THE CALIBRATION DILEMMA: REDUCING MODEL UNCERTAINTY WHEN CALIBRATING TO MEASURED HEADS

One recurring insight from the application of the Analytic Element Method is that in the absence of local flux information it is only possible to calibrate the ratio of recharge (N) to permeability (k). There are an infinite number of N and k values that will fit a set of head measurements and head-specified boundaries equally well.

Commonly, the permeability is selected for a groundwater model based on standard pumping test results, and then the recharge is determined by model calibration: e.g. minimizing the sum of the squares of the calibration errors. We argue that better results are often achieved by embracing uncertainty rather than by merely minimizing residuals.

We compute the posterior distributions of the uncertain parameters, N and k, by applying a simple analytic element model, Bayes Theorem, and a modified profile likelihood representation. This approach incorporates the available qualitative and quantitative information through the prior distributions. These prior distributions are then optimally updated to incorporate the noisy head measurements.

As an example, we present an application of the method to evaluate the likely capture area of a well with known discharge in an aquifer of known thickness and porosity from the frequency distributions characterizing N and k, and uncertain head calibration data.

The a priori lognormal frequency distribution of k, when unconstrained by recharge information, generates a wide range of likely capture areas. The upper end of this range is particularly problematic as it extends quite far from the well and, at its far end, can be subject to significant uncertainty resulting from small uncertainties in the head calibration data. However, the recharge conditioned frequency distribution of k is nearly “normal” resulting in significantly smaller capture areas of equivalent confidence.