Toward a priori evaluation of relativeworth 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 eK could be approximated by a polynomial function with first-order terms of H and K data densities μH and μK, 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.