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Published byKari Sweeney Modified about 1 year ago

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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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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

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

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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

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Takens’ theorem (1981) z(t) x(t) example: attracteur de Lorenz(1963) ( ) y(t)

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

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

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

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

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Pyrénées Mt Liban Atlas Portraits dynamiques

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

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Pyrénées Mt Liban Atlas (…)

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yearly analysis Pyrénées Pyreneous

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Pyreneous

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Pyreneous

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Pyreneous

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Pyreneous

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Pyreneous

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yearly analysis Mont Liban Mt Liban

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Mt Liban

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Mt Liban

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Mt Liban

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Mt Liban

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Mt Liban

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Mt Liban

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yearly analysis Atlas

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Atlas

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Atlas

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Atlas

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Atlas

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Atlas

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Atlas

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