Toward a Priori Evaluation of Relative Worth of Head and Conductivity Data as Functions of Data Densities in Inverse Groundwater Modeling

Groundwater hydraulic head (H) measurements and point-estimates of hydraulic conductivity (K) both contain information about the K field. There is no simple, a priori estimate of the relative worth of H and K data. Thus, there is a gap in our conceptual understanding of the value of the K inversion procedure. Here, using synthetic calibration experiments, we quantified the worth of H and K data in terms of reducing calibrated K errors. We found that normalized K error e K could be approximated by a polynomial function with first-order terms of H and K data densities μ H and μ K , which have been normalized by the correlation lengths of the K field, and a mutually inhibitive interaction term. This equation can be applied to obtain a rough estimate of the uncertainty prior to the inversion for a case with a similar configuration. The formulation suggests that the inversion is valuable even without K data. The relative worths of H and K depend heavily on existing data densities and heterogeneity. K can be ten times more informative when it is sparse. Noise perturbation experiments show that we should incorporate noisy K data when K is sparse, but not a large amount of low-quality K estimates. Our conclusions establish a crude, baseline estimate of the value of calibration. A similar assessment method for information content can be employed for more complex problems.