A Bayesian inversion of hydrological and thermal parameters in the hyporheic zone

Abstract:

Reliable estimates of hydrological properties at the stream-aquifer interface are necessary for quantifying surface-subsurface exchanges but are challenging to get due to spatial variability and field data scarcity. Our study introduces a novel approach for inferring uncertainty-quantified hydrological and thermal parameters from a combination of pressure and temperature measurements in the hyporheic zone (HZ).

We use a stochastic approach to infer thermal and hydrological parameters in a HZ vertical profile. The column is forced by pressure and temperature time series at the boundaries and conditioned on temperature at multiple depths. The inversion process is based on a Bayesian algorithm called Method of Anchored Distribution (MAD) and on the associated open-source program MAD++, with extensions in the post-processing toolbox. This approach has several benefits. First, the hierarchical framework built-in in MAD allows the specification of a non-parametric and assumption-free likelihood function. Moreover, the Bayesian approach yields data-driven and naturally uncertainty-quantified parameter estimates.

We present two outcomes of the inversion approach. (1) Repeating the analysis at multiple locations yields spatially-distributed snapshots of uncertainty-quantified HZ parameters. (2) The unconditional posterior distribution of hydrological parameters is integrated in a Monte-Carlo error estimation framework to provide statistical distributions of surface-subsurface exchanges time series.

We present the methodology and demonstrate its application using field measurements from the Avenelles basin, France.