Balancing Particle Diversity in Markov Chain Monte Carlo Methods for Dual Calibration-Data Assimilation Problems in Hydrologic Modeling

Abstract:

Given the inherent uncertainty in almost all of the variables involved, recent research is re-addressing the problem of calibrating hydrologic models from a stochastic perspective: the focus is shifting from finding a single parameter configuration that minimizes the model error, to approximating the maximum likelihood multivariate probability distribution of the parameters. To this end, Markov chain Monte Carlo (MCMC) formulations are widely used, where the distribution is defined as a smoothed ensemble of particles or members, each of which represents a feasible parameterization. However, the updating of these ensembles needs to strike a careful balance so that the particles adequately resemble the real distribution without either clustering or drifting excessively. In this study, we explore the implementation of two techniques that attempt to improve the quality of the resulting ensembles, both for the approximation of the model parameters and of the unknown states, in a dual calibration-data assimilation framework. The first feature of our proposed algorithm, in an effort to keep members from clustering on areas of high likelihood in light of the observations, is the introduction of diversity-inducing operators after each resampling. This approach has been successfully used before, and here we aim at testing additional operators which are also borrowed from the Evolutionary Computation literature. The second feature is a novel arrangement of the particles into two alternative data structures. The first one is a non-sorted Pareto population which favors 1) particles with high likelihood, and 2) particles that introduce a certain level of heterogeneity. The second structure is a partitioned array, in which each partition requires its members to have increasing levels of divergence from the particles in the areas of larger likelihood. Our newly proposed algorithm will be evaluated and compared to traditional MCMC methods in terms of convergence speed, and the ability of adequately representing the target probability distribution while making an efficient use of the available members. Two calibration scenarios will be carried out, one with invariant model parameter settings, and another one allowing the parameters to be modified through time along with the estimates of the model states.