Chaos in Snow Cover Dynamics of Mountains

This article discusses the evidences of chaos in the dynamics of snow cover in Pyrenees, Lebanon and High Atlas mountains. A global modelling approach is used to investigate the dynamics which is well adapted to low dimensional system. Furthermore, the article discusses the hypothesis, knowledge and requirements for chaotic behaviour in the system.

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1. Evidences of chaos from the dynamics of snow cover in Pyrenees, Lebanon and High- Atlas mountains le 17/07/2013

2. Global Modelling Phenomenological approach of the dynamics well adapted to low-dimensionnal system several underlying hypothesis Few knowledge about the dynamics is required The dynamics is directly investigated from a time series It can provide a strong evidence of chaotic behaviour System should be ergodic, deterministic, autonomous and stationnary approach

3. Gouesbet & Letellier (1994) Reformulation Polynomial approximation approach Global Modelling

4. approach Sunspot cycles Canadian lynx cycles Human respiration Rainfed wheat Snow cover - natural - ecological - human - agricultural - climatic .. systems Maquet et al. 2007 Letellier et al. 2006 Mangiarotti et al. 2011, 2013 Previous applications to real world systems .. this work ! Letellier et al. 2013

5. Takens theorem (1981) z(t) x(t) example: attracteur de Lorenz(1963) (1941-2010) y(t)

6. diffeomorphism (differentiable & differentiable inverse) z(t) x(t) y(t) x(t) x(t +2 ) x(t + ) (1941-2010) Takens theorem (1981)

7. diffeomorphism (differentiable & differentiable inverse) z(t) x(t) y(t) x(t) x(t +2 ) x(t + ) Takens theorem (1981)

8. Phase Space Portrait On drive n fois NDVI(t) approach

10. Pyrnes (0-40000km) Mt Liban (0-12000km) Atlas (0-30000km)

11. Pyrnes Mt Liban Atlas Portraits dynamiques 2000-2012

12. Models selection algorithm interaction Main GloMo Interface Algorithmic tools R-packages PoMoS GloMo Packages available on CRAN: http://cran.cict.fr approach

13. Pyrnes Mt Liban Atlas () () () 2000-2012

14. yearly analysis Pyrnes Pyreneous

15. 2000-2001 Pyreneous

16. 2001-2002 Pyreneous

17. 2002-2003 Pyreneous

18. 2003-2004 Pyreneous

19. 2010-2011 Pyreneous

20. yearly analysis Mont Liban Mt Liban

21. 2001-2002 Mt Liban

22. 2003-2004 Mt Liban

23. 2005-2006 Mt Liban

24. 2006-2007 Mt Liban