High-resolution moisture profiles from full-waveform probabilistic inversion of TDR signals

•We infer 1D soil moisture profiles with 1-cm resolution by spatial TDR inversion.•We quantify uncertainty in the moisture estimates by a novel Bayesian scheme.•We provide a detailed analysis of the accuracy of the method.•We observe a mean RMSE of 0.04 cm3 cm−3 for a series of sand column experiments.•We observe a mean RMSE of 0.02 cm3 cm−3 for a field application in a podzol.

SummaryThis study presents an novel Bayesian inversion scheme for high-dimensional undetermined TDR waveform inversion. The methodology quantifies uncertainty in the moisture content distribution, using a Gaussian Markov random field (GMRF) prior as regularization operator. A spatial resolution of 1 cm along a 70-cm long TDR probe is considered for the inferred moisture content. Numerical testing shows that the proposed inversion approach works very well in case of a perfect model and Gaussian measurement errors. Real-world application results are generally satisfying. For a series of TDR measurements made during imbibition and evaporation from a laboratory soil column, the average root-mean-square error (RMSE) between maximum a posteriori (MAP) moisture distribution and reference TDR measurements is 0.04 cm3 cm−3. This RMSE value reduces to less than 0.02 cm3 cm−3 for a field application in a podzol soil. The observed model-data discrepancies are primarily due to model inadequacy, such as our simplified modeling of the bulk soil electrical conductivity profile. Among the important issues that should be addressed in future work are the explicit inference of the soil electrical conductivity profile along with the other sampled variables, the modeling of the temperature-dependence of the coaxial cable properties and the definition of an appropriate statistical model of the residual errors.