The tipping bucket equations as a model for macropore flow

Abstract

The tipping bucket model, a computationally efficient scheme for simulating soil water transport which requires few input parameters, implicitly assumes that all water flow occurs through macropores. The model is limited in its elimination of both micropore flow and macropore flow with unsaturated micropores and its reliance on a fixed time step, normally taken to be daily. The reformulation of the tipping bucket model as a set of differential equations for macropore water and solute transport removes the above limitations. Previous work on simulation of water transport through oxisols using the Richards equation showed that an accurate fit to measured water contents could be obtained only by making the probably false assumption that the saturated water content is only 70% of the total porosity. Combining the tipping bucket equation for macropore water transport with the Richards equation for micropore water transport produces an equally good fit to measured water contents under the more reasonable assumption that saturated water content is equal to total porosity. A critical assumption in the production of a good fit is that the saturated water content is scale-invariant, i.e. the macropore and micropore domains have the same saturated water content. The tipping bucket equations introduce two parameters that are difficult to estimate, the macropore drainage parameter and the mass transfer coefficient for drainage from macropores into micropores. However, for the particular data set studied in this paper, the above parameters are largely irrelevant as long as macropore water does not drain downwards through macropores faster than it drains into micropores, i.e. as long as the macropore and micropore domains are not decoupled.