Distributed Soil Moisture from Crosshole Ground-Penetra ng Radar Travel Times using Stochas c Inversion

Geophysical methods off er several key advantages over conven onal subsurface measurement approaches, yet their use for hydrologic interpreta on is o en problema c. We developed the theory and concepts of a novel Bayesian approach for high-resolu on soil moisture es ma on using travelme observa ons from crosshole ground-penetrating radar experiments. The recently developed Mul -Try Diff eren al Evolu on Adap ve Metropolis algorithm with sampling from past states, MT-DREAM(ZS), was used to infer, as closely and consistently as possible, the posterior distribu on of spa ally distributed vadose zone soil moisture and porosity under saturated condi ons. Two diff ering and opposing model parameteriza on schemes were considered, one involving a classical uniform grid discre za on and the other based on a discrete cosine transforma on (DCT). We illustrated our approach using two diff erent case studies involving geophysical data from a synthe c water tracer infi ltra on study and a real-world fi eld study under saturated condions. Our results demonstrate that the DCT parameteriza on yields superior Markov chain Monte Carlo convergence rates along with the most accurate es mates of distributed soil moisture for a large range of spa al resolu ons. In addi on, DCT is admirably suited to inves gate and quan fy the eff ects of model trunca on errors on the MT-DREAM(ZS) inversion results. For the fi eld example, lateral anisotropy needed to be enforced to derive reliable soil moisture es mates. Our results also demonstrate that the posterior soil moisture uncertainty derived with the proposed Bayesian procedure is signifi cantly larger than its counterpart es mated from classical smoothness-constrained determinis c inversions.