Models of water flow in the upper soil layer of spatially variable fields are developed. Field variability is assumed to take place in the horizontal plane. The saturated hydraulic conductivity is assumed to be a random variable of lognormal distribution, and head suction and moisture content are related to it by simple analytical relationships. The aim of the study is to derive the expectation and variances of the moisture content, suction heads, hydraulic conductivity, and water flux as functions of depth and time for infiltration and redistribution. Toward this aim a simplified solution of vertical flow in a homogeneous column, based on the concept of moving front, is developed. The statistical procedure for using this solution in a spatially variable field is outlined.

Determinations of the sorptivity (S) and five parameters describing the hydraulic conductivity [K(h)] and soil water retentivity [θ(h)] functions have been used to analyze the spatial distribution of the hydraulic properties in an experimental field. The parameters are: saturated hydraulic conductivity (Ks); water entry value (hw); saturated (θs) and residual (θr) water contents; and a constant β characterizing the pore size distribution of the soil. For a given depth, each of these parameters is described as a realization of a stationary two‐dimensional isotropic and random process. These stochastic processes are characterized by truncated normal or log‐normal probability density functions independent of the spatial position, and by autocorrelation functions between any two spatial points in the field which depend solely on the size of the vector separating the two points. The spatial variability of each of the six parameters has a structure that is characterized by a characteristic length—the integral scale, J, representing the largest distance for which the parameter is correlated with itself. Values of J, which are calculated from the autocorrelation functions for each parameter generally decrease with depth. On the average over depth the calculated values of J are 21, 44, 55, 25, 35, and 15 meters for the parameters Ks, hw, θs, θr, S, and β, respectively. The spatial variability of the hydraulic functions are described by the probability density functions and the autocorrelation functions. Since the integral scales of K(h) and θ(h) vary with both h and depth, the characteristic length of the field has been chosen as the integral scale of the weighted mean diffusivity which is 18 m.

Data obtained from careful water balance studies on water uptake by the roots of red cabbage are compared with results obtained from a modified numerical model of Nimah and Hanks. In the modified model the air dry moisture content at the soil surface may vary with time depending on meteorological conditions. The maximum possible rate of evapotranspiration is calculated by considering both meteorological conditions and crop properties. Data are quoted to suggest that the coefficient of the root sink may sometimes vary exponentially with depth. A period of 7 weeks was simulated, and the calculated weekly moisture profiles did not agree completely with those measured in the field. On the other hand, the calculated cumulative rates of evaporation and transpiration were in excellent agreement with the field data. When the original model was used without the suggested modifications, the agreement of these rates with the field data was not as good, an indication that some of these modifications actually improve the predictive capabilities of the model.

In a heterogenous field whose hydraulic properties vary from point to point the transport of solute also differs from profile to profile. In this paper solute concentration on the field scale was treated as a random variable. The field heterogeneity was described in terms of the statistical distribution of the hydraulic parameters, which implies a corresponding distribution of the concentration. Equations for computing this distribution, as well as its average and variance, in a heterogeneous field were derived explicitly for a simple, but representative case, of leaching under random recharge distribution on the surface. The water and solute flow in unsaturated soil was assumed to be vertical and steady. The randomness of the hydraulic properties was reduced to that of the saturated hydraulic conductivity by adopting a scaling hypothesis and a log normal distribution.