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Evidences of chaos from the dynamics of snow cover

le 17/07/2013. Evidences of chaos from the dynamics of snow cover. in Pyrenees, Lebanon and High-Atlas mountains. approach. Global Modelling. Phenomenological approach of the dynamics well adapted to low-dimensionnal system several underlying hypothesis.

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Evidences of chaos from the dynamics of snow cover

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

  2. approach 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

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

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

  5. Takens’theorem (1981) example: attracteur de Lorenz(1963) z(t) (1941-2010) x(t) y(t)

  6. Takens’theorem (1981) z(t) x(t +2 τ ) (1941-2010) x(t + τ ) x(t) y(t) x(t) (differentiable & differentiable inverse) diffeomorphism

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

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

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

  10. 2000-2012 Portraits dynamiques Pyrénées Mt Liban Atlas

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

  12. 2000-2012 Pyrénées (…) Mt Liban (…) Atlas (…)

  13. Pyreneous yearly analysis Pyrénées

  14. Pyreneous 2000-2001

  15. Pyreneous 2001-2002

  16. Pyreneous 2002-2003

  17. Pyreneous 2003-2004

  18. Pyreneous 2010-2011

  19. Mt Liban yearly analysis Mont Liban

  20. Mt Liban 2001-2002

  21. Mt Liban 2003-2004

  22. Mt Liban 2005-2006

  23. Mt Liban 2006-2007

  24. Mt Liban 2007-2008

  25. Mt Liban 2009-2010

  26. Atlas yearly analysis Atlas

  27. Atlas 2001-2002

  28. Atlas 2002-2003

  29. Atlas 2004-2005

  30. Atlas 2005-2006

  31. Atlas 2006-2007

  32. Atlas 2009-2010

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