Stochastic modeling of soil water fluxes in the absence of measured hydraulic parameters requires a knowledge of the expected distribution of the hydraulic parameters in different soil types. Predictive relationships describing the hydraulic parameter distributions must be developed based on the common descriptors of the physical properties of soils (e.g., texture, structure, particle size distribution). Covariation among the hydraulic parameters within these relationships must be identified. Data for 1448 soil samples were examined in an evaluation of the usefulness of qualitative descriptors as predictors of soil hydraulic behavior. Analysis of variance and multiple linear regression techniques were used to derive quantitative expressions for the moments of the hydraulic parameters as functions of the particle size distributions (percent sand, silt, and clay content) of soils. Discriminant analysis suggests that the covariation of the hydraulic parameters can be used to construct a classification scheme based on the hydraulic behavior of soils that is analogous to the textural classification scheme based on the sand, silt, and clay content of soils. INTRODUCTIONApplication of the classical theory of soil water movement requires knowledge of the relationships among matric potential, moisture content, and hydraulic conductivity. The physical attributes of the soil giving rise to these interrelationships are understood in a qualitative sense [e.g., Childs, 1969]. A comprehensive theory to allow derivation of the relationships from fundamental properties of the medium (e.g., grain size distribution) is, however, not yet fully developed, although recent work suggests that certain aspects of the hydraulics may be amenable to a theoretical treatment [Nakano, 1976;Arya and Paris, 1981]. In most cases, curves of matric potential versus moisture content (the moisture characteristic) and of hydraulic conductivity versus either matric potential or moisture content must be determined for a given soil by direct measurement. Statistical analyses can be used to identify what soil properties are important in describing the observed variation in these curves, thereby providing information of practical value as well as suggesting how theoretical exploration might proceed.One approach that has been used to define the moisture characteristic is the construction of regression equations to predict the moisture content at specified values of matric potential using properties such as bulk density, percent sand, and other measured properties such as organic matter content [Ghosh, 1980;Gupta and Larson, 1979;Rawls and Brakensiek, 1982]. Results from these studies indicate that reasonable predictions can be made when the necessary data are available.

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Abstract. The fate of materials undergoing transport and reactions in natural porous media sometimes depends on the time of exposure of the conveyed material to other materials present in the system. The distribution of groundwater age, the effects of mineral chemical heterogeneity on reactive solute transport, and the occurrence of lag in reaction systems are some areas of hydrogeology that involve exposure time in an important way. A general balance equation for accounting for such effects is provided through an extended transport operator that incorporates generalized exposure time as an additional independent coordinate. Evolution of material distributions over exposure time appears within this transport operator as a convective process that represents space-and time-dependent generalized exposure of material constituents undergoing physical transport and nonequilibrium chemical and microbiological mass transformations. The general equation is derived from basic mass balance arguments by treating the constituents as a mixture of overlapping continua and developing evolution equations for the mixture material densities in the new dimensions of space, time, and exposure time. Example applications of the approach to each of the three examples above are described. IntroductionThe fate of materials undergoing transport in porous media sometimes depends on the time of exposure of the conveyed material to other materials present in the system. Such dependency appears in diverse ways, three of which are introduced here as example phenomena that will be analyzed in this article. In the case where the conveyed material is the water itself and the other material is the aquifer solid phase, the exposure time is the groundwater age [e.g., Goode, 1996; Varni and Cartera, 1998]. This quantity is important in recharge source

[1] A new equation for the collector efficiency (h) of the colloid filtration theory (CFT) is developed via nonlinear regression on the numerical data generated by a large number of Lagrangian simulations conducted in Happel's sphere-in-cell porous media model over a wide range of environmentally relevant conditions. The new equation expands the range of CFT's applicability in the natural subsurface primarily by accommodating departures from power law dependence of h on the Peclet and gravity numbers, a necessary but as of yet unavailable feature for applying CFT to large-scale field transport (e.g., of nanoparticles, radionuclides, or genetically modified organisms) under low groundwater velocity conditions. The new equation also departs from prior equations for colloids in the nanoparticle size range at all fluid velocities. These departures are particularly relevant to subsurface colloid and colloid-facilitated transport where low permeabilities and/or hydraulic gradients lead to low groundwater velocities and/or to nanoparticle fate and transport in porous media in general. We also note the importance of consistency in the conceptualization of particle flux through the single collector model on which most h equations are based for the purpose of attaining a mechanistic understanding of the transport and attachment steps of deposition. A lack of sufficient data for small particles and low velocities warrants further experiments to draw more definitive and comprehensive conclusions regarding the most significant discrepancies between the available equations.

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