By Jason J. Gurdak1, John E. McCray2, Geoffrey D. Thyne2, and Sharon L. Qi3
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 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 groundwater. 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 Latin hypercube sampling 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.
1 U.S. Geological Survey, Denver, Colorado
2 Colorado School of Mines, Golden, Colorado
3 U.S. Geological Survey, Vancouver, Washington
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