Hydrogeophysical Inversion of Time‐Lapse ERT Data to Determine Hillslope Subsurface Hydraulic Properties

Abstract

As geophysical data allow for the monitoring of hydrological processes at relatively fine spatial resolutions, these data can help identify otherwise poorly constrained hydraulic parameters within hydrologic models. For example, Binley et al. ( 2002) constrained the saturated hydraulic conductivity value of one layer in a three-layer subsurface flow model by calculating the first and second spatial moments of the change in water content from petrophysically transformed resistivity and radar data. Many studies have since extended the usefulness of geophysical data to, for example, calibrate hydrologic models of salt water intrusion (e.g.,

A Comparison of Hydrological and Geophysical Calibration Data in Layered Hydrologic Models of Mountain Hillslopes

“…The inflection between the two slopes again occurred at roughly 10 𝐴𝐴 Ω , where 𝐴𝐴 𝐴𝐴 < 10 𝐴𝐴 Ω correlated to electrode combinations with larger spacing between current injection electrodes (spacing between electrodes >22 m on average). The preference to fitting 𝐴𝐴 𝐴𝐴 from relatively closely spaced electrodes was consistent with the results of Pleasants et al (2022) since current injected between two closely spaced electrode should lead to a larger current density in the near surface compared to the deeper subsurface (Roy & Apparao, 1971).…”

“…Previous work by Pleasants et al. (2022) highlighted that van Genuchten‐Mualem parameters $${\theta }_{\mathrm{r}}$$, $${\theta }_{\mathrm{s}}$$, and $${K}_{\mathrm{s}}$$ are most sensitive to changes in $${d}_{\mathrm{F}\mathrm{E}}$$ while $$\alpha $$ and $${n}_{\mathrm{v}\mathrm{g}}$$ are relatively insensitive to $${d}_{\mathrm{F}\mathrm{E}}$$. The reader is directed to Engda et al.…”

“…As in Pleasants et al. (2022), the value of $${\theta }_{\mathrm{s}}$$ from $${d}_{\mathrm{F}\mathrm{E}}$$ optimization and $$\theta (h)$$ fitting was used for $${\phi }_{\mathrm{a}}$$ in Equation . We expect that subsurface coarse fragments effectively reduce the subsurface volume through which electricity can be conducted and thus increase the resistivity of the subsurface.…”

“…The hydrologic model used in this study, described in detail by Pleasants et al (2022), employs the coordinate-transformed finite-difference method (An et al, 2010) with a variable time step scheme to solve a 2-D coupled surface-subsurface flow system. Variably saturated subsurface flow occurs in a vertical cross section and is described by the mixed form of Richards' equation: (m s −1 ), and 𝐴𝐴 𝐴𝐴S is a source/sink term (s −1 ).…”

“…While the logical approach to hydrologic model calibration may be to include all available data, the difference in measurement scale between data such as ERT and water content may lead to significantly different hydraulic parameters. Recent work by the current authors indicated that even using different ERT data sets (i.e., transfer resistance and inverted resistivity) in hillslope model calibrations can lead to different optimum hydraulic parameters (Pleasants et al, 2022). This recent work presented a method of brute-force hydrogeophysical inversion using fine-earth fraction optimization (Engda et al, 2016;Fullhart et al, 2018Fullhart et al, , 2019 to limit the number of parameters needing estimation in defining subsurface hydraulic properties.…”