Evidences of chaos from the dynamics of snow cover
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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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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


Global modelling

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


Evidences of chaos from the dynamics of snow cover

approach

Global Modelling

Gouesbet & Letellier (1994)

  • Reformulation

Polynomial

approximation


Evidences of chaos from the dynamics of snow cover

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 !


Takens theorem 1981

Takens’theorem (1981)

example: attracteur de Lorenz(1963)

z(t)

(1941-2010)

x(t)

y(t)


Takens theorem 19811

Takens’theorem (1981)

z(t)

x(t +2 τ )

(1941-2010)

x(t + τ )

x(t)

y(t)

x(t)

(differentiable & differentiable inverse)

diffeomorphism


Takens theorem 19812

Takens’theorem (1981)

z(t)

x(t +2 τ )

x(t + τ )

x(t)

y(t)

x(t)

(differentiable & differentiable inverse)

diffeomorphism


Evidences of chaos from the dynamics of snow cover

approach

Phase Space Portrait

NDVI(t)

On dérive

n fois


Evidences of chaos from the dynamics of snow cover

Pyrénées (0-40000km²)

Mt Liban (0-12000km²)

Atlas (0-30000km²)


Evidences of chaos from the dynamics of snow cover

2000-2012

Portraits dynamiques

Pyrénées

Mt Liban

Atlas


Algorithmic tools r packages

approach

Algorithmic tools R-packages

PoMoS

GloMo

Models selection algorithm interaction

Main GloMo Interface

Packages available on CRAN: http://cran.cict.fr


Evidences of chaos from the dynamics of snow cover

2000-2012

Pyrénées

(…)

Mt Liban

(…)

Atlas

(…)


Evidences of chaos from the dynamics of snow cover

Pyreneous

yearly analysis

Pyrénées


Evidences of chaos from the dynamics of snow cover

Pyreneous

2000-2001


Evidences of chaos from the dynamics of snow cover

Pyreneous

2001-2002


Evidences of chaos from the dynamics of snow cover

Pyreneous

2002-2003


Evidences of chaos from the dynamics of snow cover

Pyreneous

2003-2004


Evidences of chaos from the dynamics of snow cover

Pyreneous

2010-2011


Evidences of chaos from the dynamics of snow cover

Mt Liban

yearly analysis

Mont Liban


Evidences of chaos from the dynamics of snow cover

Mt Liban

2001-2002


Evidences of chaos from the dynamics of snow cover

Mt Liban

2003-2004


Evidences of chaos from the dynamics of snow cover

Mt Liban

2005-2006


Evidences of chaos from the dynamics of snow cover

Mt Liban

2006-2007


Evidences of chaos from the dynamics of snow cover

Mt Liban

2007-2008


Evidences of chaos from the dynamics of snow cover

Mt Liban

2009-2010


Evidences of chaos from the dynamics of snow cover

Atlas

yearly analysis

Atlas


Evidences of chaos from the dynamics of snow cover

Atlas

2001-2002


Evidences of chaos from the dynamics of snow cover

Atlas

2002-2003


Evidences of chaos from the dynamics of snow cover

Atlas

2004-2005


Evidences of chaos from the dynamics of snow cover

Atlas

2005-2006


Evidences of chaos from the dynamics of snow cover

Atlas

2006-2007


Evidences of chaos from the dynamics of snow cover

Atlas

2009-2010


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