Chaotic attractors captured from remote sensing time series for the dynamics of cereal crops

Abstract

A chaotic attractor was obtained from remote sensing data, for the first time, in the early 2010s, its Poincaré section revealing a weakly dissipative dynamics. This attractor was captured from a time series of vegetation index, for the cycles of cereal crops in semi-arid region. This attractor was fully unexpected, since it was also the first attractor of a weakly dissipative dynamics directly extracted from observational time series. The generality of this result is questioned here by applying the same modelling approach – the global modelling technique – to four provinces in coastal and inland Morocco: Safi, El Jadida, Khourigba and Khenifra. Several experimentations are considered, applying the analyses at the provinces scale, or to several provinces in association and in aggregation. The obtained models confirm the results obtained in the early 2010s: the dynamics of cereal crops is chaotic and can be approximated by a weakly dissipative three-dimensional dynamics.

Keywords:

• NDVI
• vegetation cycle
• global modelling
• determinism
• complexity
• unpredictability

Mathematics Subject Classifications:

• ODE
• Poincaré sections
• time series analysis

Acknowledgements

S. M. would like to thank Lionel Jarlan and Christophe Letellier for stimulating discussions, respectively, about land cover maps and weakly dissipative chaos. SM would like to thank Pr. Yves Couder (1941–2019) for the stimulating discussions we had at the 19e Rencontres du Non Linéaires in 2016, and for his warm encouragements to publish the present results. We would like to dedicate this work to his memory.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the French programs Les Enveloppes Fluides et l'Environnement (LEFE) of the Institut National des Sciences de l'Univers (INSU), Programme National de Télédétection Spatiale (PNTS) of the Centre National de la Recherhce Scientifique, and Spirales of the Institut de Recherche pour le Développement (IRD); by the Centre National d'Etudes Spatiales (CNES), and by Université Paul Sabatier Toulouse III.