Scale- and location-dependent correlations of soil strength and the yield of wheat

The relationship between soil strength and crop yield may be summarized by a linear correlation coefficient (usually negative). It is likely, however, that this over-simplifies a complex situation in which the relationship between these variables depends on spatial scale and location. We used the wavelet transform to assess this scale- and location-dependence. We established a transect on an arable field in Eastern England, and studied the correlations of soil strength (top- and subsoil) with crop yield. The transect comprised 267 contiguous 0.72 m × 0.72 m plots. Measurements were taken during two consecutive growing seasons of winter wheat (harvest dates of August 2004 and 2005). Soil strength was measured with a penetrometer in the spring of each growing season. As expected, the overall correlation of soil strength with yield was negative but weak. Wavelet analysis revealed that, at fine spatial scales, topsoil and subsoil strength were correlated more or less equally with yield; however, at coarse spatial scales, topsoil strength had a stronger correlation with yield than did subsoil strength. The correlation of topsoil strength with yield at fine spatial scales (corresponding to about 1 m on the ground) was negative. A likely source of this fine-scale variation was the soil compaction associated with tractor wheelings. The correlation of topsoil strength with yield at the coarsest spatial scale (corresponding to about 50 m on the ground) was positive. This correlation was temporally stable, and might have reflected how soil strength can act as a proxy for other soil attributes. In the 2005 growing season, we found evidence that, at intermediate spatial scales, the correlation of soil strength with yield changed depending on the position on the transect. This was probably due to an interaction between the compaction associated with tractor wheelings and the local soil conditions. There was no evidence of such location-dependence in the correlation of soil strength with yield in the 2004 growing season. In summary, the effect of soil strength on crop yield was not expressed in a constant negative correlation across all spatial scales and locations: the negative correlation occurred mainly at fine spatial scales, and the correlation changed according to the position in the landscape and the prevailing local soil conditions.