Statistical and geostatistical analyses were conducted to estimate both correlation and spatial distributions of trace elements in soils and plants within a corn field. Statistical analysis of AB-DTPA-extractable trace elements in soils and the total elemental content of plants indicated that Mo in corn leaves was negatively correlated with soil Cu and Fe. Copper aggravates Mo deficiency in plants because Cu interferes with the role of Mo in enzymatic reduction of NO3. Geostatistical analyses of the soil trace elements, Cu, Zn, Mn, Fe, and Mo, showed that these elements were spatially interdependent. Iron, Mn, and Mo in corn leaves were spatial variables characterized by linear, spherical, and exponential variogram models, respectively. However, Cu and Zn contents in corn leaves were randomly distributed in the field. Using the relationship between soil Cu and plant Mo, and a cokriging technique, plant Mo estimation was significantly improved by incorporating the soil Cu information. Compared with kriging, cokriging reduced the mean error of the estimates by about 5 times, reduced the mean square error and the mean kriging variance up to 48%, and increased the correlation of estimates and measurements from 0.49 to 0.61.

The convection-dispersion (CDE) equation and stochasticconvective models are the most commonly used process representa-soltions for predicting solute transport in the field. The convection dispersion equation assumes that the solute is perfectly mixing in the lateral direction, whereas the stochastic-convective model assumes that the solute moves at different velocities in isolated stream tubes without lateral mixing. However, solute transport in heterogeneous preporous media cannot always be conceptualized as being either a convective-dispersive or a stochastic-convective process. In this study, a generalized transfer function model (GTF) was proposed to describe various solute transport processes in heterogenous soils. The model is similar to the convective lognormal transfer function model, but two parameters, lm and ls, are introduced to characterize the depthdependency of the mean (m) and standard deviation (s) of the loga rithm of travel time, respectively. The GTF can describe well the two extremes of solute dispersion, the convective-dispersive and stochastic-convective processes, and transport processes between the two extremes. In addition, the GTF can be used to characterize other solute transport processes in heterogeneous soils, such as those in which the mean of travel time increases with depth nonlinearly, and those in which the dispersivity is a scale-dependent function of the travel distance with any power values.

Estimation of soil particle size fractions (percentage of sand, clay and silt) with sparse data can be improved by taking into account the spatial correlation with other variables. Reflectance of the near infrared band (0.76-0.90μm) is used as an auxiliary variable in the prediction of soil particle size fractions on a 100m×100m grid in a 2200m×1300m field. The results of kriging using the textural information alone are compared with those of cokriging with the auxiliary variable. Cokriging gives a higher correlation coefficient and a lower mean squared error between estimates and measurements than kriging. The most significant improvement of the estimation is in areas of the field with sparse data for the estimated variables. The relative improvement is up to 90% in terms of reduced kriging variance and up to 33% for the mean squared error between actual measurements and estimated values. Only 17-25% of the original observations of texture are needed to obtain relatively accurate estimation when cokriging with reflectance data.

Estimating mass and distributions of chemicals in soils is one of the key steps to study chemical transport in the vadose zone and groundwater systems. In this study, solute mass and distributions were computed in an 800 by 800 by 1.8m soil volume using kriging and cokriging with nonsymmetric pseudo-cross-variograms. Among the measured chemicals of Cl-, SO42-, Ca+2, Mg+2, Na+, P2O5-, K+, and NO-3 in the three-dimensional system, Cl- was used as the model to show the estimation process and results. Using pseudo-crossvario- grams maximized the use of available information at different soil depths and improved solute estimation. All sample pseudo-crossvariograms between depths were modeled successfully with common variogram functions such as spherical and linear. Therefore, it was relatively easier to test the positive definiteness of the cokriging coefficient matrix adapted to pseudo-crossvariograms. Cokriging allows easily obtained information at shallower depths to be used to improve solute estimations at deeper depths. Compared to kriging, cokriging reduced the mean squared errors of estimations between 30 and 60% at different depths, and reduced the mean kriging variances between 35 to 58%. In the total mass estimation of Cl- in the soil, cokriging with non-symmetric pseudo-crossvariograms, used less than half the data; potentially it could reduce more than half the sampling cost of kriging estimation. Meanwhile, cokriging reduced the estimation error by about 18%, when compared with kriging estimates using all observations. Using same data at each layer, cokriging would reduce the estimation error 40% more than kriging because cokriging efficiently incorporated information at upper layers without increasing sample requirement. Cokriging with non-symmetric pseudo-crossvariograms is an accurate and economical way to calculate solute distributions and total mass in a large field.

Stochastical analysis was performed to assess the effect of soil spatial variability and heterogeneity on the recovery of denser-than-water nonaqueous phase liquids (DNAPL) during the process of surfactant-enhanced remediation. UTCHEM, a three-dimensional, multicomponent, multiphase, compositional model, was used to simu-late water flow and chemical transport processes in heterogeneous soils. Soil spatial variability and heterogeneity were accounted for by heteroconsidering the soil permeability as a spatial random variable and a geostatistical method was used to generate random distributions of the permeability. The randomly generated permeability fields were develincorporated into UTCHEM to simulate DNAPL transport in hetero- examgeneous media and stochastical analysis was conducted based on the simulated results. From the analysis, an exponential relationship between average DNAPL recovery and soil heterogeneity (defined as the standard deviation of log of permeability) was established with a coefficient of determination (r2) of 0.991, which indicated thatDNAPL recovery decreased exponentially with increasing soil heterogeneity. Temporal and spatial distributions of relative saturations in the water phase, DNAPL, and microemulsion in heterogeneous soils were compared with those in homogeneous soils and related to soil heterogene-ity. Cleanup time and uncertainty to determine DNAPL distributions in heterogeneous soils were also quantified. The study would provide useful information to design strategies for the characterization and beremediation of nonaqueous phase liquid-contaminated soils with spatial variability and heterogeneity.