The surface map on the bottom is a model of the change in the local mean across the field.  One can remove, or account for, this change in the mean spatial structure across a region by generating a data set of residuals - the magnitude (+ or -) each particular value departs from the estimated mean at the observation's particular location.  These residuals from the mean structure can then be used to analyze the point-to-point dependency (covariance structure) of the response variable.  Below a contour map of the residuals hovers above the surface depiction of the mean spatial structure.  This contour of the residuals illustrates that there is a lot of local variability (residual error or local departures from the mean spatial structure) in the observations, hence the low R² associated with the trend model. updated:  27 September 2000