Statistical and geostatistical methods are utilized to investigate soil variability. Methodology includes block kriging, cokriging and simulations of random fields. The ramifications of the variability are numerous, including the effect on soil water, soil fertility, evapotranspiration, and crop yields. Block kriging can be used to estimate crop yields and infiltration rates on a large scale using small scale or point data. Results based on variograms and geostatistics are compared to the classical relationship developed by Smith in 1938, that the variance is reduced from V₁ to V₁/nᵇ as the support area increases from 1 to n plots. These results establish a firm theoretical basis for the variance within a finite domain as a function of sample support size. Applications include not only uniformity trials, but also measurement theory. Based on 20 data sets, indices of soil heterogeneity are derived. With these indices, optimal sample sizes and shapes can be determined. The ordinary kriging and cokriging estimators are investigated in order to examine their utilization. Soil moisture content and soil water retained at 1.5 MPa within the root zone are predicted by cokriging with surface moisture and texture as auxiliary variables. Compared with ordinary kriging, cokriging gave a significant improvement in terms of the average kriging variance and the sum of squared errors between the actual and the predicted values. With soil spectral properties and cokriging, soil texture is estimated successfully. Cokriging is also used for temporal variables and compared with a time invariant relationship. Recently-developed pseudo-cross variograms and cokriging are utilized to predict soil chemicals. The main advantage of this approach is that the computation of sample cross-variograms does not require that measured variables be sited at the same locations. Lastly, several simulation methods are studied. A new simulation procedure is developed and compared with other simulation methods, such as the Turning Bands Method. Conditional simulation is used to simulate random fields for soil water and reflectance.

Water with entrained disease-causing virus entering soil normally passes through water saturated and unsaturated regions before reaching the groundwater. Twelve experiments were conducted to evaluate the effect of saturated versus unsaturated flow, and the effect of organic matter in unsaturated flow on the survival and transport of a virus, MS-2 bacteriophage, in soil columns. Additional experiments were conducted to characterize the soil, to assure that the experimental equipment did not remove virus, and to determine the extent of reversible adsorption of virus to soil. The virus were added to well water and applied to soil columns 0.052 m in diameter and 1.05 m long. KBr was used as a chemical tracer. In two experiments organic matter in the soil water was increased by using soil humic material or extract from sewage sludge. The soil material was Vint loamy fine sand (a sandy, mixed, hyperthermic Typic Torrifluvent) mixed with recent alluvium. Water samples were extracted from 0.10, 0.20, 0.40, and 0.80 m depths through porous stainless steel samplers, and from the 1.05 m depth through the percolate tube. Four different eluants were tested to remove virus from soil, and one, tryptic soy broth, was used to elute virus after three transport experiments. For saturated flow the virus concentrations reached the influent concentration in less than 2 pore volumes (T), with a retardation coefficient R at 1.05 m = 0.80. For unsaturated flow with low organic matter the relative concentrations reached steady-state values (C/C₀)(s) ranging from a mean of 27% of inflow at 0.20 m (5 to 18 T) to a mean of 5% at 1.05 m (1 to 3.3 T). Under unsaturated conditions with increased organic matter, virus (C/C₀)(s) at 1.05 m was from 41% to 49% of influent, 8 to 10 times greater than with low organic matter. Elution permitted calculation of a partition coefficient k(p) essentially equal to 0 (saturated average k(p) = -0.07 mL/g, SD = 0.15 mL/g; unsaturated average k(p) = 0.28 mL/g, SD = 0.40 mL/g), indicating little or no adsorption of virus to soil solids. Under unsaturated flow conditions enhanced removal of this virus occurs, and the removed virus are apparently inactivated. Organic matter reduced the removal of virus during transport by unsaturated flow. Virus concentrations reached and maintained a steady-state, exponentially-declining profile with depth.

Effects of trellising on water use, absorption of photosynthetically active radiation (PAR, 400 to 700 nm wavelength) by foliage and potentially by fruit, fruit composition, and yield were studied in 1988 under semi-arid conditions on field-grown Vitis vinifera L. 'Petite Sirah' grapevines in a mature vineyard. The positioning of shoots on trellises resulted in canopies that were (1) positioned vertically (vertical canopy), (2) positioned in a "V" pattern with sides inclined 60° from horizontal (inclined canopy), and (3) inclined toward the vineyard floor (standard canopy). Seasonal water use values determined from neutron scattering data were 393 ± 61, 554 ± 73, and 455 ± 57 mm for the standard, vertical and inclined canopies, respectively. On average, about 50% of seasonal water consumption occurred between fruit set and filling stages for each type of canopy. Average crop factors (ratio of actual to reference crop evapotranspiration) of 0.383, 0.540 and 0.444 were for the period bud burst to harvest for standard, vertical and inclined canopy systems, respectively. The diurnal water use patterns of the three trellising canopies were very similar when measured by either the heat pulse technique or by porometer. The average daily heat pulse velocity (HPV) for selected vertical, inclined and standard canopies for 6 days were 8.77, 7.58 and 6.85 cm h⁻¹, respectively. The HPV technique indicated that the average daily water use of the whole plant was 0.227, 0.192 and 0.137 kg/m² leaf area/d for standard, vertical and inclined canopies, respectively. The daily average transpiration rates as measured by the HPV technique were 32, 31, and 25% higher than the average transpiration rates estimated from porometer data for standard, vertical and inclined canopies, respectively. Stomatal conductances of the vertical and inclined canopies were 20 and 40%, respectively, below that of standard canopy. PAR absorption by foliage during mid-day was highest in the standard trellis, and lowest in the inclined trellis. PAR potentially available for absorption by fruits was lowest in the standard trellis, and highest in the inclined trellis. In both inclined and vertical canopies, the average sunfleck values were 26%, but was only 2% in the standard canopy. Analysis of fruit composition at harvest revealed that total dissolved solids (°Brix) was significantly higher in the inclined trellis than for the vertical trellis or the standard trellis. The inclined trellis resulted in the highest alcohol content of wine. Per vine yields did not differ significantly among the three trellis systems. Overall, the standard trellis was optimum because grapevines consumed less water and produced a shading which protected the fruit from direct solar radiation.

A computer simulation model was developed to simulate the impact of irrigating soils containing gypsic horizons on soil water quality and percolated water quality. The model simulates saturated - unsaturated solute movement using the mixing cell approach to simulate dispersion and movement of soluble salts. Dissolution and precipitation of slightly soluble salts and the formation of ion pairs is considered as a function of temperature. Van Genuchten closed form equation is used to find soil water retention function. Finite difference method was applied to Richards equation for moisture movement simulation in the profile. The model predicts the concentration of the major cations and anions in each segment. The regression coefficients of the observed vs. simulated concentration of the major ions were higher than 0.961 in all the three replicates with slopes ranging between 0.717 and 0.940. Running the model at 1 and 41 °C showed significant differences in Ca, SO₄, and HCO₃ concentrations in the percolated water. However, the differences in Cl, Na, and Mg concentrations were not significant. The presence of high Ca and SO₄ concentrations in the irrigation water reduced gypsum solubility in soils containing a layer of gypsum compared with the presence of Mg and Cl in the irrigation water.

Transient laboratory experiments are evaluated for their use in inverse methods to estimate soil-water parameters for unsaturated flow. The experiments are upward infiltration, One-Step outflow, stepwise inflow and evaporation. The experiments are simulated numerically for three inch standard size cores. A theoretical sandy and a clayey soil are used and are described by the closed-form van Genuchten soil-water relations. During each numerical experiment, for each soil, measurements of different auxiliary variables are simulated. These auxiliary variables are the inflow or outflow at the boundary, and the water content and matric potential within the soil core at three different locations. For each auxiliary variable the sensitivity to estimate the parameters α, n and the saturated hydraulic conductivity is studied by plotting the objective function surface in the parameter planes defined by these parameters. The objective function is calculated for 900 points in each parameter plane and describes the error between the measured and generated auxiliary variable. The shape of these surfaces indicates how well an inverse procedure can find a unique and accurate solution. From these surfaces auxiliary variables, or combinations thereof, are selected which provide sensitive parameter estimates. The surfaces indicate that the contours are nonconvex and that confidence regions for parameters are not symmetric. The hydraulic conductivity is the least sensitive parameter to estimate. For a wetting experiment the parameter sensitivity will increase when the measurement of the auxiliary variable is taken further away from the inflow boundary. To obtain sensitive parameter estimates the auxiliary variable used in the inverse procedure needs to be least similar to the known and changed boundary variable. The shape of the objective function surface for the degenerate case, where an auxiliary variable would be measured at the changed boundary, can provide prior information regarding the sensitivity of estimating parameters from an auxiliary variable and regarding the start values of the parameters for the parameter search. The difference in parameter sensitivity between the sandy and clayey soil is small.

Crop coefficients (K(c)) are a useful means of predicting how much water is needed for irrigating a crop. The crop water stress index (CWSI), on the other hand, is a means of knowing when to irrigate. Two field experiments were conducted during the summers of 1990 and 1991 at Maricopa Agricultural Center and Marana Agricultural Center, respectively, to evaluate water use (evapotranspiration, ET) of different cotton varieties, to develop crop coefficients for cotton grown in the state of Arizona, and to evaluate empirical and theoretical crop water stress indices under field conditions. For the 1990 experiment, ET from the cotton variety DPL 77 was obtained using soil water balance (SWB) and steady state heat balance (SSHB) techniques. For the 1991 experiment, ET from two cotton varieties (DPL 20 and Pima S-6) was estimated using the Bowen ratio energy balance (BREB) method and the steady state heat balance method. Reference evapotranspiration (ETᵣ) was obtained from weather stations located close to the experimental plots. Average daily ET from the SSHB measurements ranged from 8.24 to 15.13 mm and from 10.34 to 12.12 mm for the 1990 and 1991 experiments, respectively. Total ET from the SWB was approximately 19% less than the total ET estimated by the SSHB. Total ET from individual plants was well correlated with average stem area over the evaluation periods. Daily ET from the two cotton varieties (DPL20 and Pima S-6) was approximately similar when irrigation conditions were the same, but differed later by as much as 48.4% as irrigation continued for the variety Pima S-6 only. Daily ET from the BREB measurements and ETᵣ were used to develop a crop coefficient curve for cotton grown at Marana, Arizona, which had a maximum smoothed value of 1.21. A critical value of CWSI equal to 0.3 was obtained by observing the pattern of the CWSI values over well-watered and drier conditions, and from previous research. Using the developed crop coefficient curve and the CWSI should provide a useful means of scheduling irrigation for cotton grown under climatic conditions similar to those at Marana, Arizona.