1"
2"
3"
The$Eastward$Shift$of$the$Walker$Circulation$
in$response$to$Global$Warming$and$its$
relationship$to$ENSO$variability$
5"
Tobias$Bayr1,$Dietmar$Dommenget2,$Thomas$Martin1$and$Scott$
Power3$
6"
$
7"
Abstract$
4"
8"
9"
10"
11"
$This$article$investigates$the$global$warming$response$of$the$Walker$Circulation$and$
the$ other$ zonal$ circulation$ cells$ (represented$ by$ the$ zonal$ stream$ function)$ in$ a$ CMIP5$
multiMmodel$ensemble$(MMEns)$under$the$RCP4.5$scenario.$The$changes$in$the$mean$state$
are$presented$as$well$as$the$changes$in$the$modes$of$variability.$$
12"
13"
14"
15"
16"
17"
18"
19"
20"
The$mean$zonal$circulation$weakens$nearly$everywhere$along$the$equator.$Over$the$
Pacific$the$Walker$cell$also$shows$a$significant$eastward$shift.$These$changes$in$the$mean$
circulation$ are$ very$ similar$ to$ the$ leading$ mode$ of$ interannual$ variability$ in$ the$ tropical$
zonal$circulation$cells,$which$is$dominated$by$ENSO$variability.$During$an$El$Nino$event$the$
circulation$weakens$and$the$rising$branch$over$the$Maritime$Continent$shifts$to$the$east$in$
comparison$to$neutral$conditions$(vice$versa$for$a$La$Nina$event).$Two$thirds$of$the$global$
warming$ forced$ trend$ of$ the$ Walker$ cell$ can$ be$ explained$ by$ a$ longMterm$ trend$ in$ this$
interannual$variability$pattern,$i.e.$a$shift$towards$more$El$NinoMlike$conditions$in$the$multiM
model$mean$under$global$warming.$$
21"
22"
23"
24"
25"
26"
In$ interannual$ variability$ the$ zonal$ circulation$ exhibits$ an$ asymmetry$ between$ El$
Nino$and$La$Nina$events.$$El$Nino$anomalies$are$located$more$to$the$east$compared$to$La$
Nina$anomalies.$Consistent$with$this$asymmetry$we$find$a$shift$to$the$east$of$the$dominant$
mode$ of$ variability$ of$ zonal$ stream$ function$ under$ global$ warming.$ All$ these$ results$ vary$
among$ the$ individual$ models,$ but$ the$ MMEns$ of$ CMIP3$ and$ CMIP5$ show$ in$ nearly$ all$
aspects$very$similar$results,$which$underline$the$robustness$of$these$results.$
27"
28"
29"
30"
31"
32"
The$observed$data$(ERA$Interim$reanalysis)$from$1979$to$2012$shows$a$westward$
shift$and$strengthening$of$the$Walker$Circulation.$This$is$opposite$to$what$the$results$in$the$
CMIP$models$reveal.$However,$75%$of$the$trend$of$the$Walker$Cell$can$again$be$explained$
by$ a$ shift$ of$ the$ dominant$ mode$ of$ variability,$ but$ here$ towards$ more$ La$ NinaMlike$
conditions.$Thus$longMterm$trends$of$the$Walker$cell$seem$to$follow$to$a$large$part$the$preM
existing$dominant$mode$of$internal$variability.$$$
33"
1"
"
34"
35"
36"
37"
38"
39"
40"
41"
42"
43"
44"
45"
1. Introduction0
46"
47"
48"
49"
50"
51"
52"
53"
54"
55"
56"
57"
58"
59"
Most$ recent$ studies$ focus$ on$ the$ Walker$ Circulation$ and$ predict$ that$ it$ weakens$
under$global$warming$(Knutson$and$Manabe$1995;$Vecchi$and$Soden$2007;$DiNezio$et$al.$
2009;$Power$and$Kociuba$2011).$This$picture$has$not$changed$in$the$climate$model$runs$of$
the$5th$Phase$of$the$Coupled$Model$Intercomparison$Project$(CMIP),$that$were$carried$out$
for$ the$ 5th$ Assessment$ Report$ (AR5)$ of$ the$ Intergovernmental$ Panel$ on$ Climate$ Change$
(IPCC):$ Figure$1$ shows$ the$ trend$ of$ the$ strength$ of$ the$ Walker$ cell$ based$ on$ the$ sea$ level$
pressure$(SLP)$and$SST$gradient$over$the$equatorial$Pacific$of$the$individual$CMIP3$models$
under$ the$ A1B$ scenario$ and$ of$ the$ individual$ CMIP5$ models$ under$ the$ RCP4.5$ scenario.$$
The$multiMmodel$ensemble$(MMEns)$and$most$models$show$a$consistent$reduction$in$both$
SST$and$SLP$gradients,$i.e.$a$weakening$of$the$Walker$Circulation.$The$CMIP5$MMEns$shows$
a$stronger$weakening$than$the$CMIP3$MMEns,$despite$a$lower$greenhouse$gas$increase$in$
the$CMIP5$RCP4.5$scenario$than$in$the$CMIP3$A1B$scenario.$But$in$both$CMIP3$and$CMIP5$
there$ are$ models$ that$ show$ no$ significant$ trend$ or$ even$ a$ strengthening$ of$ the$ Walker$
Circulation.$Thus$a$spread$in$the$signal$can$be$found$in$the$individual$models.$
60"
61"
62"
63"
64"
65"
66"
67"
68"
69"
70"
Knutson$ and$ Manabe$ (1995)$ indicate$ two$ different$ mechanisms,$ which$ determine$
the$ response$ of$ the$ Walker$ Circulation$ in$ a$ warmer$ climate.$ The$ first$ mechanism$ works$
with$a$horizontal$homogeneous$warming$in$the$atmosphere$that$increases$with$height,$and$
is$ a$ pure$ atmospheric$ one.$ In$ a$ warmer$ climate$ an$ enhanced$ hydrological$ cycle$ leads$ to$
enhanced$ upper$ level$ warming,$ which$ increases$ the$ static$ stability.$ This$ mechanism$ was$
further$ investigated$ by$ Held$ and$ Soden$ (2006)$ and$ Vecchi$ and$ Soden$ (2007)$ and$ $ they$
concluded$ that$ an$ atmospheric$ warming$ weakens$ the$ tropical$ circulations.$ In$ contrast$ an$
atmospheric$cooling$strengthens$the$Walker$Circulation,$as$found$in$a$paleoMclimate$study$
(DiNezio$et$al.$2011).$In$the$following$we$will$refer$to$this$mechanism$as$the$homogeneous$
warming$ mechanism,$ as$ it$ does$ not$ require$ any$ horizontal$ gradients$ in$ the$ warming$
pattern.$
71"
72"
73"
74"
75"
76"
$The$ second$ mechanism$ works$ with$ horizontal$ inhomogeneous$ temperature$
changes,$ i.e.$ the$ change$ in$ zonal$ temperature$ gradients.$ This$ depends$ on$ the$ local$
differences$ in$ the$ strength$ of$ evaporative$ cooling$ (Knutson$ and$ Manabe$ 1995),$ the$ ocean$
dynamical$ thermostat$ cooling$ (Clement$ et$ al.$ 1996),$ cloud$ cover$ feedbacks$ (Meehl$ and$
Washington$ 1996)$ and$ the$ landMsea$ warming$ contrast$ (Bayr$ and$ Dommenget$ 2013a).$
Further$ DiNezio$ et$ al.$ (2009)$ found$ that$ in$ a$ CMIP3$ MMEns$ the$ evaporative$ cooling$ and$
The$ equatorial$ zonal$ circulation$ of$ the$ atmosphere$ originates$ from$ the$ zonal$
temperature$ differences$ along$ the$ equator$ due$ to$ the$ landMsea$ distribution$ and$ ocean$
circulation$within$the$tropics.$The$main$zonal$circulation$cells$are$the$Indian$Ocean$cell,$the$
Pacific$Ocean$(or$Walker)$cell$and$the$Atlantic$Ocean$cells$(Hastenrath$1985).$The$Walker$
cell$is$the$most$prominent$and$its$variability$is$strongly$linked$to$sea$surface$temperature$
(SST)$ variations$ associated$ with$ the$ El$ Nino$ Southern$ Oscillation$ (ENSO)$ phenomenon.$
Mean$ state$ and$ variability$ of$ these$ zonal$ circulation$ cells$ have$ large$ socioMeconomical$
impacts$ via$ modulating$ the$ distribution$ of$ e.g.$ precipitation,$ severe$ weather$ and$ stream$
flow$(Power$et$al.$1999).$It$is$therefore$of$great$interest$to$know,$how$the$zonal$circulation$
cells$ might$ change$ in$ mean$ state$ and$ variability$ in$ response$ to$ a$ warmer$ climate,$ and$
whether$they$have$already$changed.$
2"
"
77"
78"
79"
80"
81"
82"
cloud$cover$feedbacks$reduce$the$warming$over$the$warm$pool$region$more$effectively$than$
the$ ocean$ dynamical$ thermostat$ cools$ the$ cold$ tongue$ region,$ hence$ reduce$ the$ SST$
gradient$ over$ the$ Pacific$ and$ weakens$ the$ Walker$ Circulation.$ In$ general,$ this$ second$
mechanism$can$act$in$both$directions$in$a$warmer$climate:$it$can$weaken$or$strengthen$the$
zonal$ circulation.$ In$ the$ following$ we$ will$ refer$ to$ this$ mechanism$ as$ the$ inhomogeneous$
warming$mechanism,$as$it$requires$changes$in$the$horizontal$temperature$gradients.$$
83"
84"
85"
Vecchi$ and$ Soden$ (2007)$ and$ Yu$ et$ al.$ (2012)$ also$ found$ an$ eastward$ shift$ under$
global$ warming,$ $ in$ addition$ to$ the$ weakening$ the$ Walker$ Circulation.$ Both$ studies$ relate$
this$eastward$shift$to$a$trend$towards$more$El$NinoMlike$conditions.$$
86"
87"
88"
89"
90"
91"
92"
93"
94"
95"
ENSO$ is$ a$ coupled$ airMsea$ interaction$ phenomena$ with$ associated$ changes$ in$ SST$
gradient,$ SLP$ gradient$ and$ surface$ winds$ over$ the$ Pacific$ (Philander$ 1990):$ El$ Nino$ is$
characterised$ by$ anomalous$ warm$ SST$ over$ the$ East$ and$ Central$ Pacific,$ weaker$ surface$
winds$ over$ the$ West$ Pacific,$ a$ weaker$ SLP$ gradient$ over$ the$ Pacific$ and$ more$ convection$
over$the$Eastern$Pacific.$For$La$Nina$the$situation$is$vice$versa,$with$more$convection$over$
the$ West$ Pacific,$ thus$ ENSO$ variability$ is$ associated$ with$ a$ zonal$ shift$ of$ convection.$
Another$important$feature$of$ENSO$variability$is$its$spatial$asymmetry$(e.g.$Hoerling$et$al.$
1997;$Rodgers$et$al.$2004;$Yu$and$Kim$2011;$Dommenget$et$al.$2013),$i.e.$that$the$warming$
of$SST$during$El$Nino$events$occurs$a$bit$further$to$the$east$than$the$SST$cooling$during$La$
Nina$events.$$
96"
97"
98"
99"
100"
101"
102"
103"
104"
105"
106"
107"
108"
109"
110"
111"
112"
113"
114"
115"
116"
117"
The$ aim$ of$ this$ study$ is$ investigate$ the$ eastward$ shift$ of$ the$ Walker$ Circulation$
under$global$warming$and$its$relationship$to$ENSO$variability.$Further,$we$want$to$analyse$
the$ changes$ in$ the$ modes$ of$ variability$ and$ find$ out$ if$ the$ trends$ of$ the$ zonal$ circulation$
cells$ follow$ a$ preMexisting$ mode$ of$ internal$ variability.$ In$ our$ analyses$ we$ use$ the$ zonal$
stream$ function$ for$ the$ representation$ of$ the$ zonal$ circulation$ cells,$ including$ the$ Walker$
Circulation,$ as$ defined$ by$ Yu$ and$ Zwiers$ (2010)$ and$ Yu$ et$ al.$ (2012).$ This$ is$ a$ direct$
measure$ of$ the$ circulation$ in$ the$ free$ atmosphere$ and$ not$ like$ the$ SLP$ a$ surface$ based$
approximation.$ It$ has$ the$ advantage$ that$ it$ measures$ the$ zonal$ circulation$ over$ all$ levels.$
Thus$includes$both$areas$where$the$two$mechanisms$mentioned$above$influence$the$zonal$
circulation.$ We$ address$ the$ following$ questions:$ 1)$ What$ is$ the$ response$ of$ the$ zonal$
circulation$ cells$ to$ global$ warming$ in$ the$ mean$ state$ and$ how$ do$ its$ modes$ of$ variability$
change$ in$ the$ CMIP3$ and$ CMIP5$ database$ under$ global$ warming?$ 2)$ Does$ the$ Walker$
Circulation$shift$eastward$and$if$yes,$what$causes$the$eastward$shift$under$global$warming?$
3)$Is$ the$ projected$ response$ already$ evident$ in$ reanalysis$ data$ for$ recent$ decades?$ The$
paper$is$organised$as$follows:$Section$2$gives$an$overview$of$the$data$and$the$definition$of$
the$ zonal$ stream$ function$ used$ in$ this$ study.$ The$ response$ of$ the$ mean$ state$ in$ the$ CMIP$
MMEns$is$shown$in$Section3.$The$eastward$shift$is$examined$in$Section$4.$The$asymmetry$of$
the$ Walker$ Circulation$ in$ ENSO$ variability$ is$ investigated$ in$ Section$ 5$ and$ the$ changes$ in$
the$ modes$ of$ variability$ in$ Section$6.$ The$ observed$ trends$ in$ the$ recent$ decades$ in$
reanalysis$data$are$shown$in$Section$7.$In$the$final$analysis$section$we$discuss$how$changes$
in$ SLP$ relate$ to$ changes$ in$ the$ zonal$ circulation$ cells$ and$ conclude$ our$ analysis$ with$ a$
summary$and$discussion$in$Section$9.$
3"
"
118"
119"
120"
121"
122"
123"
124"
125"
126"
127"
128"
129"
130"
131"
132"
133"
2. Data0and0Methods0
134"
135"
136"
137"
138"
139"
For$comparison$with$observations$and$analysing$the$trends$over$recent$decades$we$
use$ ERA$ Interim$ reanalysis$ data$ (Simmons$ et$ al.$ 2007)$ for$ the$ period$ 1979$ until$ 2012$ in$
lack$ of$ “real”$ observations$ of$ tropospheric$ winds.$ We$ choose$ ERA$ Interim$ because$ the$
tropical$ tropospheric$ temperature$ trends$ in$ this$ data$ set$ are$ in$ a$ good$ agreement$ with$
satellite$observations$(Bengtsson$and$Hodges$2009).$These$data$sets$are$also$interpolated$
onto$a$regular$2.5°x2.5°$grid.$$
140"
141"
As$ a$ measure$ for$ the$ zonal$ circulation$ along$ the$ equator$ we$ use$ the$ zonal$ stream$
function$as$defined$in$Yu$and$Zwiers$(2010)$and$Yu$et$al.$(2012):$$
The$data$analysed$in$this$study$are$taken$from$the$Climate$Model$Intercomparison$
Project$ Phase$ 3$ and$ 5$ (CMIP3,$ Meehl$ et$ al.$ 2007$ and$ CMIP5,$ Taylor$ et$ al.$ 2012).$ From$
CMIP3$we$use$data$from$the$20C$and$A1B$scenarios,$from$CMIP5$we$use$the$historical$and$
RCP4.5$scenarios.$The$RCP4.5$scenario$has$a$smaller$increase$in$greenhouse$gases$than$the$
A1B$ scenario.$ We$ choose$ these$ greenhouse$ gas$ emission$ scenarios$ because$ most$ of$ the$
available$ models$ simulated$ these$ scenarios;$ see$ legend$ in$ Figure$ 1$ for$ a$ list$ of$ climate$
models.$ We$ have$ the$ following$ variables$ available$ from$ 22$ CMIP3$ models$ and$ 36$ CMIP5$
models:$sea$level$pressure$(SLP),$sea$surface$temperature$(SST),$atmospheric$temperature$
(T),$tropospheric$temperature$(Ttropos;$mass$weighted$average$of$atmospheric$temperature$
between$ 1000$ and$ 100hPa),$ zonal$ wind$ (U),$ meridional$ wind$ (V)$ and$ vertical$ wind$ (W).$
Each$data$set$is$interpolated$onto$a$regular$2.5°$x$2.5°$grid$and$for$each$CMIP$phase,$CMIP3$
and$CMIP5$we$build$a$multiMmodel$ensemble$(MMEns)$with$one$ensemble$member$for$each$
model.$For$the$trend$analysis$in$Section$3$we$calculate$the$multiMmodel$mean.$For$all$other$
analysis$ using$ the$ MMEns$ we$ concatenate$ all$ data$ sets$ to$ get$ one$ long$ data$ set,$ where$
detrended$anomalies$are$defined$for$each$model$individually$first.$$
!
Ψ = 2!"!
!!
!
!"
!
!
142"
143"
144"
145"
with$the$divergent$component$of$the$zonal$wind$uD,$the$radius$of$the$earth$a,$the$pressure$p$
and$ gravity$ constant$ g.$ The$ zonal$ wind$ is$ averaged$ for$ the$ meridional$ band$ between$ 5°N$
and$ 5°S$ and$ integrated$ from$ the$ top$ of$ the$ atmosphere$ to$ surface.$ In$ the$ figures$ only$ the$
levels$below$100$hPa$are$shown,$as$the$stream$function$is$nearly$zero$above$that$level.$$
146"
147"
148"
149"
150"
151"
152"
153"
154"
155"
156"
3. Mean0state0and0response0
The$ mean$ state$ of$ the$ zonal$ stream$ function$ in$ the$ CMIP3$ and$ CMIP5$ multiMmodel$
mean$ for$ the$ period$ 1950$ until$ 1979$ agree$ quite$ well$ with$ each$ other$ (see$ Fig.$ 2a,b)$ and$
with$ reanalysis$ data$ (not$ shown),$ as$ already$ investigated$ previously$ for$ CMIP3$ (Yu$ et$ al.$
2012).$Positive$values$indicate$a$clockwise$circulation$and$negative$values$an$anticlockwise$
circulation.$ The$ three$ main$ convection$ regions$ (Africa,$ the$ Maritime$ Continent$ and$ South$
America)$ and$ the$ descending$ regions$ (West$ Indian$ Ocean,$ the$ Pacific$ cold$ tongue$ region$
and$the$Atlantic$Ocean)$together$form$the$main$circulation$cells$(the$Indian$Ocean$cell,$the$
Pacific$ or$ Walker$ cell$ and$ the$ Atlantic$ Ocean$ cells).$ The$ trend$ patterns$ under$ global$
warming$ over$ the$ period$ 1950$ until$ 2099$ are$ very$ similar$ in$ the$ CMIP3$ and$ CMIP5$ (Fig.$
2c,d)$and$to$the$results$of$Yu$et$al.$(2012).$Thus,$the$trend$pattern$seems$to$be$very$robust$
4"
"
157"
158"
159"
160"
despite$ different$ models,$ resolutions,$ ensemble$ sizes$ and$ emission$ scenarios$ in$ the$
different$MMEns.$The$MMEns$predict$more$ascending$over$the$West$Indian$Ocean$and$the$
Pacific$and$more$descending$over$Africa,$the$Maritime$Continent$and$South$America$under$
global$warming$(see$also$Fig.$3).$$
161"
162"
163"
164"
165"
166"
167"
168"
169"
170"
171"
172"
173"
174"
We$ can$ build$ the$ vertical$ averages$ of$ the$ stream$ functions$ to$ get$ a$ clearer$ picture:$
The$ global$ warming$ trend$ of$ the$ tropical$ zonal$ circulations$ over$ most$ of$ the$ Indian$ and$
Atlantic$Ocean$is$opposite$to$the$mean$state$(Fig.$2e,f,$note$the$reversed$sign$of$the$trend$for$
better$comparison),$which$indicates$a$weakening$of$the$circulation$in$agreement$with$the$
arguments$of$Vecchi$and$Soden$(2007).$If$we$focus$on$the$Pacific$ocean,$the$MMEns$predict$
only$ a$ small$ change$ in$ strength$ of$ the$ circulation$ (the$ maximum$ of$ the$ Walker$ cell$ at$
150°W):$in$the$CMIP3$MMEns$it$slightly$increases,$in$agreement$with$the$results$from$Yu$et$
al.$ (2012),$ in$ the$ CMIP5$ MMEns$ it$ slightly$ decreases.$ But$ in$ these$ figures$ the$ striking$
difference$between$the$mean$states$in$20C$and$21C$over$the$Pacific$is$the$eastward$shift$of$
the$Walker$cell$(compare$the$blue$and$green$curves$in$Fig.$2e,f).$This$can$also$be$seen$in$the$
vertical$wind$at$the$500hPa$level$along$the$equator$(Fig.$3):$Over$the$East$Indian$Ocean$and$
Maritime$Continent$the$vertical$wind$decreases,$whereas$over$the$Pacific$Ocean$increases.$
Thus$ an$ eastward$ shift$ of$ the$ Walker$ Circulation$ can$ be$ seen$ in$ zonal$ stream$ function$ as$
well$as$in$the$vertical$wind$in$both$CMIP3$and$CMIP5.$$
175"
176"
177"
178"
179"
180"
181"
182"
183"
184"
The$zero$line$of$the$stream$function$over$the$Maritime$Continent$warm$pool$region$
determines$ the$ western$ edge$ of$ the$ Walker$ cell$ and$ coincides$ approximately$ with$ the$
maximum$ of$ convection$ in$ Fig.$ 3.$ This$ zero$ line$ shifts$ 6°$ to$ the$ east$ in$ the$ CMIP5$ MMEns$
and$ 8°$ in$ the$ CMIP3$ MMEns$ (Fig.$ 2e,f).$ Figure$ 4$ shows$ the$ shift$ in$ the$ position$ of$ the$
western$edge$of$the$Walker$cell$under$global$warming$on$the$xMaxis$and$the$average$trend$
in$ the$ box$ over$ the$ ascending$ branch$ of$ the$ Walker$ and$ Indian$ cell$ on$ the$ yMaxis$ (120°EM
180°,$ 700M300hPa)$ for$ each$ individual$ CMIP3$ and$ CMIP5$ model.$ Most$ models$ show$ a$
negative$trend$and$an$eastward$shift$under$global$warming.$These$two$quantities$appear$to$
have$ a$ weak$ linear$ relation:$ models$ that$ tend$ to$ weaken$ most$ also$ tend$ to$ have$ a$ larger$
eastward$shift.$$
185"
186"
187"
188"
189"
190"
191"
192"
193"
4. East:west0shift0of0the0Walker0Circulation0during0El0Nino/La0Nina0
194"
195"
196"
197"
198"
The$Walker$Circulation$in$ERA$Interim$reanalysis$data$reveals$an$eastMwest$shift$in$
ENSO$ variability$ (Fig.$ 5a,b):$ The$ zonal$ circulation$ cells$ over$ the$ IndoMPacific$ are$
considerably$weaker$during$El$Nino$than$during$La$Nina.$Additionally,$the$western$edge$of$
the$Walker$Circulation$shifts$to$the$east$of$its$mean$state$position$during$El$Nino$(176°E)$
and$ to$ the$ west$ during$ La$ Nina$ (140°E).$ $ Figure$ 5c$ shows$ the$ difference$ between$ the$ El$
The$ centers$ of$ large$ scale$ convection$ and$ precipitation$ shift$ in$ the$ eastMwest$
direction$during$El$Nino/La$Nina$events$(e.g.$Philander$1990).$$Whether$the$eastMwest$shift$
of$ the$ convection$ during$ El$ Nino$ is$ associated$ with$ an$ eastMwest$ shift$ in$ the$ zonal$
circulation$cells$can$be$analysed$using$composites$of$the$stream$function$for$El$Nino$and$La$
Nina$events.$As$selection$criteria$for$these$composites$we$use$the$normalised$Nino3.4$index$
(normalised$with$its$standard$deviation)$from$detrended$SST$anomalies.$These$composites$
contain$all$months$with$normalised$Nino3.4$index$>$1$for$El$Nino$and$normalised$Nino3.4$
index$<$M1$for$La$Nina.$$
5"
"
199"
200"
Nino$and$La$Nina$composites.$An$interesting$point$is$that$ENSO$affects$not$only$the$Pacific$
cell,$but$also$has$a$significant$impact$on$the$circulation$cell$over$the$Indian$Ocean.$$
201"
202"
203"
204"
205"
206"
207"
208"
209"
Figures$ 5dMf$ show$ the$ same$ composites$ as$ in$ Fig.$ 5aMc$ but$ for$ all$ CMIP5$ models$
together$ over$ the$ period$ 1950M1979.$ The$ Nino3.4$ index$ is$ again$ used$ as$ the$ selection$
criterion,$normalised$in$each$model$with$its$standard$deviation$of$Nino3.4$index$to$account$
for$the$interMmodelMdifferences$in$variability$strength.$The$western$edge$of$the$Walker$cell$
is$at$133°E$during$La$Nina$years,$$at$141°E$averaged$across$all$years$and$at$165°E$in$El$Nino$
years.$This$corresponds$to$a$32°$difference$between$El$Nino$and$La$Nina$years$and$is$a$very$
similar$eastMwest$shift$as$in$reanalysis$data,$but$all$three$states$located$roughly$10°$further$
west$than$they$are$in$the$reanalysis.$The$amplitude$of$the$ENSO$variability$(Fig.$5f)$over$the$
West$Pacific$is$30%$lower$and$also$10°$further$west$than$in$the$reanalysis$data.$$
210"
211"
212"
213"
214"
215"
216"
217"
It$is$interesting$to$note$that$the$trend$pattern$from$Fig.$2c,d$has$some$similarities$to$
the$ENSO$amplitude$pattern$in$Fig.$5f.$The$pattern$correlation$coefficient$is$0.61$in$CMIP3$
and$0.73$in$CMIP5.$This$suggests$that$large$parts$of$the$trend$under$global$warming$might$
be$linked$to$more$El$NinoMlike$conditions,$as$already$seen$in$the$trend$of$the$box$index$of$
SST$in$Fig.$1.$However,$there$is$no$linear$relation$between$the$eastward$shift$during$El$Nino$
and$the$eastward$shift$under$global$warming$in$the$individual$models,$i.e.$that$the$models$
with$ a$ stronger$ eastward$ shift$ in$ ENSO$ variability$ do$ not$ show$ a$ stronger$ eastward$ shift$
under$global$warming$(not$shown).$$
218"
219"
220"
221"
222"
223"
224"
225"
226"
From$the$similarity$of$the$Walker$cell$response$to$ENSO$and$to$global$warming$the$
question$arises$if$they$have$the$same$mechanism.$Figure$6a$shows$the$vertical$profile$of$the$
ENSO$ pattern$ (El$ Nino$ minus$ La$ Nina$ composite$ as$ in$ Fig.$ 5f)$ in$ the$ CMIP5$ MMEns$ of$
atmospheric$ temperature$ along$ the$ equator.$ The$ strongest$ warming$ appears$ over$ the$
Pacific$ with$ a$ maximum$ at$ the$ surface$ and$ at$ 300hPa.$ According$ to$ the$ two$ mechanisms$
mentioned$ in$ the$ introduction,$ we$ can$ decompose$ this$ pattern$ into$ a$ horizontal$
homogeneous$and$inhomogeneous$part.$Homogeneous$warming,$that$increases$with$height,$
acts$to$weaken$the$tropical$circulations$and$an$inhomogeneous$warming$may$cause$more$
ascending$where$it$is$relatively$warm$and$more$descending$where$it$is$relatively$cold.$$
227"
228"
229"
230"
231"
232"
First$of$all$we$can$note$that$ENSO$is$also$associated$with$a$homogeneous$warming$
that$increases$with$height$(Fig.$6b).$$In$Fig.$6c$we$can$see$that$variability$in$the$zonal$stream$
function$ associated$ with$ ENSO$ (contours)$ fits$ quite$ well$ to$ the$ inhomogeneous$ warming$
(shading).$ $ This$ is$ evident$ because$ additional$ ascending$ occurs$ where$ the$ atmospheric$
warming$is$stronger$and$additional$descending$where$the$atmosphere$warms$less.$In$ENSO$
the$homogeneous$part$is$of$the$same$order$as$the$inhomogeneous$(Fig.$6b,c).$
233"
234"
235"
236"
237"
238"
239"
240"
Under$ global$ warming$ (Fig.$ 6dMf)$ the$ homogeneous$ and$ inhomogeneous$ warming$
have$a$similar$structure$as$in$the$ENSO$composite:$both$show$the$strongest$warming$near$
the$300hPa$level$in$the$homogeneous$warming$and$a$stronger$warming$over$the$East$and$
Central$Pacific$than$over$the$East$Indian$Ocean$and$Maritime$Continent$in$the$levels$below$
200hPa$ and$ vice$ versa$ above.$ But$ under$ global$ warming$ the$ homogeneous$ warming$ is$
roughly$ 10$ times$ larger$ than$ the$ inhomogeneous$ warming.$ Here$ the$ response$ of$ zonal$
stream$ function$ (contours$ in$ Fig.$ 6f)$ only$ roughly$ fits$ to$ the$ inhomogeneous$ warming$
(shading$in$Fig.$6f),$strongest$disagreeing$over$the$Maritime$Continent.$$
6"
"
241"
242"
243"
244"
245"
246"
247"
248"
249"
250"
251"
252"
253"
254"
255"
256"
5. Asymmetry0in0the0response0of0the0Walker0Circulation0during0El0
Nino/La0Nina0
Next$we$want$to$investigate,$if$the$Walker$Circulation$exhibits$a$spatial$asymmetry$
in$ ENSO$ variability$ as$ one$ can$ find$ in$ SST$ (e.g.$ Dommenget$ et$ al.$ 2013).$ We$ repeat$ the$
composite$analysis$described$above,$but$now$with$detrended$anomalies$instead$of$the$full$
field$values$of$the$zonal$stream$function.$Additionally$we$normalised$each$composite$with$
its$ mean$ Nino3.4$ index$ to$ account$ for$ the$ skewness$ of$ SST.$ In$ reanalysis$ data$ we$ get$
abnormal$ ascending$ over$ the$ West$ Indian$ Ocean$ and$ Central$ Pacific$ and$ abnormal$
descending$over$most$of$the$Maritime$Continent$region$(between$60°E$and$160°E)$during$
El$Nino$(Fig.$7a)$and$vice$versa$during$La$Nina$(Fig.$7b,$note$the$reversed$sign),$but$with$the$
anomalies$ shifted$ more$ to$ the$ west$ and$ having$ a$ weaker$ amplitude.$ These$ eastMwest$
asymmetries$in$location$and$strength$are$a$nonMlinearity.$The$amplitude$in$Figure$7c$shows$
the$region$where$the$variability$of$the$Walker$Circulation$linked$to$ENSO$is$nonMlinear,$as$in$
a$ linear$ case$ the$ sum$ of$ El$ Nino$ and$ La$ Nina$ composite$ would$ be$ zero$ due$ to$ the$
normalisation$by$the$mean$Nino3.4$index.$The$zonal$circulation$cells$anomalies$over$most$
of$the$IndoMPacific$region$are$nonMlinear,$with$a$maximum$between$110°E$to$140°W.$$
257"
258"
259"
260"
261"
262"
263"
264"
265"
266"
267"
268"
269"
270"
271"
272"
273"
274"
275"
276"
277"
278"
279"
280"
281"
The$composites$of$the$CMIP5$MMEns$over$the$period$1950M1979$(Fig.$7dMf)$are$very$
similar$to$the$composites$of$reanalysis$data$(Fig.$7aMc).$They$show$that$over$the$West$Pacific$
the$ La$ Nina$ amplitude$ is$ more$ in$ the$ west$ and$ weaker$ than$ the$ El$ Nino$ amplitude.$ The$
ENSO$nonMlinearity$is,$however,$confined$to$a$smaller$region$(110°E$to$140°W;$see$Fig.$7f)$
and$has$weaker$amplitude$than$in$reanalysis$data.$In$order$to$quantify$how$well$the$MMEns$
and$ the$ individual$ climate$ models$ simulate$ the$ spatial$ nonMlinearity$ of$ the$ Walker$
Circulation,$we$define$a$simple$two$box$index:$The$westMeast$difference$between$a$western$
box$(120°EM150°E,$200$hPaM700$hPa)$and$eastern$box$(170°EM160°W,$200$hPaM700$hPa)$in$
the$ difference$ plot$ of$ the$ composites$ as$ shown$ for$ reanalysis$ data$ in$ Fig.$ 7c.$ We$ can$
compare$ this$ with$ a$ measure$ for$ the$ spatial$ nonMlinearity$ of$ ENSO$ in$ SST,$ as$ defined$ in$
Dommenget$ et$ al.$ (2013):$ As$ for$ stream$ function$ we$ calculate$ for$ SST$ the$ eastMwest$
difference$between$an$eastern$box$(80°WM140°W,$5°SM5°N)$and$western$box$(140°EM160°W,$
5°SM5°N)$ of$ the$ sum$ of$ normalised$ El$ Nino$ and$ La$ Nina$ composites.$ Figure$ 8$ shows$ these$
two$ measures$ for$ ERA$ Interim$ reanalysis$ data$ (1979M2012)$ and$ all$ climate$ models$ of$ the$
CMIP3$and$CMIP5$data$base$for$the$period$1900$to$1999.$The$MMEns$of$CMIP3$and$CMIP5$
both$ have$ a$ much$ weaker$ nonMlinearity$ than$ ERA$ Interim,$ but$ CMIP5$ is$ closer$ to$ the$
observed$ than$ CMIP3.$ From$ the$ individual$ models$ we$ can$ see$ two$ interesting$ features:$
First,$ most$ of$ the$ models$ have$ problems$ in$ simulating$ a$ realistic$ nonMlinearity$ (cluster$ of$
models$around$zero).$Second,$from$the$strong$linear$relationship$we$can$see$that$the$skill$to$
simulate$a$strong$nonMlinearity$in$SST$seems$to$be$related$to$the$skill$in$simulating$a$strong$
nonMlinearity$ in$ the$ zonal$ stream$ function.$ We$ cannot$ say$ from$ this$ analysis$ if$ the$ nonM
linearity$of$the$SST$is$caused$by$the$nonMlinearity$of$the$atmosphere$or$vice$versa.$But$in$a$
recent$ study$ of$ Frauen$ and$ Dommenget$ (2010)$ found$ out$ that$ nonMlinear$ atmospheric$
feedbacks$in$ENSO$variability$can$exist$with$a$linear$ocean,$indicating$that$the$atmosphere$
alone$can$cause$a$substantial$ENSO$nonMlinearity.$$
282"
283"
284"
6. Changes0in0the0modes0of0variability0in0response0to0global0warming0
We$now$analyse$the$changes$in$the$modes$of$variability$under$global$warming.$We$
will$base$this$on$Empirical$Orthogonal$Function$(EOF)$analysis,$which$is$a$common$way$to$
7"
"
285"
286"
287"
288"
289"
determine$ the$ modes$ of$ variability.$ We$ will$ focus$ on$ two$ questions:$ Do$ the$ EOF–patterns$
change$ and$ thus$ indicate$ changes$ in$ the$ spatial$ patterns$ of$ variability?$ Second,$ do$ the$
principal$ component$ (PC)$ time$ series$ of$ the$ leading$ modes$ have$ a$ longMterm$ trend$ under$
global$warming?$If$yes$this$would$indicate$that$the$trendMpattern$may$be$related$to$leading$
modes$of$internal$variability.$
290"
291"
292"
293"
294"
295"
296"
297"
298"
299"
For$the$first$question$we$have$a$closer$look$at$the$EOF$patterns$in$the$CMIP5$MMEns$
in$ the$ two$ time$ periods$ 1950M1979$ (20C)$ and$ 2070M2099$ (21C).$ The$ EOFM1$ patterns$
(Fig.$9a,b)$over$these$periods$are$very$similar$to$the$composite$of$El$Nino$and$La$Nina$(Fig.$
7d,e).$They$are$also$similar$to$the$combined$EOFM1$of$zonal$stream$function$and$SST,$where$
the$SST$pattern$is$the$typical$ENSO$pattern$(e.g.$Kang$and$Kug$2002,$not$shown).$Thus$the$
EOFM1$is$associated$with$ENSO$variability$in$zonal$stream$function$and$describes$an$eastM
west$shift$of$the$edge$between$the$Indian$and$Pacific$cell.$The$western$Pacific$pole$of$EOFM1$
is$further$east$in$21C$and$this$pole$becomes$a$bit$weaker$than$during$20C.$EOFM2$describes$
a$strengthening$or$weakening$of$the$eastern$part$of$Indian$cell$and$the$western$part$of$the$
Pacific$cell$and$also$shifts$a$little$bit$to$the$east$in$21C.$
300"
301"
302"
303"
304"
305"
306"
307"
308"
309"
310"
311"
312"
For$ a$ more$ detailed$ analysis$ of$ the$ spatial$ changes$ we$ can$ use$ Distinct$ Empirical$
Orthogonal$Function$(DEOF)$analysis$as$described$by$Bayr$and$Dommenget$(2013b).$This$
method$ compares$ all$ the$ leading$ modes$ of$ variability$ in$ two$ data$ sets$ on$ the$ basis$ of$ the$
multiMvariate$ EOF$ patterns$ and$ finds$ the$ patterns$ of$ the$ largest$ changes$ in$ variability.$ In$
DEOF$ analysis$ the$ two$ EOF$ sets$ from$ 20C$ and$ 21C$ are$ compared$ against$ each$ other$ via$
projecting$ one$ set$ of$ EOF$ patterns$ onto$ the$ other$ to$ find$ the$ pattern$ that$ has$ the$ largest$
difference$in$explained$variance$in$these$two$sets$of$EOF$pattern$(see$Bayr$and$Dommenget$
(2013b)$for$further$details).$The$projected$explained$variances$(Fig.$10a,b)$show$both$that$
the$ variability$ becomes$ more$ large$ scale$ under$ global$ warming$ as$ the$ leading$ modes$ of$
variability$ have$ a$ lower$ explained$ variance$ in$ 20C$ than$ in$ 21C.$ This$ means$ that$ fewer$
modes$are$needed$in$21C$to$explain$the$largest$part$of$the$variance.$The$spatial$degrees$of$
freedom$from$Bretherton$et$al.$(1999)$decrease$from$10.2$in$20C$to$9.5$in$20C.$Additionally,$
EOFM1$has$the$largest$difference$in$terms$of$explained$variance$in$the$two$data$sets.$$
313"
314"
315"
316"
317"
318"
319"
320"
321"
322"
323"
324"
325"
The$projection$of$the$EOFs$of$20C$onto$the$EOFs$of$21C$(DEOFM1!"!→!"! )$maximizes$
the$ explained$ variance$ differences$ between$ 20C$ and$ 21C.$ It$ is$ the$ pattern$ that$ loses$ the$
largest$ amount$ of$ variance$ in$ 21C$ relative$ to$ 20C.$ The$ DEOFM1!"!→!"! $ (Fig.$ 10c)$ mainly$
shows$that$the$variance$in$the$Indian$Ocean$cell$is$reduced$by$14%$in$21C$relative$to$its$20C$
value$(a$change$in$explained$variance$from$11.1%$to$9.5%).$The$DEOFM1!"!→!"! $maximizes$
the$ explained$ variance$ differences$ between$ 21C$ and$ 20C.$ It$ is$ the$ pattern$ that$ gains$ the$
largest$ amount$ of$ variance$ in$ 21C$ relative$ to$ 20C.$ The$ DEOFM1!"!→!"! $ (Fig.$ 10d)$ mainly$
shows$that$the$variance$in$the$central$Pacific$pole$has$increased$by$21%$in$21C$relative$to$
its$ 20C$ value$ (a$ change$ in$ explained$ variance$ from$ 14.0%$ to$ 17.0%).$ Combined$ the$ two$
leading$DEOFMmodes$indicate$a$shift$in$the$variability$from$the$Indian$Ocean$into$the$central$
Pacific$ in$ EOFM1.$ DEOFM1!"!→!"! $ is$ also$ of$ smaller$ spatial$ scale$ (e.g.$ distance$ between$ the$
main$ poles)$ than$ DEOFM1!"!→!"! .$ This$ again$ suggests$ that$ the$ variability$ in$ 21C$ tends$
towards$larger$scales.$
326"
327"
This$shift$from$the$Indian$into$the$Pacific$Ocean$is$consistent$with$the$spatial$nonM
linearity$discussed$in$Section$5.$The$El$Nino$composite$pattern$in$zonal$stream$function$is$
8"
"
328"
329"
further$ east$ than$ the$ La$ Nina$ composite$ pattern,$ thus$ an$ eastward$ shift$ of$ the$ dominant$
mode$of$variability$can$be$linked$to$a$shift$towards$more$El$NinoMlike$conditions.$$
330"
331"
332"
333"
334"
335"
336"
337"
338"
339"
340"
Next$we$have$a$look$at$the$longMterm$trend$in$the$PC$time$series.$We$therefore$use$
the$ EOFM1$ pattern$ of$ 20C$ and$ calculate$ the$ PC$ timeseries$ for$ this$ pattern$ over$ the$ period$
from$1950$to$2099.$The$similarity$of$the$trend$pattern$in$Fig.$2d$with$EOFM1$from$Fig.$9a,b$is$
already$ a$ strong$ hint$ that$ the$ zonal$ circulation$ shifts$ in$ its$ dominant$ mode$ of$ variability$
towards$more$El$NinoMlike$conditions.$Indeed$a$positive$trend$in$PCM1$(El$NinoMlike)$can$be$
seen$ in$ the$ average$ over$ all$ CMIP5$ models$ (red$ line$ in$ Fig.$ 11).$ But$ the$ decadal$ (natural)$
variability$ of$ the$ individual$ models$ is$ still$ much$ larger$ than$ the$ trend$ in$ the$ MMEns,$
indicating$that$detection$of$a$Walker$Circulation$trend$due$to$increased$greenhouse$gases$
will$be$very$difficult$in$the$next$decades,$if$we$are$not$able$to$separate$the$climate$change$
signal$ from$ internal$ variability.$ No$ other$ PC$ time$ series$ exhibit$ a$ strong$ trend$ in$ the$
MMEns.$$
341"
342"
343"
344"
345"
346"
347"
348"
349"
350"
351"
Finally$we$want$to$find$out$how$much$of$the$global$warming$trend$from$Fig.$2c,d$is$
related$to$the$trend$in$the$dominant$mode$of$variability.$In$each$individual$model$we$can$
remove$the$variability$and$trend$associated$with$the$EOFM1$pattern.$After$removing$EOFM1$
in$each$model$individually$we$can$calculate$a$new$MMEns$and$the$residual$trend$of$this$new$
MMEns$(Fig.$12).$Much$of$the$trend$has$vanished$over$the$IndoMPacific$region$and$the$trend$
in$PCM1$can$explain$52%$of$the$trend$in$CMIP5$over$the$entire$tropics$or$69%$of$the$Walker$
Circulation$ changes$ (49%$ and$ 67%$ in$ CMIP3,$ respectively).$ The$ residual$ trend$ pattern$
shows$a$reduction$of$convection$over$Africa$and$South$America,$consistent$with$the$general$
weakening$ as$ found$ by$ Vecchi$ and$ Soden$ (2007),$ less$ descending$ over$ the$ cold$ tongue$
region,$consistent$with$the$strong$warming$there,$and$an$upward$expansion$the$Indian$and$
Pacific$cell.$$
352"
353"
354"
355"
356"
357"
358"
7. Recent0trends0in0ERA0Interim0reanalysis0data0
359"
360"
361"
362"
363"
364"
365"
366"
367"
368"
369"
370"
The$ trend$ pattern$ over$ the$ Pacific$ for$ the$ period$ 1979$ until$ 2012$ is$ mostly$ the$
opposite$ of$ the$ CMIP$ trend$ pattern$ (compare$ Fig.$ 13a$ with$ Fig.$ 2c,d),$ thus$ shows$ a$
westward$shift$of$the$western$edge$and$a$strengthening$of$the$Walker$Circulation$(see$also$
Fig.$13c).$The$trend$is$roughly$10$times$larger$than$in$the$CMIP$MMEns$and$the$pattern$has$
again$a$high$correlation$with$the$dominant$mode$of$variability$(M0.70),$thus$indicating$that$
the$Walker$Circulation$shifted$towards$more$La$NinaMlike$conditions$in$the$recent$decades.$
As$ in$ the$ CMIP$ models,$ the$ trend$ of$ EOFM1$ can$ explain$ 49%$ of$ the$ trend$ over$ the$ entire$
tropics$and$even$75%$over$the$Pacific$(Fig.$13b).$The$residual$trend$shows$a$strong$increase$
of$convection$over$South$America$in$the$last$decades.$From$the$time$series$of$EOFM1$of$zonal$
stream$function$in$Fig.$13d$we$can$see$that$there$was$a$strong$interMdecadal$fluctuation$of$
ENSO$in$the$last$decades,$with$more$and$stronger$El$Nino’s$in$the$time$period$1979$till$1998$
and$more$and$stronger$La$Nina’s$in$the$time$period$1999$till$2012,$as$also$stated$by$Kosaka$
Next$ we$ have$ a$ look$ on$ the$ observed$ zonal$ circulation$ trends$ in$ the$ last$ three$
decades.$ We$ have$ to$ keep$ in$ mind$ that$ in$ comparison$ to$ simulated$ trends$ the$ observed$
trend$ has$ a$ lower$ signal$ to$ noise$ ratio$ due$ to$ the$ shorter$ time$ period$ and$ a$ stronger$
influence$ of$ natural$ variability$ as$ it$ is$ only$ one$ realization,$ whereas$ the$ CMIP$ MMEns$
includes$many$realizations.$Thus$the$observed$trends$are$much$more$uncertain$and$contain$
a$larger$fraction$of$natural$variability$than$the$CMIP$MMEns.$$
9"
"
371"
372"
373"
and$Xie$(2013).$Thus,$although$the$sign$of$the$trends$in$reanalysis$data$is$opposite$to$that$of$
the$simulated$global$warming$trend$in$the$CMIP$models,$the$trend$of$the$dominant$mode$of$
variability$again$plays$a$crucial$role$for$the$trend$in$the$Walker$Circulation.$$$
374"
375"
376"
377"
378"
379"
380"
8. Relation0of0Stream0function0and0SLP0
381"
382"
383"
384"
385"
386"
387"
388"
389"
390"
391"
392"
393"
394"
395"
In$ the$ mean$ state$ (Fig.$ 14a)$ we$ see$ good$ agreement$ between$ all$ four$ variables:$
Convection$ takes$ place$ were$ the$ temperatures$ are$ high$ (the$ three$ ‘heat$ sources’$ Africa,$
Maritime$Continent$and$South$America),$SLP$is$low$and$the$stream$function$gradients$are$
large.$$However,$this$general$agreement$is$not$seen$in$the$changes$21CM20C$(Fig.14b).$The$
change$ in$ vertical$ wind$ again$ agrees$ with$ the$ zonal$ gradient$ of$ the$ zonal$ stream$ function$
(correlation$0.74)$and$the$Ttropos$and$SLP$response$are$very$similar$(correlation$M0.94),$as$
already$ found$ in$ Bayr$ and$ Dommenget$ (2013a).$ But$ over$ most$ regions$ the$ changes$ in$
stream$ function$ and$ vertical$ wind$ do$ not$ agree$ with$ the$ changes$ in$ SLP$ and$ Ttropos,$
especially$over$Africa$and$South$America.$Here$the$landMsea$warming$contrast$reduces$the$
SLP$ according$ to$ Bayr$ and$ Dommenget$ (2013a),$ which$ would$ suggest$ an$ increase$ in$
convection.$In$contrast,$the$vertical$wind$and$the$stream$function$show$more$descending.$
There$is$no$explanation$for$this$discrepancy$yet,$but$it$indicates$that$changes$in$SLP$cannot$
reveal$ the$ full$ picture$ of$ changes$ over$ the$ entire$ troposphere,$ like$ convection$ and$
associated$precipitation$patterns.$Further$investigation$is$needed$to$better$understand$the$
causes$of$these$discrepancies.$
396"
397"
398"
399"
400"
401"
402"
403"
404"
405"
406"
407"
408"
409"
410"
9. Summary0and0discussion0
411"
412"
In$ the$ MMEns$ we$ $ see$ that$ the$ trend$ pattern$ has$ some$ similarities$ with$ ENSO$
associated$ variability$ of$ the$ zonal$ stream$ function.$ Indeed$ a$ large$ part$ of$ the$ global$
An$open$question$is$the$relation$of$our$results$based$on$zonal$stream$function$to$the$
results$of$previous$studies$using$SLP.$Figure$14$shows$the$meridional$average$(5°SM5°N)$of$
SLP$ and$ vertical$ wind$ at$ the$ 500$ hPa$ level,$ the$ vertical$ and$ meridional$ mean$ of$
tropospheric$ temperature$ (Ttropos)$ and$ the$ zonal$ gradient$ of$ vertical$ and$ meridional$
averaged$zonal$stream$function$in$the$CMIP5$MMEns.$For$a$better$comparison$we$removed$
the$area$means$for$SLP$and$Ttropos$and$all$variables$are$normalised.$$$
The$ main$ purpose$ of$ this$ study$ is$ to$ analyze$ the$ response$ of$ the$ zonal$ circulation$
cells$(with$a$special$focus$on$the$Walker$Circulation)$to$global$warming$and$its$relation$to$
ENSO$using$the$last$two$generations$of$climate$models.$The$focus$is$on$the$eastward$shift$of$
the$ Walker$ Circulation$ and$ the$ changes$ in$ the$ modes$ of$ variability.$ We$ choose$ the$ zonal$
stream$function$for$this$analysis,$as$it$is$a$direct$representation$of$the$zonal$circulation$and$
also$available$over$all$levels$of$the$troposphere.$We$find$that$the$trend$patterns$of$the$zonal$
circulation$ under$ global$ warming$ (Fig.$ 2$ cMd)$ are$ very$ similar$ in$ the$ two$ CMIP$ MMEns,$
despite$ the$ differences$ in$ models,$ resolution,$ ensemble$ size$ and$ emission$ scenario.$ This$
underlines$the$robustness$of$the$signal.$The$trend$pattern$shows$more$ascending$air$over$
the$ West$ Indian$ Ocean,$ Central$ and$ East$ Pacific,$ and$ more$ descending$ air$ over$ the$ three$
main$ convection$ regions$ Africa,$ the$ Maritime$ Continent$ and$ South$ America,$ thus$ a$
weakening$of$the$zonal$circulations.$Additionally$we$show$that$the$CMIP$MMEns$predict$a$
substantial$eastward$shift$of$the$western$part$of$the$Walker$cell,$by$6°$in$CMIP5$MMEns$and$
8°$in$the$CMIP3$MMEns.$$
10"
"
413"
414"
415"
416"
417"
418"
419"
420"
421"
422"
423"
424"
warming$ response$ corresponds$ to$ a$ shift$ towards$ more$ El$ NinoMlike$ conditions.$ The$ El$
NinoMlike$trend$in$zonal$stream$function$will$cause$that$neutral$ENSO$conditions$at$the$end$
of$the$21st$century$resemble$El$Nino$conditions,$if$referred$to$the$20th$century$climate.$How$
El$ NinoMlike$ the$ global$ warming$ trend$ is$ in$ comparison$ with$ an$ average$ El$ Nino$ can$ be$
calculated:$ An$ average$ El$ Nino$ in$ the$ CMIP5$ MMEns$ is$ associated$ with$ an$ amplitude$
of$ M3.6*10M10$ kg$ sM1$ in$ the$ box$ (120°EM180°,$ 700M300hPa)$ as$ defined$ for$ Fig.$ 4$ and$ an$
eastward$shift$of$25°$longitude.$Thus$a$global$warming$trend$of$the$same$size$would$mean$a$
100%$ shift$ towards$ an$ average$ El$ Nino,$ with$ 20th$ century$ as$ reference$ climate.$ The$
eastward$shift$of$6°$and$the$trend$of$M1.1*1010$kg$sM1$(100$yrM1)$in$the$CMIP5$MMEns$in$this$
box$ (Fig.$ 4)$ would$ thus$ mean$ a$ longMterm$ shift$ of$ 30%$ in$ amplitude$ and$ 26%$ in$ location$
towards$ an$ average$ El$ Nino$ event$ over$ the$ next$ century$ (31%$ and$ 37%$ in$ CMIP3,$
respectively).$$
425"
426"
427"
428"
429"
430"
431"
Further$ we$ could$ show$ that$ the$ internal$ variability$ of$ the$ zonal$ stream$ function$
exhibits$ a$ substantial$ spatial$ nonMlinearity,$ as$ the$ El$ Nino$ anomaly$ pattern$ of$ the$ zonal$
stream$ function$ is$ more$ in$ the$ east$ than$ the$ La$ Nina$ anomaly$ pattern.$ The$ spatial$ nonM
linearity$in$the$zonal$stream$function$is$linear$related$to$the$nonMlinearity$of$ENSO$in$SST$in$
the$individual$models.$However,$most$models$have$problems$in$simulating$a$realistic$ENSO$
nonMlinearity$ in$ both$ variables,$ subsequently$ the$ nonMlinearity$ of$ the$ CMIP$ MMEns$ is$ less$
than$half$as$strong$as$in$the$ERA$Interim$reanalysis$data.$$
432"
433"
434"
435"
436"
437"
438"
439"
440"
441"
442"
The$ similarity$ of$ the$ eastward$ shift$ in$ the$ zonal$ stream$ function$ during$ global$
warming$ and$ strong$ El$ Nino$ events$ may$ indicate$ a$ common$ forcing$ mechanism$ for$ these$
shifts.$Several$studies$have$shown$that$the$ENSO$nonMlinearity$is$caused$by$the$atmospheric$
response$to$SST$anomalies$(Kang$and$Kug$2002;$Philip$and$van$Oldenborgh$2009;$Frauen$
and$ Dommenget$ 2010),$ in$ particular$ the$ eastward$ shift$ of$ strong$ El$ Nino$ events$
(Dommenget$ et$ al.$ 2013).$ Thus$ the$ atmosphere$ responds$ with$ an$ eastward$ shift$ to$ SST$
warming.$ Under$ global$ warming$ the$ enhanced$ hydrological$ cycle$ to$ first$ order$ leads$ to$ a$
horizontally$ homogenous$ but$ vertically$ enhanced$ warming.$ $ This$ warming$ trend$ is$ also$
associated$ with$ an$ eastward$ shift,$ indicating$ that$ horizontally$ homogenous$ and$ vertically$
enhanced$ warming$ patterns,$ as$ in$ both$ global$ warming$ trend$ and$ during$ El$ Nino,$ may$
induce$an$eastward$shift$of$the$zonal$circulation$cell$over$the$Pacific.$
443"
444"
445"
446"
447"
448"
$The$ prominent$ changes$ in$ the$ modes$ of$ variability$ under$ global$ warming$ are$ an$
eastward$ shift$ from$ the$ Indian$ Ocean$ to$ the$ central$ Pacific$ of$ EOFM1$ and$ a$ shift$ towards$
larger$ scale$ variability.$ EOFM1$ is$ associated$ with$ ENSO$ variability$ and$ has$ a$ positive$ (El$
NinoMlike)$ trend$ under$ global$ warming.$ After$ removing$ the$ trend$ associated$ with$ EOFM1,$
two$ third$ of$ the$ trends$ vanishes$ over$ the$ Pacific,$ i.e.$ are$ related$ to$ more$ El$ NinoMlike$
conditions.$$
449"
450"
451"
452"
453"
454"
455"
456"
The$ spread$ in$ the$ response$ of$ the$ individual$ models$ is$ quite$ large.$ Most$ of$ the$
individual$ climate$ models$ predict$ a$ weakening$ and$ an$ eastward$ shift$ of$ the$ Walker$ cell$
under$global$warming,$but$some$models$show$no$significant$trends$and$some$even$predict$
a$strengthening$and$westward$shift.$This$indicates$that$the$homogeneous$warming,$which$
can$only$weaken$the$Walker$cell$in$a$warmer$climate,$can’t$be$the$dominant$mechanism$in$
all$climate$models.$The$inhomogeneous$warming$must$be$the$dominant$mechanism$in$the$
models$ with$ a$ strengthening$ Walker$ cell,$ as$ this$ mechanism$ can$ act$ in$ general$ to$ both$
directions,$$either$weakening$or$strengthening$the$Walker$Circulation.$$
11"
"
457"
458"
459"
460"
461"
462"
463"
464"
465"
466"
467"
468"
469"
470"
471"
472"
473"
474"
475"
476"
In$ERA$Interim$reanalysis$data$we$found$a$strengthening$of$the$Walker$Circulation$
and$westward$shift$over$the$last$three$decades.$In$recent$literature$there$is$a$debate$about$
the$ changes$ of$ the$ Walker$ Circulation$ over$ the$ last$ decades:$ Analysing$ observations$ and$
model$runs$forced$with$observed$SST$and/or$greenhouse$gas$concentrations$the$studies$of$
Sohn$ and$ Park$ (2010),$ Meng$ et$ al.$ (2011),$ Luo$ et$ al.$ (2012)$ and$ L’Heureux$ et$ al.$ (2013)$
found$ a$ strengthening$ of$ the$ Walker$ Circulation.$ These$ studies$ explain$ the$ strengthening$
with$a$more$La$NinaMlike$SST$warming$or$a$stronger$warming$over$the$Indian$Ocean$than$
over$the$Pacific$over$the$last$decades.$ But$several$other$studies$found$a$weakening$of$the$
Walker$ Circulation$ (Vecchi$ et$ al.$ 2006;$ Power$ and$ Kociuba$ 2010;$ Yu$ and$ Zwiers$ 2010;$
Tokinaga$et$al.$2012a,b;$DiNezio$et$al.$2013),$caused$by$the$pure$atmospheric$mechanism$
mentioned$in$the$introduction.$A$recent$study$form$Solomon$and$Newman$(2012)$found$out$
that$ there$ are$ large$ discrepancies$ in$ the$ SST$ trends$ over$ the$ IndoMPacific$ in$ the$ different$
observed$ data$ sets,$ which$ are$ caused$ by$ different$ representations$ of$ El$ Nino$ in$ these$
observed$ datasets.$ A$ second$ problem$ is$ the$ distinction$ between$ externally$ forced$ trends$
and$ internal$ variability$ in$ relative$ short$ records,$ so$ that$ Power$ and$ Kociuba$ (2011)$
conclude,$ that$ external$ forcing$ accounts$ for$ 30M70%$ of$ the$ observed$ Walker$ Circulation$
changes$over$the$20th$century,$with$internal$variability$making$up$the$rest.$To$sum$up:$due$
to$relative$short$records$it$is$difficult$to$say$what$part$of$the$trend$in$ERA$Interim$reanalysis$
data$ is$ caused$ by$ global$ warming,$ by$ natural$ variability$ or$ even$ is$ just$ a$ measure$
uncertainty.$
477"
478"
479"
480"
481"
482"
483"
484"
485"
486"
487"
488"
489"
490"
491"
With$the$opposite$direction$between$the$predicted$trend$in$the$CMIP$MMEns$and$the$
trends$ of$ the$ recent$ decades$ in$ ERA$ Interim,$ there$ are$ two$ conclusions$ possible:$ One$
conclusion$could$be$that$the$trend$in$ERA$Interim$is$due$to$increased$greenhouse$gases$and$
the$CMIP$MMEns$predict$the$wrong$sign$of$ENSO$response.$The$other$conclusion$is$that$the$
trends$in$ERA$Interim$are$just$natural$decadal$variations$of$ENSO$variability$and$that$under$
global$warming$the$Walker$Circulation$will$shift$eastward$and$weaken,$as$the$CMIP$models$
predict.$We$think$this$is$quite$likely,$as$both$CMIP$MMEns$predict$it$and$the$dominant$mode$
of$ variability$ exhibits$ strong$ decadal$ trends$ in$ Fig.$ 11.$ Nevertheless,$ both$ possible$
conclusions$ have$ one$ important$ thing$ in$ common:$ a$ large$ part$ of$ the$ Walker$ Circulation$
trend$ follows$ a$ preMexisting$ mode$ of$ variability,$ thus$ can$ be$ described$ to$ some$ extend$ as$
more$El$NinoMlike$or$more$La$NinaMlike.$We$have$to$keep$in$mind$that$the$ENSO$response$of$
the$climate$models$under$global$warming$is$still$quite$uncertain$(e.g.$Latif$and$Keenlyside$
2009),$ $ but$ the$ MMEns$ of$ climate$ models$ calculated$ for$ the$ IPCC$ AR5$ predict$ an$ more$ El$
NinoMlike$ response$ and$ therefore$ an$ eastward$ shift$ and$ weakening$ of$ the$ Walker$
Circulation$in$future$climate.$
0
492"
493"
Acknowledgements0
494"
495"
496"
497"
498"
499"
We$acknowledge$the World Climate Research Programme's Working Group on Coupled
Modeling,$ the$ individual$ modeling$ groups$ of$ the$ Climate$ Model$ Intercomparison$ Project$
(CMIP3$and$CMIP5)$and$ECMWF$for$providing$the$data$sets.$This$work$was$supported$by$
the$Deutsche$Forschungsgemeinschaft$(DFG)$through$project$DO1038/5M1,$the$ARC$Centre$
of$Excellence$in$Climate$System$Science$(CE110001028), the RACE Project of BMBF and the
NACLIM Project of the European Union. We thank Hanh$ Nguyen$ for$ providing$ the$ code$ to$
12"
"
500"
501"
502"
calculate$the$zonal$stream$function$and$Hardi$Bordbar$and$Sabine$Haase$for$discussion$and$
useful$comments.$$
13"
"
503"
References0
504"
505"
506"
Bayr,$T.,$and$D.$Dommenget,$2013a:$The$Tropospheric$Land–Sea$Warming$Contrast$as$the$
Driver$of$Tropical$Sea$Level$Pressure$Changes.$J.)Clim.,$26,$1387–1402,$
doi:10.1175/JCLIMDM11M00731.1.$
507"
508"
509"
Bayr,$T.,$and$D.$Dommenget,$2013b:$Comparing$the$spatial$structure$of$variability$in$two$
datasets$against$each$other$on$the$basis$of$EOFMmodes.$Clim.)Dyn.,$
doi:10.1007/s00382M013M1708Mx.$
510"
511"
Bengtsson,$L.,$and$K.$I.$Hodges,$2009:$On$the$evaluation$of$temperature$trends$in$the$
tropical$troposphere.$Clim.)Dyn.,$36,$419–430,$doi:10.1007/s00382M009M0680My.$
512"
513"
514"
Bretherton,$C.$S.,$M.$Widmann,$V.$P.$Dymnikov,$J.$M.$Wallace,$and$I.$Bladé,$1999:$The$
effective$number$of$spatial$degrees$of$freedom$of$a$timeMvarying$field.$J.)Clim.,$12,$
1990–2009.$
515"
516"
Clement,$A.$C.,$R.$Seager,$M.$A.$Cane,$and$S.$E.$Zebiak,$1996:$An$ocean$dynamical$thermostat.$
J.)Clim.,$9,$2190–2196.$
517"
518"
519"
DiNezio,$P.$N.,$A.$C.$Clement,$G.$A.$Vecchi,$B.$J.$Soden,$B.$P.$Kirtman,$and$S.MK.$Lee,$2009:$
Climate$Response$of$the$Equatorial$Pacific$to$Global$Warming.$J.)Clim.,$22,$4873–4892,$
doi:10.1175/2009JCLI2982.1.$
520"
521"
522"
523"
DiNezio,$P.$N.,$A.$Clement,$G.$a.$Vecchi,$B.$Soden,$a.$J.$Broccoli,$B.$L.$OttoMBliesner,$and$P.$
Braconnot,$2011:$The$response$of$the$Walker$circulation$to$Last$Glacial$Maximum$
forcing:$Implications$for$detection$in$proxies.$Paleoceanography,$26,$n/a–n/a,$
doi:10.1029/2010PA002083.$
524"
525"
526"
DiNezio,$P.$N.,$G.$a.$Vecchi,$and$A.$C.$Clement,$2013:$Detectability$of$Changes$in$the$Walker$
Circulation$in$Response$to$Global$Warming.$J.)Clim.,$130114154537002,$
doi:10.1175/JCLIMDM12M00531.1.$
527"
528"
529"
Dommenget,$D.,$T.$Bayr,$and$C.$Frauen,$2013:$Analysis$of$the$nonMlinearity$in$the$pattern$
and$time$evolution$of$El$Niño$southern$oscillation.$Clim.)Dyn.,$40,$2825–2847,$
doi:10.1007/s00382M012M1475M0.$
530"
531"
Frauen,$C.,$and$D.$Dommenget,$2010:$El$Niño$and$La$Niña$amplitude$asymmetry$caused$by$
atmospheric$feedbacks.$Geophys.)Res.)Lett.,$37,$L18801,$doi:10.1029/2010GL044444.$
532"
533"
Hastenrath,$S.,$1985:$Climate)and)Circulation)of)the)Tropics.$D.$Reisel$Publishing$Company,$
Dordrecht,$Netherlands,.$
534"
535"
Held,$I.$M.,$and$B.$J.$Soden,$2006:$Robust$responses$of$the$hydrological$cycle$to$global$
warming.$J.)Clim.,$19,$5686–5699,$doi:10.1175/JCLI3990.1.$
14"
"
536"
537"
538"
Hoerling,$M.$P.,$A.$Kumar,$and$M.$Zhong,$1997:$El$Niño,$La$Niña,$and$the$Nonlinearity$of$
Their$Teleconnections.$J.)Clim.,$10,$1769–1786,$doi:10.1175/1520M
0442(1997)010<1769:ENOLNA>2.0.CO;2.$
539"
540"
541"
Kang,$I.MS.,$and$J.MS.$Kug,$2002:$El$Niño$and$La$Niña$sea$surface$temperature$anomalies:$
Asymmetry$characteristics$associated$with$their$wind$stress$anomalies.$J.)Geophys.)Res.,$
107,$4372,$doi:10.1029/2001JD000393.$
542"
543"
544"
Knutson,$T.$R.,$and$S.$Manabe,$1995:$TimeMMean$Response$over$the$Tropical$Pacific$to$
Increased$C0$2$in$a$Coupled$OceanMAtmosphere$Model.$J.)Clim.,$8,$2181–2199,$
doi:10.1175/1520M0442(1995)008<2181:TMROTT>2.0.CO;2.$
545"
546"
Kosaka,$Y.,$and$S.MP.$Xie,$2013:$Recent$globalMwarming$hiatus$tied$to$equatorial$Pacific$
surface$cooling.$Nature,$doi:10.1038/nature12534.$
547"
548"
549"
L’Heureux,$M.$L.,$S.$Lee,$and$B.$Lyon,$2013:$Recent$multidecadal$strengthening$of$the$Walker$
circulation$across$the$tropical$Pacific.$Nat.)Clim.)Chang.,$3,$1–6,$
doi:10.1038/nclimate1840.$
550"
551"
Latif,$M.,$and$N.$S.$Keenlyside,$2009:$El$Niño/Southern$Oscillation$response$to$global$
warming.$Proc.)Natl.)Acad.)Sci.,$106,$20578–20583.$
552"
553"
Luo,$J.MJ.,$W.$Sasaki,$and$Y.$Masumoto,$2012:$Indian$Ocean$warming$modulates$Pacific$
climate$change.$Proc.)Natl.)Acad.)Sci.,$doi:10.1073/pnas.1210239109.$
554"
555"
Meehl,$G.,$and$W.$Washington,$1996:$El$NiñoMlike$climate$change$in$a$model$with$increased$
atmospheric$CO$2$concentrations.$Nature,$382,$56–60.$
556"
557"
558"
Meehl,$G.$A.,$C.$Covey,$T.$Delworth,$M.$Latif,$B.$McAvaney,$J.$F.$B.$Mitchell,$R.$J.$Stouffer,$and$
K.$E.$Taylor,$2007:$THE$WCRP$CMIP3$Multimodel$Dataset:$A$New$Era$in$Climate$
Change$Research.$Bull.)Am.)Meteorol.)Soc.,$88,$1383,$doi:10.1175/BAMSM88M9M1383.$
559"
560"
561"
Meng,$Q.,$M.$Latif,$W.$Park,$N.$S.$Keenlyside,$V.$A.$Semenov,$and$T.$Martin,$2011:$Twentieth$
century$Walker$Circulation$change:$data$analysis$and$model$experiments.$Clim.)Dyn.,$1–
17,$doi:10.1007/s00382M011M1047M8.$
562"
563"
North,$G.$R.,$T.$L.$Bell,$and$R.$F.$Cahalan,$1982:$Sampling$Errors$in$the$Estimation$of$
Empirical$Orthogonal$Functions.$Mon.)Weather)Rev.,$110,$699–606.$
564"
565"
Philander,$S.,$1990:$El)Niño,)La)Niña,)and)the)southern)oscillation.$Academic$Press,$San$Diego,$
USA,.$
566"
567"
Philip,$S.,$and$G.$J.$van$Oldenborgh,$2009:$Significant$Atmospheric$Nonlinearities$in$the$
ENSO$Cycle.$J.)Clim.,$22,$4014–4028,$doi:10.1175/2009JCLI2716.1.$
568"
569"
Power,$S.,$T.$Casey,$C.$Folland,$A.$Colman,$and$V.$Mehta,$1999:$InterMdecadal$modulation$of$
the$impact$of$ENSO$on$Australia.$15,$319–324.$
15"
"
570"
571"
Power,$S.$B.,$and$G.$Kociuba,$2010:$The$impact$of$global$warming$on$the$Southern$
Oscillation$Index.$Clim.)Dyn.,$37,$1745–1754,$doi:10.1007/s00382M010M0951M7.$
572"
573"
Power,$S.$B.,$and$G.$Kociuba,$2011:$What$caused$the$observed$20$th$century$weakening$of$
the$Walker$circulation?$J.)Clim.,$110629145325000,$doi:10.1175/2011JCLI4101.1.$
574"
575"
576"
Rodgers,$K.$B.,$P.$Friederichs,$and$M.$Latif,$2004:$Tropical$Pacific$Decadal$Variability$and$Its$
Relation$to$Decadal$Modulations$of$ENSO.$J.)Clim.,$17,$3761–3774,$doi:10.1175/1520M
0442(2004)017<3761:TPDVAI>2.0.CO;2.$
577"
578"
Simmons,$A.,$S.$Uppala,$D.$Dee,$and$S.$Kobayashi,$2007:$ERAMInterim:$New$ECMWF$
reanalysis$products$from$1989$onwards.$ECMWF)Newsl.,$110,$25–35.$
579"
580"
581"
Sohn,$B.$J.,$and$S.MC.$Park,$2010:$Strengthened$tropical$circulations$in$past$three$decades$
inferred$from$water$vapor$transport.$J.)Geophys.)Res.,$115,$D15112,$
doi:10.1029/2009JD013713.$
582"
583"
584"
Solomon,$A.,$and$M.$Newman,$2012:$Reconciling$disparate$twentiethMcentury$IndoMPacific$
ocean$temperature$trends$in$the$instrumental$record.$Nat.)Clim.)Chang.,$2,$691–699,$
doi:10.1038/nclimate1591.$
585"
586"
Taylor,$K.$E.,$R.$J.$Stouffer,$and$G.$a.$Meehl,$2012:$An$Overview$of$CMIP5$and$the$Experiment$
Design.$Bull.)Am.)Meteorol.)Soc.,$93,$485–498,$doi:10.1175/BAMSMDM11M00094.1.$
587"
588"
589"
Tokinaga,$H.,$S.MP.$Xie,$C.$Deser,$Y.$Kosaka,$and$Y.$M.$Okumura,$2012a:$Slowdown$of$the$
Walker$circulation$driven$by$tropical$IndoMPacific$warming.$Nature,$491,$439–443,$
doi:10.1038/nature11576.$
590"
591"
592"
593"
Tokinaga,$H.,$S.MP.$Xie,$A.$Timmermann,$S.$McGregor,$T.$Ogata,$H.$Kubota,$and$Y.$M.$
Okumura,$2012b:$Regional$Patterns$of$Tropical$IndoMPacific$Climate$Change:$Evidence$
of$the$Walker$Circulation$Weakening*.$J.)Clim.,$25,$1689–1710,$doi:10.1175/JCLIMDM11M
00263.1.$
594"
595"
Vecchi,$G.$A.,$and$B.$J.$Soden,$2007:$Global$Warming$and$the$Weakening$of$the$Tropical$
Circulation.$J.)Clim.,$20,$4316–4340,$doi:10.1175/JCLI4258.1.$
596"
597"
598"
Vecchi,$G.$A.,$B.$J.$Soden,$A.$T.$Wittenberg,$I.$M.$Held,$A.$Leetmaa,$and$M.$J.$Harrison,$2006:$
Weakening$of$tropical$Pacific$atmospheric$circulation$due$to$anthropogenic$forcing.$
Nature,$441,$73–76,$doi:10.1038/nature04744.$
599"
600"
Yu,$B.,$and$F.$W.$Zwiers,$2010:$Changes$in$equatorial$atmospheric$zonal$circulations$in$
recent$decades.$Geophys.)Res.)Lett.,$37,$L05701.$
601"
602"
603"
Yu,$B.,$F.$W.$Zwiers,$G.$J.$Boer,$and$M.$F.$Ting,$2012:$Structure$and$variances$of$equatorial$
zonal$circulation$in$a$multimodel$ensemble.$Clim.)Dyn.,$doi:10.1007/s00382M012M1372M
6.$
16"
"
604"
605"
606"
Yu,$J.MY.,$and$S.$T.$Kim,$2011:$Reversed$Spatial$Asymmetries$between$El$Niño$and$La$Niña$
and$their$Linkage$to$Decadal$ENSO$Modulation$in$CMIP3$Models.$J.)Clim.,$
110506133859050,$doi:10.1175/JCLIMDM11M0024.1.$
607"
$
608"
17"
"
609"
610"
611"
612"
613"
614"
615"
616"
617"
618"
619"
620"
621"
622"
623"
624"
625"
626"
627"
628"
629"
630"
631"
632"
633"
634"
635"
636"
637"
638"
639"
640"
641"
642"
643"
644"
645"
646"
647"
648"
649"
650"
651"
652"
653"
654"
Figure0Captions0
Figure0 1:$ Trend$ of$ the$ Δbox$ index$ difference$ (W−E)$ of$ SST$ and$ (E−W)$ of$ SLP$ in$ the$
individual$models$of$the$CMIP3$and$CMIP5$data$base,$with$box$E$=$(80M160°W,$5°SM5°N)$and$
box$W$=$(80M160°E,$5°SM5°N)$over$the$period$1950M2099;$The$black$and$blue$circles$are$the$
MMEns$values.$
$
Figure02:$(a)$Mean$state$of$zonal$stream$function$along$the$equator$in$CMIP3$MMEns$over$
the$ period$ from$ 1950$ to$ 1979$ (20C),$ averaged$ from$ 5°S$ to$ 5°N;$ black$ bold$ lines$ at$ the$
bottom$ indicate$ the$ three$ continents$ Africa,$ Maritime$ Continent$ and$ South$ America,$ (b)$
same$as$(a)$but$here$for$CMIP5$MMEns,$(c)$shading:$linear$trend$of$zonal$stream$function$in$
CMIP3$MMEns$in$the$period$1950$to$2099,$contours:$mean$state$from$(a),$(d)$same$as$(c)$
but$ here$ for$ CMIP5$ MMEns,$ (e)$ vertical$ average$ of$ (a)$ in$ kg$ sM1$ (blue$ line),$ (c)$ in$ kg$ sM1$
(500yr)M1$ (red$ line)$ $ and$ mean$ state$ over$ the$ period$ from$ 2070$ to$ 2099$ in$ kg$ sM1$ (21C)$
(green$line),$(f)$vertical$average$of$(b)$in$kg$sM1$(blue$line)$and$(d)$in$kg$sM1$(500yr)M1$(red$
line)$and$mean$state$in$21C$in$kg$sM1$(green$line).$
$
Figure0 3:$ Mean$ state$ of$ the$ vertical$ wind$ (positive$ upward)$ at$ 500$ hPa,$ 5°SM5°N$ in$ 20C$
(blue$ line),$ 21C$ (green$ line)$ in$ Pa$ sM1$ and$ trend$ over$ the$ period$ 1950$ to$ 2099$ in$ Pa$ sM1$
(500yr)M1$(red$dashed)$in$CMIP5$MMEns.$
$
Figure04:$Response$of$zonal$stream$function$under$global$warming$in$the$individual$models$
of$the$CMIP3$and$CMIP5$data$base,$on$the$xMaxis$the$shift$of$the$western$edge$(zero$line$of$
stream$function)$of$Walker$cell,$on$the$yMaxis$the$trend$of$zonal$stream$function$averaged$
over$the$box$120°EM180°,$700M300hPa.$$
$
Figure0 5:$ Composites$ of$ zonal$ stream$ function$ (a)M(c)$ in$ ERA$ Interim,$ with$ normalised$
Nino3.4$index$(170°WM120°W,$5°SM5°N)$as$selection$criterion,$(a)$for$Nino3.4$>$1$(El$Nino),$
(b)$ for$ Nino3.4$ <$ M1$ (La$ Nina),$ (c)$ shading:$ difference$ El$ Nino$ −$ La$ Nina$ (i.e.$ ENSO$
amplitude),$contours:$mean$state$in$ERA$Interim;$(d)M(f)$same$as$(a)M(c)$but$here$for$CMIP5$
MMEns$in$20C.$$
$
Figure06:0(a)$Same$as$Fig.$5f,$but$here$for$atmospheric$temperature$in$the$CMIP5$MMEns$
(i.e.$ the$ atmospheric$ warming$ in$ an$ El$ Nino$ M$ La$ Nina$ composite),$ (b)$ horizontal$
homogeneous$ warming$ (zonal$ mean$ of$ (a)),$ (c)$ shading:$ horizontal$ inhomogeneous$
warming$((a)$M$(b)),$contours:$ENSO$amplitude$from$Fig.$5f,$(d)$linear$trend$of$atmospheric$
temperature$over$the$period$from$1950$till$2099$in$the$CMIP5$MMEns,$(e)M(f)$same$as$(b)M
(c),$but$here$for$(d),$but$in$(f)$the$trend$pattern$of$Fig.$2d$as$contours.$
$
Figure0 7:$ Same$ as$ Fig.$ 5,$ but$ here$ composites$ of$ detrended$ anomalies,$ normalised$ with$
mean$Nino3.4$index$(170°WM120°W,$5°SM5°N),$shading:$(a)$for$Nino3.4$>$1$(El$Nino),$(b)$for$
Nino3.4$ <$ M1$ (La$ Nina),$ (c)$ sum$ El$ Nino$ +$ La$ Nina$ (i.e.$ a$ measure$ for$ the$ nonMlinearity);$
contours$in$figures$(aMc):$mean$state$in$ERA$Interim;$(dMf)$same$as$(aMc)$but$here$for$CMIP5$
MMEns$in$20C.$
$
Figure0 8:$ NonMlinearity$ of$ ENSO$ in$ the$ individual$ models$ of$ CMIP3$ and$ CMIP5$ data$ base$
and$ERA$Interim,$on$the$xMaxis$a$measure$of$the$nonMlinearity$of$the$SST:$the$difference$of$
18"
"
655"
656"
657"
658"
659"
660"
661"
662"
663"
664"
665"
666"
667"
668"
669"
670"
671"
672"
673"
674"
675"
676"
677"
678"
679"
680"
681"
682"
683"
684"
685"
686"
687"
688"
689"
690"
691"
692"
693"
eastern$box$(80°WM140°W,$5°SM5°N)$and$western$box$(140°EM160°W,$5°SM5°N)$of$the$sum$of$
El$ Nino$ and$ La$ Nina$ composites$ (as$ defined$ in$ Dommenget$ et$ al.$ 2013);$ on$ the$ yMaxis$ a$
measure$ of$ the$ nonMlinearity$ of$ the$ zonal$ stream$ function:$ the$ difference$ of$ western$ box$
(120°EM150°E,$700M200hPa)$and$eastern$box$(170°EM160°W,$700M200hPa)$of$the$sum$of$El$
Nino$and$La$Nina$composites,$like$in$Fig.$7c.$
$
Figure0 9:0 EOFs$ of$ zonal$ stream$ function$ in$ CMIP5$ MMEns,$ shading:$ (a)$ EOFM1$ in$ 20C,$ (b)$
EOFM1$in$21C,$(c)$EOFM2$in$20C,$(d)$EOFM2$in$21C,$explained$variance$is$given$in$the$header$
in$brackets$respectively;$contours$in$all$figures:$mean$state$20C$from$Fig.$2b.$
$
Figure0 10:$ (a)$ Explained$ variances$ of$ the$ eigenvalues$ in$ 20C$ (black$ solid$ line)$ and$
explained$ variances$ of$ 20C$ projected$ onto$ the$ eigenvalues$ of$ 21C$ (red$ dashed$ line),$ the$
error$ bars$ show$ the$ statistical$ uncertainties$ of$ the$ explained$ variances$ due$ to$ sampling$
errors$according$to$North$et$al.$(1982);$(b)$same$as$(a),$but$here$for$the$eigenvalues$of$21C$
(red$ solid$ line)$ and$ the$ explained$ variances$ of$ 21C$ projected$ onto$ the$ eigenvalues$ of$ 20C$
(black$dashed$line),$(c)$DEOF$20C→21C$pattern;$the$values$given$in$the$header$in$brackets$
is$ the$ explained$ variance$ of$ this$ pattern$ in$ 20C$ and$ 21C,$ respectively,$ (d)$ as$ (c),$ but$ here$
DEOF$21C→20C$pattern;$contours$in$(c)M(d):$EOFM1$in$20C$from$Fig.$9a.$
$
Figure011:$10$year$running$mean$of$PCM1$of$zonal$stream$function$in$all$individual$CMIP5$
models;$the$thick$red$line$is$the$average$of$all$36$individual$models.$
$
Figure0 12:$ (a)$ Shading:$ residual$ trend$ in$ zonal$ stream$ function$ in$ CMIP3$ MMEns$ after$
removing$the$trend$of$EOFM1$in$each$model$individually,$contours:$trend$in$stream$function$
from$Fig.$2c$(before$removing$the$trend$of$EOFM1)$for$comparison,$(b)$same$as$(a)$but$here$
for$CMIP5$MMEns.$
$
Figure013:$(a)$Same$as$Fig.$2c,$but$here$the$trend$in$ERA$Interim$over$the$period$1979$to$
2012,$ mean$ state$ of$ ERA$ Interim$ over$ this$ period$ as$ contours,$ (b)$ shading:$ the$ residual$
trend$in$ERA$Interim$after$removing$trend$of$EOFM1,$contours:$the$trend$of$(a),$(c)$same$as$
Fig.$2e,f,$but$here$for$mean$state$(in$kg$sM1)$and$trend$(in$kg$sM1$(50yr)M1)$in$ERA$Interim,$(d)$
time$series$of$EOFM1$of$zonal$stream$function$in$ERA$Interim.$
$
Figure014:0Meridional$average$(5°SM5°N)$of$SLP$and$vertical$wind$(W)$at$the$500$hPa$level,$
the$ vertical$ and$ meridional$ mean$ of$ tropospheric$ temperature$ (Ttropos,$ as$ defined$ in$ Bayr$
and$Dommenget$2013a)$and$the$zonal$gradient$of$vertical$ and$meridional$averaged$zonal$
stream$ function$ in$ the$ CMIP5$ MMEns,$ area$ mean$ for$ SLP$ and$ Ttropos$ removed$ and$ all$
variables$are$normalised;$(a)$mean$state$in$20C,$(b)$difference$21C$–$20C.$
$
19"
"
Figures
September 15, 2013
Weakening of the Walker Circualtion?
CMIP5
strengthening
1
regession (R2 = 0.55)
0.8
0.6
Trend in Δ SLP [hPa/100yrs]
0.4
11
13
0.2
20
0
−0.2
−0.4
−0.6
weakening
13
−0.8
−1
3
26
10
36
9
8
25
14 16
16
17
7 10
827
2
412
35
5
11
1
283
14 5 9
32
619
23
30
1 21217
31
19
15
24
22
18
20
434
33
18
17
22
152 6
12
29
−0.5
−0.4
weakening
−0.3
−0.2
−0.1
0
0.1
0.2
Trend in Δ SST [K/100yrs]
0.3
0.4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
ACCESS1−0
ACCESS1−3
BCC−CSM1−1
BCC−CSM1−1−m
BNU−ESM
CanESM2
CCSM4
CESM1−BGC
CMCC−CM
CMCC−CMS
CNRM−CM5
CSIRO−Mk3−6−0
FGOALS−g2
FIO−ESM
GFDL−CM3
GFDL−ESM2G
GFDL−ESM2M
GISS−E2−H
GISS−E2−H−CC
GISS−E2−R
GISS−E2−R−CC
HadGEM2−AO
HadGEM2−CC
HadGEM2−ES
INM−CM4
IPSL−CM5A−LR
IPSL−CM5A−MR
IPSL−CM5B−LR
MIROC5
MIROC−ESM
MIROC−ESM−CHEM
MPI−ESM−LR
MPI−ESM−MR
MRI−CGCM3
NorESM1−M
NorESM1−ME
CMIP3
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
BCCR−BCM2.0
CGCM3.1(T63)
CGCM3.1(T47)
CNRM−CM3
CSIRO−Mk3.0
CSIRO−Mk3.5
GFDL−CM2.0
GFDL−CM2.1
GISS−AOM
GISS−EH
GISS−ER
IAP−FGOALS−g1.0
INM−CM3.0
IPSL−CM4
MIROC3.2(hires)
MIROC3.2(medres)
MPI−ECHAM5
MRI−CGCM2.3.2
NCAR−CCSM3
NCAR−PCM
UKMO−HadCM3
UKMO−HadGEM1
0.5
strengthening
Figure 1: Trend of the ∆box index difference (W−E) of SST and (E−W) of SLP in the individual models of the
CMIP3 and CMIP5 data base, with box E = (80-160W,5S-5N) and box W = (80-160E, 5S-5N) over the period
1950-2099; The black and blue circles are the MMEns values.
1
CMIP3
a) 100
CMIP5
Mean state of zonal stream function in 20C
b)100
Mean state of zonal stream function in 20C
15
12
150
300
400
500
600
−1
6
250
3
300
kg s
250
9
200
0
10
200
400
−3
500
−6
600
700
700
−9
850
850
925
1000
−12
1000
0
30E
60E
c) 100
90E
120E 150E
180 150W 120W 90W
Longitude
60W
−15
0
30W
Trend of zonal stream function
10
Pressurelevel / hPa
Pressurelevel / hPa
150
30E
60E
90E 120E 150E 180 150W 120W 90W 60W 30W
Longitude
d)100
Trend of zonal stream function
3
2.4
150
1.6
250
−1.6
300
−1.6
400
−3.2
−4.8
−14.4
−6.4
−1.6
−8
500
600
1.6
−9.6
−8
−11.2
850
−6.4
−6.4
6.4
4.8
−3.2
−4.8
−6.4
0
30E
11
1
60E
90E
x 10
Mean state 20C
Mean state 21C
(−) Trend
120E 150E
180 150W 120W 90W
Longitude
60W
1.2
250
−1.8
300
−5.4
400
−7.2
3.2
f)
30E
11
1
0
0
−0.5
−0.5
−3.6
−5.4
−1.8
5.4
−7.2
−1.8
3.6
1.8
1.8
−2.4
−3
90E 120E 150E 180 150W 120W 90W 60W 30W
x 10
Mean state 20C
Mean state 21C
(−) Trend
−1
0
0
5.4
−7.2 −5.4
1.8
60E
−0.6
−1.2
12.6
7.2 9 10.8
3.65.4
−3.6
−3.6 −5.4
−7.2
−9
−1.8
0.5
30E 60E 90E 120E 150E 180 150W120W 90W 60W 30W
Longitude
−9
1.8
−10.8
−9
0.5
−1
0
−1.8
−12.6 −10.8
0
30W
0
7.2
−14.4
600
850
925
1000
Vertical average
−16.2
−1.8
−3.6
500
0.6
−3.6
1.8
700
6.4
4.8
3.2
1000
e)
8
−8
12.8
11.2
9.6
−4.8
−3.2
−3.2
−1.6
−3.2
8
−4.8
−12.8
−11.2
−9.6
700
−1.6
1.8
200
1010 kg s−1 100 yrs−1
1.6
200
Pressurelevel / hPa
Pressurelevel / hPa
150
Longitude
Vertical average
30E 60E 90E 120E 150E 180 150W120W 90W 60W 30W
Longitude
0
Figure 2: (a) Mean state of zonal stream function along the equator in CMIP3 MMEns over the period from
1950 to 1979 (20C), averaged from 5S to 5N; black bold lines at the bottom indicate the three continents Africa,
Maritime Continent and South America, (b) same as (a) but here for CMIP5 MMEns, (c) shading: linear trend
of zonal stream function in CMIP3 MMEns in the period 1950 to 2099, contours: mean state from (a), (d) same
as (c) but here for CMIP5 MMEns, (e) vertical average of (a) in kg s−1 (blue line), (c) in kg s−1 (500yr)−1 (red
line) and mean state over the period from 2070 to 2099 (21C) in kg s−1 (green line), (f) vertical average of (b) in
kg s−1 (blue line) and (d) in kg s−1 (500yr)−1 (red line) and mean state in 21C in kg s−1 (green line).
2
Vertical wind at 500 hPa (pos. upward)
0.06
0.04
0.02
0
−0.02
−0.04
−0.06
0
20C
21C
Trend
30E
60E
90E
120E 150E 180 150W 120W 90W
longitude
60W
30W
Figure 3: Mean state of the vertical wind (positive upward) at 500 hPa, 5S-5N in 20C (blue line), 21C (green
line) in Pa s−1 and trend over the period 1950 to 2099 in Pa s−1 (500yr)−1 (red line) in CMIP5 MMEns.
3
0
10
5
CMIP5
Response in zonal stream function
x 10
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Trend of stream function [kg s−1 100 yrs−1]
strengthening
2
regession (R = 0.34)
4
3
13
2
1129
1
16 31
30
36
20
10 912
35
16
11
26
3
23
25
10
2827 1
1 47 81422
17 24
9 28
21
32 15 20
18
4 19 5
22 736
33 5 34
17
21
0
−1
13
−2
weakening
−3
2
14
18
19
15
−4
6 12
−5
−40
−30
westward
−20
−10
0
10
20
30
o
shift [ longitude]
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
ACCESS1−0
ACCESS1−3
BCC−CSM1−1
BCC−CSM1−1−m
BNU−ESM
CanESM2
CCSM4
CESM1−BGC
CMCC−CM
CMCC−CMS
CNRM−CM5
CSIRO−Mk3−6−0
FGOALS−g2
FIO−ESM
GFDL−CM3
GFDL−ESM2G
GFDL−ESM2M
GISS−E2−H
GISS−E2−H−CC
GISS−E2−R
GISS−E2−R−CC
HadGEM2−AO
HadGEM2−CC
HadGEM2−ES
INM−CM4
IPSL−CM5A−LR
IPSL−CM5A−MR
IPSL−CM5B−LR
MIROC5
MIROC−ESM
MIROC−ESM−CHEM
MPI−ESM−LR
MPI−ESM−MR
MRI−CGCM3
NorESM1−M
NorESM1−ME
CMIP3
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
BCCR−BCM2.0
CGCM3.1(T63)
CGCM3.1(T47)
CNRM−CM3
CSIRO−Mk3.0
CSIRO−Mk3.5
GFDL−CM2.0
GFDL−CM2.1
GISS−AOM
GISS−EH
GISS−ER
IAP−FGOALS−g1.0
INM−CM3.0
IPSL−CM4
MIROC3.2(hires)
MIROC3.2(medres)
MPI−ECHAM5
MRI−CGCM2.3.2
NCAR−CCSM3
NCAR−PCM
UKMO−HadCM3
UKMO−HadGEM1
40
eastward
Figure 4: Response of zonal stream function in global warming in the individual models of the CMIP3 and
CMIP5 data base, on the x-axis the shift of the western edge (zero line of stream function) of Walker cell, on the
y-axis the trend of zonal stream function averaged over the box 120E-180, 700-300hPa.
4
ERA Interim
b)
El Nino composite
100
150
Pressurelevel / hPa
Pressurelevel / hPa
150
c)
La Nina composite
100
200
250
300
400
500
600
200
250
300
400
500
600
700
700
850
925
1000
850
925
1000
0
30E
60E
90E
120E 150E
180 150W 120W 90W
Longitude
60W
30W
diff. El Nino − La Nina composite
100
150
Pressurelevel / hPa
a)
200
250
300
400
500
600
700
850
925
1000
0
30E
60E
90E
120E 150E
180 150W 120W 90W
Longitude
60W
30W
0
30E
60E
90E
120E 150E
180 150W 120W 90W
Longitude
60W
30W
CMIP5 MMEns
e)
El Nino composite
100
150
Pressurelevel / hPa
Pressurelevel / hPa
150
f)
La Nina composite
100
200
250
300
400
500
600
200
250
300
400
500
600
700
700
850
925
1000
850
925
1000
0
30E
60E
90E
120E 150E
180 150W 120W 90W
Longitude
60W
30W
diff. El Nino − La Nina composite
100
150
Pressurelevel / hPa
d)
200
250
300
400
500
600
700
850
925
1000
0
30E
60E
90E
120E 150E
180 150W 120W 90W
Longitude
60W
30W
0
30E
60E
90E
120E 150E
180 150W 120W 90W
Longitude
60W
30W
Figure 5: Composites of zonal stream function (a-c) in ERA Interim, with normalised Nino3.4 index
(170W-120W, 5S-5N) as selection creterion, (a) for Nino3.4 > 1 (El Nino), (b) for Nino3.4 < -1 (La Nina), (c)
shading: difference El Nino − La Nina (i.e. ENSO amplitude), contours: mean state in ERA Interim; (d-f) same
as (a-c) but here for CMIP5 MMEns in 20C.
5
Atmospheric temperature in CMIP5 MMEns
ENSO composite
2
1
0.4
300
0
400
−0.4
500
−0.8
600
700
−1.2
850
925
1000
−1.6
−2
0
30E
60E
0.6
200
0.4
250
0.2
300
0
400
−0.2
500
−0.4
600
700
−0.6
850
925
1000
−0.8
90E 120E 150E 180 150W 120W 90W 60W 30W
Longitude
30E
60E
0.8
0.6
−3.9
−5.2
200
0.4
−6.5
250
3.9
−7.8
−10.4−9.1
300
1.3
5.2
6.5
0.2
2.6
0
−11.7
400
7.8
−0.2
5.2
3.9 6.5
500
2.6
−0.4
600
−0.6
1.3
700
−0.8
850
925
1000
−1
0
1
−1.3
−2.6
150
Pressurelevel / hPa
0.8
250
Pressurelevel / hPa
150
1.2
200
Inhomogeneous part of (a)
100
0.8
K
Pressurelevel / hPa
150
c)
Homogeneous part of (a)
100
1.6
90E 120E 150E 180 150W 120W 90W 60W 30W
−1
0
Longitude
K
b)
Total warming
100
K
a)
30E
60E
90E 120E 150E 180 150W 120W 90W 60W 30W
Longitude
Global warming trend
4
Homogeneous part of (d)
−0.8
500
−1.6
600
−2.4
700
−3.2
850
925
1000
−4
0
30E
60E
90E 120E 150E 180 150W 120W 90W 60W 30W
Longitude
0.32
200
1.6
250
0.8
300
0
400
−0.8
500
−1.6
600
−2.4
700
−3.2
850
925
1000
−4
0
30E
60E
90E 120E 150E 180 150W 120W 90W 60W 30W
Longitude
Pressurelevel / hPa
0
400
0.4
−0.6
150
2.4
−1
0.8
300
−1
1.6
250
Pressurelevel / hPa
150
2.4
200
Inhomogeneous part of (d)
100
3.2
K 100yrs
Pressurelevel / hPa
150
f)
4
3.2
0.24
−0.3
200
0.16
−0.9
−0.6
−0.3
250
300
−0.9
−1.2
−0.9
0.6
1.2
1.5
−1.5
−1.2
0.08
0.9
0.6
−0.6
0
1.8
2.1
400
−0.08
2.4
500
0.3
−0.16
0.3
600
700
−0.3
0.9
0.3
0
30E
0.3
60E
−0.24
−0.32
0.6
850
925
1000
K 100yrs−1
e)100
Total warming
K 100yrs
d)100
−0.3
−0.4
90E 120E 150E 180 150W 120W 90W 60W 30W
Longitude
Figure 6: (a) Same as Fig. 5f, but here for atmospheric temperature in the CMIP5 MMEns (i.e. the
atmospheric warming in an El Nino − La Nina composite), (b) horizontal homogeneous warming (zonal mean of
(a)), (c) shading: horizontal inhomogeneous warming ((a) - (b)), contours: ENSO amplitude from Fig. 5f; (d)
linear trend of atmospheric temperature over the period from 1950 till 2099 in the CMIP5 MMEns, (e)-(f) same
as (b)-(c), but here for (d), but in (f) the trend pattern of Fig. 2d as contours.
6
ERA Interim
b)
El Nino composite
100
150
Pressurelevel / hPa
Pressurelevel / hPa
150
c)
−La Nina composite
100
200
250
300
400
500
600
200
250
300
400
500
600
700
700
850
925
1000
850
925
1000
0
30E
60E
90E
120E 150E
180 150W 120W 90W
Longitude
60W
30W
sum El Nino + La Nina
100
150
Pressurelevel / hPa
a)
200
250
300
400
500
600
700
850
925
1000
0
30E
60E
90E
120E 150E
180 150W 120W 90W
Longitude
60W
30W
0
30E
60E
90E
120E 150E
180 150W 120W 90W
Longitude
60W
30W
60W
30W
CMIP5 MMEns
e)
El Nino composite
100
150
Pressurelevel / hPa
Pressurelevel / hPa
150
f)
−La Nina composite
100
200
250
300
400
500
600
200
250
300
400
500
600
700
700
850
925
1000
850
925
1000
0
30E
60E
90E
120E 150E
180 150W 120W 90W
Longitude
60W
30W
sum El Nino + La Nina
100
150
Pressurelevel / hPa
d)
200
250
300
400
500
600
700
850
925
1000
0
30E
60E
90E
120E 150E
180 150W 120W 90W
Longitude
60W
30W
0
30E
60E
90E
120E 150E
180 150W 120W 90W
Longitude
Figure 7: Same as Fig. 5, but here composites of detrended anomalies, normalised with mean Nino3.4 index
(170W-120W, 5S-5N), shading: (a) for Nino3.4 > 1 (El Nino), (b) for Nino3.4 < -1 (La Nina), (c) sum El Nino +
La Nina (i.e. a measure for the non-linearity); contours in figures (a-c): mean state in ERA Interim; (d-f) sames
as (a-c) but here for CMIP5 MMEns in 20C.
7
11
1
CMIP5
Non−linearity of ENSO
x 10
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
regession (R2 = 0.66)
17
−1
east−west difference in stream function [kg s ]
0.8
5
14
7
8
29
0.6
3635
28
18 4 8 11
610
13
9 7
15
21
20
34
3 24
19
1
14
3
22
20
2
2
17
2333
5
9
194
1
22
11
32
26
10
15
18
121625
631
30 16
21
12 13 27
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
ACCESS1−0
ACCESS1−3
BCC−CSM1−1
BCC−CSM1−1−m
BNU−ESM
CanESM2
CCSM4
CESM1−BGC
CMCC−CM
CMCC−CMS
CNRM−CM5
CSIRO−Mk3−6−0
FGOALS−g2
FIO−ESM
GFDL−CM3
GFDL−ESM2G
GFDL−ESM2M
GISS−E2−H
GISS−E2−H−CC
GISS−E2−R
GISS−E2−R−CC
HadGEM2−AO
HadGEM2−CC
HadGEM2−ES
INM−CM4
IPSL−CM5A−LR
IPSL−CM5A−MR
IPSL−CM5B−LR
MIROC5
MIROC−ESM
MIROC−ESM−CHEM
MPI−ESM−LR
MPI−ESM−MR
MRI−CGCM3
NorESM1−M
NorESM1−ME
CMIP3
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
BCCR−BCM2.0
CGCM3.1(T63)
CGCM3.1(T47)
CNRM−CM3
CSIRO−Mk3.0
CSIRO−Mk3.5
GFDL−CM2.0
GFDL−CM2.1
GISS−AOM
GISS−EH
GISS−ER
IAP−FGOALS−g1.0
INM−CM3.0
IPSL−CM4
MIROC3.2(hires)
MIROC3.2(medres)
MPI−ECHAM5
MRI−CGCM2.3.2
NCAR−CCSM3
NCAR−PCM
UKMO−HadCM3
UKMO−HadGEM1
ERA Interim
1
east−west difference in SST [K]
Figure 8: Non-linearity of ENSO in the individual models of CMIP3 and CMIP5 data base and ERA Interm, on
the x-axis a measure of the non-linearity of the SST: the difference of eastern box (80W-140W, 5S-5N) and
western box (140E-160W, 5S-5N) of the sum of El Nino and La Nina composites (as defined in Dommenget et al.
2013); on the y-axis a measure of the non-linearity of the zonal stream function: the difference of western box
(120E-150E, 700-200hPa) and eastern box (170E-160W, 700-200hPa) of the sum of El Nino and La Nina
composites, like in Fig. 6c.
8
EOFs in 20C
150
150
200
200
250
300
400
500
300
400
500
600
700
700
850
925
1000
850
925
1000
30E
60E
90E
120E
c) 100
150E
180
150W
Longitude
120W
90W
60W
30W
0
150
200
200
Pressurelevel / hPa
150
250
300
400
500
700
850
925
1000
150E
180
150W
Longitude
120W
90W
60W
150E
180
150W
Longitude
120W
90W
60W
30W
120W
90W
60W
30W
EOF−2 (14.8 %)
500
850
925
1000
120E
120E
400
600
90E
90E
300
700
60E
60E
250
600
30E
30E
d) 100
EOF−2 (14.5 %)
0
EOF−1 (24.3 %)
250
600
0
Pressurelevel / hPa
b) 100
EOF−1 (23.0 %)
Pressurelevel / hPa
Pressurelevel / hPa
a) 100
EOFs in 21C
30W
0
30E
60E
90E
120E
150E
180
150W
Longitude
Figure 9: EOFs of zonal stream function in CMIP5 MMEns, shading: (a) EOF-1 in 20C, (b) EOF-1 in 21C, (c)
EOF-2 in 20C, (d) EOF-2 in 21C, explained variance is given in the header in brackets respectively; contours in
all figures: mean state 20C from Fig. 2b.
9
DEOFs 20C → 21C
a)
DEOFs 21C → 20C
b)
Explained variances
explained variance / %
ev
ev
20C→21C
15
10
5
0
1
2
3
c) 100
4
5
6
eigenvalues of 20C
7
8
9
10
5
0
150
150
200
200
250
300
400
500
700
850
925
1000
120E
150E
180
150W
Longitude
120W
90W
60W
4
5
6
eigenvalues of 21C
7
8
9
10
DEOF−1 ( 14.0 %) ( 17.0 %)
500
850
925
1000
90E
3
400
600
60E
2
300
700
30E
1
250
600
0
21C→20C
15
d) 100
DEOF−1 ( 9.7 %) ( 8.1 %)
21C
pev
20
10
Pressurelevel / hPa
Pressurelevel / hPa
20C
pev
20
Explained variances
25
explained variance / %
25
30W
0
30E
60E
90E
120E
150E
180
150W
Longitude
120W
90W
60W
30W
Figure 10: (a) Explained variances of the eigenvalues in 20C (black solid line) and explained variances of 20C
projected onto the eigenvalues of 21C (red dashed line), the error bars show the statistical uncertainties of the
explained variances due to sampling errors according to North et al. (1982); (b) same as (a), but here for the
eigenvalues of 21C (red solid line) and the explained variances of 21C projected onto the eigenvalues of 20C
(black dashed line), (c) DEOF 20C → 21C pattern; the values given in the header in brackets is the explained
variance of this pattern in 20C and 21C respectively, (d) as (c), but here DEOF 21C → 20C pattern; contours in
(c)-(d): EOF-1 in 20C from Fig. 9a.
10
10 year running mean of PC−1
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
1950
1960
1970
1980
1990
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
2100
year
Figure 11: 10 year running mean of PC-1 of zonal stream function in all individual CMIP5 models; the thick
red line is the average of all 36 individual models.
11
CMIP3
a) 100
CMIP5
b)100
Residual trend (trend of EOF−1 removed)
Residual trend (trend of EOF−1 removed)
3
2.4
150
0.6
−1.2
250
−0.3
0.9
300
0.3
0.3
1.2
0.3
0.3
400 0.6
500
−0.6
−1.8
−1.5
−1.2
600
−0.9
−0.9
0.6
0.9
−2.4
−1.8
−1.5
−1.2
−0.3 −2.1
−0.6
0.6
1.8
1.2
1.5
−0.3
700
1.2
−0.9
250
−0.3
0.3
0.9
300
0.6
−0.6
0.3
0.6
400
0
0.6
−1.2
−0.9
−0.6
500
1.2
600
−0.6
2.41.8
2.1
−1.2
−1.5
−0.6
−0.3
−0.9
−1.2
1.5
1.2
−0.3
−1.8
0.9
0.6
0.9
−0.3
0.3
1000
0
−0.3
700
−0.3
850
1.8
200
1010 kg s−1 100 yrs−1
200
Pressurelevel / hPa
Pressurelevel / hPa
150
30E
60E
90E
120E 150E
180 150W 120W 90W
Longitude
60W
30W
850
925
1000
0.6
0.3
0
30E
60E
−2.4
−3
90E 120E 150E 180 150W 120W 90W 60W 30W
Longitude
Figure 12: (a) Shading: residual trend in zonal stream function in CMIP3 MMEns after removing the trend of
EOF-1 in each model individually, contours: trend in stream function from Fig. 2c (before removing the trend of
EOF-1) for comparison, (b) same as (a) but here for CMIP5 MMEns.
12
a) 100
b) 100
Trend in ERA Interim
Residual trend (trend of EOF−1 removed)
50
40
−3
150
−6
−3
−5
6
−12
−15
250
3
Pressurelevel / hPa
Pressurelevel / hPa
−9
200
3
−18
9
300
6
12
9
−9
−21
400
15
−9
−3
500
−12
600
700
−6
−3
−6
−6
−3
0
30E
11
c) 1.5 x 10
1
60E
90E
120E
150E
180
150W
Longitude
120W
90W
200
−5
−10
250
300
−5
−10
−10
−20
−15
−30
−15
−15
51015
20
−10
−20
10
10
15
0
−25
−35
−40
25
400
5
20
5
−5
−10
500
−20
600
−9
−6
−12
3
850
925
1000
30
3
1010 kg s−1 100 yrs−1
150
60W
−30
700
−40
850
925
1000
−50
0
30W
Vertical average
d) 4
Mean state 1979−1995
Mean state 1996−2012
Trend
30E
60E
90E
120E
150E
180
150W 120W
Longitude
90W
60W
30W
Time series of EOF−1
3
2
0.5
1
0
0
−0.5
−1
−1
−1.5
0
−2
30E 60E 90E 120E 150E 180 150W120W 90W 60W 30W
Longitude
0
monthly data
5 years running mean
−3
1978 1982 1986 1990
1994 1998
year
2002
2006
2010
Figure 13: (a) Same as Fig. 2c, but here the trend in ERA Interim over the period 1979 to 2012, and mean
state of ERA Interim over this period as contours; (b) shading: the residual trend in ERA Interim after removing
trend of EOF-1, contours: the trend of (a); (c) same as Fig. 2e, but here for mean state (in kg s−1 ) and trend (in
kg s−1 (50yr)−1 ) in ERA Interim, (d) time series of EOF-1 of zonal stream function in ERA Interim.
13
a)
Mean state 20C (vertically averaged and normalised)
b)
1
Difference 21C−20C (vertically averaged and normalised)
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
−0.2
−0.2
−0.4
−0.4
grad. str. func.
W
(−) SLP
Ttropos
−0.6
−0.8
−1
0
30E
60E
90E
120E 150E
180 150W 120W 90W
−0.6
−0.8
60W
30W
−1
0
0
30E
60E
90E
120E 150E
180 150W 120W 90W
60W
30W
0
Figure 14: Meridional average (5S-5N) of SLP and vertical wind (W) at the 500 hPa level, the vertical and
meridional mean of tropospheric temperature (Ttropos , as defined in Bayr and Dommenget 2013a) and the zonal
gradient of vertical und meridional averaged zonal stream function in the CMIP5 MMEns, area mean for SLP
and Ttropos removed and all variables are normalised; (a) mean state in 20C, (b) difference 21C − 20C.
14