Optimization of neural networks for precipitation analysis in a humid region to detect drought and wet year alarms

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1 METEOROLOGICAL APPLICATIONS Meteorol. Appl. 23: (2016) Published online 25 November 2015 in Wiley Online Library (wileyonlinelibrary.com) DOI: /met.1533 Optimization of neural networks for precipitation analysis in a humid region to detect drought and wet year alarms Mohammad Valipour* Young Researchers and Elite Club, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran ABSTRACT: In this study, annual precipitation was forecast by coding in MATLAB software environment based on a non-linear autoregressive neural network (NARNN), non-linear input output (NIO) and NARNN with exogenous input (NARNNX). Historical precipitation data (27 precipitation gauge stations located in Gilan, Iran) were used as two 21 year sets from 1968 to 1988 and from 1989 to 2009 for calibration and testing of the networks, respectively. Results showed that the accuracy of the NARNNX was better than that of the NARNN and NIO, based on r values. However, performance of the networks was not satisfactory because the number of neurons in the hidden layer and the roles of training, validation and testing phases were lacking flexibility and change. Optimization of the number of neurons in the hidden layer and the determination of the best role among the different phases led to improvement of network accuracy. The r values were <0.73 only for five stations in the optimized NARNN and <0.74 only for those stations with optimized NIO. KEY WORDS drought alarm; forest cover; meteorological conditions; seasonal trend; wet year alarm Received 4 February 2015; Revised 9 June 2015; Accepted 21 June Introduction Precipitation plays an important role in the global energy and water cycle. An accurate knowledge of precipitation amounts reaching the land surface is of special importance for fresh water assessment and management related to land use, agriculture and hydrology, including the risk reduction of flood and drought (Schneider et al., 2011). Therefore, several studies have been performed on precipitation analysis. Yu et al. (2006) evaluated long-term trends in annual and seasonal precipitation in Taiwan. Valipour (2012) identified critical areas for agricultural water management in Iran based on the region s annual rainfall and showed that five synoptic stations in Iran had a relative error of >20%. Thus, agricultural water management and selection of cropping pattern should be performed very carefully in these five areas. Hasan and Dunn (2010) presented a simple Poisson gamma model for forecasting rainfall occurrence and amount of precipitation simultaneously. Their model allowed for a disaggregation of the monthly rainfall into the number of rainfall events per month and the mean amount of rainfall per event. Burlando et al. (1993) forecasted short-term rainfall using Auto regressive moving average (ARMA) models. Their results showed that the event-based estimation approach yields better forecasts. Other useful methods for precipitation analysis are Tropical rainfall measuring mission (TRMM) Multi-satellite Precipitation Analysis (Pombo et al., 2014; Dasari and Salgado 2015), fuzzy technique (Yu et al., 2004; Hasan et al., 2008; Kisi and Shiri, 2011; Kisi and Shiri, 2012; Rossi et al., 2014), radar data method (Burlando et al., 1996; Korsholm et al., 2015) and spatial and temporal variability analyses (Wagesho et al., 2013; * Correspondence: M. Valipour, Young Researchers and Elite Club, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran. vali-pour@hotmail.com Foresti and Seed, 2015; Kim and Lee, 2015; Wu et al., 2015). On the other hand, although there are many methods to model hydrological phenomena (Valipour and Eslamian, 2014; Valipour, 2014a, 2014b, 2014c, 2015a, 2015b, 2015c; Mahdizadeh Khasraghi et al., 2015; Rahimi et al., 2015; Valipour et al., 2015a, 2015b), artificial neural network (ANN) is a powerful model for agricultural and forest meteorology analysis. Banihabib et al. (2012) and Valipour et al. (2012a, 2012b, 2013) forecasted the inflow using ARMA, Auto regressive integrated moving average (ARIMA) and ANN models. They showed that the ANN model was more accurate than the ARMA and ARIMA models. The river flow was simulated by using ANN models in many studies (Cigizoglu, 2005; Kisi and Cigizoglu, 2007). There are several studies in which the rainfall values are forecasted using ANNs. However, the advantage of the current study is the optimization of the networks to enhance forecasting, especially during peak points. The importance of precipitation analysis has been addressed in many previous studies. In some of the mentioned studies, ANNs had a better accuracy than the other methods such as linear and non-linear regression, ARMA and ARIMA. However, the effect of the region s climate has not been considered in many cases and the trend of precipitation has not been studied in detail. On the other hand, the use of ANN models has not been shown to improve initial forecasts. In addition, it does not attempt to increase the network accuracy as well, especially in cases where the observation data is less. In humid regions, wet year occurrence seems more likely; however, climate change in recent years indicates that it is not always true. Figure 1 shows the condition of agricultural and paddy fields in Gilan. In 2008 there was a drought, but >1000 hectares of farm fields were destroyed in this region only after 4 years, because of wet year occurrence in Contrasting climate conditions (drought and wet years) reveal a need for more attention towards optimization of the methods used for precipitation analysis and consequently for achieving more accurate forecasting Royal Meteorological Society

2 92 M. Valipour Figure 1. Conditions of agricultural and paddy fields in Gilan. 2. Materials and methods In this study, the annual data of 27 precipitation gauge stations and their average (as average of Gilan precipitation) were applied to three different structures of ANNs for compression and optimization. Precipitation data from 1968 to 1988 and from 1989 to 2009 were used for the training and testing phases, respectively. The non-linear autoregressive neural network (NARNN) is identified as follows (MATLAB Toolboxes, 2010): ( ) P F = f,, P (t i) (1) P (t 1) F where P F is the forecasted precipitation, t is the time step and i is the number of past time steps. This structure was applied to cases where the available data was less. In this state, there is no input set and precipitation data related to the output set are used as input with a time delay. In addition, the non-linear input output (NIO) is identified as follows (MATLAB Toolboxes, 2010): ( P F = f P (t 1) O F ),, P (t i) where P O is the observed precipitation. This structure is applied for cases where previous values of P F will not be available when deployed. In addition, the NARNN with exogenous input (NARNNX) was applied for increasing the accuracy of forecasting as follows (MATLAB Toolboxes, 2010): ( P F = f P (t 1) O,, P (t i) O O, P(t 1) F ),, P (t i) In each of the three structures, the numbers of neurons in input, hidden and output delays were 1, 50 and 1, respectively. In addition, the number of epoch and delay was 1 and the sigmoid activity function (due to its better performance than linear, radial and tangent activity functions) was used. The output of the ANN includes two decades of forecasted precipitation data from 1990 to 2009 because of a delay that occurred in the neural network. In the network design, 70% of precipitation data were considered for training, 15% for validation and 15% for testing. The best number of neurons in the hidden layer was determined for all F (2) (3) structures for increasing the accuracy of forecasting, especially during peak points. In addition, the role of each phase was modified and the optimized values were obtained for training, validation and testing stages. Other information (temperature in C and forest cover for Gilan) was gathered for analysing the results and for better discussion about the performance of the ANN in each station. Precipitation isohyet, isothermal and forest cover maps for the study area were designed using the above-mentioned information and precipitation data. The r index was calculated as follows: r = ( ) nσp F ΣP O ΣP F ΣP O (nσp 2F ( ) ) ΣP F ( nσp 2 O ( ) ) ΣP O (4) where n = 20 is the number of forecasted data (from 1990 to 2009). However, Equation (4) could not be used during peak points because of point-to-point compression for scrutiny of the performance of initial and optimized models. For this purpose, the relative error index was used as follows: RE = 100 ( ) P F P O P 1 (5) O where RE(%) is the relative error. The training phase was performed using the Levenberg-Marquardt backpropagation in the ANN and the total value for the stages was assessed for designing the initial and optimized ANNs by coding in MATLAB software environment. A short section of the coded program has been presented in the Appendix for optimized NARNNX. 3. Results and discussion The results obtained from the programmed networks in the MATLAB environment are indicated in Figure 2 for the best structure (NARNNX). For the NARNN, the minimum r value was 0.50 for the Masuleh station, the maximum r value was 0.69 for the

3 Precipitation analysis in humid regions 93 Figure 2. Observed precipitation amounts (mm) versus non-linear autoregressive neural network with exogenous input (NARNNX) for all the stations and their average (Gilan) Royal Meteorological Society Meteorol. Appl. 23: (2016)

4 94 M. Valipour Table 1. Obtained results in optimized NARNN for the best values of the number of neurons in the hidden layer and the role of each phase in the network structure. Table 2. Obtained results in optimized NIO for the best values of the number of neurons in the hidden layer and the role of each phase in the network structure. Station name Number of neurons in hidden layer Training Validation Testing r Station name Number of neurons in hidden layer Training Validation Testing r Loshan Nav Masuleh Astara Shirabad Tutkabon Kalaj Tutaki Kolchal Abvier Shahrbijar Lemir Rasht Astaneh Anzali Parudbar Kharjegil Manjil Masal Haratbar Shalman Ghalerudkhan Kasma Gilvan Bashmahaleh Mashinkhaneh Hashtpar Gilan Loshan Nav Masuleh Astara Shirabad Tutkabon Kalaj Tutaki Kolchal Abvier Shahrbijar Lemir Rasht Astaneh Anzali Parudbar Kharjegil Manjil Masal Haratbar Shalman Ghalerudkhan Kasma Gilvan Bashmahaleh Mashinkhaneh Hashtpar Gilan Mashinkhaneh station and the average r value was 0.67 for Gilan. For the NIO, the minimum r value was 0.51 for the Kharjegil and Bahsmahaleh stations, and the maximum r value was 0.68 for the Lemir station and the average r value was 0.64 for Gilan. These results indicate that the r values were always <0.70 in the NARNN and the NIO. As shown in Figure 2, for the NARNNX, the minimum r value was 0.46 for the Shalman station, the maximum rvalue was 0.94 for the Shirabad and Anzali stations and the average r value was 0.82 for Gilan. These findings imply that the r values were always >0.70 in the NARNNX except in the Shalman station. The accuracy of the NARNNX was better than that of the NARNN and the NIO; however, according to Figure 2, the performance of the NARNNX was not acceptable during peak points. The forecasted precipitations were much lower than their observed values in the Masuleh, Kalaj and Mashinkhaneh stations and were much higher than their observed values in the Kalaj, Kolchal, Lemir, Manjil, Ghalerudkhan, Kasma and Bashmahaleh stations, for the peak points. However, according to Figure 2, the NARNNX was suitable for limited agricultural schedule, but increasing the accuracy of the ANN was required for better forecasting in order to deal with natural disasters, as shown in Figure 1. For this purpose, the ANN was optimized by using improved structures. After evaluation of the possible parameters for optimization, it was found that the best value for the number of epoch, delay and neurons of input and output layers was 1 and also the ability of the sigmoid activity function was better than the radial, linear and tangent, and only the number of neurons in the hidden layer and the role of training, validation and testing phases were changeable. Thus, the networks were optimized by revision of written codes for the initial ANN, and the best values were obtained for the structures. Tables 1 3 show the obtained r values for the optimized ANN. Performance of all the ANNs was improved by increasing the number of neurons in the hidden layer. The best r values belonged to the Shahrbijar (0.87), Abvier (0.88) and Abvier (0.99) stations for the optimized NARNN (193 neurons), the optimized NIO (269 neurons) and the optimized NARNNX (144 neurons), respectively, which had the most number of neurons in the hidden layer. However, the number of neurons in the hidden layer had increased in the NARNN and the NIO than in the NRANNX, but the accuracy of the NARNNX was more than that of other methods due to the roles of the training, validation and testing phases. According to Table 3, 90% of the data were used for network training in many stations. However, this amount was 80% in the NARNN (Table 2) only for the Shahrbijar station and <80% for the other stations, and the maximum amount was 65% for network training in the NIO. Figure 3 shows the structure of the optimized ANN for precipitation analysis in Gilan. The duration of the training phase was decreased (by 70% of that in the initial ANN) in the optimized NIO because of not using the outputs of the model (lack of autoregressive effect). In this case, over-training occurs for more training, and the accuracy of forecasting decreases. The duration of the training phase was increased (only 5%) in optimized NARNN because

5 Precipitation analysis in humid regions 95 Table 3. Obtained results in the optimized NARNNX for the best values of the number of neurons in the hidden layer and the role of each phase in the network structure. Station name Number of neurons in hidden layer Training Validation Testing Loshan Nav Masuleh Astara Shirabad Tutkabon Kalaj Tutaki Kolchal Abvier Shahrbijar Lemir Rasht Astaneh Anzali Parudbar Kharjegil Manjil Masal Haratbar Shalman Ghalerudkhan Kasma Gilvan Bashmahaleh Mashinkhaneh Hashtpar Gilan of using output with a delay as the input. More training led to over-training also because of using limited data (lack of input layer) in the NARNN. Finally, the duration of the training phase was increased by 90% in the optimized NARNNX because of the simultaneous impact of the input layer and using output with a delay as the input. Therefore, the r values were >0.90 in all of the precipitation gauge stations in Gilan because of adequate training (not over-training). The accuracy of forecasting was improved in the optimized NARNNX, especially during peak points. Better forecasting of the optimized NARNNX is undetectable in the Kalaj, Kolchal, Lemir, Parudbar, Ghalerudkhan and Kasma stations when compared with the initial NARNN. In addition, a better comparison between the initial and the optimized ANN can be done using Figure 4. According to Figure 4, the relative errors were decreased in the optimized ANN than in the initial ANN during However, the amounts of decrease were more in the optimized NARNNX. Performance of the optimized NARNNX improved significantly in 1994, 1998, 2000, 2002, 2003 and 2007 than the initial NARNNX. However, the initial NARNNX had a better forecasting for 1990, 2004 and 2008 than the optimized NARNNX. Although the error was increased in the optimized NARNNX than in the initial NARNNX for the minimum precipitation in 2008, it would not cause a problem if the necessary measures are implemented in the drought year because of lower forecasting by the optimized NARNNX (P F < P O ). However, the amounts of precipitation were forecast to be more than the r observed precipitation in the peak year of optimized NARNN and optimized NIO (2008). Therefore, there could be more damage to the agricultural fields than expected, if the optimized NARNN and optimized NIO are used. However, Figure 4 confirms the drought occurrence shown in Figure 1 for Figure 4 also compares the initial and optimized ANNs for average of Gilan; however, Table 4 can be used for evaluating the performance of the ANN during the peak points of the precipitation gauge stations. Selection criteria for the peak points were the mean of precipitation for each station, as in Table 4. Precipitations that were more than twice the mean were selected as peak points with wet year alarm, and precipitations that were less than half of the mean were selected as peak points with drought alarm. The relative errors were decreased in the optimized ANN rather than in the initial ANN, except in one case related to the optimized NARNNX in the Loshan precipitation gauge station for Therefore, the optimized ANN had appropriate proficiency in peak precipitation forecasting. However, the amounts of relative error were high for the NARNNX and the NIO in some stations even in optimized structures. Comparison of the average of relative errors indicated that RE NARNN < RE NARNNX < RE NIO and optimized RE NARNN < optimized RE NARNNX < optimized RE NIO. This implies that the NARNN had a better performance than the NIO and even the NARNNX in peak point forecasting. The reason for this observation could be related to the input data to the ANN. According to Figure 3, the input data included 21 annual precipitations from 1968 to 1989 as an input layer in the NARNNX and the NIO, but the input data that entered the network included output data without delay as the input layer in the NARNN. As only one peak was observed (389.5 mm related to the Mashinkhaneh station in 1982), based on Table 4, for annual precipitation data from 1968 to 1989, when there was no peak precipitation forecasting in the input data of the ANN in Loshan, Kalaj, Parudbar, Manjil and Gilvan stations, the NARNNX and the NIO were trained based on these data. Thus, they did not expect any peak precipitation to occur during However, the NARNN was trained better than the NARNNX and the NIO due to the lack of input layer and the use of annual precipitations from 1968 to 1989, and it could forecast peak points of precipitation for the gauge stations with a relative error <10% of the optimized structure. The NARNN is superior to the NARNNX and the NIO in cases where the input data lacked peak points, because of more suitable training. According to Table 4, 1994 was reported as wet year alarm twice (Parudbar and Gilvan) and Figure 5 also shows that the amount of precipitation in this year was higher than that of other years (except 1993), for the average of Gilan. In addition, 2008 has also been reported twice for the Loshan and Manjil stations, but in the context of drought alarm, Figures 1 and 4 show that the average of Gilan had similar conditions in this year. However, although 1999 was reported in all the stations in Table 4 (except Mashinkhaneh) as drought year, Figure 4 shows that this year has a mean precipitation as the average of Gilan (not minimum). Table 4 shows that these stations had a different situation than other precipitation gauge stations, especially in The data about climate and location of each station were gathered for a more detailed study about precipitation gauge stations in Gilan, and then Figure 5 was obtained by using this information. According to Figure 5, the Loshan, Kalaj, Parudbar, Manjil and Gilvan stations are in the south of Gilan with precipitations <400 mm (the minimum of precipitation), temperature >16.5 C (the maximum of temperature) and without forest cover (the poorest stations of forest cover). This information indicates that

6 96 M. Valipour Figure 3. Structure of optimized artificial neural network (ANN) for precipitation analysis in Gilan; w reflects the weight vector and b reflects the bias vector. NARNN, non-linear autoregressive neural network; NARNNX, NARNN with exogenous input; NIO, non-linear input output. Table 4. Relative errors of ANN for the peak points at the precipitation gauge stations. Station name Year of occurrence Peak value (mm) Alarm type NARNN (%) Optimized NARNN (%) NIO (%) Optimized NIO (%) NARNNX (%) Optimized NARNNX (%) Loshan Drought Drought Kalaj Drought Wet year Parudbar Wet year Drought Manjil Drought Drought Gilvan Wet year Drought Mashinkhaneh Drought This is related to the training data Average the conditions of these stations are distinct from those of other stations of Gilan, which is a humid region. Tables 1 3 also show that the accuracy of optimized ANN was low for these five stations. The r values were <0.73 only for these stations in the optimized NARNN (Table 1) and they were <0.74 only for these stations in the optimized NIO (Table 2). However, according to Figure 5, the r values were >0.80 for Tutaki (precipitation >1400 mm), Ghalerudkhan (precipitation >1500 mm) and Anzali stations (precipitation >1700 mm), in the optimized ANN (Tables 1 3). This implies that the performance of the optimized ANN was satisfactory even in high precipitation stations except these five stations. Figure 5 and Tables 1 4 show that not only the probability of wet years and drought occurrences was low (Table 4) in stations near to the Caspian Sea or stations located in areas with appropriate forest cover because of climate stabilization (the lack of abrupt changes of weather), but rather the precipitation forecasting was also more accurate (Tables 1 3).

7 Precipitation analysis in humid regions 97 Figure 4. Observed precipitation (mm) and amounts of relative error in initial and optimized ANN for the average of Gilan. NARNN, non-linear autoregressive neural network; NARNNX, NARNN with exogenous input; NIO, non-linear input output. 4. Conclusion In this study, the ability of three different structures of artificial neural network (ANN), the non-linear autoregressive neural network (NARNN), the non-linear input output (NIO) and the NARNN with exogenous input (NARNNX) was compared with the annual precipitation forecasting in Gilan. All the models were optimized by determining the best number of neurons in the hidden layer and the role of each phase (training, validation and testing) based on the number of data dedicated to them for increasing the accuracy of forecasting, especially during the peak points. The results showed that optimized NARNN and optimized NIO were more sensitive to the duration of network training than optimized NRANNX because of the lack of input layer and autoregressive effect, respectively. The NARNN was suitable for cases where the number of available data for precipitation analysis was limited or peak points were not observed in recorded precipitation data, implying that the NARNNX could be used for other conditions. It could also be applied successfully for precipitation forecasting for the 20 next years with an r value >0.90. The results also showed that optimized ANNs are applicable not only for the case study but also for all humid regions with various precipitation ranges (based on the performance of three different structures in the mentioned conditions). In

8 98 M. Valipour Figure 5. Location of precipitation gauge stations and climate conditions in Gilan; (a) precipitation isohyet map (mm), (b) isothermal map ( C) and (c) forest cover map. addition, the analysis of peak precipitation shows that deforestation creates difficulty for forecasting processes by disrupting the region s ecosystem and increasing the probability of wet years and drought occurrences and causes more damage to the agricultural fields. The distinguishing aspect of this study is the optimization of ANNs to increase the accuracy of forecasting peak points, which indicates the advantages of the work compared with other investigations in different domains of hydrology without accurate evaluations of peak points (Ju et al., 2009; Maier et al., 2010; Valipour and Montazar, 2012a, 2012b; Valipour, 2015 Royal Meteorological Society 2014d, 2014e, 2015d, 2015e, 2015f, 2015g, 2015h; Kan et al., 2015). Appendix inputseries = tonndata(narnnx_valipour1,false,false); targetseries = tonndata(narnnx_valipour2,false,false); inputdelays = 1:1; feedbackdelays = 1:1; hiddenlayersize = 129; Meteorol. Appl. 23: (2016)

9 Precipitation analysis in humid regions 99 net = narxnet(inputdelays,feedbackdelays,hiddenlayersize); net.inputs{1}.processfcns = { removeconstantrows, mapminmax }; net.inputs{2}.processfcns = { removeconstantrows, mapminmax }; [inputs,inputstates,layerstates,targets] = preparets(net, inputseries,{},targetseries); net.dividefcn = dividerand ; net.dividemode = value ; net.divideparam.trainratio = 90/100; net.divideparam.valratio = 5/100; net.divideparam.testratio = 5/100; net.trainfcn = trainlm ; net.performfcn = mse ; net.plotfcns = { plotperform, plottrainstate, plotresponse, ploterrcorr, plotinerrcorr }; [net,tr] = train(net,inputs,targets,inputstates,layerstates); outputs = net(inputs,inputstates,layerstates); errors = gsubtract(targets,outputs); performance = perform(net,targets,outputs) traintargets = gmultiply(targets,tr.trainmask); valtargets = gmultiply(targets,tr.valmask); testtargets = gmultiply(targets,tr.testmask); trainperformance = perform(net,traintargets,outputs) valperformance = perform(net,valtargets,outputs) testperformance = perform(net,testtargets,outputs) view(net) netc = closeloop(net); netc.name = [net.name - Closed Loop ]; view(netc) [xc,xic,aic,tc] = preparets(netc,inputseries,{},targetseries); yc = netc(xc,xic,aic); closedloopperformance = perform(netc,tc,yc) nets = removedelay(net); nets.name = [net.name - Predict One Step Ahead ]; view(nets) [xs,xis,ais,ts] = preparets(nets,inputseries,{},targetseries); ys = nets(xs,xis,ais); earlypredictperformance = perform(nets,ts,ys) References Banihabib ME, Valipour M, Behbahani SMR Comparison of autoregressive static and artificial dynamic neural network for the forecasting of monthly inflow of Dez reservoir. J. Environ. Sci. Technol. 13(4): Burlando P, Montanari A, Ranzi R Forecasting of storm rainfall by combined use of radar, rain gages and linear models. Atmos. Res. 42(1 4): Burlando P, Rosso R, Cadavid LG, Salas JD Forecasting of short-term rainfall using ARMA models. J. Hydrol. 144(1 4): Cigizoglu HK Generalized regression neural network in monthly flow forecasting. Civil Eng. Environ. Syst. 22(2): Dasari HP, Salgado R Numerical modelling of heavy rainfall event over Madeira Island in Portugal: sensitivity to different micro physical processes. Meteorol. Appl. 22: Foresti L, Seed A On the spatial distribution of rainfall nowcasting errors due to orographic forcing. Meteorol. Appl. 22: Hasan MM, Dunn PK A simple Poisson gamma model for modelling rainfall occurrence and amount simultaneously. Agric. For. Meteorol. 150(10): Hasan M, Tsegaye T, Shi X, Schaefer G, Taylor G Model for predicting rainfall by fuzzy set theory using USDA scan data. Agric. Water Manage. 95(12): Ju Q, Yu Z, Hao Z, Ou G, Zhao J, Liu D Division-based rainfall-runoff simulations with BP neural networks and Xinanjiang model. Neurocomputing 72(13): Kan G, Yao C, Li Q, Li Z, Yu Z, Liu Z, et al Improving event-based rainfall-runoff simulation using an ensemble artificial neural network based hybrid data-driven model. Stoch. Environ. Res. Risk Assess., 29(5): Kim DK, Lee D Atmospheric thickness and vertical structure properties in wintertime precipitation events from microwave radiometer, radiosonde and wind profiler observations. Meteorol. Appl. 22: , DOI: /met Kisi O, Cigizoglu HK Comparison of different ANN techniques in river flow prediction. Civil Eng. Environ Syst. 24(3): Kisi O, Shiri J Precipitation forecasting using wavelet-genetic programming and wavelet-neuro-fuzzy conjunction models. Water Resour. Manage. 25(13): Kisi O, Shiri J Reply to discussion of Precipitation forecasting using wavelet-genetic programming and wavelet-neuro-fuzzy conjunction models. Water Resour. Manage. 26(12): Korsholm US, Petersen C, Sass BH, Nielsen NW, Jensen DG, Olsen BT, et al A new approach for assimilation of 2D radar precipitation in a high-resolution NWP model. Meteorol. Appl. 22: Mahdizadeh Khasraghi M, Gholami Sefidkouhi MA, Valipour M Simulation of open- and closed-end border irrigation systems using SIRMOD. Arch. Agron. Soil Sci. 61(7): Maier HR, Jain A, Dandy GC, Sudheer KP Methods used for the development of neural networks for the prediction of water resource variables in river systems: current status and future directions. Environ. Model Softw. 25(8): MATLAB Toolboxes MATLAB/Toolboxes/Neural Network. Version (R2010b). (accessed 25 June 2010). Pombo S, de Oliveira RP, Mendes A Validation of remote-sensing precipitation products for Angola. Meteorol. Appl. 22: , DOI: /met Rahimi S, Gholami Sefidkouhi MA, Raeini-Sarjaz M, Valipour M Estimation of actual evapotranspiration by using MODIS images (a case study: Tajan catchment). Arch. Agron. Soil Sci. 61(5): Rossi PJ, Hasu V, Koistinen J, Moisseev D, Makela A, Saltikoff E Analysis of a statistically initialized fuzzy logic scheme for classifying the severity of convective storms in Finland. Meteorol. Appl. 21(3): Schneider U, Becker A, Meyer-Christoffer A, Ziese M, Rudolf B Global precipitation analysis products of the GPCC. Global Precipitation Climatology Centre (GPCC), Deutscher Wetterdienst, Offenbach a. M., Germany. Valipour M Critical areas of iran for agriculture water management according to the annual rainfall. Eur. J. Sci. Res. 84(4): Valipour M. 2014a. Drainage, waterlogging, and salinity. Arch. Agron. Soil Sci. 60(12): Valipour M. 2014b. Future of the area equipped for irrigation. Arch. Agron. Soil Sci. 60(12): Valipour M. 2014c. Application of new mass transfer formulae for computation of evapotranspiration. J. Appl. Water Eng. Res. 2(1): Valipour M. 2014d. Use of average data of 181 synoptic stations for estimation of reference crop evapotranspiration by temperature-based methods. Water Resour. Manage. 28(12): Valipour M. 2014e. Temperature analysis of reference evapotranspiration models. Meteorol. Appl. 22: , DOI: /met Valipour M. 2015a. Comparative evaluation of radiation-based methods for estimation of potential evapotranspiration. J. Hydrol. Eng. 20(5): Valipour M. 2015b. Importance of solar radiation, temperature, relative humidity, and wind speed for calculation of reference evapotranspiration. Arch. Agron. Soil Sci. 61(2): Valipour M. 2015c. Long-term runoff study using SARIMA and ARIMA models in the United States. Meteorol. Appl. 22: , DOI: /met Valipour M. 2015d. Evaluation of radiation methods to study potential evapotranspiration of 31 provinces. Meteorol. Atmos. Phys. 127(3): Valipour M. 2015e. A comprehensive study on irrigation management in Asia and Oceania. Arch. Agron. Soil Sci. 61(9): Valipour M. 2015f. Future of agricultural water management in Africa. Arch. Agron. Soil Sci. 61(7): Valipour M. 2015g. Study of different climatic conditions to assess the role of solar radiation in reference crop evapotranspiration equations. Arch. Agron. Soil Sci. 61(5):

10 100 M. Valipour Valipour M. 2015h. Investigation of Valiantzas evapotranspiration equation in Iran. Theor. Appl. Climatol., 121(1 2): Valipour M, Banihabib ME, Behbahani SMR. 2012a. Monthly inflow forecasting using autoregressive artificial neural network. J. Appl. Sci. 12(20): Valipour M, Banihabib ME, Behbahani SMR. 2012b. Parameters estimate of autoregressive moving average and autoregressive integrated moving average models and compare their ability for inflow forecasting. J. Math. Stat. 8(3): Valipour M, Banihabib ME, Behbahani SMR Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir. J. Hydrol. 476: Valipour M, Eslamian S Analysis of potential evapotranspiration using 11 modified temperature-based models. Int. J. Hydrol. Sci. Technol. 4(3): Valipour M, Gholami Sefidkouhi MA, Eslamian S. 2015a. Surface irrigation simulation models: a review. Int. J. Hydrol. Sci. Technol. 5(1): Valipour M, Montazar AA. 2012a. Optimize of all effective infiltration parameters in furrow irrigation using visual basic and genetic algorithm programming. Aust. J. Basic Appl. Sci. 6(6): Valipour M, Montazar AA. 2012b. Sensitive analysis of optimized infiltration parameters in SWDC model. Adv. Environ. Biol. 6(9): Valipour M, Ziatabar Ahmadi M, Raeini-Sarjaz M, Gholami Sefidkouhi MA, Shahnazari A, Fazlola R, et al. 2015b. Agricultural water management in the world during past half century. Arch. Agron. Soil Sci. 61(5): Wagesho N, Goel NK, Jain MK Temporal and spatial variability of annual and seasonal rainfall over Ethiopia. Hydrol. Sci. J. 58(2): Wu M, Lam H, Li K Characterization and indexing of heavy rainstorms in Hong Kong. Meteorol. Appl. 22: Yu PS, Chen ST, Wu CC, Lin SC Comparison of grey and phase-space rainfall forecasting models using a fuzzy decision method. Hydrol. Sci. J. 49(4): Yu PS, Yang TC, Kuo CC Evaluating long-term trends in annual and seasonal precipitation in Taiwan. Water Resour. Manage. 20(6):