Statistical inferences of soil properties and crop yields as spatial random functions

Crop yields are often highly variable due (partly) to spatial heterogeneity of soil properties. The conditional multivariate normal (CMVN) method is systematically described and applied to 24 spatial random functions. These include: 12 soil properties, four soil variables, and two yield components of each of four field crops [wheat (Triticum aestivum L.), vetch (Vicia sativum L.), corn (Zea mays L.), and peanut (Arachis hypogaea L.)]. The statistical parameters characterizing the joint probability density function in a two-dimensional field were estimated, from 20 to 60 measurements, by the maximum likelihood procedure. An estimation procedure for three parameters of four covariance models (piecewise linear, exponential, spherical, and Gaussian), constant mean, and linear drift, is described. It was found that the covariance function of all the 24 spatial functions can be represented by the four models and that there is a significant two-dimensional linear drift of the mean. The parameter that represents the nugget effect (i.e. the variance of uncorrelated values of the spatial function) is estimated to be either zero or nonsignificant for the soil properties but has a small significant value for most crop yield components. Soil properties as well as crop yield components are characterized by the existence of a significant correlation scale on the order of 10 to 30 m. Estimations of conditional expectation, conditional covariance, the variance, and the variance of the estimated variance were made and demonstrate that the CMVN method can be applied to real field data. The specific covariance model used generally has a small effect on the estimated results. Comparisons with kriged values and kriging variance demonstrate the similarity and differences in the results.