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Published byKari Sweeney Modified over 9 years 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. 2007 Letellier et al. 2006 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) (1941-2010) 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 ) (1941-2010) 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 (0-40000km²) Mt Liban (0-12000km²) Atlas (0-30000km²)
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Pyrénées Mt Liban Atlas Portraits dynamiques 2000-2012
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Models selection algorithm interaction Main GloMo Interface Algorithmic tools R-packages PoMoS GloMo Packages available on CRAN: http://cran.cict.fr approach
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Pyrénées Mt Liban Atlas (…) 2000-2012
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yearly analysis Pyrénées Pyreneous
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2000-2001 Pyreneous
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2001-2002 Pyreneous
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2002-2003 Pyreneous
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2003-2004 Pyreneous
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2010-2011 Pyreneous
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yearly analysis Mont Liban Mt Liban
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2001-2002 Mt Liban
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2003-2004 Mt Liban
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2005-2006 Mt Liban
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2006-2007 Mt Liban
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2007-2008 Mt Liban
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2009-2010 Mt Liban
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yearly analysis Atlas
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2001-2002 Atlas
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2002-2003 Atlas
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2004-2005 Atlas
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2005-2006 Atlas
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2006-2007 Atlas
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2009-2010 Atlas
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