Use of Pseudo‐Crossvariograms and Cokriging to Improve Estimates of Soil Solute Concentrations

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Abstract
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 1.8 m soil volume using kriging and cokriging with nonsymmetric pseudo‐crossvariograms. Among the measured chemicals of Cl−, SO2−4, Ca2+, Mg2+, Na+, P2O−5, K+, and NO−3 in the three‐dimensional system, Cl− was used as the model to show the estimation process and results. Using pseudo‐crossvariograms 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 with kriging, cokriging reduced the mean squared errors of estimations between 30 and 60% at different depths, and reduced the mean kriging variances between 35 and 58%. In the total mass estimation of Cl− in the soil, cokriging with nonsymmetric 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 the 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 the sample requirement. Cokriging with nonsymmetric pseudo‐crossvariograms is an accurate and economical way to calculate solute distributions and total mass in a large field.

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