Transcript Jin two-strip model

ENSO sensitivity to change in stratification in CMIP3
Boris Dewitte
Sulian Thual, Sang-Wook Yeh, Soon-Il An, Ali Belmadani
CLIVAR Workshop, Paris, France, 17-19 November 2010
New strategies for evaluating ENSO processes in climate models
Impact of climate change on the mean stratification
in ensemble models
ΔT (2xCO2 – PI)
Yeh et al. (2009)
Dinezio et al. (2009)
Conclusions/Perspectives
• The characteristics of the thermocline (depth, sharpness,
intensity) needs to be taken into account for determining
the stability of ENSO
• SODA tells us that an increased stratification leads to
more energetic and low-frequency ENSO (Climate change
paradox..)
• Need to understand the impact of stratification changes
on ENSO non-linearities.
Motivation
Understand the physical mechanism associated to
the ‘rectification’ of ENSO variability/stability by the
change in mean state?
?
T
 b.T (t   )  c.T  e.T 3  k . N 2
(t   2 )


t


,
t
t
~6 months
η~10-20 years
2~?
k~?
Cf. Battisti and Hirst (1989)
Change in thermocline depth at
decadal timescales
On thermocline depth: small amplitude
(Wang and An, 2001)
Levitus data
Change in mean temperature associated to the 1976/77 climate shift
T(1960-2001)
T(1980-1997)-T(1960-1975)
D20 (1980-1997)
D20 (1960-1975)
(Moon et al., 2004; Dewitte et al., 2009)
• The ‘Moon pattern’ indicates that change in mean state
cannot be account for just one baroclinic mode..!
T(1980-1997)-T(1960-1975)
(modes 1 to 3)
TM ( x, y , z, t )  
1
T
M
 sl
n 1
n
( x, y , t ).
dFn ( x, z, t ' )
dz
Sensitivity of ENSO to stratification
• Ocean dynamics perspective
Shallow-water equations
Stratification defined by (c, H)
Multimode context
Stratification defined by (cn, Pn)
y

v
  yu  g

t
y  0 H
u n
 n
 yv n  g
 Pn . x
t
x
v n
 n
 yu n  g
 Pn . y
t
y
 u v  c 2 
  

0
t
 x y  g
 u n v n  c n2  n




0
y  g
t
 x
x

u
  yv  g

t
x  0 H
A ‘finer’ representation of the thermocline allows for taking into account
the ‘loss’ of energy associated to vertical propagation: Implication for
ENSO energetics and feedbacks
Interannual variability of vertical displacements
in a OGCM simulation (1985-1994)
(Dewitte and Reverdin, 2000)
Sensitivity of ENSO to stratification
• Thermodynamics perspective
T '
T '
T
T '
T
T '
T '
T '
 (u.
 u'.
 w.
 w'.
 u'.
 v'.
 w'.
 ...)
t
x
x
z
z
x
y
z
Nonlinear Dynamical Heating
Zonal Advective Feedback
Thermocline Feedback
Mean circulation (U, W ) in CMIP3
1 : BCCR-BCM2.0
2 : CCCMA-CGCM3.1
3 : CCCMA-CGCM3.1 (t63)
4 : CNRM-CM3
5 : CSIRO-MK3.0
6 : CSIRO-MK3.5
7 : GFDL-CM2.0
8 : GFDL-CM2.1
9a : GISS-AOM (run1)
9b : GISS-AOM (run2)
11 : GISS-MODEL-E-R
12 : IAP-FGOALS1.0-g
13 : INGV-ECHAM4
14 : INM-CM3.0
15 : IPSL-CM4
16 : MIROC3.2-HIRES
17 : MIROC3.2-MEDRES
18 : MIUB-ECHO-g
19 : MPI-ECHAM5
20 : MRI-CGCM2.3.2A
21 : NCAR-CCSM3.0
22 : UKMO-HadCM3
23 : UKMO-HadGem1
Belmadani et al. (2010)
Thermocline depth bias in CMIP3
1 : BCCR-BCM2.0
2 : CCCMA-CGCM3.1
3 : CCCMA-CGCM3.1 (t63)
4 : CNRM-CM3
5 : CSIRO-MK3.0
6 : CSIRO-MK3.5
7 : GFDL-CM2.0
8 : GFDL-CM2.1
9a : GISS-AOM (run1)
9b : GISS-AOM (run2)
11 : GISS-MODEL-E-R
12 : IAP-FGOALS1.0-g
13 : INGV-ECHAM4
14 : INM-CM3.0
15 : IPSL-CM4
16 : MIROC3.2-HIRES
17 : MIROC3.2-MEDRES
18 : MIUB-ECHO-g
19 : MPI-ECHAM5
20 : MRI-CGCM2.3.2A
21 : NCAR-CCSM3.0
22 : UKMO-HadCM3
23 : UKMO-HadGem1
Sensitivity of ENSO to stratification
• Thermodynamics perspective
T '
T '
T
T '
T
T '
T '
T '
 (u.
 u'.
 w.
 w'.
 u'.
 v'.
 w'.
 ...)
t
x
x
z
z
x
y
z
Nonlinear Dynamical Heating
Zonal Advective Feedback
Thermocline Feedback
The Jin twostrip model
(An and Jin,
2001)
  L 2 
 e ( x, y)   A(Te , x) exp   y 0  / 2
  La  
~3°N

Hmix
Equator
T
Te
T
 u e .
 w . e   .Te
t
x
z
with
Te
~ f (he )
z
Rossby waves (hn)
y=yn
he=rWhn
hn=rEhe
y=0°
Kelvin waves (he, ue)
u
h
u e  he  h n
y=0°-> ( e  )e(h xeh 
 hx ehe  avec
t
m
e
n) m
xe
x

 t
2
(h t   m )hhn   x hn / y n   y ( x / y )
c
c

y y
y=yn->  n  C R n  Curl ( )   m hn avec CR n   f 2 ~ y 2
n
x conditions
f (reflexion, rE et rW )

t2 boundary
2
2

 he 
 
with X   hn 
T 
 e
X
 A  X
t
Solution of the mode [Xµ=X0.e.t.cos(β.t +φ)] as a
function of coupling efficiency 
=1
The Jin twostrip model
(An and Jin,
2001)
X
 A  X
t
α
=0
(basin mode)
β
~4 yrs
~ 9 months
Stability of ENSO as a function of thermocline depth
Period
Increased thermocline depth ------->lower frequency stronger
ENSO
Growth rate
Federov and Philander (2001)
• Defining thermocline…
• Depth (P1)
• Intensity, Sharpness (Pn, n>1)
Gent and Luyten (1985)
Decadal variability of Pn – CNRM-CM3
<P1>=0.5, <P2>=0.5, <P3>=0.2
dD20<0
dD20>0
Dewitte et al. (2007)
dPn(t)
180°
dD20>0
dD20<0
CNRM-CM3
N3VAR
90°W
Conceptual Model
(Thual et al., 2010)
comparable to the Jin two-strip model (Jin 1997b, An &
Jin 2001) except for the ocean dynamics.
Atmospherical component :
 x   f (SST )
Statistical relationship (SVD)
with a coupling coefficient µ.
Ocean dynamics :
Kelvin and Rossby wave on
3 baroclinic modes : Kn, Rn
Thermodynamics :
( t   n ) K n  cn  x K n  Pn   x . K n 
cn
( t   n ) Rn   x Rn  Pn   x . Rn 
3
 t SST  FH ( x) H  FU ( x)U  FD SST
Thermocline depth and
zonal currents : H, U
Variables :
X ( x, t )  ( K1 , K 2 , K3 , R1 , R2 , R3 , SST )
Thermodynamical feedbacks
Adimentionalised feedback intensity
 t SST  FH ( x) H  FU ( x)U  FD SST
Thermocline feedback
FH  w  dT 
dH
Zonal advective feedback
FU   x SST
SODA dataset (1958-2008)
Stability Analysis
Find eigenvalues (a+ ib) of J from
X  J X
Each eigenmode (a,b) has the form
X ( x, t )  exp( at ) A cos(bt   ( x, t ))
Dominant eigenmode=ENSO mode
Eigenvectors of the ENSO mode (µ=1)
Sensitivity to Stratification
δ
P1(1-δ), P2(1+δ/2), P3(1+δ/2)
Stratification acts as a coupling parameter, but with physical meaning.
Sensitivity of ENSO mode to stratification in the TD model
Model parameters:
P1(1-δ), P2(1+δ/2),
P3(1+δ/2)
frequency
Growth rate
The 1976/77 Climate shifts:
Pre-70s to Post-70s : Strong
increase in stratification (δ
=120%).
=> Stronger, lower frequency
ENSO
Data: SODA
The 2000 shifts:
Post-2000 : Slight decrease in
stratification (δ =95%).
=> ENSO variability displaced toward
the west. Processes ?
Data: SODA
Change in ENSO stability in the GFDL model
« Metrics » for the sensitivity to stratification
change using the extended Jin’s two-strip
model

f
2xCO2 - PI
EOF1 of low-passed filtered T(x,z,y=0) (PI runs)
MRI
GFDL
Yeh et al. (2010)
Sensitivity of ENSO to a
warming climate: GFDL
versus MRI
Yeh et al. (2010)
Change in feedback processes
Conclusions/Perspectives
• The characteristics of the thermocline (depth, sharpness,
intensity) needs to be taken into account for determining
the stability of ENSO
• SODA tells us that an increased stratification leads to
more energetic and lower-frequency ENSO (Climate
change paradox.?.)
• Need to understand the impact of stratification changes
on ENSO non-linearities.
« Metrics » for the sensitivity to stratification
change using the extended Jin’s two-strip
model

f
Low frequency change of temperature (EOF1) in
the MRI and GFDL models
MRI
GFDL
Change in stratification tends to
project on the high-order or « very
slow » modes (n>3)
 impact Ekman layer physics
Change in stratification does
project on the gravest modes
(n=1,3)
 Impact ENSO stability
Change in feedback processes
Yeh et al. (2010)
Yeh et al. (2010)
Low frequency change of temperature (EOF1) in
CMIP3
MIROC3_3_HIRES
MIROC3_3_MEDRES
MRI_CGCM2_3_2A
NCAR_CCSM3_0
MPI_ECHAM5
UKMO_HADCM3
CCCMA_CGCM3_1_t63
CNRM_CM3
CSIRO_MK3_5
GFDL_CM2_0
INMCM3_0
MIUB_ECHO_G
CCCMA_CGCM3_1
FGOALSrun1
GFDL_CM2_1
INVG_ECHAM4
IPSL_CM4
GISS_AOMrun1
Low
frequency
change of
temperatu
re (EOF1)
in CMIP3