A STOCHASTIC-MODEL OF INFILTRATION WHICH SIMULATES MACROPORE SOIL-WATER FLOW

Estimates of "macropore" soil water phenomena are calculated from a simple stochastic model of infiltration. Probability density functions (pdf) for cumulative infiltration (I), infiltration rate (I'), and infiltrating-water flux (upsilon) are proposed. Cumulative infiltration is defined here as the maximum quantity of water the soil can accept from unponded water supplied at a given location on the soil surface. Similarly, infiltration rate is defined as the maximum rate at which unponded water can enter the soil. The pdfs for cumulative infiltration (f(I)) and infiltration rate (f(I')) are derived by assuming that the saturated hydraulic conductivity (K(s)) is a lognormal-distributed random variable. The actual infiltrating-water flux will depend on I', rainfall rate (R0), slope, and surface roughness. For a flat and smooth soil surface the pdf for infiltrating-water flux f-upsilon is derived from f(I') by assuming that water failing to infiltrate into portions of the soil with lower infiltration rates will flow over the soil surface, eventually being accepted by areas with higher infiltration rates. The pdf f-upsilon predicts that macropore soil water flow phenomena will become more pronounced as the rainfall rate approaches the mean infiltration rate, when macropore flux predicted by f-upsilon is many times the rainfall rate. These results indicate that stochastic description of soil hydraulic properties shows promise in describing macropore soil water phenomena. Models of the field-scale effects of macropore soil water flow should include infiltration rate variability and runoff contributions to infiltrating-water flux.