Determining nugget: sill ratios of standardized variograms from aerial photographs to krige sparse soil data

Maps of kriged soil properties for precision agriculture are often based on a variogram estimated from too few data because the costs of sampling and analysis are often prohibitive. If the variogram has been computed by the usual method of moments, it is likely to be unstable when there are fewer than 100 data. The scale of variation in soil properties should be investigated prior to sampling by computing a variogram from ancillary data, such as an aerial photograph of the bare soil. If the sampling interval suggested by this is large in relation to the size of the field there will be too few data to estimate a reliable variogram for kriging. Standardized variograms from aerial photographs can be used with standardized soil data that are sparse, provided the data are spatially structured and the nugget:sill ratio is similar to that of a reliable variogram of the property. The problem remains of how to set this ratio in the absence of an accurate variogram. Several methods of estimating the nugget:sill ratio for selected soil properties are proposed and evaluated. Standardized variograms with nugget:sill ratios set by these methods are more similar to those computed from intensive soil data than are variograms computed from sparse soil data. The results of cross-validation and mapping show that the standardized variograms provide more accurate estimates, and preserve the main patterns of variation better than those computed from sparse data.