An Iterative Local Updating Ensemble Smoother for Estimation and Uncertainty Assessment of Hydrologic Model Parameters With Multimodal Distributions

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 cl...

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Vydané v:Water resources research Ročník 54; číslo 3; s. 1716 - 1733
Hlavní autori: Zhang, Jiangjiang, Lin, Guang, Li, Weixuan, Wu, Laosheng, Zeng, Lingzao
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Washington John Wiley & Sons, Inc 01.03.2018
American Geophysical Union (AGU)
Predmet:
Algorithms
Clustering
Computation
Computer applications
Data processing
Distribution
ensemble smoother
Hydrologic models
Hydrologic systems
Hydrology
inverse modeling
Iterative methods
Mathematical models
Modelling
Motivation
multimodal distribution
Nonlinear systems
Nonlinearity
Parallel processing
Parameter uncertainty
Parameters
Problems
Uncertainty
water
ISSN:0043-1397, 1944-7973
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Popis
Shrnutí: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
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USDOE
ISSN:0043-1397
1944-7973
DOI:10.1002/2017WR020906