A Bayesian Hierarchical Approach to Multivariate Nonstationary Hydrologic Frequency Analysis. Issue 1 (19th January 2018) - Bracken, C.; Holman, K. D.; Rajagopalan, B.; Moradkhani, H.
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. Plain Language Summary: In this study, we develop a method for determining the probability of occurrence of rare hydrologic events (e.g., floods). Utilizing modern statistical methods, we are able to estimate occurrence probabilities for multiple hydrologic variables simultaneously while incorporating climate information that changes in time. We apply this technique to estimate occurrence probabilities for streamflow, reservoir elevation, and snow levels for the Taylor Park reservoir in Colorado, USA. This method provides several benefits over traditional methods including reduction of uncertainty and a flexible model structure which allows for the incorporation of climate information. Key Points: A model for nonstationary multivariate hydrologic frequency analysis is developed The model allows for the incorporation of climate covariates and the specification of a nonlinear dependence between variables Multivariate frequency analysis capture the dependence between multiple hydrologic variables