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
Received: 19 May 2016 – Discussion started: 22 Jun 2016
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.
Revised: 19 Dec 2016 – Accepted: 04 Jan 2017 – Published: 06 Feb 2017
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.
Tarquis, A. M., Castellanos, M. T., Cartagena, M. C., Arce, A., Ribas, F., Cabello, M. J., de Herrera, J. L., and Bird, N. R. A.: Scale and space dependencies of soil nitrogen variability, Nonlin. Processes Geophys., 24, 77-87, doi:10.5194/npg-24-77-2017, 2017.