Specifying a hierarchical mixture of experts for hydrologic modeling: Gating function variable selection

Authors

  • Erwin Jeremiah,

    1. School of Civil and Environmental Engineering, University of New South Wales, Sydney, New South Wales, Australia
    2. Now at the Strategic Asset Unit of State Water Corporation, New South Wales, Australia
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  • Lucy Marshall,

    1. Land Resources and Environmental Science, Montana State University, Bozeman, Montana, USA
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  • Scott A Sisson,

    1. School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales, Australia
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  • Ashish Sharma

    Corresponding author
    1. School of Civil and Environmental Engineering, University of New South Wales, Sydney, New South Wales, Australia
    • Corresponding author: A. Sharma, School of Civil and Environmental Engineering, University of New South Wales, Sydney, NSW 2052, Australia. (a.sharma@unsw.edu.au)

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Abstract

[1] The complexity of predicting surface runoff from hydrological models is compounded by uncertainties associated with the model structure, parameters and inputs. A hierarchical mixture of experts (HME) is recognized as one of the ways of incorporating model structural uncertainty into hydrological simulations. In this article, a framework capable of incorporating parameter and structural uncertainties is implemented via the use of a hierarchical mixture of experts together with sequential Monte Carlo parameter sampling. The use of a HME enables aggregation of multiple constituent models at the same instance, mixed to different extents in a dynamic manner as specified by a gating function, allowing the modeler to better characterize the uncertainty associated with the obtained predictions. This article presents a mechanism for better specifying the structure of the gating function used for combining models in a HME approach, by investigating the combination of predictor variables that allows the best model mixing. These predictors exist in various forms, each of which represents information on the catchment. We apply three different types of predictors to a case study, the Never Never River catchment in Australia. The outcomes from this case study consistently demonstrate improved Bayesian information criterion (BIC) readings for the HME especially when used with a combination of predictors. The predictor coefficients are further used for regionalization with the Manning River catchment, having similar characteristics to the Never Never River catchment, and also demonstrate satisfactory improvement in BIC when compared with a single structure model.

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