An iterative local updating ensemble smoother for estimation and uncertainty assessment of hydrologic model parameters with multimodal distributions

TL;DR

This paper introduces ILUES, an efficient iterative ensemble method for estimating parameters and their uncertainties in nonlinear hydrologic models with multimodal distributions, outperforming traditional approaches especially in high-dimensional spaces.

Contribution

The paper proposes ILUES, a simple and efficient iterative local updating ensemble smoother that effectively explores multimodal parameter distributions in complex hydrologic systems.

Findings

ILUES accurately quantifies parametric uncertainties in complex models.

ILUES outperforms clustering-based methods in high-dimensional spaces.

Numerical tests demonstrate ILUES's robustness with nonlinear and multimodal distributions.

Abstract

Ensemble smoother (ES) has been widely used in inverse modeling of hydrologic systems. However, for problems where the distribution of model parameters is multimodal, using ES directly would be problematic. One popular solution is to use a clustering algorithm to identify each mode and update the clusters with ES separately. However, this strategy may not be very efficient when the dimension of parameter space is high or the number of modes is large. Alternatively, we propose in this paper a very simple and efficient algorithm, i.e., the iterative local updating ensemble smoother (ILUES), to explore multimodal distributions of model parameters in nonlinear hydrologic systems. The ILUES algorithm works by updating local ensembles of each sample with ES to explore possible multimodal distributions. To achieve satisfactory data matches in nonlinear problems, we adopt an iterative form of ES to assimilate the measurements multiple times. Numerical cases involving nonlinearity and multimodality are tested to illustrate the performance of the proposed method. It is shown that overall the ILUES algorithm can well quantify the parametric uncertainties of complex hydrologic models, no matter whether the multimodal distribution exists.