BIVARIATE FLOOD FREQUENCY ANALYSIS USING GUMBEL COPULA
DOI:
https://doi.org/10.11113/mjce.v30.16024Keywords:
Flood frequency analysis, Gumbel copula, bivariate probability distributionAbstract
A copula based methodology is presented in this study for bivariate flood frequency analysis over a station over a Kelantan river basin located in Northeast Malaysia. The joint dependence structures of three flood characteristics, namely, peak flow, flood volume and flood duration were modelled using Gumble Copula. Various univariate distribution functions of flood variables were fitted with observed flood variables to find the best distributions (eg. generalized pareto, log-normal, exponential, gamma distribution, weibull, gumbel, cauchy). The results of study revealed that different variable fits with different distributions and the correlation analysis among variables showed a strong association. Cumulative joint distribution functions (CDF) of peakflow and volume, peakflow and duration and volume and duration revealed that return period of joint return periods are much higher.References
Chen L, Singh, VP, Shenglian G, Hao Z, & Li T (2012). Flood coincidence risk analysis using multivariate copula functions. Journal of Hydrologic Engineering, 17(6): 742-755.
Chen LS, Tzeng IS, Lin CT (2013). Bivariate generalized gamma distributions of Kibble's type. Statistics, (ahead-of-print), 1-17.
Chowdhary H, Escobar LA, Singh VP (2011). Identification of suitable Copulas for bivariate frequency analysis of flood peak and flood volume data. Hydrology Research; 42: 193-215.
De Michele, C., & Salvadori, G. (2003). A generalized Pareto intensityâ€duration model of storm rainfall exploiting 2â€copulas. Journal of Geophysical Research: Atmospheres, 108(D2).
Fu, G., & Kapelan, Z. (2013). Flood analysis of urban drainage systems: Probabilistic dependence structure of rainfall characteristics and fuzzy model parameters. Journal of Hydroinformatics, 15(3), 687-699
Kao, S. C., & Chang, N. B. (2011). Copula-based flood frequency analysis at ungauged basin confluences: Nashville, Tennessee. Journal of Hydrologic Engineering, 17(7), 790-799.
Keef, C., Tawn, J. A., & Lamb, R. (2013). Estimating the probability of widespread flood events. Environmetrics, 24(1), 13-21.
Reddy MJ, Ganguli P (2012). Bivariate flood frequency analysis of upper Godavari River flows using Archimedean Copulas. Water Resources Management, 26(14): 3995-4018.
Requena A I, Mediero L, Garrote L (2013). Bivariate return period based on copulas for hydrologic dam design: comparison of theoretical and empirical approach. Hydrology and Earth System Sciences Discussions, 10: 557-596.
Salarpour M, Yusop Z, Yusof F, Shahid S, Jajarmizad M (2013) Flood frequency analysis based on t-copula for Johor River, Malaysia Journal of Applied Sciences 13:1021-1028
Salvador G, Michele CD (2004). Frequency analysis via Copulas: Theoretical aspects and applications to hydrological events. Water Resources Research; 12:W12511.
Salvadori, G., & De Michele, C. (2013). Multivariate extreme value methods. In Extremes in a changing climate (pp. 115-162). Springer Netherlands.
Sklar, A. Fonctions de répartition à n dimensions et leurs marges. Paris Institute of Statistics. 1959, 8, 229-231.
Xie H, Wang K (2013). Joint-probability Methods for Precipitation and Flood Frequencies Analysis. Third International Conference on Intelligent System Design and Engineering Applications.
Zhang, L.; Singh, V.P. Bivariate Rainfall and Runoff Analysis Using Entropy and Copula Theories. Entropy. 2012. 14, 1784-1812. DOI: 10.3390/e14091784.
