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https://doi.org/10.5194/egusphere-2024-337
https://doi.org/10.5194/egusphere-2024-337
11 Mar 2024
 | 11 Mar 2024

Feature scale and identifiability: How much information do point hydraulic measurements provide about heterogeneous head and conductivity fields?

Scott K. Hansen, Daniel O'Malley, and James P. Hambleton

Abstract. We systematically investigate how the spacing and type of point measurements impacts the scale of subsurface features that can be identified by groundwater flow model calibration. To this end, we consider the optimal inference of spatially heterogeneous hydraulic conductivity and head fields based on three kinds of point measurements that may be available at monitoring wells: of head, permeability, and groundwater speed. We develop a general, zonation-free technique for Monte Carlo (MC) study of field recovery problems, based on Karhunen-Loève (K-L) expansions of the unknown fields whose coefficients are recovered by an analytical, continuous adjoint-state technique. This allows unbiased sampling from the space of all possible fields with a given correlation structure and efficient, automated gradient-descent calibration. The K-L basis functions have a straightforward notion of period, revealing the relationship between feature scale and reconstruction fidelity, and they have an a priori known spectrum, allowing for a non-subjective regularization term to be defined. We perform automated MC calibration on over 1100 conductivity-head field pairs, employing a variety of point measurement geometries and evaluating the mean-squared field reconstruction accuracy, both globally and as a function of feature scale. We present heuristics for feature scale identification, examine global reconstruction error, and explore the value added by both the groundwater speed measurements and by two different types of regularization. We find that significant feature identification becomes possible as feature scale exceeds four times measurement spacing and identification reliability subsequently improves in a power law fashion with increasing feature scale.

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Journal article(s) based on this preprint

24 Mar 2025
Feature scale and identifiability: how much information do point hydraulic measurements provide about heterogeneous head and conductivity fields?
Scott K. Hansen, Daniel O'Malley, and James P. Hambleton
Hydrol. Earth Syst. Sci., 29, 1569–1585, https://doi.org/10.5194/hess-29-1569-2025,https://doi.org/10.5194/hess-29-1569-2025, 2025
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We consider how well one can identify hydraulic conductivity that varies from place to place by...
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