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Moore C.,Institute of Environmental Science and Research Ltd | Moore C.,Butler Partners Pty Ltd | Wohling T.,Lincoln Ventures Ltd | Doherty J.,Watermark Numerical Computing | Doherty J.,Flinders University
Water Resources Research | Year: 2010

The concept of the Pareto front has received considerable attention in the model calibration literature, particularly in conjunction with global search optimizers that have been developed for use in contexts where objective function surfaces are pitted with local optima or characterized by multiple broad regions of attraction in parameter space. In this paper, use of the Pareto concept in such calibration contexts is extended to include regularization and model predictive uncertainty analysis. Both of these processes can be formulated as constrained optimization problems in which a trade-off is analyzed between a set of constraints on model parameters on the one hand and maximization/ minimization of one or a number of model outputs of interest on the other hand. In both cases, the optimal trade-off point, though being calculable on a theoretical basis for synthetic cases, must be chosen subjectively when working with real-world models. Two cases are presented to illustrate the methodology: one a synthetic groundwater model and the other a real-world surface water model. © 2010 by the American Geophysical Union. Source

Doherty J.,Watermark Numerical Computing | Doherty J.,Flinders University | Welter D.,South Florida Water Management District
Water Resources Research | Year: 2010

"Structural noise" is a term often used to describe model-to-measurement misfit that cannot be ascribed to measurement noise and therefore must be ascribed to the imperfect nature of a numerical model as a simulator of reality. As such, it is often the dominant contributor to model-to-measurement misfit. As the name "structural noise" implies, this type of misfit is often treated as an additive term to measurement noise when assessing model parameter and predictive uncertainty. This paper inquires into the nature of defect-induced model-to-measurement misfit and provides a conceptual basis for accommodating it. It is shown that inasmuch as defect induced model-to-measurement misfit can be characterized as "noise," this noise is likely to show a high degree of spatial and temporal correlation; furthermore, its covariance matrix may approach singularity. However, the deleterious impact of structural noise on the model calibration process may be mitigated in a variety of ways. These include adoption of a highly parameterized approach to model construction and calibration (including the strategic use of compensatory parameters where appropriate), processing of observations and their model generated counterparts in ways that are able to filter out structural noise prior to fitting one to the other, and/or through implementation of a weighting strategy that gives prominence to observations that most resemble predictions required of a model. Copyright 2010 by the American Geophysical Union. Source

Sepulveda N.,U.S. Geological Survey | Doherty J.,Watermark Numerical Computing | Doherty J.,Flinders University
Groundwater | Year: 2015

A groundwater flow model for east-central Florida has been developed to help water-resource managers assess the impact of increased groundwater withdrawals from the Floridan aquifer system on heads and spring flows originating from the Upper Floridan Aquifer. The model provides a probabilistic description of predictions of interest to water-resource managers, given the uncertainty associated with system heterogeneity, the large number of input parameters, and a nonunique groundwater flow solution. The uncertainty associated with these predictions can then be considered in decisions with which the model has been designed to assist. The "Null Space Monte Carlo" method is a stochastic probabilistic approach used to generate a suite of several hundred parameter field realizations, each maintaining the model in a calibrated state, and each considered to be hydrogeologically plausible. The results presented herein indicate that the model's capacity to predict changes in heads or spring flows that originate from increased groundwater withdrawals is considerably greater than its capacity to predict the absolute magnitudes of heads or spring flows. Furthermore, the capacity of the model to make predictions that are similar in location and in type to those in the calibration dataset exceeds its capacity to make predictions of different types at different locations. The quantification of these outcomes allows defensible use of the modeling process in support of future water-resources decisions. The model allows the decision-making process to recognize the uncertainties, and the spatial or temporal variability of uncertainties that are associated with predictions of future system behavior in a complex hydrogeological context. © 2014, National Ground Water Association. Source

Herckenrath D.,Technical University of Denmark | Langevin C.D.,U.S. Geological Survey | Doherty J.,Watermark Numerical Computing | Doherty J.,Flinders University
Water Resources Research | Year: 2011

Because of the extensive computational burden and perhaps a lack of awareness of existing methods, rigorous uncertainty analyses are rarely conducted for variable-density flow and transport models. For this reason, a recently developed null-space Monte Carlo (NSMC) method for quantifying prediction uncertainty was tested for a synthetic saltwater intrusion model patterned after the Henry problem. Saltwater intrusion caused by a reduction in fresh groundwater discharge was simulated for 1000 randomly generated hydraulic conductivity distributions, representing a mildly heterogeneous aquifer. From these 1000 simulations, the hydraulic conductivity distribution giving rise to the most extreme case of saltwater intrusion was selected and was assumed to represent the "true" system. Head and salinity values from this true model were then extracted and used as observations for subsequent model calibration. Random noise was added to the observations to approximate realistic field conditions. The NSMC method was used to calculate 1000 calibration-constrained parameter fields. If the dimensionality of the solution space was set appropriately, the estimated uncertainty range from the NSMC analysis encompassed the truth. Several variants of the method were implemented to investigate their effect on the efficiency of the NSMC method. Reducing the dimensionality of the null-space for the processing of the random parameter sets did not result in any significant gains in efficiency and compromised the ability of the NSMC method to encompass the true prediction value. The addition of intrapilot point heterogeneity to the NSMC process was also tested. According to a variogram comparison, this provided the same scale of heterogeneity that was used to generate the truth. However, incorporation of intrapilot point variability did not make a noticeable difference to the uncertainty of the prediction. With this higher level of heterogeneity, however, the computational burden of generating calibration-constrained parameter fields approximately doubled. Predictive uncertainty variance computed through the NSMC method was compared with that computed through linear analysis. The results were in good agreement, with the NSMC method estimate showing a slightly smaller range of prediction uncertainty than was calculated by the linear method. Copyright 2011 by the American Geophysical Union. Source

Nolan B.T.,U.S. Geological Survey | Malone R.W.,U.S. Department of Agriculture | Doherty J.E.,Watermark Numerical Computing | Doherty J.E.,Flinders University | And 3 more authors.
Pest Management Science | Year: 2015

BACKGROUND: Complex environmental models are frequently extrapolated to overcome data limitations in space and time, but quantifying data worth to such models is rarely attempted. The authors determined which field observations most informed the parameters of agricultural system models applied to field sites in Nebraska (NE) and Maryland (MD), and identified parameters and observations that most influenced prediction uncertainty. RESULTS: The standard error of regression of the calibrated models was about the same at both NE (0.59) and MD (0.58), and overall reductions in prediction uncertainties of metolachlor and metolachlor ethane sulfonic acid concentrations were 98.0 and 98.6% respectively. Observation data groups reduced the prediction uncertainty by 55-90% at NE and by 28-96% at MD. Soil hydraulic parameters were well informed by the observed data at both sites, but pesticide and macropore properties had comparatively larger contributions after model calibration. CONCLUSIONS: Although the observed data were sparse, they substantially reduced prediction uncertainty in unsampled regions of pesticide breakthrough curves. Nitrate evidently functioned as a surrogate for soil hydraulic data in well-drained loam soils conducive to conservative transport of nitrogen. Pesticide properties and macropore parameters could most benefit from improved characterization further to reduce model misfit and prediction uncertainty. © 2015 Society of Chemical Industry. Source

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