Scale and space dependencies of soil nitrogen variability

Abstract. In this study, we use multifractal analysis, through generalized dimensions (D_q) and the relative entropy (E(δ)), to investigate the residual effects of fertigation treatments applied to a previous crop on wheat and grain biomass and nitrogen content. The wheat crop covered nine subplots from a previous experiment on melon responses to fertigation. Each subplot had previously received a different level of applied nitrogen (N_app), and the plants from the previous melon crop had already taken up part of it. Many factors affect these variables, causing them to vary at different scales and creating a non-uniform distribution along a transect. Correlations between the four variables and N_app showed high volatility, although the relationships between grain weight and wheat weight versus wheat nitrogen content presented a statistically significant logarithmic trend.

The D_q values were used to study the relation between scales and E(δ) values, and their increments between scales were used to identify the scale at which the variable had the maximum structure and were compared with the scaling behaviour of the N_app. E(δ) is particularly appropriate for this purpose because it does not require any prior assumptions regarding the structure of the data and is easy to calculate.

The four variables studied presented a weak multifractal character with a low variation in D_q values, although there was a distinction between variables related to nitrogen content and weight. On the other hand, the E(δ) and the increments in E(δ) help us to detect changes in the scaling behaviour of all the variables studied. In this respect, the results showed that the N_app through fertigation dominated the wheat and grain biomass response, as well as the nitrogen content of the whole plant; surprisingly, the grain nitrogen content did not show the same structure as N_app. At the same time, there was a noticeable structure variation in all the variables, except wheat nitrogen content, at smaller scales that could correspond to the previous cropping root arrangement due to uptake of the N_app.