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 τ ) x(t + τ ) (1941-2010) Takens’ theorem (1981)

7. diffeomorphism (differentiable & differentiable inverse) z(t) x(t) y(t) x(t) x(t +2 τ ) x(t + τ ) Takens’ theorem (1981)

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

10. Pyrénées (0-40000km²) Mt Liban (0-12000km²) Atlas (0-30000km²)

11. Pyrénées 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. Pyrénées Mt Liban Atlas (…) 2000-2012

14. yearly analysis Pyrénées 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

25. 2007-2008 Mt Liban

26. 2009-2010 Mt Liban

27. yearly analysis Atlas

28. 2001-2002 Atlas

29. 2002-2003 Atlas

30. 2004-2005 Atlas

31. 2005-2006 Atlas

32. 2006-2007 Atlas

33. 2009-2010 Atlas