Time to ponding: Comparison of analytic, quasi‐analytic, and approximate predictions

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Abstract
An analytic expression for time to ponding is introduced using the nonlinear model of Broadbridge and White (1987). The hydraulic properties of this model can encompass properties ranging from those of a highly nonlinear Green‐Ampt‐like soil to those satisfying the weakly nonlinear Burgers' equation. Because of its versatility, this analytic solution is used as a benchmark against which extant analytic, quasi‐analytic, and approximate expressions are compared. Time to ponding is parameterized here in terms of the readily measured field properties, sorptivity and hydraulic conductivity. In the limit of Green‐Ampt‐like properties the analytic solution reduces exactly to the Parlange and Smith (1976) approximation. A similar functional dependence of time to ponding on rainfall rate is found from quasi‐analytic approximations. Based on this, a modified approximation is suggested which should give time to ponding for most soils to within ±10%. Some existing approximations are found to have unacceptable deviations from the analytic solution, and their continued use appears unwarranted. Finally, we address the field problem of predicting time to ponding at any antecedent water content, given sorptivity measured at only one initial water content.