Spatial prediction of soil organic carbon from data on large and variable spatial supports. I. Inventory and mapping

We consider approaches for calculating and mapping statistical predictions of soil organic carbon (SOC), and attendant uncertainty, from data across a region of France. The data were collected from farms across the region. To protect the anonymity of farms that contributed, the locations and values of individual observations were unavailable, and we were only able to use the average value, sample variance, and number of observations from each commune. Communes varied in size up to a maximum of 130?km 2, with a mean of 10?km 2. The uncertainty due to data being commune-wide averageswith sample error varying between communes as a result of variations in their size and the number of samples drawn from within themraises an important methodological issue. We show how a residual maximum likelihood method can be used to estimate covariance parameters on the basis of this form of data and use the empirical best linear unbiased predictor to calculate predictions. Cross-validation shows that by properly representing the commune-wide averaged data, the predictions and attendant uncertainty assessments are more reliable than those from a naive approach based on the summary means only. We compare maps produced using the approaches showing the SOC predictions and the attendant uncertainty. Copyright (c) 2012 John Wiley & Sons, Ltd