Journal of Applied Research in Water and Wastewater 10(2018) 454-460

Original paper

The efficiency of genetic programming model in simulating rainfall-runoff process (Case Study: Khorramabad river basin)

Hamidreza Babaali*,1, Zohreh Ramak2, Reza Sepahvand3

1Department of Civil Engineering, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran. 2Department of Civil Engineering, Science and Research of Branch, Islamic Azad University, Tehran, Iran. 3Faculty of Civil Engineering, Isfahan University of Technology, Isfahan, Iran.

ARTICLE INFO ABSTRACT

Article history: Predicting the river discharge is one of the important subjects in water resources Received 25 November 2018 engineering. This subject is of utmost importance in terms of planning, Received in revised form 20 December 2018 management, and policy of water resources with the aim of economic and Accepted 30 December 2018 environmental development, especially in a country like Iran with limited water resources. Awareness of the relation between rainfall and runoff of basins is an inseparable past of water design studies. Lack of sufficient data on rainfall-runoff Keywords: due to the absence of appropriate hydrometric stations reveals the importance Simulation of using indirect methods and heuristic algorithms for estimating the basins' Rainfall-runoff runoff more than before. In the present research, the genetic programming Heuristic algorithm model has been employed to simulate the rainfall-runoff process of Genetic programming Khorramabad River basin, and in order to introduce the patterns and identify the best pattern dominating the nature of flow, all statistical data were divided into two groups of training and experiment (52 percent training and 48 percent experiment) and the program was implemented for 1000 replications using fitting functions and going through replication and developmental processes so as to find the optimal replication. Moreover, in order to evaluate the relations obtained from the simulator model, Root Mean Square Error (RMSE) and Mean Squared Error (MSE) indexes and Coefficient of Determination (R2) have been used. The investigations demonstrate that the employed equation 3 has the greatest relevance with the observational data. Therefore, it is recommended that the said equation be used for the rainfall-runoff studies of the abovementioned basin. Based on the results, the genetic programming model is an accurate direct method for predicting the discharge of Khorramabad River basin. ©2018 Razi University-All rights reserved.

1. Introduction In recent years, artificial intelligence (AI) techniques such as artificial neural network (ANN) and genetic programming (GP) have Accurate prediction of streamflow is an essential ingredient for both been pronounced as a branch of computer science to model wide range water quantity and quality management. Generally, there are two of hydrological processes (Whigham and Crapper,2001; Dolling and possible approaches to predict streamflow. The first approach is the Varas, 2002). Following this, comparative studies between different AI process modelling that involves the study of rainfall-runoff processes in techniques have been appeared in the relevant literature and still order to model the underlying physical laws (Kuchment et al. 1996). The attempting to find out the most appropriate one (Ghorbani et al. 2010; rainfall–runoff process can be influenced by many factors such as Nourani et al. 2011; Abrahart et al. 2012). Hence we initially developed weather conditions, land-use and vegetation cover, infiltration, and a hybrid waveletartificial neural network (WANN) model as an optimized evapotranspiration. Therefore, it is subject to many simplification ANN technique for monthly streamflow prediction in a particular assumptions or excessive data requirements about the physics of the catchment in this investigation. Then we, as a first time, compared the catchment. The second approach to streamflow prediction is the pattern results of WANN with those of linear genetic programming (LGP) recognition methodology which attempts to recognize streamflow technique. The pattern recognition methodology is adopted as our patterns based on their antecedent records. In this approach, thorough prediction approach in this study. ANN is an effective approach to understanding of the physical laws is not required and the data manage large amounts of dynamic, non-linear and noisy data, requirements are not as extensive as for the process model (Nourani et especially when the underlying physical relationships are not necessary al. 2011). The logic behind this approach is to find out relevant spatial to fully understanding (Nourani et al. 2011). ANNs were widely used in and temporal features of historical streamflow records and to use these various fields of hydrological predictions and successful results have to predict the evolution of prospective flows. As inputs of the models in also been reported in streamflow prediction (Abrahart et al. 2012; pattern recognition method are only time-lagged streamflow Besaw et al. 2010; Can et al. 2012; Dolling and Varas 2002; Kisi and observations, this approach appears more useful for the catchments Cigizoglu 2007; Nourani et al. 2011). In the last decade, GP has been with no or sparse rain gauge stations (Besaw et al. 2010). pronounced as a new robust method to solve wide range of modelling

e g a P * Corresponding author Email: [email protected]

|

Please cite this article as: H.R. Babaali, Z. Ramak, R. Sepahvand, The efficiency of genetic programming model in simulating rainfall-runoff 454 process (Case Study: Khorramabad river basin), Journal of Applied Research in Water and Wastewater, 5 (2), 2018, 454-460.

Babaali et al./ J. App. Res. Wat. Wast. 10(2018) 454-460

problems in water resources engineering such as rainfall-runoff and on the other hand, the non-linear feature and inherent uncertainty modelling (Dorado et al. 2003; Nourani et al. 2012; Whigham and of the rainfall-runoff process, have led the researchers to using artificial Crapper. 2001), unit hydrograph determination (Rabunal et al. 2007), intelligence methods and heuristic algorithms. The methods inspired by flood routing (Sivapragasam et al. 2008), and sea level forecasting nature such as genetic programming (GP), which are introduced as soft (Ghorbani et al. 2010). It was observed that a few studies existed in the computing, are among those models that are used in complex accurate literatures related to the comparison of the performance of GP and ANN researches (Qolizadeh et al. 2016; Fazaeili. 2010; Harun et al. 2002). in time series modelling of streamflow. Guven (2009) applied LGP, a Zahiri and Azamathulla (2014) used two methods of linear genetic variant of GP, and two versions of neural networks for prediction of daily programming and M5 tree model in order to predict the flow rate in flow of Schuylkill River in the USA and showed that the performance of compound cross-sections. the results showed that although both LGP was moderately better than that of ANN. Wang et al. (2009) models had high accuracy in predicting the flow rate, the accuracy of developed and compared several AI techniques include ANN, neural- the linear genetic programming was greater than the M5 tree model. based fuzzy inference system (ANFIS), GP and support vector machine Using genetic programming and artificial neural networks, (Ghorbani et (SVM) for monthly flow forecasting using long-term observations in al. 2010) modeled the fluctuations of the surface of water on Cocos China. Their results indicated that the best performance can be Island in Indian Ocean with 12-hour, 24-hour, 5-day, and 10-day data. obtained by ANFIS, GP and SVM, in terms of different evaluation According to the results, in most of the cases, the results obtained from criteria. Londhe and Charhate (2010) used ANN, GP and model trees genetic programming were more accurate than those obtained from (MT) to forecast river flow one day in advance at two stations in artificial neural networks. Whigham and Crapper (2001) modeled the Narmada catchment of India. The results showed the ANNs and MT daily rainfall-runoff process in Teifi and Namoi basins using genetic techniques performed almost equally well, but GP performed better programming and IHACRES. The results obtained from genetic than its counterparts. All aforementioned researches show that GP programming had higher accuracy than those obtained from the models result in higher accuracy than regular ANN based modelling model.In a research on Orgeval basin in France, (Khu et al., 2001) took approaches. The fact behind this is that the ANN models are not very advantage of genetic programing to predict the hourly runoff and satisfactory in terms of precision when a time series is highly non- compared the results obtained from observational values and those stationary and hydrologic process being operated under a large range produced through classic methods. The research results indicated the of time scales (Nourani et al. 2012). To improve the results of the ANN acceptable accuracy of genetic programming. models, input and/or output data pre-processing by wavelet Studying the rainfall-runoff relation in different times, Liong et al. decomposition technique (hybrid wavelet-ANN models) are suggested (2001) came to the conclusion that using the genetic programming and successful results have been reported (Kisi. 2008; Labat 2005; method in predicting the rainfall-runoff behavior in basins had fewer Nourani et al. 2009a, 2011). In recent years, this hybrid model was also errors. Jayawardena et al. (2005) modeled the rainfall-runoff process of compared with some other classic models such as multiple linear a small basin in Hong Kong and two almost big basins in China using regressions and regular ANNs. The findings deduced that the hybrid genetic programming. The results obtained from the modeling with daily WANN model can be considered as an effective tool in modelling data for the basin with steep slope and small area were not appropriate, complex hydrological processes (Anctil and Tape. 2004; Adamowski and to solve this problem, they suggested using data with shorter time and Sun. 2010; Partal and Kisi. 2007; Rajaee et al. 2010). Using genetic intervals (15 to 30 minutes). The results of two other basins were in line programming, Soltani et al. (2009) modeled the daily rainfall-runoff of with the real data. Lighvan basin. In that research, the initial modeling of rainfall-runoff was To the best of our knowledge, there is no research examining the done with 15 variables to determine meaningful variables, and the final performance of WANN and LGP models in monthly streamflow modeling was done with meaningful variables and two sets of prediction. Thus, in this study we initially developed WANN and LGP mathematical operators. The obtained model was recommended as the models to predict monthly streamflow at a particular river and then model of Lighvan basin's rainfall-runoff because of its simplicity and compared the prediction results with the observations. Following this, higher accuracy. based upon two successive gauging stations records we put forward Gholizadeh et al. (2016) investigated the function of genetic six black-box ANN structures as reference models for monthly programming as an intelligent modern method for estimating Kasilian streamflow prediction on Coruh River located in eastern Black Sea basin's rainfall-runoff. The results revealed that the aforementioned region (Turkey). Then we applied wavelet transform to our ANN-based model had a proven ability in estimating rainfall-runoff of Kasilian basin reference models. The ANN component of the models can handle the using meteorological and hydraulic parameters. While introducing the nonlinearity and non-stationary elements, while the wavelet component genetic programming method as a direct method for predicting the river can deal with seasonal (cyclic) non-stationary elements of the flow, Danandeh Mehr and Majdzadeh. (2010) used this method in order phenomenon. In the second step, we developed monthly streamflow to investigate the effect of daily river discharge in predicting the daily prediction models based on explicit LGP technique. Ultimately, we discharge of Absardeh River basin located in Lorestan Province and discussed the both accuracy and applicability of ANN, WANN, and LGP compared the results with those obtained from the artificial neural techniques via the comparison of their performances. Such a network. The results indicated that genetic programming had proper comparison has also been done by Wang et al. (2009) among GP and efficiency and high accuracy in predicting the rivers flow in comparison ANN for monthly discharge forecasting but they did not consider with the artificial neural network. Farboodnam et al. (2009) predicted wavelet transform in their neural networks. Aytec et al. (2008) made the daily discharge of Lighvan River using the genetic programming use of neural networks and genetic programming for modeling daily method and compared the results with the artificial neural network. rainfall-runoff of Juniata River basin in Pennsylvania in the US and According to the results of their research, the genetic programming found out that genetic programming models the rainfall-runoff process method had much higher accuracy in predicting daily river discharge in more accurately than neural networks. comparison with the artificial neural network. One of the most complex hydrologic processes is the process of 2. Materials and methods changing rainfall to runoff that is affected by different physical and 2.1. The region under study hydrological parameters. Modeling the rainfall-runoff model and predicting the river discharge is an important measure to take in Khorramabad River basin with an area of 1640 square kilometers managing and controlling floodwater, designing hydraulic structures in is located in the southwest of Iran in Lorestan Province with basins and managing drought (Salajghe et al. 2009). Since when (Sherman. 1932) suggested the concept of unit hydrograph, several geographical location of 33 degrees and 26 minutes and 76 seconds of linear and non-linear hydrological models have been widely used for northern latitude to 48 degrees and 14 minutes and 77 seconds of simulating the rainfall-runoff process. These models have developed eastern longitude. This basin makes up about 16 percent of the over time, quality of the recommended models has constantly improved Kashkan River basin. The maximum height of the basin under study is as a result of the introduction of new devices and enhancement of 2876 meters and its minimum height is 1112 meters. Fig. 1 the location human knowledge. Despite the long history of statistical hydraulic and of the basin under study. hydrological models, experience shows that regardless of their strengths, such models have lots of weaknesses as well. The fact that The required data for conducting the current research include daily most of the hydrometric stations are new, the defects in the statistics of rainometric and hydrometric data of between 1991 and 2013, the data most of these stations, the need to long historical information and related to the basin physiography as well as the data related to CN different meteorological parameters, the need to various parameters value or curve number. Cham Anjir Station has been used as the such as river geometry, time-consuming deduction of physical models, rainometric and hydrometric station in the present research. The fact

e g a P

| Please cite this article as: H.R. Babaali, Z. Ramak, R. Sepahvand, The efficiency of genetic programming model in simulating rainfall-runoff

455 process (Case Study: Khorramabad river basin), Journal of Applied Research in Water and Wastewater, 5 (2), 2018, 454-460.

Babaali et al./ J. App. Res. Wat. Wast. 10(2018) 454-460 that the data are more complete in such stations, these stations have 1- An initial population of compound functions indicating prediction been selected. The following table illustrates the features of employed patterns are considered randomly (creation of chromosomes). 2- rainometric and hydrometric stations. Introducing the initial population (chromosomes) to the computer and evaluating each person (genes) of the said population using fitting 2.2. Genetic Programming functions (identification of the most effective individuals in the nature of phenomenon). 3- Selecting the effective genes in order to replicate, Genetic programming, which was initially innovated by (Cramer, mutate, have sexual intercourse, and reproduce new individuals with 1985) and then developed by (Koza. 1992), is a method of evolutionary modified traits (children). 4- Initiating the repetitive developmental algorithms that is practically developed from Genetic Algorithm (GA). process for children in each reproduction. The fourth step will be The step-by-step process of genetic programming is as follows: repeated in a specified number of times until the best response is obtained.

Fig. 1. Geographical location of the basin under study.

Table 1. The features of employed rainometric and hydrometric stations. Station Name Type of Station Geographical Longitude Geographical Latitude Height Cham Anjir Hydrometric 48°-10' 33°-26' 1140 Cham Anjir Rainometric 48°-35' 33°-25' 1166

Like GA, GP starts its work with the initial sets of random solution. In addition, this software is capable of using any type of solutions called population. Each individual in the population is called a functions, phrases and parameters in the solution process and system. chromosome that represents the solution for the intended problem. GP-LAB has a parametric structure that is shown as a tree and is made up of three main patterns including Set Vare, Gen Pop, and Then, the chromosomes, which are illustrated as an Element Tree (ET), generation. Each pattern has a substructure set that does a particular are examined by a fitting function so that the level of appropriateness task depending on the type of problem. Furthermore, each of the of a solution to a particular problem can be determined. This population patterns can use one to several parameters and functions depending evolves with the help of genetic operators in many future generations. on the conditions. The purpose of this, exactly like genetic natural compatibility, is to create populations or generations which are more adaptable to the 3. Modeling the flow using the genetic programing method environment than the previous ones (Liong. 2002). Fig. 2 demonstrates the structure of the genetic programing algorithm. In the present In this section of the research, the genetic programming method research, the GP-LAB software has been employed to use genetic has been employed in order to make and produce a model that can predict and estimate Khorramabad River discharge based on the rate programing, which will be explained in the following. of precipitation. In this method, the following parameters have been GP-LAB software is a simple understandable application in the used as the inputs of the simulated model so as to make close-to-reality MATLAB programming language that is adjusted as a set of predictions. programming codes and functions. One of the most important advantages of this method is the possibility to change and adjust the  Precipitation on day t (Pt) application for different status or to develop its codes as desired. This  Precipitation on day t-1 (Pt-1) software application, like other black box applications, make use of  Precipitation on day t-2 (Pt-2) reverse engineering viewpoint as a strategy to reach the proper

e g a P

Please cite this article as: H.R. Babaali, Z. Ramak, R. Sepahvand, The efficiency of genetic programming model in simulating rainfall-runoff

| process (Case Study: Khorramabad river basin), Journal of Applied Research in Water and Wastewater, 5 (2), 2018, 454-460. 456

Babaali et al./ J. App. Res. Wat. Wast. 10(2018) 454-460

 Discharge on day t-1 (Qt-1) the highest relevance with the observational data in each prediction In the current research, we have tried to use the abovementioned time step. Table 3 represents the initial settings of the simulator model parameters to present an equation to simulate the river discharge with to this aim.

Fig. 2. The cycle and structure of genetic programming (Koza. 1992).

Table 2. Statistical characteristics of the data used by cham anjir hydrometric station. Statistical Characteristic Discharge (m3/s) Number of Data 3652 Maximum Value 186.35 Minimum Value 0 Mean 11.03 Variance 141.41 Standard Deviation 11.89

Table 3. Initial settings employed in the simulator model of genetic programming. Number of Trees of each Generation Depth of each Tree Number of Replications Possibility of Mutation Possibility of Coupling 250 3 450 0.5 0.6

In order to introduce the patterns and identify the best pattern of replications is the optimal number for replications of the simulator dominating the nature of flow in the present research, we firstly used model. Fig. 3 illustrates the results obtained from the optimal number of fitting functions and conducted replication and developmental replications to be used in the simulator model of genetic programming. processes to find the number of optimal replication and after dividing all After specifying the initial settings of the simulator model as well statistical data into two sets of training and experiment (52% training as determining the number of optimal replications to be used in the and 48% experiment), we implemented the program for 1000 genetic programming model, we began to determine the optimal replications and observed that after 450 replications, RMSE value equations obtained from the simulator model. the optimal equations became almost constant and the tilt-shift turned to zero. This number obtained from the simulator model have been presented in Table 4.

Table 4. Three optimal equations obtained in the simulator model of genetic programming. Equations Obtained from the Simulator Model

1) 0.36 (Qt-1) Plus 0.366(Pt) Plus COS(Pt) Plus(0.8)

2) Tan(Qt-1) Plus (Pt) Plus (SQRT(SQRT(Pt-2) Plus (Pt))) Plus SQRT(Sin(Pt-1))

3) Plus(Plus(Plus(Plus(Plus(Pt,cos(Mysqrt(Plus(Pt,Minus(Mysqrt(Qt-1,Qt-1)))))

e g a P

| Please cite this article as: H.R. Babaali, Z. Ramak, R. Sepahvand, The efficiency of genetic programming model in simulating rainfall-runoff

457 process (Case Study: Khorramabad river basin), Journal of Applied Research in Water and Wastewater, 5 (2), 2018, 454-460.

Babaali et al./ J. App. Res. Wat. Wast. 10(2018) 454-460

Fig. 3. Determining the number of optimal replication to be used in the simulator model of genetic programming.

In order to examine the aforementioned equations, Root Mean ∑푛 |푋 − 푌 | 푀퐴퐸 = 푖=1 푖 푖 (3) Square Error (RMSE) and Mean Squared Error (MSE) indexes and 푛 2 Coefficient of Determination (R ) have been used, which can be Where Xi and Yi are the ith real and estimated datum, 푋̅ is the mean calculated through equations 1, 2, and 3, respectively. of the real data, 푌̅ is the mean of the estimated data, and n is the (∑푛 (푋 − 푋̅)(푌 − 푌̅))2 number of evaluation samples. Low values of RMSE and MSE and the 푅2 = 푖=1 푖 푖 (1) 푛 ̅ 2 ̅ 2 high value of R2 can show the accuracy of each pattern in comparison (∑푖=1(푋푖 − 푋) (푌푖 − 푌) ) with other competitive patterns. The results of the mentioned equations ∑푛 (푋 − 푌 )2 푅푀푆퐸 = √ 푖=1 푖 푖 (2) have been given in Table 5. 푛 Table 5. Results of evaluating the obtained optimal equations from the simulator model of genetic programming. Equation Training Experiment RMSE MSE R2 RMSE MSE R2 1 0.75 0.65 0.92 1.01 1.33 0.89 2 0.77 0.5 0.94 0.98 1.2 0.92 3 0.65 0.433 0.97 0.9 1.02 0.96

According to Tables 4 and 5, using equation 3 in Table 4 had the through genetic programming in comparison with the real discharge. As highest relevance with the observational data. Therefore, simulating the seen in that Fig., high consistency is evident between the real data and discharge corresponding to different precipitations has been done using the simulated ones this equation. Fig. 4 shows the simulated discharge using this equation

Fig. 4. Results of the simulator model of genetic programming.

4. Conclusions research by (Danandeh Mehr and Majdzadeh Tabatabaei. 2010) on In the current research, the genetic programming model was used predicting Absardeh River discharge using genetic programing. to simulate the rainfall-runoff process. The statistical indexes related to Consequently, genetic programing can be considered among the most using equations 1 to 3 in table 5 indicate that equation 3 with the lowest accurate available methods in predicting river discharge. RMSE and MSE and the highest R2 have the best efficiency and Acknowledgement consistency in simulating this process. According to the results of this study, the genetic programming model is generally a direct accurate The authors would like to thank Islamic Azad University for financial way for predicting the river discharge in Khorramabad River basin. In support of this study, Khorramabad, Iran. addition, the results of this research are in line with the results of (Guven. 2009) on predicting Schuylkill River discharge as well as the

e g a P

Please cite this article as: H.R. Babaali, Z. Ramak, R. Sepahvand, The efficiency of genetic programming model in simulating rainfall-runoff | process (Case Study: Khorramabad river basin), Journal of Applied Research in Water and Wastewater, 5 (2), 2018, 454-460. 458

Babaali et al./ J. App. Res. Wat. Wast. 10(2018) 454-460

References

Abrahart R.J., Anctil F., Coulibaly P., Dawson C.W., Mount N.J., See Kisi O., and Cigizoglu H.K., Comparison of different ann techniques in L.M., Shamseldin A.Y., Solomatine D.P., Toth E., Wilby R.L., Two river flow prediction, Civil Engineering and Environmental Systems decades of anarchy emerging themes and outstanding challenges 24 (2007) 211–231. for neural network modelling of surface hydrology, Progress in Kisi O., Stream flow forecasting using neuro-wavelet technique, Physical Geography 36 (2012) 480–513. Hydrological Processes 22 (2008) 4142–4152. Anctil F., Tape D., An exploration of artificial neural network rainfall- Koza J.R., Genetic programming: on the programming of computers by runoff forecasting combined with wavelet decomposition, Journal of means of natural selection, Cambridge, MA: MIT Press, (1992) 35- Environmental Engineering and Science 3 (2004) 121–128. 80. Aytek A., and Asce M., An application of artificial intelligence for rainfall Kuchment L.S., Demidov V.N., Naden P.S., Cooper D.M., Broadhurst runoff modeling, Journal of Earth System Science 117 (2008) 145- P., Rainfall-runoff modelling of the ouse basin, north yorkshire: an 155. application of a physically based distributed model, Journal of Aytek A.. and Kisi O.A., Genetic programming approach to suspended Hydrology 181 (1996) 323–342. sediment modelling, Journal of Hydrology 351 (2007) 288-298. Labat D., Recent advances in wavelet analyses: Part 1 – a review of Besaw L.E., Rizzo D.M., Bierman P.R., Hackett W.R., Advances in concepts, Journal of Hydrology (Amsterdam) 314 (2005) 275–288. ungauged streamflow prediction using artificial neural networks, Liong S.Y., Gautam T.R., Khu S.T., Babovic V., and Muttil N., Genetic Journal of Hydrology 386 (2010) 27–37. programming: a new paradigm in rainfall- runoff modelling, Journal Can I., Tosunogulu F., Kahya E., Daily streamflow modelling using of American Water Resources Association 38 (2001) 705-718. autoregressive moving average and artificial neural networks Londhe S., Charhate S., Comparison of data-driven modelling models: case study of Coruh basin, Turkey, Water and Environment techniques for river flow forecasting, Hydrological Sciences Journal Journa 26 (2012) 567–576. 55 (2010) 1163–1174. Danandeh Mehr A., and Majdzadeh Tabatabaei M., Investigating the Lopes HS., and Weinert WR., EGIPSYS: An enhanced gene effect of daily discharge on predicting the rivers' flow using genetic expression programming approach for symbolic regression programing, Water and Soil Magazine (Science and Agricultural problems, International Journal of Applied Mathematics and Industries) 24 (2010) 325-333. Computer Science 14 (2004) 375-384. Dolling O.R., Varas E.A., Artificial neural networks for streamflow Mallat S., A wavelet tour of signal processing, second ed. Academic prediction, Journal of Hydraulic Research 40 (2002) 547–554. Press, San Diego (CA), (1998). Dorado J., Rabunal J.R., Pazos A., Rivero D., Santos A., Puertas J., Mohammad Salehi P., Raeini Sarjaz M., and Zia Tabar Ahmadi M., Prediction and modeling of the rainfall–runoff transformation of a Simulating rainfall-runoff with the mathematical model based on typical urban basin using ANN and GP, Engineering Applications of geographical information system for emameh basin, Journal of Artificial Intelligence 17 (2003) 329–343. Agricultural Sciences and Natural Resources, Natural Resources Farboodnam N., Ghorbani M.A., and A'alami M., Predicting river flow Special 15 (2007) 1-11. using genetic programing (CaseStudy: Lighvan River), Water and Nourani V., Alami M.T., Aminfar M.H., A combined neural-wavelet Soil Science Journal, University of Tbariz 19 (2009) 107-123. model for prediction of Ligvanchai watershed precipitation, Fazaeili H., Using the genetic programing method in modeling rainfall- Engineering Applications of Artificial Intelligence 22 (2009a) 466– runoff, ms thesis, Water Engineering Department, University of 472. Tabriz (2010). Nourani V., Kisi O., Komasi M., Two hybrid artificial intelligence Ghorbani M., Khatibi R., Aytek A., Makarynskyy O., Sea water level approaches for modeling rainfall–runoff process, Journal of forecasting using genetic programming and artificial neural networks, Hydrology 402 (2011) 41–59. Comput. Geosci. UK 36 (2010) 620–627. Nourani V., Komasi M., Alami M.T., Hybrid wavelet–genetic Ghorbani M.A., Kisi O., Aalinezhad M., A probe into the chaotic nature programming approach to optimize ANN modelling of rainfall–runoff of daily streamflow time series by correlation dimension and largest process, Journal of Hydrologic Engineering 17 (2012) 724–741. lyapunov methods, Applied Mathematical Modelling 34 (2010) 4050– Omidi R., Comparing the prediction of khorramabad river discharge 4057. using time series and the artificial neural network, hydrology and Guven A., Linear genetic programming for time-series modelling of daily water resources department, ms thesis, Faculty of Water Sciences, flow rate, Journal of Earth System Science 118 (2009) 137–146. Shahid Chamran Univeristy, Ahwaz (2014). Harun S., Ahmat Nor N.I., and Kassim A.H.M., Artificial neural network Ozger M., Significant wave height forecasting using wavelet fuzzy logic model for rainfall-runoff relationship, Journal Technology 37 (2002) approach, Ocean Engineering 37 (2010) 1443–1451. 1–12. Rabunal J.R., Puertas J., Suarez J., Rivero D., Determination of the unit Huo Z., Feng S., Kang S., Huang G., Wang F., and Guo P., Integrated hydrograph of a typical urban basin using genetic programming and neural networks for monthly river flow estimation in arid inland basin artificial neural networks, Hydrological Processes 21 (2007) 476– of northwest china, Journal of Hydrology 420-421 (2012) 159-170. 485. Imam Qolizadeh S., Karimi Damaneh R., and Mehdi Panah H., Rajaee T., Mirbagheri S.A., Nourani V., Alikhani A., Prediction of daily Estimating the runoff of kasilian basin using the gene expression suspended sediment load using wavelet and neuro-fuzzy combined programing method, natural resources, Environment, and Agriculture model, International Journal of Environmental Science and Studies, Vol. 3, 2nd year- No. 4 and 5 (11 and 12), (2016) 1-7. Technology 7 (2010) 93–110. Jayawardena A.W., Muttil N., and Fernando T.M.K.G., Rainfall-runoff Rathinasamy M.,Khosa R., Multi-scale nonlinearmodel formonthly modeling using genetic programming, International Congress on streamflow forecasting: a wavelet-based approach, Journal of Modeling and Simulation Society of Australia and New Zealand Hydroinformatics 14 (2012) 424–442. (2005) 1841-1847. Salajghe A., Fathabadi A., and Mahdavi M., Investigating the efficiency Khu S.T., Liong S.Y., Babovic V., Madsen H., Muttil N., Genetic of neural-fuzzy methods and statistical models in simulating the programming and its application in real-time runoff forecasting, rainfall-runoff process, Iran's Natural Resources Journal, Grassland Journal of the American Water Resources Association 37 (2001) and Watershed Management Journal 1 (2009) 65-80. 439-451.

e g a P

| Please cite this article as: H.R. Babaali, Z. Ramak, R. Sepahvand, The efficiency of genetic programming model in simulating rainfall-runoff

459 process (Case Study: Khorramabad river basin), Journal of Applied Research in Water and Wastewater, 5 (2), 2018, 454-460.

Babaali et al./ J. App. Res. Wat. Wast. 10(2018) 454-460

Sivapragasam C., Maheswaran R., Veena V., Genetic programming Whigham P.A., and Crapper P.F., Modelling Rainfall-runoff using approach for flood routing in natural channels, Hydrological genetic programming, CSIRO Land and Water, P.O. Box 1666, Processes 22 (2008) 623–628. Canberra, A.C.T. 2601, Australia, Mathematical and Computer Modellhrg 33 (2001) 707-721. Soltani A., Modeling rainfall-runoff using genetic programing and stochastic differential equations (sde) in lighvan basin, MS Thesis in Zahiri A., and Azamathulla H., Comparison between linear genetic Water Resources Filed of Study, Water Engineering Department, programming and M5 tree models to predict flow discharge in University of Tabriz (2010). compound channels, Neural Computing and Applications 24 (2014) 413-420. Wang W.C., Chau K.W., Cheng C.T., Qiu L., A comparison of performance of several artificial intelligence methods for forecasting monthly discharge time series, Journal of Hydrology 374 (2009) 294–

306.

e g a P

Please cite this article as: H.R. Babaali, Z. Ramak, R. Sepahvand, The efficiency of genetic programming model in simulating rainfall-runoff |

4

process (Case Study: Khorramabad river basin), Journal of Applied Research in Water and Wastewater, 5 (2), 2018, 454-460. 60