A nonparametric copula distribution framework for bivariate joint distribution analysis of flood characteristics for the Kelantan River basin in Malaysia

Shahid Latif; Firuza Mustafa; Shahid Latif; Firuza Mustafa

doi:10.3934/geosci.2020012

AIMS Geosciences

2020, Volume 6, Issue 2: 171-198. doi: 10.3934/geosci.2020012

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Research article

A nonparametric copula distribution framework for bivariate joint distribution analysis of flood characteristics for the Kelantan River basin in Malaysia

Shahid Latif ^,,
Firuza Mustafa

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

Received: 23 March 2020 Accepted: 11 May 2020 Published: 19 May 2020

The joint distribution analysis of multidimensional flood characteristics i.e., flood peak flow, volume and duration, often facilitates a comprehensive understanding in the hydrologic risk assessments. Copula-based methodology are frequently incorporated via parametric approach to model dependence structure of parametric based univariate marginal distributions. But, if the targeted copulas and univariate marginal distributions belongs to some specific parametric families, it might be problematic, if the underlying assumption are violated. Also, no universal rules and literatures are imposed to model any hydrologic vectors and their joint dependence structure through any fixed or pre-defined distributions. In this literature, a nonparametric copula simulation are incorporated and applied as a case study for 50 years annual maximum flood samples of the Kelantan River basin at the Gulliemard bridge station in Malaysia. In this study, a combination of both parametric and nonparametric marginal distribution separately conjoined by a nonparametric copulas framework, which is based on the Beta kernel function. The Beta kernel copula function are incorporated to estimate bivariate copula density which further used to derived joint cumulative density of flood peak-volume, volume-duration and peak-duration pairs and their associated joint as well as conditional return periods.
- flood,
- nonparametric approach,
- beta kernel copula,
- bivariate joint analysis,
- return period
Citation: Shahid Latif, Firuza Mustafa. A nonparametric copula distribution framework for bivariate joint distribution analysis of flood characteristics for the Kelantan River basin in Malaysia[J]. AIMS Geosciences, 2020, 6(2): 171-198. doi: 10.3934/geosci.2020012

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Abstract

The joint distribution analysis of multidimensional flood characteristics i.e., flood peak flow, volume and duration, often facilitates a comprehensive understanding in the hydrologic risk assessments. Copula-based methodology are frequently incorporated via parametric approach to model dependence structure of parametric based univariate marginal distributions. But, if the targeted copulas and univariate marginal distributions belongs to some specific parametric families, it might be problematic, if the underlying assumption are violated. Also, no universal rules and literatures are imposed to model any hydrologic vectors and their joint dependence structure through any fixed or pre-defined distributions. In this literature, a nonparametric copula simulation are incorporated and applied as a case study for 50 years annual maximum flood samples of the Kelantan River basin at the Gulliemard bridge station in Malaysia. In this study, a combination of both parametric and nonparametric marginal distribution separately conjoined by a nonparametric copulas framework, which is based on the Beta kernel function. The Beta kernel copula function are incorporated to estimate bivariate copula density which further used to derived joint cumulative density of flood peak-volume, volume-duration and peak-duration pairs and their associated joint as well as conditional return periods.

References

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