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

The sharp wetting front model of infiltration (Green and Ampt, 1911; P hilip, 1954) yields through simple integration an exact solution relat ing 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 fin d the infiltration rate, and furthermore, analytic manipulations are l imited using this traditional formulation of the Green-Ampt infiltrati on. In this note we present an accurate expression for the infiltratio n 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 exp ression 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/run off calculations that necessitate the time compression approximation ( TCA).