The Prediction-Focused Approach: An opportunity for hydrogeophysical data integration and interpretation in the critical zone

Two important challenges remain in hydrogeophysics: the inversion of geophysical data and their integration in quantitative subsurface models. Classical regularized inversion approaches suffer from spatially varying resolution and yield geologically unrealistic solutions, making their utilization for model calibration less consistent. Advanced techniques such as coupled inversion allow for a direct integration of geophysical data; but, they are difficult to apply in complex cases and remain computationally demanding to estimate uncertainty.
We investigated a prediction-focused approach (PFA) to directly estimate subsurface physical properties relevant in the critical zone from geophysical data, circumventing the need for classic inversions. In PFA, we seek a direct relationship between the data and the subsurface variables we want to predict (the forecast). This relationship is obtained through a prior set of subsurface models for which both data and forecast are computed. A direct relationship can often be derived through dimension reduction techniques (Figure 1). For hydrogeophysical inversion, the considered forecast variable is the subsurface variable, such as the salinity or saturation for example. An ensemble of possible solutions is generated, allowing uncertainty quantification. For data integration, the forecast variable is the prediction we want to make with our subsurface models, such as the concentration of contaminant in a drinking water production well. Geophysical and hydrological data are combined to derive a direct relationship between data and forecast.
We illustrate the methodology to predict the energy recovered in an ATES system considering the uncertainty related to spatial heterogeneity. With a global sensitivity analysis, we identify sensitive parameters for heat storage prediction and validate the use of a short term heat tracing experiment to generate informative data. We illustrate how PFA can be used to successfully derive the distribution of temperature in the aquifer from ERT during the heat tracing experiment. Then, we successfully integrate the geophysical data to predict heat storage in the aquifer using PFA. The result is a full quantification of the posterior distribution of the prediction conditioned to observed data in a relatively limited time budget.