When the one‐dimensional moisture flow equation is simplified by applying the unit gradient approximation, a first‐order partial differential equation results. The first‐order equation is hyperbolic and easily solved by the method of P. D. Lax. Three published K(θ) relationships were used to generate three analytical solutions for the drainage phase following infiltration. All three solutions produced straight lines or nearly straight lines when log of total water above a depth was plotted versus log of time. Several suggestions for obtaining the required parameters are presented and two example problems are included to demonstrate the accuracy and applicability of the method.

Steady‐state infiltration rates were measured in a field plot with infiltrometers of 5‐, 25‐, and 127‐cm inside diameter. Measurements were made with the three ringsizes along five parallel transects, spaced 125 cm apart. The infiltrometers were placed adjacent to each other along each transect (i.e., one hundred twenty‐five 5‐cm rings, twenty‐five 25‐cm rings, and five 127‐cm rings per transect). Infiltration rates were found to be lognormally distributed for all ringsizes and autocorrelated for the 5‐cm ringsize. The 5‐cm data showed that a large fraction of the water infiltrated through a small fraction of the plot area. Autocorrelation functions were determined and power spectrums computed. A first‐order autoregressive process was found to describe the 5‐cm data, and variances of samples composited along a transect agreed with sample variances. The variances for the 25‐ and 127‐cm infiltrometers were compared with sample variances, assuming a simple two‐dimensional autocovariance function. Agreement was found for the 127‐cm rings, but not for the 25‐cm rings.

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The unsaturated hydraulic properties are important parameters in any quantitative description of water and solute transport in partially saturated soils. Currently, most in situ methods for estimating the unsaturated hydraulic conductivity (K) are based on analyses that require estimates of the soil water flux and the pressure head gradient. These analyses typically involve differencing of field‐measured pressure head (h) and volumetric water content (θ) data, a process that can significantly amplify instrumental and measurement errors. More reliable methods result when differencing of field data can be avoided. One such method is based on estimates of the gravity drainage curve K'(θ) = dK/dθ which may be computed from observations of θ and/or h during the drainage phase of infiltration drainage experiments assuming unit gradient hydraulic conditions. The purpose of this study was to compare estimates of the unsaturated soil hydraulic functions on the basis of different combinations of field data θ, h, K, and K'. Five different data sets were used for the analysis: (1) θ‐h, (2) K‐θ, (3) K'‐θ (4) K‐θ‐h, and (5) K'‐θ‐h. The analysis was applied to previously published data for the Norfolk, Troup, and Bethany soils. The K‐θ‐h and K'‐θ‐h data sets consistently produced nearly identical estimates of the hydraulic functions. The K‐θ and K'‐θ data also resulted in similar curves, although results in this case were less consistent than those produced by the K‐θ‐h and K'‐θ‐h data sets. We conclude from this study that differencing of field data can be avoided and hence that there is no need to calculate soil water fluxes and pressure head gradients from inherently noisy field‐measured θ and h data. The gravity drainage analysis also provides results over a much broader range of hydraulic conductivity values than is possible with the more standard instantaneous profile analysis, especially when augmented with independently measured soil water retention data.

Annual row crop production on the naturally occurring claypan soils of the eastern Great Plains may require field operations during somewhat wet conditions and this potentially results in soil compaction by the commonly-used, heavy-weight tractors and equipment. The objectives of this experiment were (i) to determine if compaction reduced yield and growth of soybean [Glycine max (L.) Merr.] and grain sorghum [Sorghum bicolor (L.) Moench] grown on a claypan soil (fine, mixed, thermic Mollic Albaqualf) and (ii) to determine the effect of wheel tracks on selected soil properties and whether chisel plow tillage could reduce wheel-track compaction. Compaction treatments were (i) ALL-all of the plot compacted, (ii) WT-wheel-track compaction, (iii) WTC-wheel-track compaction followed by a chisel tillage operation, and (iv) NO-no intentional compaction. In general, it took until the third year of annually repeated compaction in the ALL treatment to reduce crop growth and yields compared with the NO compaction treatment. Even though nearly half of the area was compacted each year in the WT treatment, few measured crop parameters decreased. In wheel tracks, soil penetrometer resistance and bulk density increased and air permeability decreased compared with out of tracks. However, chisel tillage appeared to eliminate the compaction by reducing penetration resistance and bulk density and increasing air permeability to values similar to out of tracks. Thus, compaction of claypan soils may not often be a problem for producers in this area, especially if occasional chisel tillage is included to remove possible compacted zones.

Fixed gradient models result when the gradient term in the soil moisture equation is assumed to vary only with depth (remains invariant in time). The fixed gradient assumption results in a first‐order partial differential equation that is transformable to a mathematical form identical to that for a uniform soil. When the transformation was applied to field data, all water content data were found to plot along a single curve. Assuming a fixed gradient and an exponential form for K(Θ) resulted in a fitted curve with an r2 = 0.847 (d.f. = 405) when data from three sites and seven depths were used. Assuming a power function for K(Θ) resulted in a similar r2. Prior to applying the transform, hydraulic conductivity required 42, 42, and 63 parameters to fit data obtained at the 21 spatial points sampled, assuming a Davidson, Watson or Brooks and Corey function, respectively. With the transform 23, 23, and 24 parameters were required for the three K(Θ) functions, respectively.