Application Of Intelligent Algorithms In Providing Optimal Unit Hydrograph Using Probability Distribution Functions

Document Type : Original Article

Authors

1 M.Sc. Student, Water Resources Engineering, University of Birjand., Birjan., Iran

2 Associate Professor of Civil Engineering., University of Birjand., Birjand., Iran

3 Assistant Professor of Water Engineering Department., University of Birjand., Birjand., Iran

Abstract

The most important steps that were taken in hydrological analysis and design Hydrograph preparation, was Unit Hydrograph concept. The Unit Hydrograph was used to determine the flood, caused by the storms of duration and different intensity. The purpose of this study was the use of intelligent algorithms to provide optimal model Unit Hydrograph using the probability distribution function. For this purpose, the log-normal probability distribution function, gamma and inverse Gaussian was used. In this model, the objective function was to minimize the Sum of squared differences between the observed and predicted runoff Hydrograph at the catchment area. Computed runoff Hydrograph estimated using the proposed model by the probability distribution function. According to the values of root mean square error (RMSE), correlation coefficient (R2) and the Nash-Sutcliffe coefficient (NS), respectively 0.06,0.96,0.96 had log-normal distribution function better performance than other distribution functions at optimized Hydrograph. This distribution function had a good performance in computing peak flow. So that the calculated peak flow was near observed runoff peak flow. Also, genetic algorithms and particle swarm intelligence showed better results than other algorithms in the calibration of probability distribution functions.

Keywords


نجفی،م.ر. 1381. ترجمه سیستم های هیدرولوژیکی مدل­سازی بارش-رواناب وی پی سینگ انتشارات دانشگاه تهران دو جلد 1056 ص
Borhani Darian,A.R and Farahmandfar,Z. 2011. Calibration of Rainfall-runoff models using MBO algorithm. the Iranian Society of Irrigation & Water Engineering 1 (4), 60-71.
Bender,D.L and Roberson,J.A. 1961. The use of dimensionless unit hydrograph to derive unit hydrographs for some Pacific basins. Journal of Geophysical Research. 66: 521-527.
Bruen, M. and Dooge, J. C. I. 1984. An efficient and robust method for estimation unit hydrograph ordinations. Journal of Hydrology. 70:1-24
Deinger,R.A. 1969. Linear program for hydrologic analysis. Water Resources Research. 5: 1105-1109
Duan,Q., Sorooshian,S and Gupta,V.K. 1992. Effective and efficient global optimization for conceptual rainfall-runoff models. Water Resource Research, 28(4),PP.1015-1031.
Duan,Q., Sorooshian,S and Gupta,V.K. 1993. Shuffled Complex Evolution approach for effective and efficient global optimization”, Journal of Optimization Theory and Application, 76(3), PP.501-521.
Duan,Q., Sorooshian,S and Gupta,V.K. 1994. Optimal use of the SCE-UA global optimization method for calibration watershed models”, Journal of Hydrology, 185, PP.265-284.
Eusuff,M and Lansey,K. 2003. Optimization of Water Distribution Network Design Using the Shuffled Frog Leaping Algorithm. Journal of Water Resources Planning and Management, 129(3), 210–225
Eusuff,M.M., Lansey,K., Pasha,F.  2006. Shuffled frog-leaping algorithm: a memetic meta-heuristic for discrete optimization. Engineerin Optimization, vol. 38, no. 2, pp.129–154,
Fan,S.K.S., Liang,Y.C., Zahara,E. 2006. A Genetic algorithm and a particle swarm optimizer Hybridized with Nelder-Mead simplex search. Computers & Industrial Engineering, 50, pp. 401-425.
Kao,Y.T., Zahara, E. 2008. A hybrid genetic algorithm and a particle swarm optimization for multimodal functions. Applied Soft Computing, 8 (2), pp. 849-857.
Kennedy,J and Eberhart,R. 1995. Particle Swarm Optimization, Proc. Of the International Conference on Neural Networks, Perth, Australia, IEEE, Piscataway, 1995, pp. 1942-1948.
Liu,Y.B., Gebremeskel,S., De Smedt,F., Hoffmann,L.,  Pfister, L. 2003. A diffusive transport approach for flow routing in GIS-based flood modelling. Journal of Hydrology, 283, PP. 91-106.
Mays,L.W and Taur,C.K. 1982. Unit hydrograph via nonlinear programming. Journal of Water Resources Research, 18, 744-752.
Mays,L.W and Coles,L. 1980. Optimization of unit hydrograph determination. Journal of Hydraulic Engineering, 106, 85-97.
Molnar,P., Ramirez,J.A. 1998.  Energy dissipation theories and optimal channel characteristics of river networks. Water Resources Research. 34 (7), 1809–1818.
Nojavan,M and Akbarpur,A. 2010. Comparison of optimal design of unit hydrograph using simulated annealing and genetic algorithm(case study:Kameh watershed),Iranian Journal of Geology, 4(14),pp. 23-31.
Olivera,F and Maidment,D. 1999. Geographic information systems(GIS)-based spatially distributed model for runoff routing", Water Resources Research,Vol.35, No.4, Pages 1155-1164.
Prasad,T.D., Gupta,R and Prakash,S. 1999.  Determination of optimal loss rate Parameters and unit hydrograph. Journal of Hydrology, 4, 83-87.
Qaderi,K., Mohammad Vali Samani,J., Eslami,H.R and Saghafian,B. 2006. Automatic calibration of a rainfall-runoff model using SCE optimization method, Iran Water Resources Research, 2(2): 39-52.
Rajib,K.B. 2004.  Optimal Design of Unit Hydrographs using probability distribution and genetic algorithms. Journal of IndianAcademy of Sciences, 29, 499-508.
Singh,V.P.1988. Hydrologic Systems, Prentice Hall, Englewood Cliffs.
Singh,V.P. 1976. Unit hydrographs, A comparative study. Journal of Water Resources Research, 12, 381-392
Wang,F., Qiu,Y. 2005. A modified particle swarm optimizer with roulette selection operator, Proc. Nat. Lang. Process. Knowl. Eng. Pp. 765-768,