Time Compression Approximation Relationship for Infiltration in the Presence of a Shallow Water Table: Evaluating the Role of Péclet Number

Abstract

The time compression (or time condensation) approximation (TCA) is commonly used in conjunction with an infiltration capacity equation for predicting the postponding infiltration rate, or, more generally, infiltration under time-varying precipitation. In this paper a power function relationship for TCA between infiltration capacity and its time derivative is proposed for infiltration in the presence of a shallow water table. The results show that the exponent (β) in the power function relationship is not a constant but decreases as infiltration proceeds. The change of β indicates that the TCA relationship changes during infiltration and further suggests the necessity of using different TCA relationships for predicting infiltration rate during different stages after ponding. We argue that the change of β is due to the gradual dynamic change of the relative role of gravity and capillarity during infiltration. A Péclet number (Pe) is proposed for measuring the relative effect of gravity and capillarity. In the early times of infiltration when Pe < 1, with the increase of Pe, β decreases roughly from 3.5 to 2 for clay, silty clay loam, and silty loam, and from 3 to 2 for sandy loam and sand; during the longer times when Pe > 1, β has a linear relationship with Pe. The relationship between Pe and β provides an objective approach to select the suitable TCA function during different infiltration stages after ponding.