Probabilistic Inference Coupled with Possibilistic Reasoning for Robust Estimation of Hydrologic Parameters and Piecewise Characterization of Interactive Uncertainties

S. Wang Institute for Energy, Environment and Sustainable Communities, University of Regina, Regina, Saskatchewan, Canada

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G. H. Huang Faculty of Engineering and Applied Science, University of Regina, Regina, Saskatchewan, Canada

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B. W. Baetz Department of Civil Engineering, McMaster University, Hamilton, Ontario, Canada

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W. Huang Department of Civil Engineering, McMaster University, Hamilton, Ontario, Canada

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Abstract

This paper presents a factorial possibilistic–probabilistic inference (FPI) framework for estimation of hydrologic parameters and characterization of interactive uncertainties. FPI is capable of incorporating expert knowledge into the parameter adjustment procedure for enhancing the understanding of the nature of the calibration problem. As a component of the FPI framework, a Monte Carlo–based fractional fuzzy–factorial analysis (MFA) method is also proposed to identify the best parameter set and its underlying probability distributions in a fuzzy probability space. Factorial analysis of variance (ANOVA) coupled with its multivariate extensions are performed to explore potential interactions among model parameters and among hydrological metrics in a systematic manner. The proposed methodology is applied to the Xiangxi River watershed by using the conceptual hydrological model (HYMOD) to demonstrate its validity and applicability. Results reveal that MFA is capable of deriving probability density functions (PDFs) of hydrologic model parameters. Moreover, the sequential inferences derived from the F test and its multivariate approximations disclose the statistical significance of parametric interactions affecting individual and multiple hydrological metrics, respectively. The findings presented here indicate that parametric interactions are complex in a fuzzy stochastic environment, and the magnitude and direction of interaction effects vary in different regions of the parameter space as well as vary temporally because of the dynamic behavior of hydrologic systems.

Corresponding author address: G. H. Huang, Faculty of Engineering and Applied Science, University of Regina, 3737 Wascana Pkwy., Regina, SK S4S 0A2, Canada. E-mail: sshuo.wwang@gmail.com; huangg@uregina.ca

Abstract

This paper presents a factorial possibilistic–probabilistic inference (FPI) framework for estimation of hydrologic parameters and characterization of interactive uncertainties. FPI is capable of incorporating expert knowledge into the parameter adjustment procedure for enhancing the understanding of the nature of the calibration problem. As a component of the FPI framework, a Monte Carlo–based fractional fuzzy–factorial analysis (MFA) method is also proposed to identify the best parameter set and its underlying probability distributions in a fuzzy probability space. Factorial analysis of variance (ANOVA) coupled with its multivariate extensions are performed to explore potential interactions among model parameters and among hydrological metrics in a systematic manner. The proposed methodology is applied to the Xiangxi River watershed by using the conceptual hydrological model (HYMOD) to demonstrate its validity and applicability. Results reveal that MFA is capable of deriving probability density functions (PDFs) of hydrologic model parameters. Moreover, the sequential inferences derived from the F test and its multivariate approximations disclose the statistical significance of parametric interactions affecting individual and multiple hydrological metrics, respectively. The findings presented here indicate that parametric interactions are complex in a fuzzy stochastic environment, and the magnitude and direction of interaction effects vary in different regions of the parameter space as well as vary temporally because of the dynamic behavior of hydrologic systems.

Corresponding author address: G. H. Huang, Faculty of Engineering and Applied Science, University of Regina, 3737 Wascana Pkwy., Regina, SK S4S 0A2, Canada. E-mail: sshuo.wwang@gmail.com; huangg@uregina.ca
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