evidences of chaos from the dynamics of snow cover in pyrenees, lebanon and high- atlas mountains le...
TRANSCRIPT
Evidences of chaos from the dynamics of snow cover
in Pyrenees, Lebanon and High-
Atlas mountains
le 17/07/2013
Global Modelling
• Phenomenological approach of the dynamics
• well adapted to low-dimensionnal system
• several underlying hypothesis
Few knowledge about the dynamics is requiredThe 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
Gouesbet & Letellier (1994)
nn XXxRX
XX
Xx
,..,,
...
21
32
21
nnn
n
n
xxxfx
xxxfx
xxxfx
,..,,
...
,..,,
,..,,
21
2122
2111
• Reformulation
Polynomialapproximation
nn XXxPXXxR ,..,,,..,, 2121
approach
Global Modelling
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 applicationsto ‘‘real world’’ systems
.. this work !
Letellier et al. 2013
Takens’theorem (1981)
zyxz
yxzxy
xyx
tztytx ,,
z(t)
x(t)
example: attracteur de Lorenz(1963)
(1941-2010)
y(t)
zyxz
yxzxy
xyx
diffeomorphism(differentiable &
differentiable inverse)
tx
tztytx ,,
z(t)
x(t)y(t) x(t)
x(t +
2 τ
)
x(t + τ )
(1941-2010)
Takens’theorem (1981)
zyxz
yxzxy
xyx
diffeomorphism(differentiable &
differentiable inverse)
tx
tztytx ,,
z(t)
x(t)y(t) x(t)
x(t +
2 τ
)
x(t + τ ) tx
tx
tx
Takens’theorem (1981)
Phase Space Portrait
tx1
On dériven fois
n
n xX
xX
xX
x
...
13
12
1
1x
1x
ND
VI(t
)approach
Pyrénées (0-40000km²)
Mt Liban (0-12000km²)
Atlas (0-30000km²)
Pyrénées
Mt Liban
Atlas
Portraits dynamiques
txtxtx ,,
2000-2012
Models selection algorithm interactionMain GloMo Interface
Algorithmic tools R-packages
PoMoS GloMo
Packages available on CRAN: http://cran.cict.fr
approach
Pyrénées
Mt Liban
Atlas
(…)
(…)
(…)
2000-2012
yearly analysis
Pyrénées
Pyreneous
2000-2001
Pyreneous
2001-2002
Pyreneous
2002-2003
Pyreneous
2003-2004
Pyreneous
2010-2011
Pyreneous
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
Mt Liban
yearly analysis
Atlas
Atlas
2001-2002
Atlas
2002-2003
Atlas
2004-2005
Atlas
2005-2006
Atlas
2006-2007
Atlas
2009-2010
Atlas