern the projected mean, maximum and minimum monthly rain intensity for the next four consecutive months in Athens. The meteorological data used to estimate the rain intensity, were the monthly rain totals (mm) and the respective rain days, which were acquired from the National Observatory of Athens, for a 111-year period (1899 29). The results of the developed and applied ANN models showed a fairly reliable forecast of the rain intensity for the next four months. For the evaluation of the results and the ability of the developed prognostic models, appropriate statistical indices were taken into consideration. In general, the predicted rain intensity compared with the corresponding observed one seemed to be in a very good agreement at a statistical significance level of pb.1. 211 Elsevier B.V. All rights reserved. 1. Introduction The enhancement of the greenhouse effect, caused by continuous increasing anthropogenic emissions of greenhouse gases into the atmosphere, is expected to induce severity of damaging climate change. Solomon et al. (29) showed that climate change, which takes place due to increases in carbon dioxide concentration, is largely irreversible for years after emissions stop. The extreme events are likely to be more often in the future (IPCC, 27). During the last decades, there was a lot of discussion concerning the impacts of climate change in extreme events, such as heavy rain, resulting in significant flooding in urban environments, or in combination with tornado outbreak causing damage in properties (Mateo et al., 29; Nastos and Matsangouras, 2). Besides, recent Corresponding author at: Laboratory of Climatology and Atmospheric Environment, Faculty of Geology and Geoenvironment, University of Athens, Panepistimiopolis GR 157 84, Athens, Greece. Tel./fax: +3 2 727491. E-mail address: nastos@geol.uoa.gr (P.T. Nastos). studies have concluded that, heavy storms of convective nature in the developed mega-cities could be attributed to the urban heat island (UHI) (Paliatsos et al., 25; Nastos and Zerefos, 27; 28; Philandras et al., 2a). On the other hand, water scarcity and decreasing run off appear as adverse consequences of climatic change in vulnerable regions such as the Mediterranean region (IPCC, 27). Nastos and Zerefos (29) concluded that the temporal variability of consecutive wet days shows statistically significant (confidence level of 95%) negative trends, mainly in the western region of Greece, characterized by large orographic precipitation amounts (Metaxas et al., 1999). Insignificant positive trends for consecutive dry days appear almost all over the country with emphasis in the southeastern region. Rainfall is one of the most complex and difficult elements of the hydrology cycle to understand and to model due to the complexity of the atmospheric processes that generate rainfall and the tremendous range of variation over a wide range of scales both in space and time (French et al., 1992). Sokol and Bližňák (29) analyzed data in cases of short duration 169-895/$ see front matter 211 Elsevier B.V. All rights reserved. doi:.16/j.atmosres.211.7.2

2 P.T. Nastos et al. / Atmospheric Research xxx (211) xxx xxx heavy rainfall during the summer at the Czech Republic. They found that there was a relatively high incidence of such cases in southern and central Czech Republic, during the years 22 27. Federico et al. (29) in their work announced the first exploratory analysis and results for the precipitation in the peninsula of Calabria in southern Italy, for the period 1978 27. It was found that although the annual rainfall is greater on the west side of the peninsula, more intense precipitation is affecting mainly the east side, which is exposed to strong positive and strong storms. Thus, accurate rainfall forecasting is one of the greatest challenges in operational hydrology, despite many advances in weather forecasting in recent decades (Gwangseob and Ana, 21). For these reasons, any attempt to predict such extreme precipitation events is very important in order to protect population, infrastructure and prevent disasters due to flooding with major economic impacts. Several studies on the prediction of rainfall have been carried out during the last years. So far, long-term climate prediction using numerical models demonstrate not a useful performance (Zwiers and Von Storch, 24). During the last decade, ANN models have been applied to rainfall forecasting (Bodri and Cermak, 2; Luck et al., 2; Silverman and Dracup, 2; Sakellariou and Kambezidis, 24; Cigizoglou and Alp, 24). More specifically, Sahai et al. (2) used ANN models in order to forecast total precipitation during the summer monsoon period across India. As input data, they used rainfall recorded from 36 stations throughout India during the months of June-July-August and September for the time period 1871 1994. The prediction was based on the knowledge of the total rainfall amount for four consecutive months (June-September) of the previous four years. The results showed good forecast estimates of rainfall with Root Mean Square Error (RMSE) equal to 54.2 mm. The quite satisfactory results are primarily due to the frequency of occurrence of heavy rainfall during the summer monsoon in India as well as the large number of data used for ANN models training, which makes them able to obtain a fairly good knowledgeexperience of the phenomenon. Freiwan and Cigizoglu (25) developed a number of different multilayer perceptron ANN models that were trained with the method of back-propagation algorithm in order to predict rainfall for the next month. As input data, they used the rainfall of the previous two months and a periodic component for each month. The rainfall prediction concerned the airport area in Amman, Jordan, during the period 1924 2. The predictions for the next month, showed a satisfactory reliability: for instance, the coefficient of determination (R 2 ) between true and predicted rainfall amounts was about.112 and.466, while the RMSE was between 25.8 and 33.6 mm, depending on the used ANN model type. Iseri et al. (25) created different types of predictive models, including ANN models, in order to predict the rainfall in the Fukuoka- Japan. Prediction was based on data recorded during the time period 191 1997. Their prediction concerned the monthly amount of rainfall in August. As input data for ANN models training, they used the change of the sea surface temperature and three different climate indices regarding the previous three to twelve months before the predicted month. Between all the models, ANN models showed the best forecasting ability with R 2 values between.147 and.366. Mar and Naing (28) used ANN models for monthly rainfall amount prediction in Yangon (Myanmar-South East Asia), taking as input data monthly values of rainfall for the period 197 26. The applied ANNs resulted in RMSE between 9.9 and 22.9 mm, depending on the used ANN model type. Therefore, there are many relevant studies on the prediction of precipitation so far, but these are not enough for longterm prognosis i.e. for four consecutive months and especially for rain intensity. In the present study, the efficiency of applying ANN models in forecasting long term rain intensity in the greater Athens area (GAA) is demonstrated and analysed. 2. Data and methodology 2.1. Artificial Neural Networks The ANN models are inspired by the structure and function of the human brain. Neurons are a key component of the brain. They are essentially nerve cells that create a dense network between them. Typical ANN models use very simplified models of neurons, which only very rough characteristics of human neurons may maintain (Hecht-Nielsen, 1989). The first ANN models occurred during the decades of 194 and 195 with the basic artificial neuron model of McCulloch and Pitts (1943) and the first ANN training algorithm of Rosenblatt (1958). In the following decades there was a decline in the use of the ANNs because of high computing power required for their use, which was not readily available from the computers of that era. The recession was followed by regeneration of ANNs with the introduction of the ANN models of Hopfield (1982, 1987). These are known as Multi-Layer Perceptron (MLP) ANN models, which along with the training algorithm of back-propagation, proposed by Werbos (1974), caused the interest of the scientific community again. This interest coupled with the rapid growth of parallel computing capabilities. The structure of a feed forward MLP artificial neural network can be represented as in Fig. 1. The first layer is the input layer with one or more neurons, depending on the number of necessary input data for the proper training of an ANN model. One or more hidden layers follow with a number of artificial neurons that are necessary for the processing of the input signals. Each neuron of the hidden layer communicates with all the neurons of the next hidden layer, if any, having in each connection a typical weight factor (Fig. 1). Finally, the signal reaches the output layer, where the output value from the ANN is compared with the target value and error is estimated. Thus, the values of weight factors are appropriately amended and the training cycle is repeated until the error is acceptable, depending on the application. In general, ANN model applications can be applied in a lot of different disciplines, such as air pollution, urban bioclimatology, water quality, rainfall prediction, classification of rainfall prediction, climate analysis etc. (Zwick and Canarelli, 1996; Melas et al., 2; Michaelides et al., 21; Papanastasiou et al., 27; Sengorur et al., 26; Diamantopoulou et al., 27; Moustris et al., 29, 2).

P.T. Nastos et al. / Atmospheric Research xxx (211) xxx xxx 3 Fig. 1. Typical artificial neural network architecture (Caudill and Butler, 1992). 2.2. Rainfall data and study area The datasets used concern monthly rain totals with the respective rain days, and were acquired from the National Observatory of Athens (NOA), which is located on the Hill of Nymphs near the centre of Athens (longitude: 23 43 E, latitude: 37 58 N, altitude: 7 m a.m.s.l.), during the 111- year period (1899 29). This rain time series of NOA is the longest available record in Greece. The homogeneity of NOA time series was tested using the short-cut Bartlett test of homogeneity (Paliatsos et al., 25), resulting in considering NOA time series as homogenous and this could be attributed to the unchanged position of the station since 189. In this analysis, a rain day is considered as the day with rain total greater than 1 mm. In the process, the monthly rain intensity (mm/day) is calculated by dividing the monthly rain total with the respective rain days, for every year of the examined time series. Table 1 presents the mean monthly rain intensity along with the frequency (%) of cases with rain intensity greater than or equal to 14.4 mm/day with respect to the time series of each month during the examined period. Thus for example, the frequency 3.6% depicted for January (Table 1) means that 3.6% of the cases within the January time series (111-year period, 1899 29) corresponds to Table 1 Statistical characteristics of rain intensity in Athens. Month Mean rain intensity (mm/day) Frequency (%) of months with rain intensity 14.4 mm/day January 7.6 3.6 3 February 7.5 7.2 3 March 7.1 5.4 3 April 6.3 3.6 2 May 5.5 3.6 1 June 5.1 9. 1 July 4.2 4.5 August 3.7 7.2 September 6.2 9.9 2 October. 26.1 4 November.2 18. 4 December 9.7 15.3 4 Periodic Component (PC) rain intensity greater than or equal to 14.4 mm/day. The threshold of 14.4 mm/day concerns the sum of the mean rain intensity within the examined time period plus the respective standard deviation. Besides, a periodic component (PC) for each month according to the mean monthly rain intensity (Freiwan and Cigizoglu, 25) is depicted in Table 1. More specifically, the mean monthly rain intensity during the examined period was calculated and thereafter five classes were extracted corresponding in five particular PC values; that is, PC= for 4.2 3.7 mm/day, PC=1 for 5.5 5.1 mm/day, PC=2 for 6.3 6.2 mm/day, PC=3 for 7.6 7.1 mm/day and PC=4 for.2 9.7 mm/day (Table 1). The five classes were defined in order to include the months with rain intensity difference less than.5 mm/day within the same class. This scheme of selecting the PC values (after a series of trial and error) appears to be the most appropriate for successful ANNs predictability. The intra annual variation of the mean monthly rain intensity along with the PCs appear in Fig. 2. PC is a constant number for each month of the year and in other words represents the seasonality of precipitation (Freiwan and Cigizoglu, 25). PCs seem to be very important input data for the appropriate training of the constructed ANNs. This conclusion is based upon repeated trials, which were performed within the analysis framework. Specifically, a large number of different ANNs were constructed and trained. The results showed that the ANNs using PCs succeeded in much better results than all the others constructed ANNs. In this work, the architecture of the three developed ANNs has been decided after a series of successive trials and errors. Therefore, it was found that in each case the ANNs using PCs resulted in better predictions. 2.3. Rain intensity prediction Artificial Neural Networks methodology In this work three different ANN models were developed and trained in order to forecast the rain intensity. Specifically, ANN#1, ANN#2 and ANN#3 were created and trained to forecast the mean, the maximum and the minimum monthly rain intensity for the next four consecutive months, respectively. Each one of the above three models consist of three layers: the input layer, one hidden layer and the output layer. The three of them belongs to the MLP ANN models. The three ANN models with their detailed input data used for model training as well as their outputs are presented in Table 2. The available dataset (1899 29) consists of 1332 monthly rain intensity values (111 years 12 months) and was divided into two subsets. The first contains the monthly data from out of 111 years, which were used for the ANN models' training. The excluded 11 years (see next paragraph) were used for the evaluation of the ANNs forecasting ability. Concretely, the first subset consists of 12 monthly rain intensity values ( years 12 months). From this subset, a matrix of 1196 lines and 7 columns (Table 2) was created. This matrix was used for the ANNs training. The number of the lines (1196) is not equal to 12 due to the fact that for the prediction of the first four months of the year 1899 we needed rain intensity data concerning the year 1898. These data were not available. So, the ANNs training starts from the fifth month (May) of the year 1899.

4 P.T. Nastos et al. / Atmospheric Research xxx (211) xxx xxx 11 PC=4 PC=4 PC=4 9 8 PC=3 PC=3 PC=3 7 6 5 4 PC=2 PC=1 PC=1 PC= PC= PC=2 3 2 1 January February March April May June July August September October November December Fig. 2. Intra annual variability of mean monthly rain intensity and periodic component. The second subset consists of the monthly rain intensity data during the years 19, 19, 192, 193, 194, 195, 196, 197, 198, 199 and 2. In other words, the second subset consists of 132 monthly rain intensity values (11 years 12 months). From this subset, a matrix of 132 lines and 7 columns (Table 2) was created. These data are completely unknown to the ANN models and were used for the evaluation of their predictive ability. The selection of the second subset was done in a random way. Taking into account that the cumulative PCs as well as the cumulative expected incidence rate with rain intensityn= 14.4 mm/day for the next four months are harmonic/periodic factors of the rain intensity pattern within the year (Table 1), one can expect constant values for these two input nodes Table 2 ANNs input and output data for the prediction of rain intensity. Input data for training (input layer) Mean monthly rain intensity of the four previous months Maximum monthly rain intensity of the four previous months Minimum monthly rain intensity of the four previous months Cumulative PC of the four previous months Cumulative incidence rate with rain intensity 14.4 mm/day of the four previous months Cumulative PC of the four next months Cumulative expected incidence rate with rain intensity 14.4 mm/day for the next four months Output data (output layer) ANN#1: The mean monthly rain intensity for the four next consecutive months ANN#2: The maximum monthly rain intensity for the four next consecutive months ANN#3: The minimum monthly rain intensity for the four next consecutive months concerning future projections. More specifically, a descriptive interpretation of the above assumption is given in the process; that is during the ANNs training, the two input nodes Cumulative PC of the four next months and Cumulative expected incidence rate with rain intensity N= 14.4 mm/day for the next four months (Table 2) havealways the constant values in Table 1. For a better understanding, if the prediction concerns the rain intensity for the month e.g.may,the Cumulative PC of the four next months has the value 3+3+3+2=11 (Table 1). Simultaneously, the Cumulative expected incidence rate with rain intensityn= 14.4 mm/day for the next four months has the value 3.6+ 7.2+5.4+3.6=19.8 (Table 1) and so on. 2.4. Evaluation of predicted results The reliability of a predictive model is demonstrated through the use of some statistical indices. In this work, in order to establish the credibility and generally the capacity of a good prognosis by the trained ANNs, the following statistical indices were used: Mean Absolute Error (MAE), Mean Bias Error (MBE), Root Mean Square Error (RMSE), coefficient of determination (R 2 )andindex of Agreement (IA) (Wilmott, 1982; Willmott et al., 1985; Comrie, 1997; Walker et al., 1999; Kolehmainen et al., 21). MAE is an index, which is used in order to measure how forecasted values are close to observed values. MAE is given by the formula (1): MAE ¼ 1 n n 1 jp i O i j ð1þ MBE is used to describe whether a model under- (negative value) or over- (positive value) estimates the observation. MBE is calculated according to the formula (2): MBE ¼ 1 n n ðp i O i Þ ð2þ

P.T. Nastos et al. / Atmospheric Research xxx (211) xxx xxx 5 where n is the number of the data points, P i and O i represent predicted and observed values, respectively. RMSE is a commonly used measure of the differences between the predicted values by a model and the real-observed values. RMSE is used as a single measure that indicates the ability of the model prediction and has the same units as the predicted value. The smaller the numerical value of RMSE is, the closer to the real values are the predicted values by the model. RMSE is calculated according to the formula (3): RMSE ¼ 1 n n!1 ðp i O i Þ 2 2 R 2, the coefficient of determination, which is a number between and +1, measures the degree of association between two variables; in our case, the observed data (O i ) and the predicted data (P i ). It provides a measure of how well future outcomes are likely to be predicted by the model. The coefficient of determination is computed according to the formula (4): n ðo i P i Þ 2 R 2 ¼ 1 ð4þ n ðo i O iave Þ 2 where O i ave represents the average of the observed values. IA is a relative measure of error. The index of agreement is calculated according to the formula (5). This is a dimensionless measure that is limited within the range 1. IA equal to means no agreement between prediction and observation and IA equal to 1 means perfect agreement between prediction and observation. IA ¼ 1 n n ðp i O i Þ 2 ð3þ ð5þ ðjp i O iave jþjo i O iave jþ 2 3. Results and discussion The mean annual rain intensity (mm/day) time series along with 5-year moving average at NOA station, for the period 1899 29 are depicted in Fig. 3. The applied time series analysis showed that a statistically significant increasing trend is evident (b-coefficient=+.15 (mm/day/year), significance level p=.2), during the examined period. The scrutiny of the time series in Fig. 3 reveals that rain intensity fluctuates around approximately 8 mm/day from the beginning of the examined period until the middle of 198's and thereafter a statistically significant abrupt increasing trend appears until 22. (b-coefficient=+.3 (mm/day/year), significance level p=.33). Further to, an insignificant decreasing trend appears until nowadays. The incidence of flooding events in Athens could be attributed in the abrupt increase in rain intensity within the last decades (Tzavelas et al., 2). Koukis and Koutsoyiannis (1997) have shown that, flooding in Athens is probably the most severe among hydrometeorological hazards in Greece. Philandras et al. (2a) have given evidence that the rain intensity (mm/h) time series at NOA present significant increasing trends, starting in 199's, during fall and winter, while the increasing trends begin earlier in 198's during spring and summer. These trends become more intense in 2's. Nastos (28) studying the Simple Daily Intensity Index (SDII, mm/day) in Greece, during the period 1956 22, found that SDII in NOA appears a statistically significant (CL 95%) increasing trend, which could be attributed in the probability of increased development of convective thunderstorms due to urban climate characteristics(nastos and Zerefos, 27) and especially within summertime. Low frequency climatic variability is associated with changes of the extreme precipitation regime in Mediterranean, including North Atlantic Oscillation (NAO), Mediterranean Oscillation (MOI), North-Caspian Sea pattern (NCPI), and Eastern 2 18 Mean annual rain intensity 5 years moving average 16 14 12 8 6 4 2 1899 194 199 1914 1919 1924 1929 1934 1939 1944 1949 1954 1959 1964 1969 1974 1979 1984 1989 1994 1999 24 29 Fig. 3. Time series of mean annual rain intensity along with 5-year moving average (solid line) at NOA, for the period 1899 29.

6 P.T. Nastos et al. / Atmospheric Research xxx (211) xxx xxx Mediterranean Pattern (EMP) (Hatzaki et al., 2). Besides, Philandras et al. (2b) found that the effect of NAO in rain time series within the rainy season (October-April) showed a statistically significant (CL 95%) negative correlation throughout the Mediterranean region, particularly in the north part and in western Greece. Queralt et al. (29) concluded that extreme precipitation frequencies and intensities increase during negative NAO winters in most of the analyzed area in Spain. However, the modulation of NAO in extreme precipitation strongly depends on the particular region studied and the spea 16 Observed mean monthly rain intensity Predicted mean monthly rain intensity 14 12 8 6 4 2 19 19 192 193 194 195 196 197 198 199 2 Year b 25 Observed maximum monthly rain intensity Predicted maximum monthly rain intensity 2 15 5 c 9 19 19 192 193 194 195 196 197 198 199 2 Year Observed minimum monthly rain intensity Predicted minimum monthly rain intensity 8 7 6 5 4 3 2 1 19 19 192 193 194 195 196 197 198 199 2 Year Fig. 4. Observed (dot line) and predicted (bold solid line) rain intensity values for the prediction of mean (a), maximum (b) and minimum (c) rain intensity, for the next four consecutive months.

P.T. Nastos et al. / Atmospheric Research xxx (211) xxx xxx 7 cific month, significant responses being more frequent in mid late winter over some of the westernmost areas. The observed and model-predicted (by the trained ANNs) rain intensity time series, for the period 1899 29 are illustrated in Fig. 4. Specifically, the prediction of the mean rain intensity (Fig. 4a) the maximum rain intensity (Fig. 4b) and the minimum rain intensity (Fig. 4c) time series, for the next four consecutive months are the outputs of the applied ANNs. These outputs give evidence that the predictive ability of the developed ANN models is quite satisfactory for the mean rain intensity as well as for the maximum and minimum rain intensity during the next four consecutive months. For such an unexpected phenomenon as the rain intensity is, it seems that the ANN models can be a very important tool in the prediction of extreme precipitation. Nevertheless, ANNs show a weakness in the successful prediction of rain intensity peaks, which occur with relatively low frequency in the wider Athens area. This limitation may be due to the fact that other factors-input data are required for better training of ANNs. This phenomenon appears also in Poland where on 63% of thunderstorm days there were between.1 and. mm of rain. Cases of more than 3. mm of precipitation were very rare (2.7%) and were recorded mostly in mountainous areas. (Bielec-Bakowska and Lupikasza, 29). Besides, Marzano et al. (26) using neural-network approach in order to estimate precipitation intensity and extinction from ground, found that the NN retrieval algorithm tends to provide a better accuracy and a reduced error bias, especially for low-to-moderate rain rates. Table 3 presents the statistical fit agreement indices between the observed and the predicted rain intensity values for the three developed models; namely MBE, RMSE, IA, and finally, the coefficient of determination (R 2 ), for the prediction of the mean, maximum and minimum rain intensity, respectively. All models successfully predicted the mean, maximum and minimum rain intensity (significant level of pb.1). The best forecast is succeeded by the ANN#3 model and the worst by the ANN#2 one. Small values of both MAE and MBE indicate a fairly good prediction. According to statistical tables (for 132 predicted samples-pairs), R 2 =.242 (ANN#2) is satisfactory enough at a statistically significant level of pb.1. Nevertheless, ANN#2 does not have the ability for a very good prediction of maximum rain intensity for the next four consecutive months. This is due to the fact that maximum rain intensity is a more extreme and rare event. Thus, because the peak occurrence is rare, ANN#2 cannot gain the necessary experience to predict the event correctly. Recent studies establish the interest of using ANNs in prediction of rain intensity with quite reliable results. Orlandini and Morlini (2) revealed that ANN models may play an important role in the identification and reproduction of the Table 3 Statistical fit agreement indices for the developed predictive ANN models. ANN#1 ANN#2 ANN#3 MAE (mm/day) 1.6 3.2 1.2 MBE (mm/day) +.4 +1.5.1 RMSE (mm/day) 2. 3.9 1.7 IA.743.595.814 R 2.443.242.515 relationship between radar reflectivity and rain intensity, even when they are trained on a relatively small data set obtained from the monitoring of a single event over a small geographical area with a normal rain gage density. Manzatο (27) developed ANNs for the prediction of both the likelihood of occurrence, and intensity of storms over the region of Friuli Venezia Giulia in Italy, with satisfactory results. Wardah et al. (28) used meteorological satellite data and developed backpropagation ANNs for the estimation of rainfalls caused massive damages and flooding in the Klang river basin in Malaysia. Further research is needed in order to forecast the peaks of rain intensity for the next four consecutive months, improving the output of ANNs by using more appropriate input parameters for better training. The achievement of this target is associated with the prevention of flash floods mainly occurred in urban environments and accordingly the mitigation of the adverse impacts. 4. Conclusions In this work a modelling effort was carried out in order to investigate the potential of ANN models to forecast the rain intensity, four months ahead. The results showed that ANNs could be in the future a very reliable tool in predicting such a random phenomenon as the rain intensity is, mitigating in that way the associated socioeconomic impacts. The results produced by the ANN models were quite satisfactory, for the prediction of the rain intensity for the next four months. In general, the predicted values compared with the corresponding observed rain intensity values, seemed to be in a very good agreement at a statistical significance level of pb.1. The best forecast concerns the minimum monthly rain intensity for the next four consecutive months (ANN#3 model; MBE=.1) and the worst concerns the maximum monthly rain intensity for the next four consecutive months (ANN#2; MBE=+1.5). A limitation of this analysis is related to the weakness of the models to forecast the peaks of rain intensity, which appear low frequency. More research and effort has to be done in order ANNs be able to forecast with a remarkable ability dangerous and random phenomenon such as rain intensity. Maybe the ANNs training using satellite images and data as well as meteorological data of the middle and upper atmosphere prove a better forecasting ability in the future. Such a prognostic tool will be very important in early warning of urban floods. References Bielec-Bakowska, S., Lupikasza, E., 29. Long-term precipitation variability on thunderstorm days in Poland (1951 2). Atmos. Res. 93, 56 515. Bodri, L., Cermak, V., 2. Prediction of extreme precipitation using a neural network: application to summer flood occurrence in Moravia. Adv. Eng. Softw. 31, 211 221. Caudill, M., Butler, C., 1992. Understanding Neural Networks; Computer Explorations. MIT Press, Cambridge, MA, USA, p. 3. Cigizoglou, H.K., Alp, M., 24. Rainfall-runoff modelling using three neural network methods. Artificial Intelligence and Soft Computing-ICAISC 24 Lecture Notes in artificial Intelligence, 37, pp. 166 171. Comrie, A.C., 1997. Comparing neural networks and regression models for ozone forecasting. J. Air Waste Manage. 47, 653 663. Diamantopoulou, M.J., Georgiou, P.E., Papamichail, D.M., 27. Performance of neural network models with Kalman learning rule for flow routing in a river system. Fresenius Environ. Bull. 16 (11b), 1474 1484.

8 P.T. Nastos et al. / Atmospheric Research xxx (211) xxx xxx Federico, S., Avolio, E., Pasqualoni, L., De Leo, L., Sempreviva, A.M., Bellecci, C., 29. Preliminary results of a 3-year daily rainfall data base in southern Italy. Atmos. Res. 94, 641 651. Freiwan, M., Cigizoglu, H.K., 25. Prediction of total monthly rainfall in Jordan using feed forward back propagation method. Fresenius Environ. Bull. 14 (2), 142 151. French, M.N., Krajewski, W.F., Cuykendall, R.R., 1992. Rainfall forecasting in space and time using neural network. J. Hydrol. 137, 1 31. Gwangseob, K., Ana, P.B., 21. Quantitative flood forecasting using multisensor data and neural networks. J. Hydrol. 246, 45 62. Hatzaki, M., Flocas, H.A., Oikonomou, C., Giannakopoulos, C., 2. Future changes in the relationship of precipitation intensity in Eastern Mediterranean with large scale circulation. Adv. Geosci. 23, 31 36. Hecht-Nielsen, R., 1989. Theory of back propagation neural network. Proceedings of the International Joint Conference on Neural Networks, New York, IEEE, pp. 593 65. Hopfield, J.J., 1982. Neural networks and physical systems with emergent collective computational abilities. PNAS 9, 2554 2558. Hopfield, J.J., 1987. Learning algorithms and probability distributions in feedforward and feed-back networks. PNAS 84, 8429 8433. IPCC, 27. Summary for policymakers. In: Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K.B., Tignor, M., Miller, H.L. (Eds.), Climate Change 27: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, United Kingdom/New York, NY, USA. Iseri, Y., Dandy, G.C., Maier, H.R., Kawamura, A., Jinno, K., 25. Medium term forecasting of rainfall using artificial neural networks. Proceedings of the International Congress on Modeling and Simulation. Advances and Applications for Management and Decision Making. The Modeling and Simulation Society of Australia and New Zealand Inc, Melbourne, Australia, pp. 1834 184. Kolehmainen, M., Martikainen, H., Ruuskanen, J., 21. Neural networks and periodic components used in air quality forecasting. Atmos. Environ. 35, 815 825. Koukis, G.C., Koutsoyiannis, D., 1997.. Greece In: Embleton, C. and C. (Ed.), Geomorphological Hazards of Europe. Elsevier, Amsterdam, pp. 215 241. Luck, K.C., Ball, J.E., Sharma, A., 2. A study of optimal model lag and spatial inputs to artificial neural networks for rainfall forecasting. J. Hydrol. 227 (1 4), 56 65. Manzatο, Α., 27. Sounding-derived indices for neural network based shortterm thunderstorm and rainfall forecasts. Atmos. Res. 83, 349 365. Mar, K.W., Naing, T.T., 28. Optimum neural network architecture for precipitation prediction of Myanmmar. World Acad. Sci. Eng. Technol. 38, 13 134. Marzano, F.S., Fionda, E., Ciotti, P., 26. Neural-network approach to ground-based passive microwave estimation of precipitation intensity and extinction. J. Hydrol. 328, 121 131. Mateo, J., Ballart, D., Brucet, C., Aran, M., Bech, J., 29. A study of a heavy rainfall event and a tornado outbreak during the passage of a squall line over Catalonia. Atmos. Res. 93, 131 146. McCulloch, W., Pitts, W., 1943. A logical calculus of the ideas imminent in nervous activity. Bull. Math. Biophys. 5, 33 115. Melas, D., Kioutsoukis, I., Ziomas, I., 2. Neural network model for predicting peak photochemical pollutant levels. J. Air Waste Manage. 5, 495 51. Metaxas, D.A., Philandras, C.M., Nastos, P.T., Repapis, C.C., 1999. Variability of precipitation pattern in Greece during the year. Fresenius Environ. Bull. 8(1 2), 1 6. Michaelides, S.C., Pattichis, C.S., Kleovoulou, G., 21. Classification of rainfall variability by using artificial neural networks. Int. J. Climatol. 21, 141 1414. Moustris, K., Ziomas, I.C., Paliatsos, A.G., 29. 24 hours in advance forecasting of thermal comfort discomfort levels during the hot period of the year at representative locations of Athens city, Greece. Fresenius Environ. Bull. 18 (5), 61 68. Moustris, K.P., Ziomas, I.C., Paliatsos, A.G., 2. 3-day-ahead forecasting of regional pollution index for the pollutants NO 2, CO, SO 2 and O 3 using Artificial Neural Networks in Athens, Greece. Water Air Soil Pollut. 29, 29 43. Nastos, P.T., 28. Spatial and temporal variability of rain intensity in Greece. Proceedings of 8th International Hydrogeological Congress, Athens, pp. 651 66. Nastos, P.T., Matsangouras, J.T., 2. Tornado activity in Greece within the 2th century. Adv. Geosci. 26, 49 51. Nastos, P.T., Zerefos, C.S., 27. On extreme daily precipitation totals at Athens, Greece. Adv. Geosci., 59 66. Nastos, P.T., Zerefos, C.S., 28. Decadal changes in extreme daily precipitation in Greece. Adv. Geosci. 16, 55 62. Nastos, P.T., Zerefos, C.S., 29. Spatial and temporal variability of consecutive dry and wet days in Greece. Atmos. Res. 94, 616 628. Orlandini, S., Morlini, I., 2. Artificial neural network estimation of rainfall intensity from radar observations. J. Geophys. Res. 5 (D2), 24849 24861. Paliatsos, A.G., Nastos, P.T., Tzavelas, G., Panagiotakos, D.B., 25. Characteristics of precipitation in Athens area, Greece. Fresenius Environ. Bull. 14 (5), 422 428. Papanastasiou, D.K., Melas, D., Kioutsioukis, I., 27. Development and assessment of neural network and multiple regression models in order to predict PM levels in a medium-sized Mediterranean city. Water Air Soil Pollut. 182, 325 334. Philandras, C.M., Nastos, P.T., Paliatsos, A.G., Repapis, C.C., 2a. Study of the rain intensity in Athens and Thessaloniki, Greece. Adv. Geosci. 23, 37 45. Philandras, C.M., Douvis, K.C., Nastos, P.T., Tselioudis, G.B., Zerefos, C.S., 2b. Study of the precipitation trends in the Mediterranean region. Proceedings of the th Conference on Climatology, Meteorology and Atmospheric Physics (COMECAP2), 25 28/5/2, Patras, Greece, pp. 785 792 (in Greek). Queralt, S., Hernández, E., Barriopedro, D., Gallego, D., Ribera, P., Casanova, C., 29. North Atlantic Oscillation influence and weather types associated with winter total and extreme precipitation events in Spain. Atmos. Res. 94, 675 683. Rosenblatt, F., 1958. The Perceptron: a probabilistic model for information storage and organization in the brain. Psychol. Rev. 65 (6), 386 48. Sahai, A.K., Soman, M.K., Satyan, V., 2. All India summer monsoon rainfall prediction using an artificial neural network. Clim. Dyn. 16, 291 32. Sakellariou, N.K., Kambezidis, H.D., 24. Prediction of the total rainfall amount during August and November in the Athens area, Greece. Fresenius Environ. Bull. 13 (3), 289 292. Sengorur, B., Dogan, E., Koklu, R., Samandar, A., 26. Dissolved oxygen estimation using artificial neural network for water quality control. Fresenius Environ. Bull. 15 (9), 64 67. Silverman, D., Dracup, J.A., 2. Artificial neural networks and long-range precipitation predictions in California. J. Appl. Meteorol. 39 (1), 57 66. Sokol, Z., Bližňák, V., 29. Areal distribution and precipitation altitude relationship of heavy short-term precipitation in the Czech Republic in the warm part of the year. Atmos. Res. 94, 652 662. Solomon, S., Plattner, G.-K., Knutti, R., Friedlingstein, P., 29. Irreversible climate change due to carbon dioxide emissions. PNAS 6 (6), 174 179. Tzavelas, G., Paliatsos, A.G., Nastos, P.T., 2. Models for exceedances over high thresholds of the precipitation totals over Athens. Greece. Nat. Hazard Earth Syst., 5 8. Walker, S.E., Slordal, H.L., Guerreiro, C., Gram, F., Gronskei, E.K., 1999. Air pollution exposure monitoring and estimation Part II. Model evaluation and population exposure. J. Environ. Monit. 1, 321 326. Wardah, T., Abu Bakar, S.H., Bardossy, A., Maznorizan, M., 28. Use of geostationary meteorological satellite images in convective rain estimation for flash-flood forecasting. J. Hydrol. 356, 283 298. Werbos, P., 1974. Beyond regression: new tools for prediction and analysis in the behavioural sciences. Ph.D. dissertation, Committee on Applied Mathematics, Harvard University, Cambridge, MA. Willmott, C.J., Ackleson, S.G., Davis, R.E., Feddema, J.J., Klink, K.M., Legates, D.R., O'Donnell, J., Rowe, C., 1985. Statistics for the evaluation and comparison of models. J. Geophys. Res. 9, 8995 95. Wilmott, C.J., 1982. Some comments on the evaluation of model performance. Bull. Am. Meteorol. Soc. 63 (11), 139 1313. Zwick, A., Canarelli, P., 1996. Climate sensitivity analysis using neural networks. Fresenius Environ. Bull. 5 (11/12), 7 75. Zwiers, F.W., Von Storch, H., 24. On the role of statistics in climate research. Int. J. Climatol. 24, 665 68.