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

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Presentation on theme: "Evidences of chaos from the dynamics of snow cover in Pyrenees, Lebanon and High- Atlas mountains le 17/07/2013."— Presentation transcript:

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 Letellier et al 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) ( ) y(t)

6 diffeomorphism (differentiable & differentiable inverse) z(t) x(t) y(t) x(t) x(t +2 τ ) x(t + τ ) ( ) 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

9

10 Pyrénées ( km²) Mt Liban ( km²) Atlas ( km²)

11 Pyrénées Mt Liban Atlas Portraits dynamiques

12 Models selection algorithm interaction Main GloMo Interface Algorithmic tools R-packages PoMoS GloMo Packages available on CRAN: approach

13 Pyrénées Mt Liban Atlas (…)

14 yearly analysis Pyrénées Pyreneous

15 Pyreneous

16 Pyreneous

17 Pyreneous

18 Pyreneous

19 Pyreneous

20 yearly analysis Mont Liban Mt Liban

21 Mt Liban

22 Mt Liban

23 Mt Liban

24 Mt Liban

25 Mt Liban

26 Mt Liban

27 yearly analysis Atlas

28 Atlas

29 Atlas

30 Atlas

31 Atlas

32 Atlas

33 Atlas


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