[1] In this paper, a set of analytical infiltration equations that are commonly used to evaluate one-and three-dimensional water infiltration from a surface disc source is studied. Both the quasi-exact analytical formulation and the related approximations for short and long times are assessed. The analytical properties of the quasi-exact formulation are evaluated using a proposed scaling procedure in order to define the validity domains of related approximations. Both quasi-exact and approximate analytical equations are then studied with respect to their ability to reproduce numerically generated cumulative infiltrations from a 10 cm radius disc source for four soils (sand, loam, silt, and silty clay) at several initial saturations. The quasi-exact formulation is suitable for sand, loam, and silt when their soil-dependent and saturation-independent shape parameters, g and b, are properly chosen (between 0.75 and 1 and 0.3 and 1.7, respectively). Approximations derived for the same shape parameters can also be used, provided that their use is restricted to proposed validity intervals. However, none of these equations applies for silty clay, since its hydraulic properties do not fulfill the conditions required for the use of the quasiexact formulation.

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