The effects of scale on crop yield variability

We studied the relationships between crop yield variability (imposed mainly by the weather) and the scale of area aggregation. Empirical data comprised yields of cultivated plants in Poland in the 1956–1990 period. Starting from the general formula for calculating the variance of a sum, the yield variance in an aggregated area was described as a complex function of variances in individual area units and of correlations between them. Since the coefficient of correlation may be presented as a function of distance between fields, it was possible to construct a general formula for assessment of yield variability in areas of any desired size: log V = log v − b(n − 1)^0.2 where: V, coefficient of yield variability in an aggregated area; v, in a unit area; n, number of unit areas; b, empirical parameter. The parameters for several crops in Poland are presented.