Joint frequency analysis of rainfall characteristics using copula functions (Case study: Kasiliyan watershed)

Document Type : Research Article

Authors

1 Shahid Chamran University of Ahvaz

2 profossor of hydrology

3 Shahrekord University

Abstract

Recently, copula functions have attracted great attention of hydrologists as a practical tool for multivariate frequency analysis of climatological phenomena. In this study, we focus on the joint frequency analysis of two dependent characteristics of rainfall, including depth (mm) and duration (hr) using copulas for 522 events recorded in Sangdeh rain gauge station located in Kasiliyan watershed. To join the marginal distributions and constructing the joint distribution, seven copulas including Clyton, Ali-Mikhail-Haq, Farlie-Gumbel-Morgenstern, Frank, Galambos, Gumbel-Hougaard and Placket were used and evaluated. By comparing the mentioned parametric copulas with an empirical copula, we found that the Placket is the the best fitted copula on the considered variables. Finally, the joint probabilities, joint return periods and conditional joint return periods were calculated and plotted. For example, joint probability values for two events with duration of 12 and 24 (hr) given rainfall depth that exceeds 15 (mm) were calculated as 0.2663 and 0.7693, respectively. Also, conditional return period was calculated equal to 9.19 year for an event with depth of 30 (mm), given rainfall duration that exceeds 24 (hr) and equal to 14.94 year for an event with duration of 24 (hr), given rainfall depth that exceeds 30 (mm).

Keywords

Main Subjects


 Shiau JT. Fitting drought duration and severity with two-dimensional copulas. Water Resour Manag. 2006;20(5):795–815.
[2]. Zhang L, Singh VP. Bivariate rainfall frequency distributions using Archimedean copulas. J Hydrol. 2007;332(1–2):93–109.
[3]. Ganguli P, Reddy MJ. Analysis of ENSO-based climate variability in modulating drought risks over western Rajasthan in India. J Earth Syst Sci. 2013;122(1):253–69.
[4].          Abdul Rauf UF, Zeephongsekul P. Copula based analysis of rainfall severity and duration: a case study. Theor Appl Climatol. 2014;115(1):153–66.
[5]. Reddy MJ, Ganguli P. Bivariate flood frequency fnalysis of upper Godavari river flows using Archimedean copulas. Water Resour Manag. 2012;26(14):3995–4018.
[6]. Kao S-C, Govindaraju RS. A bivariate frequency analysis of extreme rainfall with implications for design. J Geophys Res Atmospheres. 2007;112(D13): 1–15.
[7]. Ghosh S. Modelling bivariate rainfall distribution and generating bivariate correlated rainfall data in neighbouring meteorological subdivisions using copula. Hydrol Process. 2010;24(24):3558–67.
[8]. Vandenberghe S, Verhoest NEC, Onof C, De Baets B. A comparative copula-based bivariate frequency analysis of observed and simulated storm events: A case study on Bartlett-Lewis modeled rainfall. Water Resour Res. 2011;47(7): 1–16.
[9]. Zhang Y, Habib E, Kuligowski RJ, Kim D. Joint distribution of multiplicative errors in radar and satellite QPEs and its use in estimating the conditional exceedance probability. Adv Water Resour. 2013;59:133–45.
[10]. Bárdossy A, Pegram GGS. Space-time conditional disaggregation of precipitation at high resolution via simulation. Water Resour Res. 2016;52(2):920–37.
 
[11]. Carreau J, Bouvier C. Multivariate density model comparison for multi-site flood-risk rainfall in the French Mediterranean area. Stoch Environ Res Risk Assess. 2016;30(6):1591–612.
[12]. Dai Q, Han D, Zhuo L, Zhang J, Islam T, Srivastava PK. Seasonal ensemble generator for radar rainfall using copula and autoregressive model. Stoch Environ Res Risk Assess. 2016;30(1):27–38.
[13]. Grimaldi S, Petroselli A, Salvadori G, De Michele C. Catchment compatibility via copulas: A non-parametric study of the dependence structures of hydrological responses. Adv Water Resour. 2016;90:116–33.
[14]. Guo E, Zhang J, Si H, Dong Z, Cao T, Lan W. Temporal and spatial characteristics of extreme precipitation events in the Midwest of Jilin Province based on multifractal detrended fluctuation analysis method and copula functions. Theor Appl Climatol. 2016;1–11.
[15]. Salvadori G, Michele CD, Kottegoda NT, Rosso R. Extremes in Nature: An Approach Using Copulas. Springer Science & Business Media; 2007. 304 p.
[16]. Nelsen RB. An Introduction to Copulas. Springer Science & Business Media; 2006. 277 p.
[17].        Sklar A. Fonctions de répartition à n dimensions et leursmarges. Publ Inst Statist Univ Paris. 1959;8:229–231.
 
[18]. Restrepo-Posada PJ, Eagleson PS. Identification of independent rainstorms. J Hydrol. 1982;55(1):303–19.
[19]. Christian Genest, Anne-Catherine Favre. Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask. J Hydrol Eng. 2007;12(4):347–68.
[20]. Mirabbasi R, Fakheri-Fard A, Dinpashoh Y. Bivariate drought frequency analysis using the copula method. Theor Appl Climatol. 2012;108(1):191–206.
[21]. Kisi O, Sanikhani H, Cobaner M. Soil temperature modeling at different depths using neuro-fuzzy, neural network, and genetic programming techniques. Theor Appl Climatol. 2016;1–16.
[22]. Jenq-Tzong Shiau, Hsieh Wen Shen. Recurrence Analysis of Hydrologic Droughts of Differing Severity. J Water Resour Plan Manag. 2001;127(1):30–40.
[23]. Bonaccorso B, Cancelliere A, Rossi G. An analytical formulation of return period of drought severity. Stoch Environ Res Risk Assess. 2003;17(3):157–74.
[24]. Shiau JT. Fitting Drought Duration and Severity with Two-Dimensional Copulas. Water Resour Manag. 2006;20(5):795–815.
[25]. Shiau JT. Return period of bivariate distributed extreme hydrological events. Stoch Environ Res Risk Assess. 2003;17(1):42–57.