Scale- and Location-Dependent Correlations of Soil Strength and Wheat Biomass.
M.J. Pringle and R. Murray Lark. Environmetrics Group, Bioinformatics and Biomathematics Division, Rothamsted Research, Harpenden, United Kingdom
It is well known that soil properties, and related variables, vary in space. It is also well known that the variation of these variables depends on the spatial scale at which they are observed; scales may range from microscopic to continental, though we generally deal with only a subset of the possible scales. Because variation is due to components at different spatial scales, the simple correlation coefficient between two variables may be misleading. The components of variation of two variables may show different correlations at different spatial scales. As a result, the correlation coefficient may obscure strong relationships between two variables at one scale because of random variation at other scales. A further complication is that the spatial covariance of two variables at any scale is not necessarily stationary; the correlation might change from one part of the landscape to another. In this case, the overall correlation may again obscure important aspects of the variables' joint spatial variation. Wavelet transforms offer a way of analyzing scale- and location-dependent covariation in space. This is done by partitioning the variation of two variables into scale-specific and local wavelet coefficients. We used wavelet analysis to examine the scale-and location-dependent correlations of soil strength and the above-ground biomass of wheat. We anticipated that soil strength would be negatively correlated with biomass since the exploitation of the soil by roots is limited when the soil is strong. We studied a transect of 267 adjacent square plots, each 0.72 metres wide, across a field in eastern England, in two successive seasons of winter wheat. Harvest dates were in 2004 and 2005, respectively. On one day in the spring of each season, we recorded the average strength of the topsoil (0-0.2 m; units of MPa) in each plot, using a hand-held penetrometer. The plants in each plot were hand-harvested when the crop was mature, and determined for above-ground biomass (oven-dry; units of Mg ha-1). The overall correlation of soil strength and biomass was -0.20 in 2004, and -0.15 in 2005. These correlations are weak, although their sign matches our expectation. Wavelet analysis revealed scale-dependent correlations between soil strength, and biomass. Data were decomposed into six spatial scales, equivalent to distances on the ground between 1 m and 50 m. In general, the wavelet correlations of soil strength and biomass in each season were strongest (most negative) at the finest scales, and increased (to positive values) at coarse scales. The negative correlations are expected, and the strong effects at fine scales probably reflect the compaction of soil in tractor wheelings. At the coarsest scale the correlation was positive (but not significantly different from zero since there were few degrees-of-freedom at this scale). This is thought to reflect variation in the underlying parent material of the study site. This variation affects not only soil strength, but would also influence crop performances (e.g., though heavy-textured soil is generally stronger than light-textured soil, it will have more available-water). In 2005, we found significant location-dependence of the correlations at a fine-scale. In two segments of contrasting soil texture — the lightest soils on the transect (over sandy colluvium), and the heaviest (on alluvial clay) — we found significant negative correlations between soil strength and biomass which were uncorrelated elsewhere at this scale. The correlation was moderate on the sandy loam, but was very strong on the clay. This may reflect the greater susceptibility to compaction of wet heavy soils, and weakly structured light soils. Issues of scale- and location-dependence amongst variables are important in soil science. Wavelet analysis allowed us to calculate the correlations of soil strength and biomass according to spatial scale and location. We found negative (significant) correlations between soil strength and biomass at all except the coarsest spatial scales, and we also found evidence of location-dependence at a fine spatial scale. At the finest spatial scales we felt that the presence of tractor wheelings in some plots affected the correlation between soil strength and biomass, and that these interacted with local soil texture. At the coarsest spatial scales we felt that the positive correlation between soil strength and biomass was due to a broad variation in the underlying parent material of the study site, possibly affecting the available-water capacity of the soil.