Comparison of conventional and intelligent methods in estimating Copula Function Parameters for multivariate frequency analysis of low flows (Case Study: Dez River Basin)

Document Type : Research Article

Authors

1 PhD Candidate of Water Resources Engineering. Shahid Chamran University, Ahvaz, Iran

2 Water Engineering Department, Shahid Chamran University, Ahvaz, Iran

3 Department of Statistics, Shahid Chamran University, Ahvaz, Iran

4 Water Engineering Department, Shahre Kord University, Shahre Kord, Iran

Abstract

Over the recent years, the dependence structure among hydrological variables has been taken into consideration and it resulted in employment of the multivariate analysis as a suitable alternative for univariate methods. In this study, the copula functions were employed for multivariate frequency analysis of low flows of Dez River basin at Tange Panj-Bakhtiari (TPB) and Tange Panj-Sezar (TPS) hydrometric stations. First, 7-d series of low flow was extracted from measured daily flows at the studied stations over the period of 1956-2012. In the next stage, 11 different distribution functions were fitted into the low flow data whereby logistic distribution had the best fit on the TPB station and the GEV distribution had the best fit on the low flow data of TPS station. After specifying the best fitted marginal distributions, the copula parameter should be estimated. In this study, two methods of inference function for margins (IFM) and particle swarm optimization (PSO) were used to estimate copula parameter. The results showed that the PSO method outperformed IFM in estimating the copula parameter. Among the Ali - Mikhail – Haq, Clayton, Frank, Galambos and Gumbel-Hougaard copulas, the Frank copula function had the lowest error and the highest accuracy in constructing the joint distribution of paired 7-d low flows data and was used for calculating the joint return periods in two states of “OR” and “AND”.

Keywords

Main Subjects


 
[1]. Bahremand A, Alvandi E, Bahrami M, Dashti Marvili M, Heravi H, Khosravi GHR, et al. Copula functions and their application in stochastic hydrology. Journal of Conservation and Utilization of Natural Resources. 2015; 4 (2):1-20. [Persian]
[2]. Salvadori G, De Michele C. On the use of copulas in hydrology: theory and practice. Journal of Hydrologic Engineering. 2007;12(4):369-80.
[3]. Salari Jazi M. Assessment of the Flooding Risk for River with Tidal Interaction Zones. PhD Thesis. 2013.
[4]. Sklar M. Fonctions de répartition à n dimensions et leurs marges. Université Paris. 1959.
[5]. Frees EW, Valdez EA. Understanding relationships using copulas. North American actuarial journal. 1998; 2(1):1-25.
[6]. Favre AC, El Adlouni S, Perreault L, Thiémonge N, Bobée B. Multivariate hydrological frequency analysis using copulas. Water resources research. 2004; 40(1): 25-39.
[7]. Brunner MI, Seibert J, Favre AC. Bivariate return periods and their importance for flood peak and volume estimation. Wiley Interdisciplinary Reviews: Water. 2016; 3(6):819-33.
[8]. Duan K, Mei Y, Zhang L. Copula-based bivariate flood frequency analysis in a changing climate—A case study in the Huai River Basin, China. Journal of Earth Science. 2016; 27(1):37-46.
[9]. Serinaldi F. A multisite daily rainfall generator driven by bivariate copula‐based mixed distributions. Journal of Geophysical Research: Atmospheres. 2009; 114(10): 70-91.
[10]. Seo BC, Krajewski WF, Mishra KV. Using the new dual-polarimetric capability of WSR-88D to eliminate anomalous propagation and wind turbine effects in radar-rainfall. Atmospheric Research. 2015; 153:296-309.
[11]. Mirabbasi R, Anagnostou EN, Fakheri-Fard A, Dinpashoh Y, Eslamian S. Analysis of meteorological drought in northwest Iran using the Joint Deficit Index. Journal of Hydrology. 2013; 492:35-48.
[12]. Abdi A, Hassanzadeh Y, Talatahari S, Fakheri-Fard A, Mirabbasi R. Parameter estimation of copula functions using an optimization-based method. Theoretical and Applied Climatology. 2016. DOI: 10.1007/s00704-016-1757-2.
[13]. Joe H. Multivariate models and multivariate dependence concepts. CRC Press. 1997.
[14]. Eberhart R, Kennedy J. A new optimizer using particle swarm theory. InMicro Machine and Human Science, 1995. MHS'95., Proceedings of the Sixth International Symposium on 1995, (pp. 39-43). IEEE.
[15]. Reddy MJ, Singh VP. Multivariate modeling of droughts using copulas and meta-heuristic methods. Stochastic environmental research and risk assessment. 2014; 28(3):475-89.
[16]. Rakhecha PR. Probable maximum precipitation for 24-h duration over an equatorial region: Part 2-Johor, Malaysia. Atmospheric Research. 2007; 84(1):84-90.
[17]. Khalili K, Tahoudi MN, Mirabbasi R, Ahmadi F. Investigation of spatial and temporal variability of precipitation in Iran over the last half century. Stochastic Environmental Research and Risk Assessment. 2016; 30(4):1205-21.
[18]. Zahedianfar F, Ghorbani Kh, Meftah Halaghi M, Abdolhosseini m, and Dehghani A. Flood Frequency Analysis on the basis of extreme values theory (Case study: Arazkuseh hydrometric station, Golestan). Journal of Water and Soil Conservation. 2015; 22(3): 115-135. [Persian]
[19]. Zhang Q, Chen YD, Chen X, Li J. Copula-based analysis of hydrological extremes and implications of hydrological behaviors in the Pearl River basin, China. Journal of Hydrologic Engineering. 2011;16(7): 598-607.
[20]. Hosking JR, Wallis JR. The effect of intersite dependence on regional flood frequency analysis. Water Resources Research. 1988; 24(4): 588-600.
[21]. Nelsen RB. An introduction to copulas. Springer Science & Business Media. 2007.
[22]. Eberhart R, Simpson P, Dobbins R. Computational intelligence PC tools. Academic Press Professional, Inc. 1996.
[23]. Shi Y, Eberhart RC. Parameter selection in particle swarm optimization. InInternational Conference on Evolutionary Programming 1998 Mar 25 (pp. 591-600). Springer Berlin Heidelberg.
[24]. Hamed Ensaniyat, N. Daily Runoff Simulation Using the PSO Algorithm in Catchment Model Optimization. Msc Thesis. 2013. [Persian]
[25]. Nash JE, Sutcliffe JV. River flow forecasting through conceptual models part I—A discussion of principles. Journal of hydrology. 1970; 10(3): 282-90.
[26]. Yue S, Rasmussen P. Bivariate frequency analysis: discussion of some useful concepts in hydrological application. Hydrological Processes. 2002; 16(14):2881-98.
 
 
Volume 4, Issue 2
June 2017
Pages 315-329
  • Receive Date: 24 January 2017
  • Revise Date: 04 March 2017
  • Accept Date: 15 March 2017
  • First Publish Date: 22 June 2017
  • Publish Date: 22 June 2017