using a hierarchy of models to understand wave-mean flow ... · using a hierarchy of models to...

Using a hierarchy of models to understand wave-mean flow interactionsChristopherG.FletcherDept.ofGeography&EnvironmentalManagement,InterdisciplinaryCentreonClimateChange(IC3),UniversityofWaterloo,Ontario,Canada.Incollaborationwith:PaulJ.KushnerDept.ofPhysics,UniversityofToronto.KarenL.SmithLamont-DohertyEarthObservatory.ChristopheCassouCNRM-CERFACS,Toulouse,France.IvanMinokhin,WilliamXuGraduatestudentsatUniversityofWaterloo.

1C.G. Fletcher: Modeling Hierarchies Workshop, Princeton, NJ. Nov 2-4, 2016.

• ThewintertimeNorthernAnnularMode(ThompsonandWallace2000)(NAM)isacoupledstratosphere-tropospheremodeofvariabilityinfluencedbywave-drivingfromthetroposphere

• Wewouldliketoforecastthesign/amplitudeoftheseasonalmeanNAMtoincreaseseasonalpredictabilityatthesurface,butdifferentsurfaceforcingsareassociatedwithopposite-signedNAMresponses:

2

Introduction

C.G. Fletcher: Modeling Hierarchies Workshop, Princeton, NJ. Nov 2-4, 2016.

• ThewintertimeNorthernAnnularMode(ThompsonandWallace2000)(NAM)isacoupledstratosphere-tropospheremodeofvariabilityinfluencedbywave-drivingfromthetroposphere

• Wewouldliketoforecastthesign/amplitudeoftheseasonalmeanNAMtoincreaseseasonalpredictabilityatthesurface,butdifferentsurfaceforcingsareassociatedwithopposite-signedNAMresponses:

3

Surface processes affecting the NAM


(N)AO/NAM―(weakvortex)

Reference (N)AO/NAM+(strongvortex)

Reference

ElNino (Garfinkel andHartmann2008)

LaNina (Iza etal.2016)

IndianOceancooling(?) IndianOcean warming Hurrell et al.(2004)

WestPacificwarming Nishiietal.(2010)

Eurasian surfacecooling (Cohen&Entekhabi 1999)

Arcticseaiceloss (Kimetal.2014)

Q:Whatexplainsthesign/amplitudeofthewintermeanNAMresponsetosurfaceforcing?

4

Research question


(N)AO/NAM―(weakvortex)

Reference (N)AO/NAM+(strongvortex)

Reference

ElNino (Garfinkel andHartmann2008)

LaNina (Iza etal.2016)

IndianOceancooling(?) IndianOcean warming Hurrell et al.(2004)

WestPacificwarming Nishiietal.(2010)

Eurasian surfacecooling (Cohen&Entekhabi 1999)

Arcticseaiceloss (Kimetal.2014)

• IntheGFDL-AM2.1AGCM,wefindopposite-signedJFmeanstrat-tropNAMresponsetoimposedSSTwarmingintheIndianvsPacificoceanbasins.

The NAM response to tropical warmingPACIND

Fletcher and Kushner [2011]C.G. Fletcher: Modeling Hierarchies Workshop, Princeton, NJ. Nov 2-4, 2016.

• ZonalmeancirculationanomaliesinthepolarstratospherearedrivenbyEP-fluxdivergenceofplanetarywaves,whichisproportionaltov*T*

• 𝑣∗𝑇∗ >0=NAM– and𝑣∗𝑇∗ <0=NAM+• Sowhatdeterminesthesignofv*T*?

6

Theory: linear interference

Smith and Kushner [2012]C.G. Fletcher: Modeling Hierarchies Workshop, Princeton, NJ. Nov 2-4, 2016.

TOTAL= EMLIN + EMNL +FLΔ 𝑣∗𝑇∗ = 𝑣&∗Δ 𝑇∗ + Δ 𝑣∗ 𝑇&∗ + Δ 𝑣∗ Δ 𝑇∗ + Δ{⟨𝑣∗*𝑇∗*⟩}

7

Theory: v*T* decomposition

Fletcher and Kushner [2011]

Ensemblemean <A> Ensembleeddy A’Zonalmean {A} Zonaleddy A*CtrlClimatologicalmean Ac Response(Pert – Ctrl) ΔA

EMLIN > 0 EMLIN < 0

• Oppositephasingofzonalwave-1responsewiththeclimatology

Linear interference and the NAMPACIND


wave-1 amplitude (m)


Linear interference and the NAM


PAC IND

v*T* 40N-80N@100hPa [mKs-1]ThesignandamplitudeoftheNAMresponsearelargelyexplainedbyEMLINfromzonalwave-1.

term Dfhn*ihT*ig (EM) dominates the wave driving re-sponse and the EMLIN contribution is larger than theEMNL contribution. Following from the linear inter-ference effects illustrated in Fig. 5, the EMLIN term isnegative throughout the entire stratosphere and most ofthe troposphere during days 1–22 for the Siberian case,while the westward-tilting structure of the waves indicatesthat the EMNL term is again positive (see also Fig. 8d).

We note that the structure of DhZ*i in the Siberiancase looks strikingly similar to that in the second periodof the AM2 simulation; that is, the day 1–22 SGCM re-sponse is westward shifted, especially in the stratosphere,relative to the day 1–65 AM2 response. The phase ofDhZ*i in the Siberian case in the SGCM shifts westwardand out of phase with hZc*i over the first few days of therun. This also occurs in AM2, albeit more quickly;however, unlike the AM2 case (Fig. 3), the SGCM waveresponse does not then shift eastward and in phase withhZc*i (not shown). As is the case for other differencesbetween the SGCM and AM2 simulations, it is not sim-ple to explain why the transient ensemble-mean wave

response differs so significantly between the two simu-lations (see section 4). But given the different wave re-sponses, we now understand how differences in phasingbetween DhZ*i and hZc*i exert correspondingly differentlinear interference effects on wave driving, and henceopposite sign NAM responses are obtained in the twosimulations.

c. Sensitivity to position and sign of the forcingin the SGCM

To further probe the linear interference effect, weconduct 11 additional forcing simulations with theSGCM in which the forcing is shifted zonally at inter-vals of 308 longitude [i.e., l1 and l2 in (3) are increased in308 increments; Table 1 simulations A–L]. For theseexperiments, this forcing should no longer be inter-preted as an idealized snow forcing, but rather as a low-level cooling.

One of these additional simulations, a simulation withthe forcing location given by l1 5 1508E and l2 5 2308E(henceforth the ‘‘Pacific case,’’ simulation E in Table 1),

FIG. 6. Dependence of the SGCM response on forcing location (simulations A–L in Table 1).(a) The TOTAL E–P flux divergence response averaged over 408–808N, 10–1 hPa, and days1–22 vs the 10–1-hPa DhZti averaged over the polar cap and over days 10–40. (b) Dfhn*ihT*ig(EM) at 10 hPa, averaged over 408–808N, and cumulative to day 22 vs the E–P flux divergenceresponse. (c) EMLIN vs EM. (d) The all-wave (solid circles) and wave-1 (open circles) spatialcorrelation between DhZ*i and hZc*i vs EMLIN.

15 NOVEMBER 2010 S M I T H E T A L . 6045

Linear interference and the NAM

Smith et al. [2010]

KarenSmithshowedthesamethingin2010usingtheGFDLHSmodelwithastratosphereandimposedEurasiansurfacecooling.

• TOPO:afullAGCMwithidealizedPacificSSTwarmingandperturbed(flattened)topography overEurasia

• TheNAM- responsevanishesduetoreducingwave-1amplitude(“tuningout”linearinterferenceso thatv*c and T*c-->0).

11

Idealized boundary forcingDefault TOPO


• ByaddinganotherAGCM(CAM4)weshowedthatthelinearinterferenceframeworkisrobustacross physicsschemesandvarioushorizontalandverticalresolutions.

12

Sensitivity to AGCM configuration


• InFletcherandCassou (2015)weuseda1000-yrfree-runningcontrolsimulationfromaCMIP5-classESM(CNRM-CM5)toexaminetheeffectsofocean-atmosphereinteractionandintraseasonalvariability.

• WealsoperformedoceannudgingtoisolateindependentsourcesofvariabilityemergingfromthePacificandTIObasins

13

Coupled ocean-atmosphere results


these assumptions. When the Pacific is active alone(PaIn), the linear interference is constructive later in theseason (Fig. 4b), while, when the Indian Ocean is activealone (PnIa), the linear interference is destructive earlierin the season (Fig. 4c). When the two basins are activetogether (PaIa), the early season response resembles thatfrom PnIa, while the late season response involves con-siderable cancellation and no discernible NAM re-sponse (Fig. 4a). The clear implication is that thepresence of precipitation anomalies in the TIO in PaIaweakens the constructive interference initiated from thePacific, particularly in wave 1.To understand the origin of the intraseasonal varia-

tion in the wave interference and NAM signals in

each case, it is informative to examine the time evolu-tion of the tropical SST and precipitation anomalies.As demonstrated in Fig. 1, the Pa-type cases clearlycapture significant ENSO events, and this is reflectedin their time-evolving SST anomalies, which arehighly similar (Figs. 5a,b). However, the PaIa caseinvolves a more zonally symmetric precipitation signal(i.e., the peaks in precipitation over TIO and TEPare more similar in magnitude) compared to the PaIncase, which, during DJF, shows relatively large anom-alies over the Pacific and small anomalies over theTIO (Fig. 5e). On the other hand, the PnIa cases do notdescribe ENSO events during DJF (Fig. 1c); however,these cases transition into La Niña events during

FIG. 4. Upper half of each panel shows the time–height cross section of the monthly zonalmean zonal wind anomalies at 608N (color shading; m s21), with stippling indicating areaswhere the wind anomalies are significantly different from zero (p, 0.05) for (a) PaIa, (b) PaIn,and (c) PnIa. Lower half of each panel shows the pressure-weighted correlation rzp (see section2d) for wave 1 (red) and wave 2 (blue). A threshold of rzp 5 0.5 (rzp 520.5) is used to denotemonths as having constructive (destructive) linear interference.

7994 JOURNAL OF CL IMATE VOLUME 28

• PAC(NAM-)comesfromthecanonicalresponsetoENSO

• IND(NAM+)frominternalvariabilityovertheTIO.

• Lin.interferencesuggestsinternalatmosphericvariabilityoverTIO(e.g.MJO)modulatesENSOteleconnections

14

Coupled ocean-atmosphere results

Fletcher and Cassou [2015]

PAC

IND

PAC + IND

u60N [ms-1]

• Wecomparedinterannualvariability(ELN)andclimatechange(CC).• InGFDL-AM2.1linearinterferenceinCCiscomplicatedbyradiative-

dynamicalforcing/responses.• ButlinearinterferenceisstillimportantinCC:EMLIN<0with

contributionsfromwaves1-4. Butoverallthepictureismuchlessclear,andwithgreaterintermodelvariability. 15

Linear Interference & Climate change

Fletcher and Minokhin [2015]

• Watt-MeyerandKushner(inprep):observedskewnessofv*T*distributionresultsfromnonlinearinteractionbetweenEMLIN andEMNL.

• Applicationsto:– tropical-extratropicalteleconnectionsinseasonal-to-decadalpredictability(Moltenietal.2015)

– transienteddyvariabilityanditsconnectionstotropicalconvectionandArcticwarming(Gossetal.2015).

16

Recent/ongoing work

Toy statistical model results for linear interference. Shading shows the number of DJF days (log scale). Red lines indicate constant TOTAL v*T*. Figure courtesy of Oliver Watt-Meyer (UofT).


• Linearinterferenceofplanetarywavesexplainsthesign/amplitudeoftheNAMresponsetomultiplesurfaceperturbations

• Robusttomodelconfiguration,detailsofperturbation,(timescale)

• We,likemanyothershere,employa“hierarchyofopportunity”fromthemodelsinourtoolkit.Arethereopportunitiestodesign/createmoreappropriatetools?

17

Conclusions and reflection


References•Fletcher,C.G.&Cassou,C.,2015.TheDynamicalInfluenceofSeparateTeleconnections fromthePacificandIndianOceansontheNorthernAnnularMode.JournalofClimate,28(20),pp.7985–8002.

•Fletcher,C.G.&Kushner,P.J.,2013.Linearinterference andtheNorthernAnnularModeresponsetotropicalSSTforcing:Sensitivitytomodelconfiguration.JournalofGeophysicalResearch:Atmospheres,118(10),pp.4267–4279.

•Fletcher,C.G.&Kushner,P.J.,2011.TheRoleofLinearInterference intheAnnularModeResponsetoTropicalSSTForcing.JournalofClimate,24(3),pp.778–794.

•Fletcher,C.G.&Minokhin,I.,2015.Linearinterference andthenorthernannularmoderesponse toElNiñoandclimatechange.ClimateDynamics,45(11-12),pp.2977–2991.

•Smith,K.L.,Fletcher,C.G.&Kushner,P.J.,2010.TheRoleofLinearInterference intheAnnularModeResponse toExtratropicalSurfaceForcing.JournalofClimate,23(22),pp.6036–6050.

•Wu,Y.&Smith,K.L.,2016.ResponseofNorthernHemisphereMidlatitudeCirculationtoArcticAmplificationinaSimpleAtmosphericGeneralCirculationModel.JournalofClimate,29(6),pp.2041–2058.

18C.G. Fletcher: Modeling Hierarchies Workshop, Princeton, NJ. Nov 2-4, 2016.

19

The end.


that the relative efficiency of TIO and TPO is relatedto the planetary wave driving of the zonal mean flowresponse.In contrast, in the tropics the extratropical zonal mean

geopotential response [DZ] has the same sign in all threesimulations and scales roughly with forcing strength (Figs.5a–c). On the basis of additional simulations, we will ar-gue in section 3d that the tropical–subtropical zonalmeangeopotential response is driven by the upper-troposphericheating rather than being related to the wave-drivenresponse.In the remainder of this article we will focus on ex-

plaining the dynamics of the NAM response. We need toaddress what causes the NAM response to be of oppositesign and roughly equal magnitude when the forcing in theTIO case is only 30% of that in the TPO case. To addressthese questions, wemust better understand the dynamicaldifferences between the high-latitude responses in TPOand TIO, and determine how thewaves produced by eachperturbation (Figs. 3 and 4) affect the zonal mean flow(Fig. 5).

b. Wave-activity flux decomposition

The wave-driven zonal response is related to the re-sponse of the Eliassen–Palm (EP) flux, which is qua-dratic in wave amplitude. In this section we developa decomposition of the EP flux response that has provenuseful in diagnosing the wave-driven response in thesesimulations.In the stratosphere the EP flux and its divergence are

dominated by the vertical component that is approxi-mately proportional to the zonal mean meridional fluxof sensible heat by the eddies (Newman et al. 2001). Wecall this quantity fy*T*g, where the braces f. . .g denotezonal and time averaging, and the star denotes a de-parture from the zonal mean. We decompose fy*T*gand its response into three distinct terms. The followingdecomposition, introduced in Smith et al. (2010), is illus-trated for fy*T*gwith the understanding that it applies toall the terms in the EP flux. This decomposition is thebasis for Fig. 6, which presents our key results.For each realization in the ensemble, we have

y*5 hy*i1 y*9,T*5 hT*i1T*9,

where the angle brackets denote an ensemble mean andthe prime a departure from the ensemble mean. The en-semble mean response of the wave activity flux, Dfy*T*g,is decomposed as

D hy*T*if g5D hy*ihT*if g1D hy*9T*9i! "

. (1)

The first term on the r.h.s. of (1) is the heat flux responseassociated with the ensemblemean eddy response, while

FIG. 3. The ensemble-mean JF response in 200-hPa wave geo-potential height. Contour interval is 20m and negative contours aredashed.

1 FEBRUARY 2011 F LETCHER AND KUSHNER 783

20

AGCM experimental designPacific Warming


Experimental Design:CTRL: 100 years of GFDL-AM2forced by repeating seasonal cycle of SST/ice; fixed 1990 atmospheric composition.PERT: same as CTRL but with a fixed SST anomaly added to climatology.ΔX = XPERT – XCTRL

All plots show JF mean ensemble mean responses from N=100 realizations of each experiment.








y*5 hy*i1 y*9,T*5 hT*i1T*9,



. (1)




21

Pacific Warming







y*5 hy*i1 y*9,T*5 hT*i1T*9,



. (1)




Indian Ocean Warming


STANDARD TOPO LOW TOPO

Pacific Pacific

Indian Indian22Fletcher and Kushner [2011]

Reducing the amplitude of Z*climodramatically reduces dNAMbecause EMLIN ~ 0.


23

∆{Z}PolarCap

(TRO

P)(m

)

The role of linear interference in explaining ΔNAM is robust across multiple forcing patterns and model configurations.

∆{Z}PolarCap

(STRAT)(m)

r = 0.96

r = 0.97 r = 0.95


24

|∆OLR*|Tropics (Wm-2)

|∆Ch

i*25

0|Trop

ics(10

6 m2 s

-1)

|∆Chi*250|Tropics (106m2s-1)

|∆Z*25

0|Extratrop

ics(m)

|∆Z*25

0|Extratrop

ics(m)

∆{Z}PolarCap (STRAT)(m)

(a) (b)

(c) (d)

∆{Z}PolarCap

(STRAT)(m)

Robust scaling from Tropics to extratropics across multiple forcing patterns and model configurations.


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