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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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

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

Global Modelling

Gouesbet & Letellier (1994)

  • Reformulation

Polynomial

approximation


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)

example: attracteur de Lorenz(1963)

z(t)

(1941-2010)

x(t)

y(t)


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 (1981)

z(t)

x(t +2 τ )

x(t + τ )

x(t)

y(t)

x(t)

(differentiable & differentiable inverse)

diffeomorphism


approach

Phase Space Portrait

NDVI(t)

On dérive

n fois


Pyrénées (0-40000km²)

Mt Liban (0-12000km²)

Atlas (0-30000km²)


2000-2012

Portraits dynamiques

Pyrénées

Mt Liban

Atlas


approach

Algorithmic tools R-packages

PoMoS

GloMo

Models selection algorithm interaction

Main GloMo Interface

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


2000-2012

Pyrénées

(…)

Mt Liban

(…)

Atlas

(…)


Pyreneous

yearly analysis

Pyrénées


Pyreneous

2000-2001


Pyreneous

2001-2002


Pyreneous

2002-2003


Pyreneous

2003-2004


Pyreneous

2010-2011


Mt Liban

yearly analysis

Mont Liban


Mt Liban

2001-2002


Mt Liban

2003-2004


Mt Liban

2005-2006


Mt Liban

2006-2007


Mt Liban

2007-2008


Mt Liban

2009-2010


Atlas

yearly analysis

Atlas


Atlas

2001-2002


Atlas

2002-2003


Atlas

2004-2005


Atlas

2005-2006


Atlas

2006-2007


Atlas

2009-2010


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