EXPLICIT EXPRESSIONS FOR GREEN-AMPT (DELTA-FUNCTION DIFFUSIVITY) INFILTRATION-RATE AND CUMULATIVE STORAGE

The sharp wetting front model of infiltration (Green and Ampt, 1911; Philip, 1954) yields through simple integration an exact solution relating the infiltration rate (i), cumulative infiltration (I), and time (t). The relation, however, is implicit for i or I; i.e., it is of the form t = A[I - B 1n (1 + I/B)]. Numerical iteration is required to find the infiltration rate, and furthermore, analytic manipulations are limited using this traditional formulation of the Green-Ampt infiltration. In this note we present an accurate expression for the infiltration rate in the form of a rapidly converging series in the variable tau = t/(t + chi). Truncating the series at four terms yields a useful expression for i(t). The proposed four-term expression gives less than 2% error at all times and is readily integrated to yield the cumulative infiltration I(t). In conjunction with the exact expression for time (t) given i or I, the proposed expression is useful in infiltration/runoff calculations that necessitate the time compression approximation (TCA).