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Latin Hypercube Approach to Estimate Uncertainty in Ground Water Vulnerability

Authors

  • Jason J. Gurdak,

    Corresponding author
    1. Department of Geology and Geological Engineering, Colorado School of Mines, 1516 Illinois St., Golden, CO 80401.
      U.S. Geological Survey, Colorado Water Science Center, Denver Federal Center, Mail Stop 415, Lakewood, CO 80225; (303) 236-4882; fax (303) 236-4912; jjgurdak@usgs.gov
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  • John E. McCray,

    1. Environmental Science and Engineering Division, Hydorologic Science and Engineering Program, Colorado School of Mines, 1500 Illinois St., Golden, CO 80401.
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  • Geoffrey Thyne,

    1. Department of Geology and Geological Engineering, Hydrologic Science and Engineering Program, Colorado School of Mines, 1516 Illinois St., Golden, CO 80401.
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  • Sharon L. Qi

    1. U.S. Geological Survey, Cascades Volcano Observatory, 1300 S.E. Cardinal Court, Building 10, Suite 100, Vancouver, WA 98683; slqi@usgs.gov
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U.S. Geological Survey, Colorado Water Science Center, Denver Federal Center, Mail Stop 415, Lakewood, CO 80225; (303) 236-4882; fax (303) 236-4912; jjgurdak@usgs.gov

Abstract

A methodology is proposed to quantify prediction uncertainty associated with ground water vulnerability models that were developed through an approach that coupled multivariate logistic regression with a geographic information system (GIS). This method uses Latin hypercube sampling (LHS) to illustrate the propagation of input error and estimate uncertainty associated with the logistic regression predictions of ground water vulnerability. Central to the proposed method is the assumption that prediction uncertainty in ground water vulnerability models is a function of input error propagation from uncertainty in the estimated logistic regression model coefficients (model error) and the values of explanatory variables represented in the GIS (data error). Input probability distributions that represent both model and data error sources of uncertainty were simultaneously sampled using a Latin hypercube approach with logistic regression calculations of probability of elevated nonpoint source contaminants in ground water. The resulting probability distribution represents the prediction intervals and associated uncertainty of the ground water vulnerability predictions. The method is illustrated through a ground water vulnerability assessment of the High Plains regional aquifer. Results of the LHS simulations reveal significant prediction uncertainties that vary spatially across the regional aquifer. Additionally, the proposed method enables a spatial deconstruction of the prediction uncertainty that can lead to improved prediction of ground water vulnerability.

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