A note on the error analysis of time compression approximations

The accuracy of the time compression analysis (TCA) is analyzed by comparison with a numerical solution. Both the standard TCA and a new modified TCA are considered for a power law diffusivity and constant surface flux. As expected, the error of the approximations decreases with increasing power, and the error of the modified TCA is about half the error of the standard TCA. In a second part, the errors of the two TCAs are measured using a simple analytical solution instead of a numerical solution. It is shown that the conclusions remain the same for the analytical and numerical solutions. The advantage of using the analytical solution is to obtain simple analytical expressions, showing the influence of parameters. This is done to estimate the maximum error of both TCAs. A practical estimate of the errors can be obtained from equations which only require knowledge of the soil water diffusivity. It appears that for real soils the errors of the TCA are always <1% and thus are a very reliable tool for practical problems. Although not studied systematically, it also appears that gravity effects reduce the errors of the TCA so that the error obtained in the absence of gravity provides a conservative estimate when gravity is present.