A note on the time compression approximation

In this paper the work by Sivapalan and Milly [1989] is extended beyond the time of pending to estimate the errors of the time compression approximation (TCA) when an exact solution exists. The diffusion coefficient is set to be constant, and gravitational effects are not considered here. The largest error of standard TCA in calculating cumulative infiltration is about 2.5%, while its underestimate of the time to ponding is about 19%. A modified TCA is also proposed, in which the exact time of pending is used directly instead of the flux to improve the estimate of postponding infiltration. The error for the modified TCA is about half of the error for the standard TCA in predicting cumulative infiltration, and thus the modified TCA should be preferred wherever pending time is or can be measured.