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the field and laboratory experiments. The often- observed escape of air bubbles through the wetted zone may be related to the Instability of the wetting front. Although the phenomenon is mathematically describable, it was decided not to pursue modeling such a natural, yet complicated, rain infiltration problem, For simplicity. the Richards equation is used as an unsaturated flow equation throughout this study. Idealized Rain Infiltration Problem The soil water movement under rainfall can hypothetically be described by using the concepts in continuous mechanics. The flow equation formulated on the basis of these concepts is the well.known Richards equation that can be derived by incorporat- ing Darcy's law with the equation of continuity. An initial condition such as a constant or specified initial moisture content is given. To formulate boundary conditions requires a knowledge of the rainfall infiltration process that is briefiy described as fol- lows. When rainfall starts, rain water falling on the soil surface causes an increase in the soil water content. If rainfall continues, the soil surface be. comes saturated and eventually is ponded. However, not all events of rainfall reach this ponding stage, Some rainfall intensities which are less than the limiting infiltration rate (or the saturated hydraulic conductivity) maintain the soil in an unsaturated condition. In other words, with small rainfall inten. sities, rain infiltration can continue indefinitely with- out ponding (Rubin and Steinhardt, 1963). On the other hand, some extremely high rainfall intensities could cause immediate ponding on the soil surface with a brief wetting stage to attain full saturation of the surface lamina' of soil. In general, the rain inmtration process can be divided into two stages: The first one is before ponding and the second one is after ponding. Thus, the following two different boundary conditions on the soil surface should be specified for these two different stages: Before ponding the soil surface condition is a flux condition equal to the given rainfall rate, and after ponding it becomes a pressure head boundary condition equal to the ponded water depth, After ponding, the saturated zone that began at the soil surface gradually proceeds downward with the saturated zone overlying the unsaturated zone, If the ponding situation continues, the interface be. tween the saturated and unsaturated zones (hence- forth called the saturation front) moves downward until the specified lower boundary such as the groundwater table or impelVious layer is reached provided that air is not entrapped, When the satura- tion front reaches the lower boundary, the soil layer is saturated throughout. However, the lower boundary condition may not be required if the soil layer is assumed semi-infmite, as was the assumption usually adopted in the rain infiltration study. The flow equation applicable in the saturated zone is the Laplace equation that can readily be derived frum the Richards equation, A boundary condition at the saturation front can be prescribed by the air entry value in terms of the soil capillary potentiaL If the soil air has access to the atmosphere, the pore air pressure may be assumed to remain essentially atmos- pheric and the soil capillary potential at the satura- tion front can thus be assumed equal to atmospheric pressure. A considerable amount of knowledge and understanding on the mechanism of rain infiltration has been advanced by many investigators (e,g" Philip, 1957a, 1969b, and 1973; Rubin and Steinhardt, 1963, 1964; Rubin, Steinhardt, and Reiniger 1964; Rubin, 1966a and 1966b; Parlange, 1971 and 1972; Knight and Philip, 1973; Philip and Knight, 1974), Freeze (1969) summarized available numerical mathe- matical treatments for one-d.imensional, vertical, saturated.unsaturated, unsteady, flow problems in soils, Remson, Hornberger, and Molz (1971) also outlined numerical techniques used in this area. The finite-difference method adopted in the present study is in essence the same explicit scheme as formulated by Richtmeyer (1957), In order to circumvent computational instability due to the use of the explicit scheme, the stability criterion of Richtmeyer (1957) was followed, This stability criterion is a restriction which makes the computation very long; however, Gupta and Staple (1964), Staple (1966, 1969), and Wang and Lakshminarayana (1968) have successfully applied explicit.difference methods in solving the rain infiltration problem, Although a form or scheme for a finite dif- ference equation may be arbitrary, various factors were considered when deciding on an explicit scheme. First, the programming of an explicit scheme is relatively simple, as unknowns are solved for separate- ly, one at a time. Second, the explicit scheme requires less computations than the implicit scheme for every time step, However, it should be cautioned that because the explicit solution of a parabolic equation is subject to a stability criterion which limits the size of the time step that can be used, a large amount of computer time will be required when an explicit scheme is used in solving the problem involving the length of time with such an order of magnitude as days and weeks. Use of an explicit scheme may be justified only on the case that the infiltration- capacity decay curve for a period of one hour or so after rainfall needs to be computed, The narrOW range of interest in time would probably make the explicit scheme as efficient as, if not more efficient than, the implicit scheme in the present computation, aside from other intrinsic problems resulting from the use 14