Scale as the Common Language for Soil Variations Revealed with Geophysics, Biophysics, and Remore Sensing.

Quantification and estimation of crop response to management are important for efficient use of resources. Because the spatial distribution of crop response is related to the distribution of soil properties, crop response to management practices will also have a strong spatial component.   Most plot research to quantify management practices uses blocking and repetition to address this variability.  Traditional research further utilizes discrete treatment levels in experiments designed to quantify crop response to a management factor, mainly because the statistical methods used are well established.  Statistical tools are now available, however to correct plot means for the covariance-variance structure in errors resulting from continuously varying soil properties. This would allow the use of continuously varying treatment structures.  Here we show how a random field linear model (RFLM) with a fixed (mean) component and correlated error structure can be used to analyze a field experiment where nitrogen (N) was applied to potato in a sinusoidal pattern along a transect.  Using the correlated error structure, the results of the experiments can be interpolated over the entire field to provide yield response maps for each of the four N treatments.  We show also how spatial autoregression and plant simulation models can be used with spatial surrogate information from remote sensing and topography to help interpolate a limited amount of field data to develop maps for management.