Soil variability and geostatistical applications

Abstract

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.