Snow-melt flood frequency analysis by means of copula based 2D probability distributions for the Narew River in Poland

Abstract

Study region: Narew River in Northeastern Poland. Study focus: Three methods for frequency analysis of snowmelt floods were compared. Two dimensional (2D) normal distribution and copula-based 2D probability distributions were applied to statistically describe floods with two parameters (flood peak Qmax,f and flood volume Vf). Two copula functions from different classes – the elliptical Gaussian copula and Archimedean 1-parameter Gumbel–Hougaard copula – were evaluated based on measurements. New hydrological insights for the region: The results indicated that the 2D normal probability distribution model gives a better probabilistic description of snowmelt floods characterized by the 2-dimensional random variable (Qmax,f, Vf) compared to the elliptical Gaussian copula and Archimedean 1-parameter Gumbel–Hougaard copula models, in particular from the view point of probability of exceedance as well as complexity and time of computation. Nevertheless, the copula approach offers a new perspective in estimating the 2D probability distribution for multidimensional random variables. Results showed that the 2D model for snowmelt floods built using the Gumbel–Hougaard copula is much better than the model built using the Gaussian copula.

Keywords

• Flood frequency analysis (FFA)
• 2D Normal probability distribution
• Copula functions
• Elliptical Gaussian copula
• Archimedean 1-parameter Gumbel–Hougaard copula
• Goodness-of-fit tests
• Narew River
• Poland