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Open AccessArticle

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

Civil and Environmental Engineering, Pennsylvania State University, State College, PA 16801, USA
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Author to whom correspondence should be addressed.
Now at A. Morton Thomas and Associates, Inc., Rockville, MD 20850, USA.
Water 2019, 11(6), 1202; https://doi.org/10.3390/w11061202
Received: 27 March 2019 / Revised: 26 May 2019 / Accepted: 5 June 2019 / Published: 8 June 2019
(This article belongs to the Section Hydrology)
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. View Full-Text
Keywords: modflow; PEST; uncertainty; information content modflow; PEST; uncertainty; information content
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Sun, N.; Fang, K.; Shen, C. Toward a Priori Evaluation of Relative Worth of Head and Conductivity Data as Functions of Data Densities in Inverse Groundwater Modeling. Water 2019, 11, 1202.

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