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Upper and Lower Bounds of the Ponding Time for Near Constant Surface Flux¹

ABSTRACT

Upper and lower bounds on the relation between the time course of cumulated infiltration into soil and water content at the soil surface are derived. These estimates can be used specifically to predict upper and lower bounds of the ponding time. The analytical results are derived for mildly varying surface flux. However, the accuracy of the limits is illustrated and discussed for Granoble sand with constant rainfall rates only. A numerical solution is also obtained that yields results outside the range of the more accurate analytical results. This confirms that errors are introduced in the numerical scheme during the early stages of infiltration. Less accurate, but easier to apply, analytical limits are also presented and discussed.

¹ Contribution of the Institut de Mécanique (LA n° 6) B.P. 68-F 38402 Saint Martin D'Heres, Cédex, France,

² Research Scientist, Institut de Mécanique; Professor of Agricultural Engineering, Cornell Univ., Ithaca, NY 14853; Senior Research Scientist, Institut de Mécanique; Lecturer, School of Australian Environmental Studies, Griffith Univ., Brisbane, Queensland 4111, Australia; and Senior Research Scientist, Institut de Mécanique, respectively.

Received for publication April 21, 1986.