Estimation of Transverse Dispersion Coefficient of Pollutant Transport in Rivers Using Evolutionary Computations

Document Type : Research Article


1 MSc. Student, Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran

2 Ph.D. Student, Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran

3 Associate Professor, Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran


Surface water is taken into account as one of the most important water resources available to mankind, which is used for various purposes, such as drinking and agriculture. Recently, with the growing urban population, there are many problems associated with the pollution and quality of water resources. Therefore, recognizing and studying the process of mixing and conveying materials in rivers is one of the prominent activities in water resource management programs. In the process of mixing, after the longitudinal dispersion coefficient, the transverse dispersion coefficient is considered as the most effective parameter. According to the importance of dispersion and distribution of pollution in rivers, in order to estimate the transverse dispersion coefficient of pollutants in surface flows, MT and SVM using two Kernels including radial basis function (RBF) and polynomial (Poly) are applied. To achieve this aim, 187 dataset including flow depth (H), flow velocity (U), shear rate (U*) and channel width (W) are used. The results of the evaluation criteria showed that the SVM-Poly model had higher accuracy (R = 0.992 = 0.92 OI =) compared to the SVM-RBF (R = 0.968 and O = 950) and MT (R = 0.966 and OI =0.946) in the training phase for DT estimation. The DT values ​​obtained by proposed models were also evaluated for testing dataset. Based on the result, it was found that SVM-RBF had the best ability to estimate DT with the lowest error (RMSE = 0.029). In addition, comparing the performance of intelligent methods with empirical relationships suggests that empirical relationships failed to show acceptable accuracy.


Main Subjects

[1]. Riahi-Madvar H, Ayyoubzadeh SA, Khadangi, E, Ebadzadeh, MM. An expert system for predicting longitudinal dispersion coefficient in natural streams by using ANFIS. Expert Systems with Applications. 2009; 36(4), pp.8589-8596.
[2]. Fischer, HB, List E, Koh R, Imberger J, Brooks N. Mixing in inland and coastal waters Academic Press. New York, 1979.
[3]. Chau KW. Transverse mixing coefficient measurements in an open rectangular channel. Advances in Environmental Research. 2000; 4(4), 287-294.
[4]. Fischer HB. Transverse mixing in a sand-bed channel. Professional Paper. 1967; No. 575-D, U.S. Geological Survey
[5]. Rutherford JC. River Mixing. John Wiley and Sons, Chichester, UK. 1967.
[6]. Deng ZQ, Singh VP, Bengtsson L. Longitudinal dispersion coefficient in straight rivers. J Hydraul Eng. 2001; 127:919–927
[7]. Bansal MK (1971) Dispersion in natural streams. J Hydr Div ASCE 97(11): 1867–1886.
[8]. Kisi O, Parmar KS. Application of least square support vector machine and multivariate adaptive regression spline models in long term prediction of river water pollution, Journal of Hydrology. 2015; 534, 104-112.
[9]. Khosravi A, Koury R, Machado L, Pabon, J. Prediction of wind speed and wind direction using artificial neural network, support vector regression and adaptive neuro-fuzzy inference system. Sustainable Energy Technologies and Assessments. 2018; 25, 146-160.
[10]. Najafzadeh M, Ghaemi A, Emamgholizadeh S. Prediction of water quality parameters using evolutionary computing-based formulations. International Journal of Environmental Science and Technology. 2018; 1-20.
[11]. Sahay RR. Prediction of longitudinal dispersion coefficients in natural rivers using artificial neural network, Environ, Fluid Mech. 2011; 11(3), 247-261.
[12]. Etemad-Shahidi A, Taghipour M. Predicting longitudinal dispersion coefficient in natural streams using M5′ model tree. Journal of Hydraulic Engineering, ASCE. 2012; 138(6), 542-554.
[13]. Najafzadeh M, Tafarojnoruz A. Evaluation of neuro-fuzzy GMDH-based particle swarm optimization to predict longitudinal dispersion coefficient in rivers. Environmental Earth Sciences. 2016; 75(2), 157.
[14]. Rezaei-Balf M, Noori R, Berndtsson R, Ghaemi A, Ghiasi B. Evolutionary polynomial regression approach to predict longitudinal dispersion coefficient in rivers. Journal of Water Supply: Research and Technology-Aqua. 2018; 67(5), 447-457.
[15]. Huai W, Shi H, Yang Z, Zeng Y. Estimating the Transverse Mixing Coefficient in Laboratory Flumes and Natural Rivers. Water, Air, & Soil Pollution. 2018; 229(8): p. 252.
[16]. Vapnik VN, Statistical Learning Theory. John Wiley. New York, 1998; 16-29.
[17]. Noori R, Abdoli MA, Ameri A, Jalili-Ghazizade M. Prediction of municipal solid waste generation with combination of support vector machine and principal component analysis: A case study of Mashhad. Environmental Progress and Sustainable Energy. 2008; 28 (2), 249-258.
[18]. Quinlan JR. Learning with continuous classes. In: Proceedings of the Fifth Australian Joint Conference on Artificial Intelligence, World Scientific. 1992; 343-348.
[19]. Zahiri A, Azamathulla HMd. Comparison between linear genetic programming and M5 tree models to predict flow discharge in compound channels. Neural Computing and Applications. 2012; 24(2), 413-420.
[20]. Rahimikhoob A. Comparison of M5 Model Tree and Artificial Neural Network’s Methodologies in Modelling Daily Reference Evapotranspiration from NOAA Satellite Images. Water Resources Management. 2016; 1-13.
[20]. Jeon TM, Baek KO, Seo IW. Development of an empirical equation for the transverse dispersion coefficient in natural streams. Environmental Fluid Mechanics. 2007; 7(4), 317– 329.
[21]. Tabatabaei SH, Heidarpour M, Ghasemi M, Hoseinipour EZ. Transverse mixing coefficient on dunes with vegetation on a channel wall. World Environmental and Water Resources Congress. 2013; 1903–1911.
[22]. Long T, Guo J, Feng Y, Huo G. Modulus of transverse diffuse simulation based on artificial neural network. Chongqing Environmental Science. 2002; 24(2), 25–28.
[23]. Pilechi A, Mohammadian A, Rennie CD, Zhu DZ. Efficient method for coupling field data and numerical modeling for the estimation of transverse mixing coefficients in meandering rivers. Journal of Hydraulic Engineering. 2016; 142(6), 04016009.
[24]. Beltaos S, Day TJ. A field study of longitudinal dispersion. Canadian Journal of Civil Engineering. 1974; 5(4), 572–585.
[25]. Webel, G, Schatzmann M. Transverse mixing in open channel flow. Journal of Hydraulic Engineering.1978; 110(4), 423–435.
[26]. Yotsukura, N, Sayre WW. Transverse mixing in natural channels. Water Resources Research.1976; 12(4), 695–704.
[27]. Engmann JEO, Kellerhals R. Transverse mixing in an ice-covered river. Water Resources Research. 1974; 10(4), 775– 784.
[28].  Najafzadeh M, Ghaemi A. Prediction of the five-day biochemical oxygen demand and chemical oxygen demand in natural streams using machine learning methods. Environmental monitoring and assessment. 2019; 191(6), 380.

[29]. Gandomi AH, Alavi AH, Sahab MG, Arjmandi P. Formulation of elastic modulus of concrete using linear genetic programming. Journal of Mechanical Science and Technology. 2010; 24(6), 1273-1278.
[30]. Gandomi A, Yun G, Alavi A. An evolutionary approach for modeling of shear strength of RC deep beams. Materials and Structures. 2013; 46,2109-2119.
Volume 6, Issue 4
January 2020
Pages 901-912
  • Receive Date: 30 April 2019
  • Revise Date: 15 July 2019
  • Accept Date: 15 July 2019
  • First Publish Date: 22 December 2019
  • Publish Date: 22 December 2019