P. J. Wierenga

Mass transfer in porous media with immobile water

An analytical solution is presented for the movement of a solute through a porous medium, which is leached at a constant rate. The solution takes into account diffusion into an immobile water fraction. The generalized solution is valid for both finite or semi-infinite media and for concentration or flux-type boundary conditions. The solution consists of a convolution integral of two functions. The first function is the derivative vs. time of the corresponding solutions of the solute transfer equation without lateral diffusion. The second function is the J-function, for which a series approximation was developed. The use of the solution is illustrated with displacement studies in a 30 cm long column, filled with glass beads. It is shown that effluent concentration distributions from, and solute concentration distributions inside the column, when unsaturated, cannot be explained without taking into account an immobile water fraction.

Effect of hysteresis on the prediction of infiltration, redistribution and drainage of water in a layered soil☆

Abstract In order to study the effect of hysteresis on soil water movement a large soil column, filled with Glendale clay loam over a river sand, was flood-irrigated with 10 cm water. The infiltration rate, wetting front advance, water content redistribution, and the amount of drainage water was measured. A computer model, using S/360 CSMP, was developed to simulate the flow behavior. The main drying and main wetting curves in the soil water tension-water content, and in the hydraulic conductivity-water content relationships were provided in the computer model. From these relationships, scanning curves were developed to simulate hysteretic flow behavior under both wetting and drying conditions. Experimental data were compared with data computed from either the main drying, the main wetting, or the scanning curves. Infiltration was accurately predicted using the main wetting curves. However, redistribution and drainage were better predicted when hysteresis was taken into account.

Time series analysis of soil moisture and rainfall along a line transect in arid rangeland

Soil water content and rainfall were measured at 30 m intervals along a 2730 m transect on the New Mexico State University College ranch, 40 km northeast of Las Cruces. The data were collected at 2-week intervals. Time-series techniques (autocorrelations and cross-correlations) were used to examine the relationships between the water content and rainfall and to compare the relationship of the overall average (the entire transect) soil moisture content with that of individual transect segments. Correlograms indicated the range of dependence in time for soil moisture and rainfall was different for the entire transect when compared to individual transect segments. In general, water content showed a significant correlation in time between 3 to 5 lags, whereas rainfall showed a significant correlation in time between 2 to 25 lags. Soil moisture lagged behind rainfall by a few lags. The response time to rainfall was short in the surface soil but increased with depth to as much as 10 lags at 135 cm. Wetting of dry, arid rangeland soils is a slow process and is largely a function of antecedent water content. In addition, this wetting process pattern was different for the entire transect when compared to individual transect segments.

Geostatistical analysis of soil hydrologic properties in a field plot

Abstract A 91-m transect was set up in an irrigated field near Las Cruces, New Mexico to obtain soil water tension and water content data to investigate their spatial variability. A total of 455 sampling points were monitored along a grid consisting of 91 stations placed 1 m apart by 5 depths per station (at 0.3, 0.6, 0.9, 1.2 and 1.5 m below the surface). Post-irrigation tension and wetness measurements were recorded over 45 days at 11 time periods. Soil water tension was measured with tensiometers using a hand-held pressure transducer. A neutron probe was used to obtain volumetric water content. Using the observed wetness and tension data, unsaturated hydraulic conductivity values were derived (using a cubic spline function to estimate the gradient), and an exponential model was used to fit the calculated conductivity-tension curves to obtain hydraulic conductivity parameter values. The spatial and temporal variability of wetness, tension, saturated hydraulic conductivity and pore-size distribution parameters, and texture at the 0.3-m depth were examined using geostatistical techniques. The exponential model was found to inadequately describe the hydraulic conductivity/tension relationship for the full range of tension, particularly in the tension range near saturation. The derived values of the saturated hydraulic conductivity parameter were much greater than expected and do not correspond to reasonable saturated hydraulic conductivity values. All of the soil parameters studied exhibited large spatial variability horizontally and vertically in the field. Ranges of dependence determined from semivariogram analysis over the 44-day drainage period are 3–32 m for wetness, 6–34 m for soil water tension, 5–35 m for natural log of saturated hydraulic conductivity parameters, 5–11 m for pore-size distribution parameter, and 8–24 m for percent sand, silt and clay at the 0.3 m depth. An alternate hole-effect model is suggested to describe the texture semivariograms. It was determined that the variance of volumetric water content generally increased at each depth over the measured time periods, which is consistent with certain past field studies and a stochastic analysis of unsaturated flow in heterogeneous soils. Future research is recommended relating soil texture to soil hydrologic parameters with the goal of predicting soil behavior with less extensive sampling schemes.

Stochastic models in agricultural watersheds

Abstract A stochastic time-series approach using spectral analysis theory is developed and applied to drainage analysis of an agricultural watershed, Rio Grande Valley, New Mexico, U.S.A. The spectral theory demonstrates that a linear reservoir model is a suitable approximation to the Dupuit aquifer over a wide range of frequencies. A first-order perturbation of the variables allows the system parameters to be evaluated from both the stochastic solution of the fluctuating or zero-mean process, and the temporal-mean or steady-state solution. Deep percolation is estimated by first assuming a “no storage” situation in which recharge is a constant fraction (leaching fraction) of applied water. A second approach to deep percolation incorporates a soil-moisture reservoir to simulate storage in the soil zone. The equations developed are useful for characterizing drainage systems which exhibit a statistically stationary response to rainfall and/or irrigation.

ESTIMATION OF VEGETATIVE COVER IN AN ARID RANGELAND BASED ON SOIL-MOISTURE USING COKRIGING

Soil moisture and vegetative cover (ephemeral, perennial forb and perennial grass) were measured at 30-m intervals along a 2730-m transect. The spatial correlation of vegetative cover and soil moisture, and their cross-correlations, were examined. A total of 610 estimates of vegetative cover were generated at 3-m intervals along the transect, using both ordinary kriging and cokriging methods. Jackknifed estimates of mean-reduced error and reduced variance were used to validate the cokriging models. The average kriging and cokriging variances and the mean sum of squares (SSQ) were used to compare the two methods. Based on SSQ comparisons, cokriging is the best method to estimate spring ephemeral cover (for observations from all stations) and perennial spring grass cover (for observations from alternate stations). Cokriging estimations for spring perennial grass cover and for spring ephemeral cover produced 7.14 and 2.13%, respectively, improvement over kriging. Cokriging gave better estimations when the number of observations for perennial spring grass cover and fall perennial forb and perennial grass covers were decreased.

VARIATION IN TENSION, WATER CONTENT, AND DRAINAGE RATE ALONG A 91-M TRANSECT

Recent studies on spatial variability determined means, variances, frequency distributions, and spatial correlation structures for a number of soil characteristics and soil types. In this study, we determined the spatial distribution of soil water tension, water content, and percolation rates along a 91-m transect, sampled at 1-m intervals. Coefficients of variation (CV) in soil-water tension were highest right after flooding, with values as high as 72%. As the soil dried out, CVs decreased to a range of 10 to 35% for all depths. Ranges of dependence for tension were between 13 and 35 m. Water contents showed the smallest variation near the surface (CVs less than 15%), and the highest in the subsoil (CVs of 30 to 45%) as a result of layering. Distances of dependence for water content were between 8 and 22 m. Drainage rates at 1.35 m below the soil surface varied widely, from 4.8 to 0.012 cm/d the first day after irrigation (mean 2.45 cm/d), and from 0.25 to 0.01 cm/d on Day 14 after irrigation (mean 0.15 cm/d). The extreme variability in drainage rates is expected to lead to large spatial variations in chemical transport in this and in similar soils.