An analytical solution is presented for the movement of chemicals through a sorbing porous medium with lateral or intra-aggregate diffusion. The liquid phase in the porous medium is divided into mobile and immobile regions. Diffusional transfer between the two liquid regions is assumed to be proportional to the concentration difference between the mobile and immobile liquids. Sorption processes in both the dynamic and stagnant regions of the medium are assumed to be instantaneous and the adsorption isotherm is assumed to be linear. The analytical model derived here describes the extensive tailing observed during flow through an unsaturated, aggregated sorbing medium and explains the often observed early breakthrough of chemicals in the effluent.

Six models, employing different ways of discretization of the nonlinear infiltration equation were compared in terms of execution time, accuracy, and programming considerations. All models yielded excellent agreement with water content profiles measured at various times in a sand column. The two explicit models, the θ‐based CSMP model and the h‐based explicit model, used between 5 and 10 times more computer time than the implicit models. Results obtained with the two models which used the Kirchhoff integral transformation were no better than those obtained with the two h‐based implicit models. The implicit schemes with implicit, or explicit evaluation of the hydraulic conductivity and water capacity functions appear to have the widest range of applicability for predicting water movement in soil with both saturated and nonsaturated regions. Excellent agreement was obtained between water content distributions, infiltration rates, and cumulative infiltration volumes calculated with the implicit finite difference model and Philip's quasi‐analytical solution.

Field‐measured values of soil temperature were used to calculate the apparent thermal diffusivity of the upper 10 cm of soil with six different methods. The limitations of the six methods were analyzed both in terms of the calculated results, and for the quantity and quality of data required to make the calculations. Four of the six methods, Amplitude, Phase, Arctangent, and Logarithm, provided explicit equations for the thermal diffusivity. These explicit methods required only a few measurements of temperature, and calculations were simple to perform; however, the results were found to be erratic and in general inconsistent with known or more reliable estimates of the apparent thermal diffusivity. Two methods, Numerical and Harmonic, which made use of larger numbers of temperature measurements to implicitly solve for the apparent thermal diffusivity, generally provided more reliable estimates. Calculated values of the apparent thermal diffusivity by both methods were used in predicting soil temperature for comparison with measured temperature. Even under partly cloudy conditions both methods predicted temperatures very well. In general the data requirement of the Numerical method was 12 to 24 measures of temperature per day at three depths, while the Harmonic method only required 8 to 12 measures of temperature per day at two depths.

With the increasing economic growth in the arid regions of the West, and with the growing need for waste disposal and storage, the ability to efficiently model water flow and pollutant transport through unsaturated soils is becoming more important. One of the more difficult water flow problems to model, from a numerical point of view, is infiltration into very dry soils. The presence of very steep pressure gradients combined with the large field scales leads to algorithms that are very CPU intensive. Here we develop a water content based algorithm that is suitable for modeling one‐dimensional unsaturated water flow into layered soils. We show that this algorithm is a numerical approximation of a general form of Richards equation. We compare the computational efficiency of this algorithm with that of two pressure head based finite difference water flow algorithms for several test problems. We find that the mass balance errors for the noniterative water content formulation are of the order of machine round off error for most applications. We also find that for soils with fairly wet initial conditions (h ≈ −100 cm H2O) the water content formulation requires approximately the same CPU time as the faster of the two pressure head formulations. For very dry soils (h=−1000 to −50,000 cm H2O) the CPU time required for the water content formulation is not a function of the initial water content of the soil, whereas the CPU time required for the pressure head formulation strongly increases with decreasing initial water content. Because of this lack of sensitivity to initial conditions, the water content based algorithm is from 1 to 3 orders of magnitude faster than the pressure head based algorithms when applied to infiltration into very dry soils. The water content algorithm is not suitable for combined saturated‐unsaturated or near‐saturated flow that may be present because of local heterogeneities in the soil. In addition, the water content algorithm cannot handle positive pressure upper boundary conditions such as those associated with ponded surface water.

Changes in salt concentration with time were measured at several depths inside and at the exit of a 94‐cm uniform unsaturated sand column which was leached at steady rates with solutions of calcium chloride. Observed salt distributions were compared with salt distributions calculated with a numerical procedure which was based on the dead‐end pore model of Coats and Smith (1964).Values for the dispersion coefficient, the diffusional mass transfer coefficient, and the fraction mobile water used in the model were obtained at different water contents by curve fitting observed and calculated concentrations at one depth. These same values were then used to calculate salt distributions at other depths and at the exit of the column and compared with measured salt distributions. Excellent agreement was obtained. The model presented a good description of the extensive tailing of the salt concentration distributions observed inside and at the exit of the column. The amount of stagnant water was found to increase with decreasing water content from 4% of the total water content of 0.256 cm3/cm3 to 40% of the total water content at a water content of 0.200 cm3/cm3. The apparent dispersion coefficient decreased from 6 cm2/hour to 1 cm2/hour at water contents of 0.256 and 0.200 cm3/cm3, respectively.