Abstract. In situ measurement of soil hydraulic properties may be achieved by analyzing the unconfined effiux from disc tension infiltrometers, once consistent infiltration equations can be derived. In this paper an analytical, three-dimensional infiltration equation is developed, based on the use of parameters with sound physical meaning and adjustable for varying initial and boundary conditions. The equation is valid over the entire time range. For practical purposes, a simplified solution is also derived. The full and simplified equations give excellent agreement with published experimental results and are particularly useful for determining soil hydraulic properties through application of inverse procedures.

near the soil surface, in response to biology, climate, and management (Gupta et al., 1991). Uptake of water Modeling of water and solute transport in soils is increasinglyand solutes by plants is another difficult area, and ongoimportant in hydrology and agriculture, but there remain many gaps ing research will change the modeling of these processes. and unresolved issues. One of these, the speed and robustness of numerical solutions, is important in large-scale and stochastic model-Not all progress, however, depends on better soil ing. A fast method was developed for solution of the Richards equation characterization and research into soil and plant profor water transport. Brooks-Corey soil hydraulic property descripcesses. There are many reports of modeling results in tions were used with water content as the dependent variable in the literature, but it is often difficult to assess their unsaturated regions and pressure head in saturated regions. Central general implications because of differing system paramtime weighting was used in unsaturated conditions to improve accueters and input variables and because a thorough analyracy and fully implicit weighting in saturated conditions to improve sis of sensitivity to uncertainties in parameters and instability. Water fluxes were calculated using matric flux potentials puts is often not given. Of course, such uncertainty combined with a novel spatial weighting scheme for the gravitational analysis is not easy, especially when it concerns patterns component. Flow across soil property interfaces was calculated bysuch as climatic variation (Janssen et al., 1994). In addiequating fluxes to and from the interface. Results on a test problem involving rainfall, surface ponding, evaporation, and drainage over

Simple water‐retention functions in current use do not predict zero water content at oven dryness. Using the Campbell equation θ = a ψ‐c = θs (ψ‐c − ψ‐c0) relating volumetric water content, θ, to matric suction, ψ, as an example, we examined a modification to ensure that the curve terminates in a suction ψ0 = 1000 MPa, approximating oven dryness. The new equation is θ = a(ψ‐c − ψ‐c0) = θs (ψ‐c − ψ‐c0)/(ψ‐cc − ψ‐c0. It was compared with the unmodified equation by fitting to water‐retention data from Australia, the UK, and the USA. Results showed not only that the new equation fit the data slightly better than the original equation, with a mean standard deviation of 0.014 m3 m−3 about the regression, but also that its parameters could be calculated from those of the unmodified equation if original water‐content data were unavailable for fitting. Although lack of data hampered assessment of its predictions of water content in dry soils, its use appears preferable to extrapolating the unmodified equation.

Water flow in soils with sufficiently large aggregate size or pore‐class heterogeneity may exhibit a nonequilibrium between the actual water content and that given by the water retention curve. The result is deeper penetration of infiltrating water than predicted using classical infiltration theory. Models of this process usually divide the soil into two or more exchanging flow regions. A simpler treatment is possible by combining Richards' equation with a dynamic description of the approach to equilibrium. We present a first‐order time constant equilibration model of infiltration into a hypothetical structured soil and use the model to describe published outflow responses to constant rate rainfall on six large, undisturbed cores. Using measured hydraulic properties and varying only the A and B horizon time constants, the model was fitted to cumulative outflow from one particular soil core that had measured time domain reflectometry (TDR) water contents at the 0.05‐ and 0.5‐m depths recorded during the experiment. Cumulative outflow was fitted using time constants of 4 and 5 h for A and B horizons, respectively, and this also gave good agreement with TDR measured water contents. Cumulative outflow and runoff from a further four of the six cores was described using the same A and B horizon time constants and varying only the macropore hydraulic conductivity. The remaining core contained a decayed root, which conducted water rapidly with little opportunity for lateral exchange. A description of cumulative outflow required both the macropore hydraulic conductivity and the time constant to be altered.

Two efficient finite difference methods for solving Richards' equation in one dimension are presented, and their use in a range of soils and conditions is investigated. Large time steps are possible when the mass‐conserving mixed form of Richards' equation is combined with an implicit iterative scheme, while a hyperbolic sine transform for the matric potential allows large spatial increments even in dry, inhomogeneous soil. Infiltration in a range of soils can be simulated in a few seconds on a personal computer with errors of only a few percent in the amount and distribution of soil water. One of the methods adds points to the space grid as an infiltration or redistribution front advances, thus gaining considerably in efficiency over the other fixed grid method for infiltration problems. In 17‐s computing, this advancing front method simulated infiltration, redistribution, and drainage for 50 days in an inhomogeneous soil with nonuniform initial conditions. Only 16 space and 21 time steps were needed for the simulation, which included early ponding with the development and dissipation of a perched water table.

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