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

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • CC1: 'Comment on egusphere-2024-337', Giacomo Medici, 13 Mar 2024
    • AC3: 'Reply on CC1', Scott K. Hansen, 18 Jul 2024
  • RC1: 'Comment on egusphere-2024-337', Anonymous Referee #1, 19 Apr 2024
    • AC2: 'Authors' reply to RC1', Scott K. Hansen, 18 Jul 2024
  • RC2: 'Comment on egusphere-2024-337', Anonymous Referee #2, 17 Jun 2024
    • CC2: 'Reply on RC2', James Hambleton, 17 Jun 2024
      • CC3: 'Reply on CC2', James Hambleton, 17 Jun 2024
    • AC1: 'Authors' reply to RC2', Scott K. Hansen, 18 Jul 2024
Scott K. Hansen, Daniel O'Malley, and James P. Hambleton
Scott K. Hansen, Daniel O'Malley, and James P. Hambleton


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Short summary
We consider how well one can identify hydraulic conductivity that varies from place to place by using only measurements obtained at a finite number of groundwater monitoring wells. In particular, we relate how accurately features (meaning connected high- or low-conductivity regions) are identified to their size and to well spacing, and examine which kinds of information are most valuable. When feature size exceeds four times the well spacing, better-than-random identification is possible.