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The spatiotemporal distribution of pore water in the vadose zone can have a critical control on many processes in the near-surface Earth, such as the onset of landslides, crop yield, groundwater recharge, and runoff generation. Electrical geophysics has been widely used to monitor the moisture content (theta) distribution in the vadose zone at field sites, and often resistivity (rho) or conductivity (sigma) is converted to moisture contents through petrophysical relationships (e.g., Archie's law). Though both the petrophysical relationships (i.e., choices of appropriate model and parameterization) and the derived moisture content are known to be subject to uncertainty, they are commonly treated as exact and error-free. This study examines the impact of uncertain petrophysical relationships on the moisture content estimates derived from electrical geophysics. We show from a collection of data from multiple core samples that significant variability in the theta (rho) relationship can exist. Using rules of error propagation, we demonstrate the combined effect of inversion and uncertain petrophysical parameterization on moisture content estimates and derive their uncertainty bounds. Through investigation of a water injection experiment, we observe that the petrophysical uncertainty yields a large range of estimated total moisture volume within the water plume. The estimates of changes in water volume, however, generally agree within (large) uncertainty bounds. Our results caution against solely relying on electrical geophysics to estimate moisture content in the field. The uncertainty propagation approach is transferrable to other field studies of moisture content estimation.

Plain Language Summary Maps and images of electrical resistivity have been widely applied to effectively monitor the wetting or drying of the Earths' near-surface. But how well can they quantify such change? How variable are the petrophysical model parameters that relate resistivity and moisture content? Does uncertainty in such relationships impact our confidence in moisture content estimates from resistivity imaging? Our analysis of field samples collected at a U.K. field site reveals great variability in petrophysical parameters. Using an uncertainty propagation method, which combines the uncertainty contributions from both petrophysical parameters and resistivity data errors, we find that the variable petrophysical parameters can lead to high uncertainty in moisture content estimates and they appear to be the dominating factor in many cases. These effects on uncertainty are greater than previously appreciated. The implication is that realistic uncertainty bounds are needed whenever electrical geophysical methods are used to quantify the amount of water present underground or its changes over time. The findings highlight the importance of better characterization of petrophysical parameters and the need to supplement the interpretation of resistivity-based moisture content estimates with other data sources.