Distributed Soil Moisture from Crosshole Ground‐Penetrating Radar Travel Times using Stochastic Inversion

In this paper two different subsurface parameterizations are compared for posterior soil moisture estimation from traveltime observations of crosshole GPR. The discrete cosine transform provides the most adequate and efficient results and enables linking MCMC derived parameter uncertainty to model resolution. Geophysical methods offer several key advantages over conventional subsurface measurement approaches, yet their use for hydrologic interpretation is often problematic. We developed the theory and concepts of a novel Bayesian approach for high-resolution soil moisture estimation using travel-time observations from crosshole ground-penetrating radar experiments. The recently developed Multi-Try Differential Evolution Adaptive Metropolis algorithm with sampling from past states, MT-DREAM(ZS), was used to infer, as closely and consistently as possible, the posterior distribution of spatially distributed vadose zone soil moisture and porosity under saturated conditions. Two differing and opposing model parameterization schemes were considered, one involving a classical uniform grid discretization and the other based on a discrete cosine transformation (DCT). We illustrated our approach using two different case studies involving geophysical data from a synthetic water tracer infiltration study and a real-world field study under saturated conditions. Our results demonstrate that the DCT parameterization yields superior Markov chain Monte Carlo convergence rates along with the most accurate estimates of distributed soil moisture for a large range of spatial resolutions. In addition, DCT is admirably suited to investigate and quantify the effects of model truncation errors on the MT-DREAM(ZS) inversion results. For the field example, lateral anisotropy needed to be enforced to derive reliable soil moisture estimates. Our results also demonstrate that the posterior soil moisture uncertainty derived with the proposed Bayesian procedure is significantly larger than its counterpart estimated from classical smoothness-constrained deterministic inversions.

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