Articles | Volume 24, issue 1
Nonlin. Processes Geophys., 24, 77–87, 2017

Special issue: Multifractal analysis in soil systems

Nonlin. Processes Geophys., 24, 77–87, 2017

Research article 06 Feb 2017

Research article | 06 Feb 2017

Scale and space dependencies of soil nitrogen variability

Ana M. Tarquis1,2, María Teresa Castellanos3, Maria Carmen Cartagena3, Augusto Arce3, Francisco Ribas4, María Jesús Cabello4, Juan López de Herrera1, and Nigel R. A. Bird1 Ana M. Tarquis et al.
  • 1CEIGRAM, Ciudad Universitaria sn, Technical University of Madrid, Madrid, 28040, Spain
  • 2Dpto. Matemática Aplicada, E.T.S.I. A.A.B., Technical University of Madrid, Spain
  • 3Dpto. Química y Tecnología de Alimentos, E.T.S.I. A.A.B, Technical University of Madrid, Spain
  • 4Centro de Investigación Agroambiental El Chaparrillo, Inst. Regional de Investigación y Desarrollo Agroforestal (IRIAF), Ciudad Real, Spain

Abstract. In this study, we use multifractal analysis, through generalized dimensions (Dq) 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 (Napp), 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 Napp showed high volatility, although the relationships between grain weight and wheat weight versus wheat nitrogen content presented a statistically significant logarithmic trend.

The Dq 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 Napp. 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 Dq 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 Napp 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 Napp. 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 Napp.

Short summary
Melon crop got different levels of N that constituted a contribution to the variation of soil N at mainly larger scales. During its development a proportion of the N was taken up, adding a second factor of variability at smaller scales. After the melon harvest, the wheat was sown across the plots and harvested at the end of the season. Wheat was used as a N sink crop and allowed us to evaluate the soil N residual. Multiscale and relative entropy were applied to study N scale dependencies.