A Bayesian Hierarchical Approach to Multivariate Nonstationary Hydrologic Frequency Analysis

Abstract

Abstract We present a general Bayesian hierarchical framework for conducting nonstationary frequency analysis of multiple hydrologic variables. In this, annual maxima from each variable are assumed to follow a generalized extreme value (GEV) distribution in which the location parameter is allowed to vary in time. A Gaussian elliptical copula is used to model the joint distribution of all variables. We demonstrate the utility of this framework with a joint frequency analysis model of annual peak snow water equivalent (SWE), annual peak flow, and annual peak reservoir elevation at Taylor Park dam in Colorado, USA. Indices of large‐scale climate drivers—El Niño Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), and Atlantic Multidecadal Oscillation (AMO) are used as covariates to model temporal nonstationarity. The Bayesian framework provides the posterior distribution of the model parameters and consequently the return levels. Results show that performing a multivariate joint frequency analysis reduces the uncertainty in return level estimates and better captures multivariate dependence compared to an independent model.