  Geophysical methods offer several key advantages over conventional subsurface
measurement approaches, yet their use for hydrologic interpretation is often
problematic. Here, we introduce theory and concepts of a novel Bayesian
approach for high-resolution soil moisture estimation using traveltime
observations from crosshole Ground Penetrating Radar (GPR) experiments. The
recently developed Multi-try DiffeRential Evolution Adaptive Metropolis with
sampling from past states, MT-DREAM(ZS) is being used to infer, as closely and
consistently as possible, the posterior distribution of spatially distributed
vadose zone soil moisture and/or porosity under saturated conditions. Two
differing and opposing model parameterization schemes are being considered, one
involving a classical uniform grid discretization and the other based on a
discrete cosine transformation (DCT). We illustrate 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 the most accurate
estimates of distributed soil moisture for a large range of spatial
resolutions, and superior MCMC convergence rates. 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
needs to be enforced to derive reliable soil moisture variability. 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.
