Analysis of time compression approximations

Time compression approximation (TCA) is a practical and often quite accurate tool to predict postponding infiltration for field applications. A modified approximation (MTCA) can be used just as easily and, in general, will reduce the error by about 50%. This is based on two results: (1) After ponding, TCA and MTCA predict very close infiltration rates; and (2) MTCA, but not TCA, uses the actual cumulative infiltration up to the ponding time. Thus, TCA has an additional error in its prediction of postponding infiltration. Previously, those results, including the 50% reduction in error, were observed numerically for linear and Burger's soils. They are illustrated here numerically with an actual soil (a Grenoble sand). More importantly, we developed a general analytical approximation for this problem and showed that it can provide a very convenient predictive tool which can then be used for arbitrary soil properties.