Scale and space dependencies of soil nitrogen variability

In this study, we use multifractal analysis, through generalized dimensions (<i>D</i>_q) and the relative entropy (<i>E</i>(<i>δ</i>)), 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. <br><br> The <i>D</i>_q values were used to study the relation between scales and <i>E</i>(<i>δ</i>) 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. <i>E</i>(<i>δ</i>) 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. <br><br> The four variables studied presented a weak multifractal character with a low variation in <i>D</i>_q values, although there was a distinction between variables related to nitrogen content and weight. On the other hand, the <i>E</i>(<i>δ</i>) and the increments in <i>E</i>(<i>δ</i>) 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<sub>app