An Iterative Local Updating Ensemble Smoother for Estimation and Uncertainty Assessment of Hydrologic Model Parameters With Multimodal Distributions. Issue 3 (10th March 2018) - Zhang, Jiangjiang; Lin, Guang; Li, Weixuan; Wu, Laosheng; Zeng, Lingzao
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. Plain Language Summary: Our motivation comes from hydrologic inverse modeling applications where the distributions of model parameters are multimodal. Although MCMC can handle multimodal distributions, the computational cost is prohibitive in large‐scale inverse modeling. As a computationally appealing alternative, ensemble smoother (ES) has been widely used in inverse modeling of hydrologic systems. However, its application is limited to problems where uncertain parameters approximately follow Gaussian distributions. For problems with multimodal distributions, using ES directly would be problematic. In this article, we propose an iterative local updating ensemble smoother for estimation and uncertainty assessment of hydrologic model parameters with multimodal distributions. Central to the proposed methodology is the idea of updating local ensembles of each sample in ES to explore possible multimodal distributions. To achieve satisfactory data matches in nonlinear problems, we adopt an iterative form of ES to assimilate the measurement multiple times. It is shown that the ILUES algorithm can well quantify the parametric uncertainties of complex hydrologic models, no matter whether the multimodal distribution exists. Moreover, the implementation of the ILUES algorithm can be greatly accelerated by adopting parallel computation. Key Points: We propose a simple and efficient algorithm to solve inverse problems with multimodal distributions The algorithm works by updating local ensembles of each sample in ES to explore possible multimodal distributions To achieve satisfactory data matches in nonlinear problems, we adopt an iterative form of ES to assimilate the measurement multiple times