Multivariate Regional Frequency Analysis Using Conditional Extreme Values Approach

Abstract

AbstractFloods can be characterized by various correlated variables such as peak flow, flood volume, duration, and time to peak. Hence, flood risk can be better assessed by performing frequency analysis in a multivariate (rather than a univariate) framework. However, multivariate approaches involve sophisticated analyses that require considerably more data than univariate approaches. In a univariate framework, flood risk assessment at an ungauged or data‐sparse location/site is generally performed through regional frequency analysis (RFA), based on information pooled from a group of sites resembling the target site. However, RFA has received little attention in the multivariate framework. The available literature recommends the use of index‐flood approach (IFA) for multivariate RFA (MRFA), even though IFA has theoretical shortcomings. Another issue is that marginals of all the flood‐related variables may not exhibit extreme behavior simultaneously. Conventionally used at‐site multivariate models are not suitable for describing the dependence structure of extremes in the regions of the support of the joint distribution where only some variables exhibit extreme behavior. This article proposes a conditional extreme values approach (CEA) to address the aforementioned issues in MRFA. Its effectiveness is demonstrated through Monte Carlo simulation experiments and a case study on watersheds from a flood‐prone region in India. Results indicate that the proposed approach can reliably predict the joint distribution of multiple flood‐related variables (and thus flood risk) at ungauged/sparsely gauged sites by effectively capturing the regional dependence structure between those variables.