Abstract
The existing empirical, approximate, analytical, quasi-analytical and numerical solutions for predicting time to ponding (tp) were reviewed and compared in this paper. The quasi-analytical solution can provide a rough range of tp. As it is not confined to any special soil physical property, thus its solution could be used as a benchmark to test other solutions, especially to validate the feasibility of numerical solution.
There are some doubtful points in the universal application of the Parlange and Smith (P-S) approximation and the general solution of the Broadbridge and White (B-W). These two solutions are not always warranted to use. A Taylor expansion of the P-S approximation shows that the P-S solution is identical to the quasi-analytical one only if rainfall intensity (R) is much larger than the soil saturated hydraulic conductivity (Ks). If R is at near Ks near and the soil physical property is strongly soil water content dependent, the P-S solution may cause large discrepancy. This conclusion is not consistent to the theoretical analysis by B-W. The Mein and Larson (M-L) model has a fatal weakness that is caused in the empirical decision of the suction at the wetting front. The numerical model developed in this study can present a good solution to the tested sand and clay soils.
Time to ponding decays exponentially with the increase of R at any initial soil water content (θn), but the exponent is not always equal to 2. No matter what R is high or low, tp varies linearly with n. R plays the most vital role on the decision of tp. An empirical model was put forward by us, which can express clearly the relationship between tp and R and θn, however, it needs to be validated in further study. We discussed the shape of the soil water profile and the depth of the wetting front at tp. Finally, an analysis of the sensibility of the numerical solution was also presented in this paper.
