On the relationship between the time condensation approximation and the flux concentration relation

The time condensation approximation (TCA) has been used widely in hydrological modeling since it was introduced in the 1940's. This paper proposes a theoretical foundation for the validity of the TCA applied to constant-rainfall infiltration by recourse to the flux-concentration relation (FCR) used in soil physics. When the FCR is independent of boundary conditions, the TCA is exact. The success of the TCA is the result of two important properties of the FCR. The first is the fact that for a variety of flow processes the FCR is nearly the same regardless of the actual boundary conditions. Secondly, the FCR-based solutions of the Richards equation are relatively insensitive to the form of the FCR. For a delta-function soil, the TCA is exact. The largest errors associated with the TCA occur in the case of linear soil, where it leads to a 19% error in the calculation of time to ponding.