Evaluation of WRF and Artificial Intelligence Models in Short-Term

J. Earth Syst. Sci. (2020) 129:188 Ó Indian Academy of Sciences

https://doi.org/10.1007/s12040-020-01450-9 (0123456789().,-volV)(0123456789().,-volV)

Evaluation of WRF and artiBcial intelligence models in short-term rainfall, temperature and Cood forecast (case study)

1 1, 1 EMADEDDIN SHIRALI ,ALIREZA NIKBAKHT SHAHBAZI * ,HOSSEIN FATHIAN , 1 2 NARGES ZOHRABI and ELHAM MOBARAK HASSAN 1Department of Water Resources Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran. 2Department of Environment, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran. *Corresponding author. e-mail: [email protected] [email protected]

MS received 16 July 2019; revised 25 May 2020; accepted 26 May 2020

Flood prediction is very critical for eDcient use of Cood control reservoirs, and earthen and concrete levees systems. As a result, Cood prediction has a great importance in catchment areas. In this study, rainfall and air temperature were predicted in Karun-4 basin in southwest of Iran by using three different models including WRF numerical model, ANN, and SVM model in order to evaluate accuracy in Cood forecasting. The rainfall and air temperature prediction and Cood forecasting results using different schemas of WRF model indicated that MYJLG schema has more accuracy than other schemas. Partial mutual information (PMI) algorithm was used in order to determine the eAective input variables in ANN and SVM models. The results of using PMI algorithm showed that rainfall at rain gauge stations in the next 6 hrs indicated that the eAective variables included relative humidity, current rain status (present rainfall), rainfall in 6 hrs ago, and rainfall and temperature of 12 hrs ago. Also, the PMI algorithm results for predicting air temperature in the next 6 hrs showed that the eAective input variables including the temperature of 18 hrs ago, current temperature, temperature of 12 hrs ago, and temperature of 6 hrs ago. The comparison between the peak discharge and runoA height values of the predicted Cood hydrograph in different models showed that SVM model had more eDciency and accuracy than the other two models in predicting rainfall, air temperature, and Cood hydrograph. Keywords. Rainfall prediction; WRF model; support vector machine; Cood events.

1. Introduction the reasons for developing the very short-term prediction systems along with the radar data use, An accurate Cood forecasting with long lead time in which lots of studies have been accomplished for could have a great value for Cood prevention and that Beld. Accurate Cood forecasting depends on utilization. The rainfall short-term prediction is accurate precipitation and temperature estimation. very important for watershed hydrologic forecast- Extremely heavy rainfall at shorter time scales ing with a short response time, especially, under is particularly difBcult to predict in mountainous the global warming and extreme weather condi- terrains, and continue to be a challenge to opera- tion. Warning of extreme atmospheric phenomena tional and research community (Das et al. 2008;Li like heavy rainfall caused by storms, is one of et al. 2017). Rainfall and temperature (two factors 188 Page 2 of 16 J. Earth Syst. Sci. (2020) 129:188 inCuencing Cood forecasting) are predicted by of May 2009 in Iran. This study result indicated different models. Many studies have been con- that the model skill differed in the rainfall predic- ducted for the precipitation forecast using diverse tion for different thresholds, and when the rainfall techniques including WRF models and remote threshold increased, model skill in predicting the sensing, statistical model, non-parametric nearest- rainfall amount would decrease. Sassanian et al. neighbours method, and soft computing-based (2015) evaluated the WRF model performance methods including artiBcial neural networks with nine different physical conBgurations, in order (ANN), support vector regression (SVR) and fuzzy to predict winter rainfall in southwest of Iran. logic (FL). The Weather Research and Forecasting The Cood forecasts can be obtained through the (WRF) model is a next-generation mesoscale forecasting system using the WRF’s precipitation numerical weather prediction system, which was as input. Only a few modelling studies have designed for both atmospheric research and oper- investigated rainfall forecast by WRF as an input ational forecasting requirements. The WRF model for hydrological models. Successful rainfall fore- method should be compared with other methods, casting can lead to accurate Cood forecasts through and at the end the best predicting Cood method an atmospheric hydrological modelling system in should be provided and applied by using the pre- real-time Cood forecasting (Wu et al. 2014; dicted rainfall data. In recent years, many Yesubabu et al. 2016). Zhou et al. (2018) investi- researchers around the world have begun studying gated WRF model for precipitation simulation and parameterization schemes for a mesoscale numeri- its application in real-time Cood forecasting in the cal weather predication system. Furthermore, with Jinshajiang River Basin. Results showed that the an instructive precipitation forecast (such as WRF one-way coupled hydro-meteorological model model) as the input of Cood forecast system, a Cood could be used for precipitation simulation and forecast with high precision and long lead time can Cood prediction in the Jinshajiang River Basin be estimated. Mourre et al. (2015) showed that the because of its relatively high precision and long WRF model was unrealistic for daily rainfall and lead time. Moser et al. (2015) selected 12 heavy largely overestimated the strong daily rainfall in rainfall events which were simulated by the Cordillera Blanca, Peru. Inaccurate rainfall pro- Weather Research and Forecasting model (WRF) duct also causes negative impacts on hydrological with data assimilation, and the distributed forecasts, especially in small mountainous catch- hydrological model CUENCAS was used to simu- ments with quick responses of runoA. Afandi et al. late the Coods caused by the 12 rainfall events. The (2013) investigated heavy rainfall events that results indicated that data assimilation could occurred over Sinai peninsula and caused Cash improve the WRF’s ability in capturing the char- Cood, using the WRF model. The test results acter of rainfall, providing more accurate guidance showed that the WRF model was able to capture for Cood warnings. Papadopoulos et al. (2009) also the heavy rainfall events over different regions of indicated that data assimilation can oAer sufBcient Sinai and predict rainfall in significant consistency information to increase the mesoscale model skill with in-situ measurement. Lu et al. (2016) used the and make the rainfall forecasts more suitable for WRF Model to conBrm the uncertainty of the rain operational Cood forecasting. Givati et al. (2012) prediction in Kinu watershed Brst, then will modify examined the horizontal separation eAect on the the WRF to suit the 6, 12, 24 hrs rainfall prediction WRF model rainfall accuracy to apply in runoA in Kinu watershed. Also, radar rainfall data will be prediction. They performed WRF model for eight employed to correct the WRF prediction in real- rainfall events and four different basins with hori- time meaning. Some successful rainfall forecast by zontal separation of 36, 12, 4, and 1.3 km, and WRF model causing Cash Coods also was investi- found that basins with a horizontal separation of gated in Iran. Taghavi et al. (2013) evaluated 4 and 1.3 km had a high correlation, in comparison 24- and 48-hr predictions of WRF-ARW numerical with the monitored rainfall; their correlation model in different regions of Iran, with quantitative coefBcient was calculated to be at 0.96 and 0.92. precipitation during one-month period in February Tian et al. (2019) examined WRF model and 2007. Results showed that model evaluation points the Hebei rainfall-runoA model together with the were better in predicting 24-hr rainfall predictions WRF three-dimensional variational (3DVar) data than the 48-hr rainfall predictions. Zakeri et al. assimilation module for Cood forecast. The results (2014) veriBed the WRF model output for the showed that the atmospheric–hydrological mod- rainfalls over the period from February to the end elling system can provide satisfactory Cood J. Earth Syst. Sci. (2020) 129:188 Page 3 of 16 188 forecasts. Yucel et al. (2015) have used fully- simulating Cood hydrograph in the Karun-4 dam distributed, multi-physics, multi-scale hydrologic and basin, which is located in the southwest of Iran. hydraulic modelling system, WRF-Hydro to assess the potential for skillful Cood forecasting based on precipitation inputs derived from the WRF model 2. Materials and methodology and the EUMETSAT Multi-sensor Precipitation Estimates (MPEs). Results showed that the WRF- 2.1 Area of study Hydro system was capable of skillfully reproducing observed Cood hydrographs in terms of the volume The catchment area of the Karun river is located in of the runoA produced and the overall shape of the Karun-4 dam in southwest of Iran, between the hydrograph. StreamCow simulation skill was sig- northern latitude of 20°3100 to 32°4100, and the nificantly improved for those WRF model simula- eastern longitude of 33°4900 to 45°5100 in the Zagros tions where storm precipitation was accurately Mountain range. The basin is almost mountainous depicted with respect to timing, location and with an average height of 2354 m, and height of its amount. highest point is 4200 m. The Karun river basin area The contemporary studies also focused on soft in Karun-4 dam is 12,854 km2. Karun-4 basin is computing-based methods to forecast rainfall and distributed into 10 sub-basins based on the topo- runoA. Several examples of such methods can be graphic maps, rivers network, and hydrometric mentioned. Venkatesan et al. (1997) employed the stations location. The Karun-4 basin’s average ANN to predict the all India summer monsoon annual rainfall is estimated at about 680 mm. Also, rainfall with different meteorological parameters as the average evaporation from the surface of the lake model inputs. Wu and Chau (2013) employed is 1811.2 mm. The average annual Cow of the river several soft computing approaches for rainfall is 49.427 m3 and the minimum and maximum prediction. Sivapragasam et al. (2001) established temperature of the dam site is estimated at 8°C, a hybrid model of support vector machine (SVM) 4.32°C, respectively. Figure 1 shows the sub-basin and the singular spectrum analysis (SSA) for map of Karun-4 basin to Karun-4 dam site, based rainfall and runoA predictions. The hybrid model on the maps 1:250,000, the number for each sub- resulted in a considerable improvement in the basin, and the stations location. Summary of model performance in comparison with the original Karun-4 basin physiographic and elevation char- SVM model. Recently, due to SVM’s excellent acteristics and its sub-basins is displayed in table 1. characteristics of robustness and generalization Karun-4 dam basin is located in the middle of performance, many researchers considered the the Middle Zagros and is considered as one of the SVM method in order to improve the accuracy of areas with considerable precipitation in the coun- the rainfall prediction model (Lu and Wang 2011; try. The type of precipitation of this watershed Kisi and Cimen 2012;Duet al. 2017; Young et al. varies according to geographical location and alti- 2017). Accordingly, selecting the appropriate pre- tude, and in the highlands, about half of the annual dictors for the prediction model accuracy has a precipitation is snowfall. For example, the snowfall great importance (Seo et al. 2014; Chang et al. of Koohrang station has been between 34% and 2017; Tan et al. 2018). 59% of all precipitation in different years, and for According to recent studies conducted so far, no this reason, the combined eAects of snow and rain study has been conducted on comparison and in the region’s hydroclimate may be of special evaluation of different models based on data driven interest. Most of the rainfall falls between Decem- including ANN and SVM and numerical model ber and the end of April. WRF in short-term forecast of precipitation and Karun-4 basin is one of the coldest regions of the air temperature in ground stations. This study country and the average annual temperature in concentrates on short-term rainfall prediction sys- different parts of it is different due to different tem construction development in watershed, by climatic factors which is mentioned in table 2. The comparing the prediction results with observed coldest station is Koohrang that the temperature rainfall intensity, and soft computing rainfall reaches 9.2°C, and in the tropical parts of the forecast, for providing a reliable tool for disaster. basin, such as Lordegan, it reaches 15.2°C. Due to This research used WRF, SVR, and ANN model in the presence of significant heights and the estab- order to predict heavy rainfall and temperature. lishment of huge water reserves, as well as the HEC-HMS hydrological model was used for existence of numerous rivers and water resources, 188 Page 4 of 16 J. Earth Syst. Sci. (2020) 129:188

Figure 1. Sub-basins boundary to Karun-4 dam site.

Table 1. Summary of physiographic and elevation characteristics of Karun-4 basin and its sub-basins.

Sub- Area Parameter Minimum Maximum Average height Main river Main river watershed (km2) (m) height (m) height (m) (m) length (m) slope (%) 1 1430.9 188.5 1988.0 3207 2328.5 58.5 3.1 2 1156.0 172.5 1984 3267 2246.2 58.6 3.2 3 1376.2 261.3 1648 3727 2389.1 61.8 5.4 4 1277.9 227.3 1647 4191 2667.5 99.8 8.4 5 1514.2 216.3 1127 3982 2357.6 69.5 8.0 6 1230.3 170.0 2072 3702 2526.5 48.1 4.1 7 951.8 162.9 2073 3594 2464.9 63.6 2.8 8 943.5 192.6 1128 3870 2478.2 75.8 6.3 9 802.0 146.2 852 3231 1855.8 47.8 9.2 10 2171.1 342.2 850 4132 2206.1 149.3 14.3

humidity is relatively suitable in rainy seasons. were used to predict rainfall and air temperature at The data used in this study include hourly pre- different stations in Karun-4 dam basin. Model cipitation, average air temperature, relative humi- outputs were used as an input for HEC-HMS dity, air pressure, wind speed and wind direction at hydrological model to predict runoA hydrograph. the meteorological stations of the Iran Meteoro- The eAective input variables for ANN and SVM logical Organization and hourly river Cow at the model were also determined using the PMI algo- hydrometric stations. rithm. Then, the optimal structure of ANN and SVM models for precipitation and air temperature 2.2 Methodology was obtained. The HEC-HMS hydrological model was calibrated and veriBed in terms of rainfall- In this study, three different models including runoA simulation. Then, by applying the hourly WRF numerical model, ANN and SVM models values of precipitation and air temperature J. Earth Syst. Sci. (2020) 129:188 Page 5 of 16 188

Table 2. SpeciBcations of stations in the area of study.

Height Rainfall Mean Relative Wind speed Station Type Latitude Longitude (m) (mm) temperature (°C) humidity (%) (m/s) Shahrekord Raingague 32°1700 50°5100 2048.9 310 11.5 46 4.1 Boroojen Raingague 31°5700 51°1800 2197 238 10.5 38 3.1 Koohrang Raingague 32°2600 50°0700 2285 1314 9.2 46 3.6 Lordegan Raingague 31°3100 50°4900 1580 520 15.2 7.45 3.8 Farokh shahr Raingague 32°1800 50°5600 2065 280 11 50 4.5 Saman Raingague 32°2700 50°5600 2057 320 11.5 47 3.5 Armand Hydrometery 50°4600 31°4000 1082 –– – – Marghak Hydrometery 50°2700 31°3900 913 –– – – Beheshtabad Hydrometery 50°3700 32°0100 1680 –– – – Soolgan Hydrometery 51°1400 31°3800 2086 –– – – predicted by WRF, ANN and SVM models in depicted in Bgure 2 extended from eastern HEC-HMS, Cood hydrograph was predicted for Mediterranean to the east of Iran, and the Persian each model. By comparing the graphs and statis- Gulf in south of Iran, and also to the Caspian Sea in tical indices, the accuracy of the models in Cood north of Iran. forecasting was evaluated. Data of the regular model network prediction was interpolated to the monitoring station points for validation and performance of different conBgura- 2.3 WRF model tions in the rainfall prediction, and it was compared The WRF system is a non-hydrostatic model (with to the observed rainfall. Due to the time interval a hydrostatic option) using terrain-following ver- between the model implementation and rainfall tical coordinate based on the hydrostatic pressure. start date, the 12-hr interval from 12:00 UTC on the The model uses higher-order numeric. This day 14 until the 00:00 UTC on the day 15 was con- includes the Runge-Kutta 2nd- and 3rd-order time sidered as the model setting time, and also elimi- integration schemes, and also 2nd- to 6th-order nated from the calculation. Observational data used advection schemes in its both horizontal and ver- in this study included 6-hr rainfall observational tical directions. It uses a time-split step for the data provided by the Meteorological Organization. acoustic and gravity-wave models. It has been used According to the selected basin, the Farrokhshahr, in tandem with hydrological models for simulation Koohrang, Shahrekord, Boroujen, and Lordegan and forecasting the rainfall (Hong and Lee 2009; stations were considered as the synoptic stations Ratna et al. 2014). In this study, rainfall and air and also Armand gauge-discharge station as dis- temperature amounts associated with the March played in Bgure 1. Due to the proximity of Far- 2016 event (heavy rainfall) were predicted with the rokhshahr and Shahrekord stations, and the same 6-hr intervals. The WRF model used with eight the model output in these two cities, Farakhshahr different conBgurations, including a convergent station was deleted during the analysis process. schema, two planetary boundary layer schema, two sub-physical schemes, a surface layer scheme, and two shortwave radiation schemas to obtain the 2.4 ANN and SVM models appropriate conBguration for March 2016 precipi- 2.4.1 PMI algorithm tation. Table 3 mention the conBguration of the physical part of the WRF model in eight different PMI algorithm was used in order to select the most implementations. The conBgurations are named eAective predictive variables for the rainfall and air using the letters of each scheme. temperature in ANN and SVM models (these mod- The model implementation start date was els are described in details in literature, for more determined at 12:00 UTC on the March 14, and the details refer to Nayak et al. (2013) and Du et al. prediction process had continued until 12:00 UTC (2017). The PMI algorithm was developed by on the March 16. The WRF model has been Sharma et al. (2000) for identifying the eAective implemented with a domain basin and a horizontal input variables in hydrologic models. The only spatial separation of 23 km. The Brst domain nonlinear algorithm for selecting the input variables 188 Page 6 of 16 J. Earth Syst. Sci. (2020) 129:188

Table 3. ConBguration of the physical part of the WRF model in eight different implementations.

Boundary Shortwave Longwave Surface Schema condition Subphysical radiation radiation Surface cover layer Convection YSULG YSU Lin Goddard RRTM UniBed Noah MM5 Kf MYJLG MYJ Lin Goddard RRTM UniBed Noah MM5 Kf YSUWG YSU WMS5-class(4) Goddard RRTM UniBed Noah MM5 Kf MYJWG MYJ WMS5-class(4) Goddard RRTM UniBed Noah MM5 Kf YSULD YSU Lin Dudhia RRTM UniBed Noah MM5 Kf MYJLD MYJ Lin Dudhia RRTM UniBed Noah MM5 Kf YSUWD YSU WMS5-class(4) Dudhia RRTM UniBed Noah MM5 Kf MYJWD MYJ WMS5-class(4) Dudhia RRTM UniBed Noah MM5 Kf

a member of Y, which can be deBned according to the Shannon’s entropy (Shannon 1948). But by assuming the random input variable X on the sit- uation that Y is dependent, the mutual observations (x, y) decrease this uncertainty, knowing x allows the value y to be deduced, and vice versa. According to the mutual information definition I(X;Y), reduction in the variable Y uncertainty is because of the X observation (Cover and Thomas 1991). This problem is represented as a common part between the two circles in Bgure 3. This common part is where the reduced uncertainty around X and Y is speciBed by the condi- tional entropy H(X—Y) and H(Y—X), respectively. Mutual Information (MI) can be calculated by using the following formula directly (May et al. Figure 2. The domain considered in WRF model. 2008): ZZ pxðÞ; y IXðÞ¼; Y pxðÞ; y log dxdy; ð1Þ is PMI algorithm in order to determine the eAective pxðÞpyðÞ input variables in data-driven models. The PMI f (y) and p(x) are the marginal probability density algorithm made each iteration by considering one functions (pdfs) of X and Y, respectively, and input (C) and one output (Y) and Bnding Cs (as- p(x, y) is joint probability density function. suming that Cs differs from C), which maximize the However, in practice, the probability density PMI amount with respect to the output variable functions correct form in equation (1) is unknown. (considering inputs was selected previously). The Hence, probability densities estimating are used statistical concept estimated that PMI provided for instead of that. By inserting the probability density Cs is based on the conBdence ranges determined by estimates with integral numerical approximation in the distribution, which was generated by a boot- equation (1), the following formula can be attained strap loop. If the input is significant, Cs will be (May et al. 2008): added to S (the set of selected input variables), and the selection process will continue until no signifi- Xn 1 fxðÞi; yi cant inputs remain, and after that the algorithm is IXðÞ; Y log ; ð2Þ n fxðÞfyðÞ going to stop consequently. i¼1 i i where f is the estimated density based on a sample of 2.4.2 Estimation of partial mutual information n observation of (x, y). By assuming the relationship (PMI) (2), it can be said that the accurate and eAective estimation of MI (mutual information) largely According to the random output variable Y, there depends on the method, which was used for estimat- is some uncertainty about Y observation, which is ing marginal and joint probability density functions. J. Earth Syst. Sci. (2020) 129:188 Page 7 of 16 188

2.4.3 HEC-HMS model 2.4.4 Statistical criteria

The HEC-HMS model was used in order to To evaluate the used models’ accuracy, statistical simulate Cood and extract Cood hydrograph. The error measurement indices including Nash–SutcliAe ability to create relationship with other software coefBcient, root mean square error, mean absolute including GIS is amongst the important features of percentage error, total volume error percent, and this model. This feature makes the right and agreement index are used, which are given in rela- quicker relationship with other software tools, tionship 3–7, respectively. The IOA index is usually allowing the process to investigate any hydrologi- used in order to evaluate the model (Willmott et al. cal event to be done in less time. This model uses a 2011). The IOA index varies between –1 and +1. simple relationship series, basin losses, and unit The closer the IOA is to +1, the model performance hydrograph for reconstructing the Coods from the becomes better. In equation (7), c is equal to 2. In use of rainfall data. This model considered a sur- relationships 3 to 7, n represents the Cow data face runoA relationship, which was performed number,Oi and Si indicate the observed and simu- based on the input rainfall rain gauge. The excess lated Cow discharge values in the i-th time step, O rainfall is calculated after the penetration contri- represents the observed mean discharge, and Cov is bution reduction, and a hydrological reduction the data covariance (Nash and SutcliAe 1970; series based on certain functions like curve number Abrahart et al. 2000). on the Soil Conservation Service (SCS) method. "#P The acquired excess rainfall leads to unit hydro- n 2 ðÞS À O graph throughout the output runoA extracts from NS ¼ 1 À Pi ÀÁi i ; ð3Þ n 2 each sub-basin. There are different methods for i Oi À O calculating rainfall losses and direct runoA in this sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi model including loss rates calculation and direct 1 Xn RMSE ¼ ðÞS À O 2; ð4Þ runoA calculation. Figure 4 shows the basin rain- n i i fall-runoA simulation in the HEC-HMS model i¼1

(USACE 1998). The main input datasets of HEC- Xn 1 Si À Oi HMS model include hourly precipitation, average MAPE ¼ Ã 100; ð5Þ n O air temperature, relative humidity, air pressure, i¼1 i P P wind speed and wind direction at the meteorolog- n n ical stations of the Meteorological Organization i SPi À i Oi PTVE ¼ n Ã 100; ð6Þ and hourly river Cow at the hydrometric stations. i Oi

Figure 3. Venn diagram, indicating the relationship between MI (Mutual Information) and entropy for output Y and single input variable X (May et al. 2008). Figure 4. Rainfall-runoA process in the HEC-HMS model. 188 Page 8 of 16 J. Earth Syst. Sci. (2020) 129:188 8 P > n S O Xn Xn compared. The main purpose of this comparison > Pi¼1jj i À i <> 1 À n ; when jjSi À Oi c Oi À O was to judge the good compliance with the actual c i¼1 Oi À O i¼1 i¼1 IOA ¼ P > n hydrological system. If the compliance of the > S O Xn Xn > Pi¼1 jji À i : n À 1; when jjSi À Oi [ c Oi À O hydrographs was not satisfactory, the parameters O À O i¼1 i i¼1 i¼1 should be corrected and modiBed by an optimiza- ð7Þ tion method and the process repeated. Optimiza- tion operations can be performed manually and 3. Results and discussion using engineering judging by the frequent correc- tion of parameters or automatically by the model. 3.1 Synoptic analysis: Rainfall and Cood When compliance is good and satisfactory, the on March 14 and 15, 2016 optimal and Bnal values of the parameters will be reported. The synoptic structure at 00:00 on March 14 In this model, some other models were used to presented a low pressure (state) of 1005 hPa with simulate the conversion of rainfall to runoA, pene- an elevation trough the 500 hPa levels in eastern tration losses, baseline Cow and snow melting in Mediterranean (Bgure 5). On the same day at 12:00 sub-basins known as the Clark unit hydrograph UTC, it extended to the east in the low-pressure method, soil conservation service (SCS) curve state, and one of its troughs extended to the center number method, subsidence method, and degree- of Iran and the second trough extended to the west day method, respectively. The Muskingum–Kunge of Iraq. Because of extending the elevation trough hydrologic model was also used for the Cow routing to Iran in the next 6 hr – 18:00 UTC – rainfall had in rivers. Figure 6 indicates the sub-basins and the begun in Karun-4 basin on March 14. It reinforced Karun-4 dam rivers upstream schematic con- in the low-pressure state and decreased to 995 hPa structed in the HEC-HMS hydrologic model envi- at 00:00 UTC on March 15. Its central core was ronment. Two heavy rainfall events of 9 Mar 2014 located in the north of Iran and its elevation trough and 8 Mar 2011 were considered for calibration and extended to the center of Iran. During this time, validation of HEC-HMS model, respectively. The rainfall had increased in the basin. In the next basin monthly average rainfall of March 2011 and few hours, it was transmitted to higher latitudes March 2014 was 88 and 82 mm, respectively. in the low-pressure state, and a pressure stack Figure 7 displays the comparison between the was installed on Iran. Consequently, the highest observed and simulated Cood hydrograph on 9 Mar amount of rainfall reported in Koohrang was at 46 2014 event at the Armand hydrometric station for mm at 12:00 on March 15, after that the amount of model calibration. Rainfall-runoA simulation was rainfall decreased and at 00:00 UTC on March 16, carried out for the validation time period with the raining was over. Bnal parameter’s values obtained from calibration, in order to validate the HEC-HMS calibrated 3.2 Calibration and validation of HEC-HMS model. Figure 7 presents the observed and simu- model lated Cood hydrograph comparison on 8 Mar 2011 event for model veriBcation at Armand hydro- First, before applying the HEC-HMS model for metric station. In Bgure 7, it can be seen that Cood predicting the Cood hydrograph, it was calibrated hydrograph variations, which were simulated by and veriBed. Calibration and veriBcation process HEC-HMS model on 9 Mar 2014 event at the continue to determine the optimal values of the Armand hydrometric station were close to the parameters in HEC-HMS model. This process observed Cood hydrograph and HEC-HMS model begins with data collection. The required data for was well calibrated in terms of rainfall-runoA sim- precipitation-runoA models include rainfall data, ulation. Also, due to the information of Bgure 8,it current time series, air temperature time series, can be found that Cood hydrograph variations and so on. The next step in the calibration process simulated by HEC-HMS model on 8 Mar 2011 is is to select the initial values for the parameters. By near to observed Cood hydrograph. giving the initial values of the model, it is able to Table 4 displays the goodness-of-Bt statistical calculate the hydrograph of the basin runoA in all criteria for calibration and veriBcation period of parts of the basin, especially the location of sta- HEC-HMS model in simulating Cow hydrograph at tions with observational data. At this point, the Armand hydrometric station. According to table 4, observed and the computational hydrograph were the Nash–SutcliAe coefBcient values, total volume J. Earth Syst. Sci. (2020) 129:188 Page 9 of 16 188

Figure 5. Free sea level pressure (Blled black line) hectopascal, geopotential height of 500 hPa levels (dashed line), wind direction 925 hPa (Picamen) for the times of 00:00 on March 14 (a), 12:00 on March 14 (b), 00:00 on March 15 (c), and 12:00 on March 15 (d). error percent, and mean absolute percentage error including rainfall hourly statistics, average air between the observed and simulated hydrograph in temperature, relative humidity, air pressure, wind the calibration step were equal to 0.91, –4.27%, and speed and wind direction at each station were 8.85%, respectively. In addition, the negative value considered up to 24 hrs ago to provide the potential of PTVE (percent of total volume error) indicated set of input variables. a low volume runoA estimate with the HEC-HMS The PMI algorithm was used in order to deter- model. Regarding Nash coefBcient and PTVE in mine the input variables eAect on output variables table 4, which equals to 0.74, 0.19, respectively, (rainfall and air temperature amounts in the next can be demonstrated that HEC-HMS model was 6 hrs at each station). This algorithm determines well calibrated in the veriBcation step. the eAectiveness of input variables by calculating the PMI value. Table 5 displays the PMI algorithm results for six eAective variables, by the order of 3.3 PMI algorithm results priority in predicting rainfall at different stations. Table 6 shows the PMI algorithm results for six In order to predict rainfall and air temperature at eAective variables by the order of priority in different Karun-4 basin synoptic stations, hourly predicting air temperature at different stations. rainfall, average air temperature, relative humid- In tables 5 and 6, R(t) represents the current ity, air pressure, wind speed, and wind direction for rain status (current rainfall amounts), R(tÀ1) each station were used. Each input variables represents the rainfall amount of 6 hrs ago, R(tÀ2) 188 Page 10 of 16 J. Earth Syst. Sci. (2020) 129:188

Figure 6. Topology of sub-basins and rivers upstream of Karun-4 dam made in HEC-HMS model.

450 800 400 700 350 Observed 600 300 Observed Simulated 500 250 Simulated 400 200 150 300 streamﬂow (cms) 100 Streamﬂow (cms) 200 50 100 0 0 0 24 48 72 96 120 144 168 192 216 240 264 288 0 24 48 72 96 120 144 168 192 216 240 264 me (hr) me (hr)

Figure 7. Comparison between the observed and simulated Figure 8. Comparison between the observed and simulated Cood hydrograph in 9 Mar 2014 event at Armand station for Cood hydrograph in 8 Mar 2011 event at Armand station for model calibration. model veriBcation. represents the rainfall amount of 12 hrs ago, Table 4. Goodness-of-Bt statistical criteria for calibration and R(tÀ3) represents the rainfall amount of 18 hrs validation period of HEC-HMS model. ago, H(t) represents the current relative humidity, PTVE RMSE MAPE H(tÀ1) represents the relative humidity of 6 hrs Stage NS (%) (cms) (%) ago, T(t) represents the average amount of current Calibration 0.91 –4.27 21.5 8.85 air temperature, T(tÀ1) represents the average Validation 0.74 0.19 63.5 25.70 amount of air temperature 6 hrs ago, T(tÀ2) represents the average amount of air temperature 12 hrs ago, T(tÀ3) represents the average amount of air temperature 18 hrs ago, WS(t) represents the predicting rainfall at Shahrekord station are current wind speed, WS(tÀ1) represents the wind H(t) and R(t). The eAective input variables for speed of 6 hrs ago, WS(tÀ2) represents the wind predicting rainfall at Borujen station are H(t), speed of 12 hrs ago, WD(tÀ4) represents the wind R(t) and R(tÀ1), respectively. The eAective input direction of 24 hrs ago, P(tÀ1) represents the air variables for predicting rainfall at Lordegan station pressure of 6 hrs ago, and P(tÀ2) represents the air are R(t), R(tÀ1), and R(tÀ2), respectively. Also, pressure of 12 hrs ago. the eAective input variables for predicting rainfall According to table 5 and based on the at Koohrang station are T(tÀ2), R(t), and R(tÀ1), AIC(p) criterion, eAective input variables for respectively, for the temperature of 12 hrs ago. J. Earth Syst. Sci. (2020) 129:188 Page 11 of 16 188

Table 5. Results of PMI algorithm to determine the eAective input variables for predicting rainfall at different stations.

Shahrekord Boroojen Lordegan Koohrang Variable AIC(p) Variable AIC(p) Variable AIC(p) Variable AIC(p) H(t) –312.3 H(t) –738.6 R(t) –674.7 T(t–2) –1376.4 R(t) –492.9 R(t) –839.3 R(t–1) –733.3 R(t) –2153.5 R(t–1) –483.6 R(t–1) –840.3 R(t–2) –745.0 R(t–1) –2159.3 T(t) –1472.4 WS(t–2) –838.3 R(t–3) –721.9 R(t–2) –2099.9 T(t–1) –1386.8 WS(t–1) –978.2 H(t) –679.1 T(t) –2487.1 WS(t–1) –1205.1 WS(t) –1246.3 WS(t) –801.5 WD(t–4) –2442.8

Table 6. Results of PMI algorithm to determine the eAective input variables for predicting air temperature at different stations.

Shahrekord Boroojen Lordegan Koohrang Variable AIC(p) Variable AIC(p) Variable AIC(p) Variable AIC(p) T(t–3) –7379.1 T(t–3) –7379.1 T(t–3) –3155.7 T(t) –8427.7 T(t) –8968.6 T(t) –8968.6 T(t) –3703.4 T(t–3) –11195.4 T(t–2) –9468.3 T(t–2) –9468.3 T(t–2) –4014.8 T(t–2) –11549.2 H(t) –9423.8 H(t) –9423.8 T(t–1) –4034.4 P(t–2) –11292.6 T(t–1) –9314.9 T(t–1) –9314.9 H(t–1) –3929.8 H(t) –10858.9 H(t–1) –9182.9 H(t–1) –9182.9 P(t–1) –3416.8 T(t–1) –10585.6

Furthermore, as per the information of table 6, parameters. The initial distribution of weights and and also based on the AIC(p) criterion, the biases is also an important factor for the BPA-based eAective input variables for predicting the air ANN model building process when considering the temperature at Shahrekord and Boroujen stations local minimum problem. In this study, 100 random are T(tÀ3), T(t), and T(tÀ2), respectively. The sets were explored for each combination of model eAective input variables for predicting the air parameters to select the best initial distribution of temperature at Lordegan station are T(tÀ3), T(t), weights and biases for ANN models. Table 7 sum- T(tÀ2), and T(tÀ1), respectively. Also, the eAec- marizes the selected weighting factors and model tive input variables for predicting the air temper- parameter sets for the Bve stations. ature at Koohrang station are T(t), T(tÀ3), and T(tÀ2), respectively. 3.5 Comparison of model performances

3.4 ANN and SVM model structure The one-step ahead direct prediction results and the recursive prediction results were systematically The model parameters in this study are the number compared with the station observations. The model of hidden nodes (HN), the momentum (MM), and the performance criteria using direct prediction with learning rate (a) for the ANN. Moreover, the positive the selected model parameters for the six stations trade-oA parameter (C), the tolerance of the loss was estimated. Precipitation and temperature function (e), and the kernel function parameter (r) direct prediction results are shown in tables 8 and are used for the SVM. The trial-and-error method 9. The Nash–SutcliAe model eDciency coefB- was employed for selecting the weighting factors and cient (NS) and Root Mean Square Error (RMSE) model parameters, which were allowed to vary as were used to assess the predictive power of hy- follows: wTR,wCA[ [0.0, 1.0], HN [ [2, 20], a [ [0.0005, drological models. According to NS and RMSE, 0.005], MM [ [0.0, 0.9], C [ [6.0, 14.0], e [ [0.07, 0.16], rainfall and temperature prediction by SVM is and r [ [2.0, 4.0]. The parameter set for each model better than the ANN in some stations and for two was selected among 1000 combination sets of events. 188 Page 12 of 16 J. Earth Syst. Sci. (2020) 129:188

Table 7. Selected input structure and model parameters.

Model ANN model parameters SVM model parameters Station Variable HN LR MM W C er Shahrekord Rainfall 12 0.005 0.1 0.4 7 0.1 2.9 Temperature 10 0.002 0.5 0.3 5 0.04 2 Lordegan Rainfall 12 0.004 0.6 0.5 6.5 0.05 3.5 Temperature 10 0.001 0.2 0.4 7.5 0.09 4 Koohrang Rainfall 12 0.002 0.1 0.3 12 0.2 4 Temperature 10 0.004 0.2 0.4 14 0.1 3.5 Farsan Rainfall 12 0.001 0.1 0.3 10 0.09 4 Temperature 11 0.001 0.3 0.5 8 0.05 4 Boroojen Rainfall 12 0.004 0.4 0.4 9 0.07 3 Temperature 10 0.002 0.2 0.3 7 0.08 2 Ardal Rainfall 12 0.001 0.6 0.4 8 0.09 3.5 Temperature 10 0.002 0.4 0.3 7.5 0.1 4

Table 8. Direct prediction results for precipitation. Table 9. Direct prediction results for temperature.

Event 15 Mar 2016 Event 15 Mar 2016 Model SVM ANN Model SVM ANN Station RMSE NS RMSE NS Station RMSE NS RMSE NS Shahrekord 0.62 1 1.2 0.9 Shahrekord 3.71 0 1.48 3.7 Loordegan 1 0.9 0.48 1 Loordegan 0.84 0.9 0.89 0.9 Koohrang 2.62 1 2.65 1 Koohrang 1.23 0.8 1.36 0.7 Farsan 1.18 0.6 0.55 0.9 Farsan 1.36 0.7 0.8 1 Broojen 0.16 0.8 0.41 –0.4 Broojen 0.87 0.9 1.01 0.9 Ardal 1.79 0.7 0.8 0.9 Ardal 1.65 0.7 0.92 0.9

3.6 Results of WRF model appropriate value for the hourly temperature esti- 3.6.1 Comparison of the observed rainfall mation by the model. This means that the WRF and temperature and model output model does not perform well on the temperature prediction. Except the two stations of Saman and Table 10 shows the IOA index for the hourly pre- Shahrekord, which had a coefBcient of 0.47 and dicted rainfall with different schemas. The IOA 0.52, respectively, all other stations, had the coef- coefBcient of the observed rainfall and the model Bcient of \0.5. The four MYJLG, MYJWG, with eight schemas had a value of more than 0.5 YSULG, and YSUWG schemas provided a better indicating their coordination at all stations except result than the other four schemas. Boroujen. Out of eight schemes, the four MYJLD, According to the information of table 12, the MYJLG, MYJWD, and MYJWG schemes had the observed peak discharge was 200 m3/s, and highest values. The best IOA values were attained the other two MYJLG and MYJWD schemas with at the amounts of 0.77, 0.76, 0.74, and 0.52 in the values of about 6.220 and 3.233 m3/s were Shahrekord, Saman, Koohrang, and Lordegan, the closest to the observation. The MYJLG schema respectively, with the MYJLD schema. Boroujen provided a good result in the former cases, and the has a negative coefBcient and indicates a lack of MYJWD schema had a good coordination with the output coordination of the model with the observational data in the case of rainfall. Conse- observation. quently, the schemas predicted rainfall well during Table 11 displays the r and IOA index for the the whole period, and also had a good performance hourly predicted air temperature with different on peak discharge. Moreover, the observed runoA schemas. The IOA index did not provide an height was 3.45 mm and the two MYJLG and J. Earth Syst. Sci. (2020) 129:188 Page 13 of 16 188

Table 10. IOA index for the predicted hourly rainfall with different schemas.

Station Names MYJLD MYJLG MYJWD MYJWG YSULD YSULG YSUWD YSUWG Boroojen r 0.85 0.65 0.93 0.80 0.74 0.57 0.72 0.57 IOA –0.46 –0.41 –0.38 –0.26 –0.65 –0.72 –0.58 –0.65 Koohrang r 0.69 0.59 0.70 0.56 0.62 0.52 0.61 0.49 IOA 0.74 0.70 0.74 0.69 0.73 0.68 0.72 0.67 Loordegan r 0.77 0.86 0.76 0.84 0.61 0.72 0.63 0.75 IOA 0.52 0.63 0.50 0.50 0.44 0.51 0.44 0.48 Saman r 0.74 0.61 0.82 0.65 0.63 0.54 0.65 0.59 IOA 0.76 0.77 0.73 0.76 0.69 0.69 0.67 0.67 Shahrekord r 0.74 0.17 0.82 0.21 0.32 À0.02 0.29 0.03 IOA 0.77 0.61 0.76 0.65 0.68 0.65 0.70 0.68

Table 11. r and IOA index for the predicted hourly air temperature with different schemas.

Station Index MYJLD MYJLG MYJWD MYJWG YSULD YSULG YSUWD YSUWG Boroojen r 0.85 0.85 0.84 0.85 0.82 0.82 0.81 0.81 IOA 0.20 0.26 0.20 0.27 0.19 0.27 0.21 0.27 Koohrang r 0.76 0.76 0.77 0.77 0.73 0.74 0.72 0.72 IOA 0.20 0.27 0.22 0.27 0.18 0.26 0.16 0.25 Lordegan r 0.81 0.79 0.81 0.77 0.78 0.75 0.77 0.73 IOA 0.12 0.23 0.12 0.22 0.14 0.21 0.12 0.20 Saman r 0.82 0.82 0.81 0.82 0.76 0.77 0.75 0.76 IOA 0.43 0.46 0.42 0.46 0.43 0.47 0.43 0.47 Shahrekord r 0.82 0.83 0.81 0.82 0.76 0.78 0.76 0.78 IOA 0.45 0.51 0.45 0.50 0.46 0.52 0.46 0.52

Table 12. Comparison between the peak discharge and runoA height values of the predicted Cood hydrograph for different schemas.

Variable Observed MYJLD MYJLG MYJWD MYJWG YSULD YSULG YSUWD YSUWG Peak discharge (cms) 200 249.9 220.6 233.3 242.8 366.3 467.1 323.7 386.4 RunoA (mm) 3.45 5.12 4.71 4.85 4.74 6.7 7.96 6.28 7.6

MYJWG schemas with 4.71 and 4.74 mm provided with the other schemas. Although, the MYJLD the closest value to the observation. Both of the schema was in the agreement with the observa- schemas also had good coordination with the tional data in rainfall process, but in Cood pre- observational data (observed data). dicting showed a higher error in NS coefBcient Table 13 indicates the comparison between the than MYJLD in peak discharge and runoA height. statistical indices of the predicted Cood hydro- Therefore, it seems that the MYJ boundary layer graph for different schemas. Investigating NS schema, the Lin cloud microphysics schema, and coefBcient in any of the schemas did not lead to a the GODDARD radiation schema had the best good result. But it had the smallest or nearest performance in Cood predicting in Karun-4 basin value to zero in the MYJLG schema. This schema in March 2016. also had a good result in peak discharge, total Comparison between the predicted hydrograph rainfall, hourly temperature, and average temper- at the Armand hydrometric station attained from ature. Consequently, it seems that it had a better the rainfall prediction with different schemas in performance in Cood predicting in comparison WRF model is illustrated in Bgure 9. According to 188 Page 14 of 16 J. Earth Syst. Sci. (2020) 129:188

Table 13. Comparison between the predicted Cood hydrograph statistical indices for different schemas.

Criteria MYJLD MYJLG MYJWD MYJWG YSULD YSULG YSUWD YSUWG NS –1.208 –0.293 –0.519 –0.483 –8.893 18.471 –6.082 –14.657 RMSE std dev 1.5 1.1 1.2 1.2 3.1 4.4 2.7 4 PTVE (%) 42.73 30.95 34.96 31.81 88.29 124.7 76.15 114.29 RMSE (cms) 48.4 37.0 40.1 39.7 102.4 143.7 86.7 128.9 MAPE (%) 42.91 31.93 35.92 32.79 82.70 116.60 73.00 109.62

500 450 Observed 400 MYJLD MYJLG 350 MYJWD 300 MYJWG 250 YSULD 200 YSULG 150 YSUWD 100 YSUWG

Forecasted streamﬂow (cms) streamﬂow Forecasted 50 0 020406080100 Time (hr)

Figure 9. Comparison between the predicted hydrograph at Armand hydrometric station obtained from rainfall prediction with different schemas in WRF model. the all schemas prediction, the amount of runoA 300 observed was more than the observed one (observational 250 data). Also, runoA start time in the model was WRF model (MYJLG) earlier than the observed one (observational data). 200 SVM ANN The runoA variations process obtained from each 150 of the eight schemes was similar, but their runoA 100 height was different. The most inappropriate schema was the YSULG. 50

forecasted streamﬂow streamﬂow (cms) forecasted 0 3.7 Comparison between the predicted Cood 0 24487296 me (hr) hydrograph with SVM and ANN and WRF models Figure 10. Comparison between the predicted hydrograph at the Armand hydrometric station in different models. Figure 10 displays the predicted Cood hydrograph at the Armand hydrometric station with input weather variables from including WRF, SVM and coefBcient value for WRF, SVM, and ANN models ANN models. SVM model hydrograph variations was –0.293, 0.548, and –0.607, respectively. The were nearer to the observed hydrograph than the RMSE value between the observed and predicted other models. Cow discharge values by WRF, SVM, and ANN Table 14 displays the comparison between the models was as 37, 21.9, and 41.3 m3/s, respectively. peak discharge and runoA height values of the Also, percent of total volume error (PTVE) predicted Cood hydrograph in different models. between the observed and predicted Cow discharge According to the data shown in table 15, SVM values by the use of WRF, SVM, and ANN models model had more accuracy in runoA height pre- was 30.95, 15.59, and 32.14%, respectively. dicting than the other two models of WRF and Therefore, the SVM model had more accuracy in ANN. Table 15 also shows the comparison between rainfall and air temperature predicting, and also the statistical indices of the predicted Cood Cood hydrograph in comparison with the other hydrograph in different models. The Nash–SutcliAe models. J. Earth Syst. Sci. (2020) 129:188 Page 15 of 16 188

Table 14. Comparison between peak discharge and runoA 6 hrs ago, and the rainfall and temperature of height values of the predicted Cood hydrograph in different 12 hrs ago. Also, the PMI algorithm results for air models. temperature predicting in the next 6 hrs indicated WRF that the eAective input variables included the Variable Observed (MYJLG) SVM ANN temperature of 18 hrs ago, the current tempera- Peak discharge 200 220.6 244.2 285.2 ture, the temperature of 12 hrs ago, and the tem- (cms) perature of 6 hrs ago. The results indicated that RunoA height 3.45 4.71 4.05 4.62 using the PMI algorithm for determining the (mm) eAective input variables in ANN and SVM models, caused a significant reduction in the time needed to determine the eAective variables, and consequently allowed the model development. Comparison Table 15. Comparison between the statistical indices of the between the peak discharge and runoA height val- predicted Cood hydrograph in different models. ues of the predicted Cood hydrograph in different Statistical criteria WRF (MYJLG) SVM ANN models revealed that the SVM model had more NS –0.293 0.548 –0.607 eDciency and accuracy in rainfall, air temperature, RMSE std dev 1.1 0.7 1.3 and Cood hydrograph predicting than other mod- PTVE (%) 30.95 15.59 32.14 els. In addition, the WRF model accuracy in rain- RMSE (cms) 37.0 21.9 41.3 fall, air temperature, and Cood hydrograph MAPE (%) 31.93 14.33 29.26 predicting was more than ANN model. Due to the fact that the WRF model requires a relatively long time to run to predict rainfall and air temperature, using the simple SVM model reduces the time 4. Discussion and conclusion required for short-term forecasting of rainfall and air temperature values and the results could be The purpose of this paper was to evaluate and used for Cood forecast. compare different models based on data driven model including ANN and SVM and WRF numerical model in short-term prediction of precipitation values and air temperature in ground References stations in order to evaluate more accurate model and using output of these model to forecast of Cood Abrahart R J and See L 2000 Comparing neural network and hydrograph. According to the results of this study, autoregressive moving average techniques for the provision of continuous river Cow forecasts in two contrasting the accuracy of the SVM model in predicting pre- catchments; Hydrol. Process. 14 2157–2172. cipitation and air temperature and Cood hydro- Afandi G E, Mostafa M and Hussieny F E 2013 Heavy rainfall graphy is higher than the WRF model. In addition, simulation over Sinai peninsula using the weather research the time required to run the SVM model in the and forecasting model; Int. J. Atmos. Sci. 2013 1–11. short-term forecast of precipitation and air tem- Chang T K, Talei A, Alaghmand S and Ooi M P L 2017 Choice perature is much lower than the WRF model. The of rainfall inputs for event-based rainfall-runoA modeling in a catchment with multiple rainfall stations using data- results obtained from the rainfall and air temper- driven techniques; J. Hydrol. 545 100–108. ature prediction and also the prediction of Cood by Cover T M and Thomas J A 1991 Information theory and using different schemas of WRF model, indicated statistics. Elements of Information Theory (1st edn) Cover T that MYJLG scheme was more accurate than the M and Thomas J A (eds); John Wiley and Sons, pp. 279–335. other schemas. Therefore, it seems that the MYJ Das S, Ashrit R, Iyengar G R, Mohandas S, Gupta M D, George J P, Rajagopal E and Dutta S K 2008 Skills of boundary layer scheme, the Lin cloud micro phy- different mesoscale models over Indian region during sics scheme, and the GODDARD radiation monsoon season: Forecast errors; J. Earth Syst. Sci. 117 scheme had the best performance in Cood predict- 603–620. ing in Karun-4 basin on March 2016. The results of Du J, Liu Y, Yu Y and Yan W 2017 A prediction of using PMI algorithm for determining the eDcient precipitation data based on support vector machine and input variables in order to predict rainfall at rain particle swarm optimization (PSO-SVM) algorithms; Algorithms 10 57. gauge stations in the next 6 hrs, revealed the Givati A, Lyan B, Liu Y and Rimmer A 2012 Using the WRF eAective variables as relative humidity, the current model in an operational streamCow forecast system for the rainfall (the current rain status), the rainfall of Jordan River; J. Appl. Meteorol. Climatol. 51 285–299. 188 Page 16 of 16 J. Earth Syst. Sci. (2020) 129:188

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Corresponding editor: N V CHALAPATHI RAO