A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters

TLDR

Markov Chain Monte Carlo methods are widely used to estimate posterior distributions of hydrologic model parameters, but they require a proposal distribution that strongly influences sampler efficiency and convergence; the SCEM‑UA algorithm is a modified version of the original SCE‑UA global optimization algorithm. This paper introduces the Shuffled Complex Evolution Metropolis algorithm (SCEM‑UA) as an MCMC sampler designed to infer the posterior distribution of hydrologic model parameters. SCEM‑UA merges the Metropolis algorithm, controlled random search, competitive evolution, and complex shuffling to continuously update the proposal distribution and steer the sampler toward the posterior.

Abstract

Markov Chain Monte Carlo (MCMC) methods have become increasingly popular for estimating the posterior probability distribution of parameters in hydrologic models. However, MCMC methods require the a priori definition of a proposal or sampling distribution, which determines the explorative capabilities and efficiency of the sampler and therefore the statistical properties of the Markov Chain and its rate of convergence. In this paper we present an MCMC sampler entitled the Shuffled Complex Evolution Metropolis algorithm (SCEM‐UA), which is well suited to infer the posterior distribution of hydrologic model parameters. The SCEM‐UA algorithm is a modified version of the original SCE‐UA global optimization algorithm developed by Duan et al. [1992] . The SCEM‐UA algorithm operates by merging the strengths of the Metropolis algorithm, controlled random search, competitive evolution, and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution. Three case studies demonstrate that the adaptive capability of the SCEM‐UA algorithm significantly reduces the number of model simulations needed to infer the posterior distribution of the parameters when compared with the traditional Metropolis‐Hastings samplers.