Richard’s equation revisited – the challenge to reconstruct non-equilibrium field retention data with soil hydraulic models

The origins of the Richard’s equation date back more than a century but it is still the most commonly used model to describe variably saturated soil water movement. It requires the specification of the characteristic relationships between soil water content, tensiometric pressure and hydraulic conductivity, which can be subsumed as soil hydraulic models. Numerous soil hydraulic models and variants thereof have been developed to mimic the behaviour of natural soils, including hysteresis, macro-pore flow, and dynamic non-equilibrium flow. Despite the progress being made, it is often difficult to accurately simulate retention data derived from undisturbed field soils.

This work presents a benchmark inverse modelling study for 1D soil water movement and field retention data from a wetting-drying cycle using state-of-the-art soil hydraulic models. The main aim is to test the ability of the different models to reproduce the field data. The soil hydraulic models tested are, among others, the van Genuchten-Mualem model (VGM, 1976, 1980), VGM with hysteresis (Kool and Parker, 1987), Brooks-Corey (1966), Dual porosity (Durner, 1994) and the non-equilibrium flow model by Diamantopoulus (2015).

In our study, we used an implementation of the Richards equation with the highly efficient and numerically stable Methods-of-Line scheme. Best-fit estimates and parameter posterior distributions were derived using the Markov-Chain Monte Carlo sampling algorithm DREAM_ZS and time series of soil water content and tensiometric pressure. The field data shows clear signs of non-equilibrium flow. It originates from an intensively studied, inverted-lysimeter site with Pumice soils under grass from the central part of the North Island of New Zealand.

Results demonstrate that none of the models was able to accurately mimic soil water content and tensiometric pressure data simultaneously at all times. Model deficiencies were identified particularly for the two wetting events, where all models underestimated soil water content while tensiometric pressure matched the data closely. We hypothesise that at least part of the discrepancies relate to an oversimplification of the hydraulic conductivity function for non-equilibrium flow.

This study is limited to a single data set and by several assumptions that are commonly made in inverse parameter estimation studies. The better assessment and implementation of measurement error (structures) might alleviate (or mask) some of the discrepancies between model simulations and data. However, this is apparently not the solution to the problem. Dynamic non-equilibrium flow has been observed in natural soils in several well-conducted field experiments. Our results are just one example that demonstrates the need to improve soil hydraulic modelling by revisiting the physics of fundamental processes in natural soils.