Numerical approximations based on different forms of the governing partial differential equation can lead to significantly different results for unsaturated flow problems. Numerical solution based on the standard h-based form of Richards equation generally yields poor results, characterized by large mass balance errors and erroneous estimates of infiltration depth. Conversely, numerical solutions based on the mixed form of Richards equation can be shown to possess the conservative property, so that mass is perfectly conserved. This leads to significant improvement in numerical solution performance, while requiring no additional computational effort. However, use of the mass-conservative method does not guarantee good solutions. Accurate solution of the unsaturated flow equation also requires use of a diagonal time (or mass) matrix. Only when diagonal time matrices are used can the solution be shown to obey a maximum principle, which guarantees smooth, nonoscillatory infiltration profiles. This highlights the fact that proper treatment of the time derivative is critical in the numerical solution of unsaturated flow.

A General Mass-Conservative Numerical Solution for the Unsaturated Flow Equation

Numerical simulation of infiltration, evaporation and shallow groundwater levels with the Richards equation

[1] The Surface Monitoring Of the Soil Reservoir Experiment (SMOSREX) site is used in this study to evaluate the performance of the Interaction between Soil Biosphere Atmosphere soil multilayer diffusion scheme (ISBA-DF) in reproducing short-term and long-term evolution of soil moisture and temperature profiles, surface energy fluxes, and drainage rate using both the Brooks and Corey and the van Genuchten models describing soil-water retention and conductivity curves. The site consists of a fallow field in southwestern France where intensive measurements were made during the 2001–2007 period. Two sets of four simulations describing homogeneous and heterogeneous soil properties are performed using four continuous pedotransfer functions. ISBA-DF is also compared with the ISBA “force-restore” soil scheme (ISBA-FR) since this version is currently used in several meteorological, hydrological, and/or climate applications. ISBA-DF exhibits a good performance in terms of simulating the soil moisture profile and the surface energy fluxes, especially when heterogeneous soil properties are considered. Its soil moisture dynamic does not depend on the field capacity, which is a clear advantage compared with ISBA-FR. However, it shows some drawbacks in simulating the surface temperature. The Brooks and Corey model exhibits the best skill scores in simulating the soil moisture profile and the surface fluxes compared with the van Genuchten model. Nevertheless, the differences are not significant, and the results on a single site reduce the generality of this intercomparison. Finally, two additional sets of experiments are performed to assess the scheme sensitivity to increasing soil depth and to the soil vertical discretization.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2011JD016002

Local evaluation of the Interaction between Soil Biosphere Atmosphere soil multilayer diffusion scheme using four pedotransfer functions

Numerical analysis of one-dimensional unsaturated flow in layered soils

SWAP simulates vertical transport of water, solutes and heat in variably saturated, cultivated soils The program has been developed by Alterra and Wageningen University, and is designed to simulate transport processes at field scale level and during whole growing seasons This manual describes the theoretical background and modeling concepts that were used for soil water flow, solute transport, heat flow, evapotranspiration, crop growth, multi-level drainage and interaction between field water balance and surface water management An overview is given of model use, input requirements and output tables

/pdf/reference-manual-swap-version-3-0-3-2p3xismeki.pdf

Reference Manual SWAP; version 3.0.3

Truncation errors in the numerical solution of horizontal diffusion in saturated/unsaturated media

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Truncation errors in the numerical solution of horizontal diffusion in saturated/unsaturated media