Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling |
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| Authors: | Roberta-Serena Blasone Jasper A Vrugt Henrik Madsen Dan Rosbjerg Bruce A Robinson George A Zyvoloski |
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| Institution: | 1. Department of Environmental Engineering, Technical University of Denmark, Kongens Lyngby, Denmark;2. Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, USA;3. DHI Water, Environment and Health, Hørsholm, Denmark;4. Civilian Nuclear Program Office (SPO-CNP), Los Alamos National Laboratory, Los Alamos, NM, USA;5. Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, USA |
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| Abstract: | In the last few decades hydrologists have made tremendous progress in using dynamic simulation models for the analysis and understanding of hydrologic systems. However, predictions with these models are often deterministic and as such they focus on the most probable forecast, without an explicit estimate of the associated uncertainty. This uncertainty arises from incomplete process representation, uncertainty in initial conditions, input, output and parameter error. The generalized likelihood uncertainty estimation (GLUE) framework was one of the first attempts to represent prediction uncertainty within the context of Monte Carlo (MC) analysis coupled with Bayesian estimation and propagation of uncertainty. Because of its flexibility, ease of implementation and its suitability for parallel implementation on distributed computer systems, the GLUE method has been used in a wide variety of applications. However, the MC based sampling strategy of the prior parameter space typically utilized in GLUE is not particularly efficient in finding behavioral simulations. This becomes especially problematic for high-dimensional parameter estimation problems, and in the case of complex simulation models that require significant computational time to run and produce the desired output. In this paper we improve the computational efficiency of GLUE by sampling the prior parameter space using an adaptive Markov Chain Monte Carlo scheme (the Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm). Moreover, we propose an alternative strategy to determine the value of the cutoff threshold based on the appropriate coverage of the resulting uncertainty bounds. We demonstrate the superiority of this revised GLUE method with three different conceptual watershed models of increasing complexity, using both synthetic and real-world streamflow data from two catchments with different hydrologic regimes. |
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| Keywords: | Hydrologic modeling Uncertainty estimation Generalized likelihood uncertainty estimation (GLUE) Markov Chain Monte Carlo Rainfall-runoff models Calibration |
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