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Accurate estimates of the unsaturated hydraulic properties are needed for any quantitative description of multiphase flow in porous media. This paper presents a consistent set of parametric models for the isothermal, hysteretic unsaturated fluid phase content (retention) and hydraulic conductivity functions of typical two-phase systems like water and air, or water and hydrocarbons. The equations are obtained by combining expressions for the hysteretic fluid retention curves with the statistical pore size distribution model of Mualem (1976) which predicts the hydraulic conductivity from more easily measured fluid retention data. Hysteresis is described using the model of Scott et al. (1983). The existence of residual fluid saturations for both the wetting and nonwetting fluids is justified. Theoretical and experimental considerations indicate a need to match predicted and observed hydraulic conductivities at fluid phase contents less than full saturation. 1Visiting Professor, 44(5), 892--898, 1980. van Genuchten, M. Th., and D. R. Nielsen, On describing and predicting the hydraulic properties of unsaturated soils, Ann. Geophys., 3(5), 615-628, 1985.

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To develop simplified methods of hydraulic characterization of field soils and effects of management, frequency distribution of macroporosity (or effective porosity) in a soil is investigated as a measure of its saturated hydraulic conductivity distribution. The effective porosity (φe) of a soil is related to its saturated hydraulic conductivity (Ks) by a generalized Kozeny‐Carman equation. The exponent of this relationship is assumed to vary within a narrow range (value of 4 or 5). The equation is then combined with scaling theory to derive the frequency distribution of Ks scaling factors from the φe distribution. These concepts are tested on experimental data for two widely different soils, a mollisol and an oxisol. The φe is defined as total porosity minus soil water content at −33 kPa pressure head. The exponent of the Ks‐φe relationship is found to be nearly 4 for the soil‐core data of both soils, while for a smaller set of in‐situ field data for oxisol, which was within a narrow range of φe, the value of the exponent was smaller. There was a considerable scatter in the relationships. However, with the exponent set equal to 4 or 5 the distribution of Ks scaling factors derived from φe distribution closely matched the experimental Ks‐derived distribution. The approach has a promise for large‐scale applications.

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.

This paper gives a review of our current conceptual understanding of the basic processes of water flow and chemical transport in the untsaturated (vadose) zone and of various deterministic mathematical models that are being used to describe these processes. During the past few decades, tremendous effort has been directed toward unravelling the complexities of various interactive physical, chemical, and microbiological mechanisms affecting unsaturated flow and transport, with contributions being made by soil scientists, geochemists, hydrologists, soil microbiologists, and others. Unfortunately, segmented, disciplinary research has contributed to a lack of experimental and theoretical understanding of the vadose zone, which, in turn, has precluded the accurate prediction and management of flow and contaminant transport through it. Thus a more unified and interdisciplinary approach is needed that considers the most pertinent physical, chemical, and biological processes operative in the unsaturated zone. Challenges for both fundamental and applied researchers to reveal the intricacies of the zone and to integrate these with currently known concepts are numerous, as is the urgency for progress inasmuch as our soil and ground water resources are increasingly subjected to the dangers of long‐term pollution. Specific research areas in need of future investigation are outlined.

Solute distributions within a soil profile during the leaching of water-soluble salts applied to the soil surface were measured at six depths to 182.4 cm within 20 subplots of a 150-ha field. Estimates of the pore water velocity based upon measures of solute displacement within each subplot and the entire field were found to be logarithmically normally distributed and in agreement with volumetric measures of water infiltration rates. Such agreement was only possible because it was recognized that the observed values were not normally distributed, and their mean values were calculated accordingly. The number of observations required to yield an estimate of the mean pore water velocity within a prescribed accuracy is shown to depend upon the nature and extent of the spatial variability of the field soil. For the field examined, 100 observations would allow the mean pore water velocity to be estimated within +50% of its true value. The functional relation between field-measured values of the apparent diffusion coefficient, also found to be logarithmically normally distributed, and pore water velocity is examined and interpreted in terms of solute distributions likely to be measured at specific sampling sites.

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