Towards more efficient soil-water modelling: moisture profiles for constant application or removal of water at the surface

Summary

Soil-water profiles are often calculated using models based on the application to successive soil layers of an approximate formulation of Darcy's Law. An arbitrary decision is usually made concerning the magnitude of the layer thickness, Δz, and time increment Δt, a decision often based on the intuitive criterion that both should be as small as possible. An unsuitable choice can either give rise to oscillations in the solutions that can be eliminated only by recalculation using different increments, or can culminate in an accuracy unjustified by the precision of the data, both cases resulting in unnecessarily lengthy and wasteful computing. However, mathematicians have shown, for problems which are analogous to particular soil-water models, that oscillations will not occur if τ = D(Δt)/(Δz)² ≥ 0·50 (where D is the soil-water diffusion coefficient, assumed constant).

This paper considers the development of moisture profiles in soils with a constant rate of loss (e.g. evaporation) or entry (e.g. irrigation) of water imposed at the surface, and demonstrates that the criterion τ ≥ 0·50 can be extended to apply to waterdependent diffusion coefficients by re-interpreting D as the maximum value occurring in the profile. Examples for 10-layer models suggest that it is sufficient for practical purposes to start with Δt values that give τ-values close to 0·50, and to proceed to smaller Δt-values only when necessary. The total gain or loss of water given by integrating the calculated profiles is compared with the known amount entering or leaving at the surface.

The profiles for both evaporation and irrigation are found to advance too rapidly.