Trivariate distribution modelling of flood characteristics using copula function—A case study for Kelantan River basin in Malaysia

Shahid Latif; Firuza Mustafa; Shahid Latif; Firuza Mustafa

doi:10.3934/geosci.2020007

AIMS Geosciences

2020, Volume 6, Issue 1: 92-130. doi: 10.3934/geosci.2020007

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Research article

Trivariate distribution modelling of flood characteristics using copula function—A case study for Kelantan River basin in Malaysia

Shahid Latif ^,,
Firuza Mustafa

Department of Geography, University of Malaya, Kuala Lumpur 50603, Malaysia

Received: 29 January 2020 Accepted: 10 March 2019 Published: 19 March 2020

Water resources operational planning, managements or either flood defence infrastructure designs often demand the estimations of flow exceedance probability for visualizing the risk of flood episodes. Numerous literature often incorporated copulas for the development of bivariate joint dependence structure among the flood characteristics, flood peak flow, volume and duration, but it could be more realistic and comprehensive if we focus all the three mutually correlated flood characteristics simultaneously. Actually, the inclusion of more flood characteristics could provide better and much justifiable information in correlation and dependency modelling. In this study, trivariate copulas are incorporated and applied to a case study to analyse flood episodes in the Kelantan River basin at Gulliemard bridge gauge station in Malaysia. Firstly, for describing best-fitted bivariate copulas for establishing the joint dependence structure of each flood attribute pairs, the Gaussian copula is recognized most justifiable model for peak-volume pair and the Frank copula for peak-duration and volume-duration pairs. After that, the trivariate joint distribution is modelled using one Archimedean copula, the Frank copula and one Elliptical copula, the Gaussian copula. Based on Cramer-von-Mises-type statistics, Sn and p-value, the Gaussian copula best representing the trivariate dependence structure of flood and which further employed in the deriving of trivariate joint and conditional return periods.
- flood,
- frequency analysis,
- kelantan river basin,
- copulas function,
- trivariate probability distribution,
- return periods
Citation: Shahid Latif, Firuza Mustafa. Trivariate distribution modelling of flood characteristics using copula function—A case study for Kelantan River basin in Malaysia[J]. AIMS Geosciences, 2020, 6(1): 92-130. doi: 10.3934/geosci.2020007

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Abstract

Water resources operational planning, managements or either flood defence infrastructure designs often demand the estimations of flow exceedance probability for visualizing the risk of flood episodes. Numerous literature often incorporated copulas for the development of bivariate joint dependence structure among the flood characteristics, flood peak flow, volume and duration, but it could be more realistic and comprehensive if we focus all the three mutually correlated flood characteristics simultaneously. Actually, the inclusion of more flood characteristics could provide better and much justifiable information in correlation and dependency modelling. In this study, trivariate copulas are incorporated and applied to a case study to analyse flood episodes in the Kelantan River basin at Gulliemard bridge gauge station in Malaysia. Firstly, for describing best-fitted bivariate copulas for establishing the joint dependence structure of each flood attribute pairs, the Gaussian copula is recognized most justifiable model for peak-volume pair and the Frank copula for peak-duration and volume-duration pairs. After that, the trivariate joint distribution is modelled using one Archimedean copula, the Frank copula and one Elliptical copula, the Gaussian copula. Based on Cramer-von-Mises-type statistics, Sn and p-value, the Gaussian copula best representing the trivariate dependence structure of flood and which further employed in the deriving of trivariate joint and conditional return periods.

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