Directing Sampling based on Uncertainty Analysis
Determining where and what to sample for environmental modeling of receiving waters is becoming increasingly important because the need for improved accuracy in model results conflicts with limited site sampling budgets. A quantitative approach to sampling, entitled Quantitatively Directed Exploration (QDE), provides a mathematical framework for determining the best location to sample, and what parameter should be sampled. QDE employs a first-order Taylor series expansion to estimate the uncertainty or variance in the model results. Uncertainty in input parameters is determined through data extrapolation techniques, specifically multivariate conditional probability, while model sensitivity is calculated by directly coding sensitivity derivatives into a model using ADIFOR 2.0.
Combining these two matrices produces the variance in model results, which in turn is employed to direct sampling. The next sampling location is defined as the point where the variance in model results is the largest. Which input parameter to sample is determined by evaluating the contribution to the total variance produced by each input parameter. The QDE approach is demonstrated on a water quality model where non-point source loading, stream characteristics, and contaminant behavior are uncertain input parameters and concentration is the uncertain model result.
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