A robust solution to Richards' equation for complex soil hydraulic models using the Method Of Lines

A robust solution to Richards' equation for complex soil hydraulic models using the Method Of Lines

Robust numerical solutions are required for automatic parameter estimation, uncertainty analysis of soil hydraulic models, but also to quantify and legitimate model complexity.
The Method Of Lines approach to solve Richards' equation has already be shown to be an efficient and stable alternative to established methods, namely low-order finite difference and finite element methods applied to the mixed form of Richards' equation. Besides its beneficial properties in numerical challenging scenarios, the Method Of Lines approach allows for easier integration of additional differential equations which proves advantageous where further processes should be included in the modeling.

In this work a slightly modified Method Of Lines approach is used to solve the pressure based Richards' equation. A finite differencing scheme is applied to the spatial derivative and the resulting system of ordinary differential equations is reformulated as differential-algebraic system of equations (DAE). The open-source code IDAS from the Sundials suite is used to solve the DAE system. This solution has been extended to include hydraulic models that can account for hysteresis, dual-permeability and non-equilibrium effects. The different hydraulic model implementations have been verified against results from the software Hydrus and show good agreement with those.
Bayesian model selection techniques and the concept of the model confusion matrix can be used to examine the legitimacy of a given model's complexity with regards to available input data.
To generate the necessary data a Monte Carlo Sampling over a range of soil parameters was carried out for the models of different complexity. The computations were performed at the high-performance computing facilities at TU Dresden using the developed code.

The results of the analysis show the identifiability of the models, i.e. how well a model recognizes itself through Bayesian model selection when it was the one that has generated the data. This is a useful technique when building model ensembles for diagnostic or predictive purposes.