Estimation of Statistical Moments of Spatial Field Averages for Soil Properties and Crop Yields

Crop yield variability often results from spatial variability of soil properties. The quantities of practical interest are the spatial averages of these properties over the entire field domain. In this study, correlation scales and the conditional and unconditional first two moments of field averages were estimated, by the maximum likelihood (ML) and Conditional Multi‐Variate Normal methods and numerical approach, for four soil properties, two soil variables, and two crop‐yield components of three field crops. The results show the significant contribution of the conditional approach in reducing the variances of the spatial average yield and soil properties by about an order of magnitude. It is also observed that the estimated conditional expectations of the spatial averages are practically identical to the unconditional one, although the maps of the conditional expectation over the field differ from the maps of the unconditional one. The integral scales of crop yields were found to be roughly estimated from the integral scales of the related soil properties. The use of conditional probability as a practical tool for reducing prediction uncertainty and the potential of conditional analysis to help make practical decisions are demonstrated. The principal practical conclusion is that, although unconditional analysis may be much simpler than the conditional approach, the latter may be more advantageous.