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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| Veröffentlicht in: | Water resources research Jg. 54; H. 3; S. 1716 - 1733 |
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| Hauptverfasser: | , , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
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Washington
John Wiley & Sons, Inc
01.03.2018
American Geophysical Union (AGU) |
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| ISSN: | 0043-1397, 1944-7973 |
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| 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 |
|---|---|
| AbstractList | 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 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. 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. 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. 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 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. |
| Author | Li, Weixuan Lin, Guang Zhang, Jiangjiang Wu, Laosheng Zeng, Lingzao |
| Author_xml | – sequence: 1 givenname: Jiangjiang orcidid: 0000-0002-0513-5233 surname: Zhang fullname: Zhang, Jiangjiang organization: Institute of Soil and Water Resources and Environmental Science, College of Environmental and Resource Sciences, Zhejiang University – sequence: 2 givenname: Guang orcidid: 0000-0002-0976-1987 surname: Lin fullname: Lin, Guang email: guanglin@purdue.edu organization: Purdue University – sequence: 3 givenname: Weixuan orcidid: 0000-0001-6755-3783 surname: Li fullname: Li, Weixuan organization: Pacific Northwest National Laboratory – sequence: 4 givenname: Laosheng orcidid: 0000-0001-6547-8513 surname: Wu fullname: Wu, Laosheng organization: University of California – sequence: 5 givenname: Lingzao orcidid: 0000-0002-4094-1310 surname: Zeng fullname: Zeng, Lingzao email: lingzao@zju.edu.cn organization: Institute of Soil and Water Resources and Environmental Science, College of Environmental and Resource Sciences, Zhejiang University |
| BackLink | https://www.osti.gov/biblio/1433557$$D View this record in Osti.gov |
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| Snippet | Ensemble smoother (ES) has been widely used in inverse modeling of hydrologic systems. However, for problems where the distribution of model parameters is... Abstract Ensemble smoother (ES) has been widely used in inverse modeling of hydrologic systems. However, for problems where the distribution of model... |
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| SubjectTerms | 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 |
| Title | An Iterative Local Updating Ensemble Smoother for Estimation and Uncertainty Assessment of Hydrologic Model Parameters With Multimodal Distributions |
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