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1 ATMOS-252; No of Pages 8 Atmospheric Research xxx (211) xxx xxx Contents lists available at SciVerse ScienceDirect Atmospheric Research journal homepage: 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 Athens, Greece b Department of Mechanical Engineering, Technological Education Institute of Piraeus, 25 Thivon and P. Ralli Str., GR 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 Athens, Greece d General Department of Mathematics, Technological Education Institute of Piraeus, 25 Thivon and P. Ralli Str., GR 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 ( ). 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 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 , Athens, Greece. Tel./fax: address: (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 /$ see front matter 211 Elsevier B.V. All rights reserved. doi:.16/j.atmosres

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 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 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 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 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 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 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).

3 P.T. Nastos et al. / Atmospheric Research xxx (211) xxx xxx 3 Fig. 1. Typical artificial neural network architecture (Caudill and Butler, 1992) 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: E, latitude: N, altitude: 7 m a.m.s.l.), during the 111- year period ( ). 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, ) 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 February March April May June July August September October November December 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 mm/day, PC=1 for mm/day, PC=2 for mm/day, PC=3 for mm/day and PC=4 for 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 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 ( ) 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 These data were not available. So, the ANNs training starts from the fifth month (May) of the year 1899.

4 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= PC=2 PC=1 PC=1 PC= PC= PC= 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 =11 (Table 1). Simultaneously, the Cumulative expected incidence rate with rain intensityn= 14.4 mm/day for the next four months has the value =19.8 (Table 1) and so on 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

5 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 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 , 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 Fig. 3. Time series of mean annual rain intensity along with 5-year moving average (solid line) at NOA, for the period

6 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 Year b 25 Observed maximum monthly rain intensity Predicted maximum monthly rain intensity c Year Observed minimum monthly rain intensity Predicted minimum monthly rain intensity 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.

7 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 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) MBE (mm/day) RMSE (mm/day) IA R 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. 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