STRATOSPHERE-TROPOSPHERE COUPLING: A METHOD TO DIAGNOSE SOURCES OF ANNULAR MODE TIMESCALES

Lawrence Mudryklevel, Paul Kushner p R ! ! SPARC DynVar level, Z(x,p,t)=− T (x,p,t)d ln p , (4) g !ps x,t p ( ) R ! ! Z(x,p,t)=− T (x,p,t)d ln p , (4) where p is the pressure at the surface, R is the specific gas constant and g is the gravitational acceleration s g !ps(x,t)

where p is the pressure at theat surface, the surface.R is the specific gas constant and g is the gravitational acceleration Abstract s Geopotentiallevel, Height Decomposition Separation of AM Timescales p R ! ! at the surface. This time-varying geopotentialZ( canx,p,t be)= decomposed− T into(x,p a,t cli)dmatologyln p , and anomalies from the(4) climatology AM timescales track seasonal variations in the AM index’s decorrelation time6,7. For a hydrostatic fluid, geopotential height may be describedg !p sas(x ,ta) function of time, pressure level Timescales derived from Annular Mode (AM) variability provide dynamical and as horizontalZ(x,p,t position)=Z ( asx,p a )+ temperatureδZ(x,p,t integral). Decomposing from the Earth’s the temperature surface to a and given surface pressure pressure fields inananalogous insight into stratosphere-troposphere coupling and are linked to the strengthThis of time-varying level, geopotentialwhere can beps is decomposed the pressure at into the a surface, climatologyR is the and specific anomalies gas constant from and theg is climatology the gravitational acceleration NCEP, 1958-2007 level: ^ a) o (yL ) d) o AM responses to climate forcings. These timescales reflect decorrelation times p 10 21 15 10 21 15 15 40 40 R ! ! 27 21 27 21 of geopotential height in the stratosphere and troposphere. However, sincex x x manner,at the to surface. first order wex can approximate− the geopotentialx anomalies in terms of those due to the temperature30 40 30 40 as Z( ,p,t)=Z( ,p)+δZ( ,p,t). DecomposingZ the( temperature,p,t)= and surfaceT ( pressure,p,t)d ln fieldsp , inananalogous (4) 27 27 27 15 21 21 ! 100 27 15 100 15 geopotential height involves a vertical integral via the hypsometric equation, g ps(x,t) 9 9 300 300 level, This time-varying geopotential can be decomposed into a climatology and anomalies from the climatology 9 some aspects of the dependence of the timescales on vertical level are and surface pressure as 9 manner, to first order we can approximate the geopotential anomalies in terms of those due to the temperature 1000 1000 We can decompose the p above time varying geopotential into a climatology and J A S O N D J F M A M J J A S O N D J F M A M J ambiguous. R ! ! where ps is the pressure at the− surface, R is the specific gas constant and g is the gravitational acceleration ^ _ anomalies,as ZZ ( ( x ,p,t )=)= Z ( x ,p )+ δ ZT ( ( xx ,p,t,p ,t ). ) d. Decomposing lnDecomposingp , the the temperature temperature and and(4) surface surface pressure pressure fields inananalogous b) o (yT ) e) o o (yL ) g ! x p 10 21 15 10 ps( ,t) -2 21 R 40 27 and surface pressure as in the same way, to first order we can approximate the geopotential≈− anomalies as two terms for 30 30 We present a method for decomposing AM variability into contributions from δZ(x,p,t) δT (x,p,t)d ln p 40 3 which themanner, temperature to first and order surface we can pressure approximate variability the geopotentialis decoupled:! anomalies in terms of those due to the temperature 27 2721 whereatps theis the surface. pressure at the surface, R is the specific gas constant and g is the gravitationalg ps(x acceleration) 100 15 15 100 9 surface pressure and temperature based on a linearization of the hypsometric 9 3 -2 p 300 300 equation. The decomposition is used to interpret stratosphere-troposphere R δp (x,t) 9 at the surface. and surface pressureR as s (1) 1000 15 9 15 1000 δZ(x,p,t) ≈− δT (x,p,t)d ln p + T (x,p) . J (5)A S O N D J F M A M J J A S O N D J F M A M J coupling events and the seasonal variation of AM timescales. Surface This time-varying geopotentialL can be decomposed into a climatology and anomalies from the climatologyPressure Level [hPa] ! x g p (x) c) o (y ) f) Effect of p -T correlations g ps( ) s ps s 6 pressure variations best account for AM variability in the troposphere and This time-varying geopotential can be decomposed into a climatology and anomaliesR fromp the climatology 10 9 10 6 δZ(x,p,t) ≈− δT (x,p,t)d ln p 30 12 30 stratospheric temperature variations best account for AM variability in the as Z(x,p,t)=Z(x,p)+δZ(x,p,t).R Decomposingδps(x,t the) temperature and surface pressure fields inananalogous g ! x 0 as Z(x,p,t)=Z(x,p)+δZWe(x,p,t will). Decomposing refer to the+ the temperature firstT (x term,p) and on surface the. right pressure hand fieldsps( side) inananalogous of Equation5asthetemperaturecomponentof(5) 100 100 ⎨ 0 stratosphere during coupling events, but AM timescales are not so readily ⎨ 8 = x + 4 δZ g δpZs( ) δZ ps 300 300 L T R δps(x,t) 6

separated. AM timescales involve strong coupling between the surface 9 x 1000 12 6 1000 manner,manner, to first order to first we can order approximate we can the approximate geopotential anomalies the geopotential in terms of those+ an dueTomalies( to,p the) temperature in terms. of those due to the temperature(5) 0 0 pressure and stratospheric temperature variations: the pressure-temperature “linearizedthe geopotential geopotential height” anomalies“temperature and to the component” secondg term“surface as p thepressures(x) surf component”ace pressure component of the geopotentialJ A S O N D J F M A M J J A S O N D J F M A M J cross correlation functions are small in magnitude but highly persistentWe will and refer to the first term on the right hand side of Equation5asthetemperaturecomponentof Left panels show the seasonality of the NAM time scale Right panels show d) effective timescale estimate (see and surface pressure as NCEP Geopotential Height Components at 75N (2005) below) e) difference of d-a and f) cross correlation and surface pressureWe as will refer to the first term on the right hand side of EquatioComponentsn5asthetemperaturecomponentof of geopotential height calculated for the a) linearized geopotential, b) temperature thus provide significant sources of AM persistence. These empirical results 10anomalies, and denote the terms as ZT and Zp,respectively.HigherordertermsinEquation5containsecanomalies based on NCEP data for component andond c) surface pressure component. timescale due to T-ps correlations. 5 p the year 2005, with climatologies might serve as the basis for further theoretical analysis on the originsthe of geopotentialzonal anomalies m] and to the second termR as the surface pressure component of the geopotential 2 ≈− 0 theδ geopotentialZ(x,p,t) anomaliesδT and(x,p,t to)d theln p second term as the surfdefinedace pressure over the years component 1958-2007. of the geopotential mean stratosphere-troposphere coupling. 10 g ! x p ! order temporal correlations.p We therefore expect this linearization to be accurate as long as correlationsAM timescales are not a simple combination (e.g., sum, average, harmonic mean) -5 s( ) R The solid black curve shows the full -10 ≈− 10 hPa non-linear geopotential height anomalies, and denote the terms as ZT and Zp,respectively.HigherordertermsinEquation5containsecRδZ(x,p,tδps(x),t) δT (x,p,t)d ln p ond of the surface pressure and temperature timescales: τ(yL) ≠ τ(yT) + τ(yp s ) anomalies, and denote+ T (x the,p) terms as .ZT and Zp,respectively.HigherordertermsinEquation5containsecanomalies.(5) The dotted curve shows ond 2 g !ps(x) between temperatureg and surfaceps(x) pressure remain small.scaled differences between the non- 1 linear anomalies and the linear ^ order temporal correlations. We therefore expect this linearization to be accurate as long as correlationsWe develop a procedure to estimate a timescale, τ for yL which is consistent with the timescales of yT, y p s and order temporal correlations.0 We therefore expect this linearizationR to be accurateδps(x,t)anomalies as long reconstructed as correlations using Eq. 1. their cross-correlations. The procedure allows us to estimate the seasonal contribution from T-ps cross- We will refer to the first-1 termWe on note the right that hand while side at of a givenEquatio horizontaln5asthetemperaturecomponentof+ T (x location,p) x theDifferences. temperature in the top component panel are and surface pressure(5) may 300 hPa correlations to the NAM timescale. This estimate is shown in panel f) of the above figure. Although such cross -2 between temperature and surface pressureg remain small.ps(x) plotted as 100x the actual difference; those in the bottom two panels are correlations are weak, they are extremely persistent during active vortex seasons as shown in the figure below. between temperaturethe geopotential and anomalies surface1 and pressure to the second remain term as small. the surface pressure component of the geopotential be related to one another by hydrostatic balance, knowledgeplotted of as 20x the the vertical actual difference. distribution of the temperature 0 We note that while at a given horizontal location x the temperatureThe red and component blue curves show and surface the pressure may Motivation and Background respective contributions from the Auto and Cross Correlation Functions for NAM and Component Time Series at 150 hPa We noteanomalies, thatWe while will and denote refer at a the givenGeopotential Height Anomalies [ to terms the horizontal as firstZT and termZp location,respectively.HigherordertermsinEquation5containsec on thex the right temperature hand side component of Equatio andn5asthetemperaturecomponentof surfaceond pressure may -1 temperature and surface pressure field at x does not completely determine the850 surface hPa pressure at x.Morespecifically,whilewecanwrite January beONDJ related to one another by hydrostatic F balance, MA knowledge ofcomponents. the vertical distribution of the temperature January The Northern and Southern Annular Modes (NAM, SAM) are defined as the dominantorder temporal correlations. We therefore expect this lineMontharization to be accurate as long as correlations variability patterns in the extratropical circulation of each respective hemisphere.be related1 The to the one geopotential another by hydrostatic anomalies balance, and to knowledge the secondof term the vertical as the distribution surface pressure of the component temperature of the geopotential ps ps =ˆfieldp atg/x(RTdoes)dz not,knowledgeofthefulltemperaturedistribution,stillreq completely determine the surface pressure at x.Morespecifically,whilewecanwriteuires knowledge of the pressure between temperature and surface pressure remain small. Fraction of Variance Explained strength and polarity of the AM pattern fluctuates over time as indicated by the value of the The graph on the right shows the fraction of the total variance (normalized relative a) Fraction of Variance Explained " 10 AM index. to the fully nonlinear anomalies) captured by the linearized anomalies (black field at x doesanomalies, not completely and denote determineps =ˆ thep g/ terms( theRT ) surfacedz as,knowledgeofthefulltemperaturedistribution,stillreqZT and pressureZp,respectively.HigherordertermsinEquation5containsec at x.Morespecifically,whilewecanwriteuires knowledge of the pressure ond July July CCF( ) We note that whilecurve), at a the given temperature horizontal component location (redx thecurve), temperature the surface pressure component component and surface pressure may Autocorrelation on a second reference level,p ˆ to determine ps.Thus,surfacepressureandtemperaturecanbeconsidered30 ACF(yL) (blue curve), and by " the covariance of the two components (green curve). NH: Cross Correlation Stratospheric vs. Tropospheric Modes solid curves. SH: dashed curves. The green curves measure the coupling ps =ˆp g/be( relatedRT )dz to,knowledgeofthefulltemperaturedistribution,stillreq one another by hydrostaticon a second balance, reference knowledge level,p ˆofto the determine vertical distributionps.Thus,surfacepressureandtemperaturecanbeconsidereduires of the knowledge temperature100 of the pressure In the stratosphere, the AM index varies with the strength of the polar vortex which is order temporalbetweenas correlations. the independent two contributions, We fields which therefore for is a important hydrostatic expect for understanding this fluid. line This AMarization is why, forto beexample, accurate global as climate long as models correlations use separate Lag Time [days] " timescales in the upper troposphere/lower stratosphere. Lag Time [days] strongly coupled to fluxes of vertical wave activity. In the troposphere it signals latitudinalfield at x does not completelyas determine independent the surface fields for pressure a hydrostatic at x.Morespecifically,whilewecanwrite fluid. This is why, for 300example, global climate models use separate vacillations in the mean position of the extratropical jet, connected with meridionalon a fluxes second of reference level,p ˆ to determine ps.Thus,surfacepressureandtemperaturecanbeconsideredPressure Level [hPa] ps between temperatureprognosticδZ T variability and equations surface dominates pressure for surface in remainstratosphere pressure small. and temperature1000 .ThisisanimportantcheckonthewhethertheCorrelations between yT and y , although weak, can decay very slowly, enhancing NAM wave activity. ps =ˆp g/(RT )dz,knowledgeofthefulltemperaturedistribution,stillreqprognostic equations for surface pressure anduires temperature knowledge of.Thisisanimportantcheckonthewhetherthe the-0.2 pressure0.0 0.2 0.4 0.6 0.8 1.0 δZ p s variability dominates in troposphere persistence by as much as 10 days in the lower stratosphere and upper troposphere. These distinctive dynamics are captured by simple mechanistic models of the two regions. " b) Fraction of VarianceFractional Contained inVariance Upper or Lower Half of Atmosphere as independent fieldsWe note for a that hydrostaticdecomposition while at fluid. a given (Eq. This horizontal 5) is is why, reasonable. for locationexample,x the global temperature climate10 models component use separate and surface pressure may The Holton and Mass2 model in its simplest form is a prognostic model for the stratosphericon a second reference level,p ˆ todecomposition determine ps.Thus,surfacepressureandtemperaturecanbeconsidered (Eq. 5) is reasonable. zonal wind, which can be represented by stratospheric temperature. The Vallis et al.3 We can define separate AM indices for both the temperature and surface30 pressure components Effect of Sudden Stratospheric Warmings on Timescales model is a prognostic model for the barotropic stream function, which can beprognostic representedas equations independent for fieldsabove surface for a hydrostaticby pressure Figureprojecting fluid. 1 and illustratestheir This temperature respective is why, the for anomalies decompositionexample,.Thisisanimportantcheckonthewhetherthe globalonto the climate at AM three modelsspatial diff usepatternerent separate prjustessure as for levels the total using NCEP reanalysis data be related to one anotherFigure by 1 illustrates hydrostatic the decomposition balance, knowledge at three dioffferent the100 pr verticalessure levels distribution using NCEP of reanalysis the temperature data by surface pressure. geopotential. We normalize their sum so that it has unit variance. prognostic equations for surface pressure and temperature.Thisisanimportantcheckonthewhetherthe ! a) Total! YearsOnly Without Winters SSWswithout SSWs! decomposition (Eq. 5) is reasonable.(Kalnay(Kalnay et et al. al. 1996). 1996). Fifty Fifty years years (1958—2007) (1958—2007) were were used used to300 produce to produce the climatologies. the climatologies. The agreement The agreement field at x does not completely determine the surface pressure at Pressure Level [hPa] x.Morespecifically,whilewecanwrite Longer decorrelation Stratosphere-Troposphere Coupling yL = δZL eL = δZT eL + δZ p s eL • longer decorrelation times in stratosphere decomposition (Eq. 5) is reasonable. · · 1000 · timescales in stratosphere! between the original geopotential anomalies and the linearization-0.2 0.0 is on0.2 order0.4 of0.6 1–5%.0.8 1.0 We find that the shorter decorrelation times in troposphere The two mechanistic models would imply that these two fields are, to someFigure extent, 1 illustrates the decompositionbetween the original at three geopotential different pr anomaliesessure levels and the using linear NCEPization reanalysisFractional is onVariance order data of 1–5%. We find that the • Figure 1 illustrates the decompositionAM index atlinearized three diff erentAM spatial pressure levels using NCEP reanalysis data Shorter decorrelation times dynamically separate, but observations suggest that they couple under some conditions. For p =ˆp g/(RT )dz,knowledgeofthefulltemperaturedistribution,stillreq⎨ ⎨ uires knowledge of the pressure NCEPT/p! s correlations! • no increase observed in timescale in s anomalies pattern yT yps b) in troposphere! example, while the stratospheric AM is known to be more persistent than the tropospheric " Level [hPa] Pressure upper troposphere AM,4,5 tropospheric AM persistence increases during seasons when the stratosphere(Kalnay itself et(Kalnay is al. 1996). et al. 1996). Fifty Fifty years years (1958—2007) (1958—2007) were were used used to produce to pr theoduce climatologies. the5 climatologies. The agreement The agreement No increase of timescale in most active and persistent.6 on a second referenceLinearized level, anomaliesp ˆ to determine are an excellentps.Thus,surfacepressureandtemperaturecanbeconsidered approximation5 to nonlinear anomalies Onlyupper Years troposphere With SSWs! between the original geopotentialLinearized anomalies AM time and series the linear componentsization is on order are of additive: 1–5%. We findy = that y + the y Stratosphere-troposphere coupling is also implied by “dripping paint” type plotsbetween such as the the original geopotential anomalies and the linearization is on order of 1–5%.L T Weps find that the \! 10 10 c) Total! •Onlyshorter Winters decorrelation with SSWs! times in stratosphere a) 0.9 0.5 -0.1 b) 0.9 0.5

-0.1 ! one below. Stratospheric anomaly patterns0.1 propagate downwards from the upper-0.1 and mid- as independent0.1-0.1 fields for a hydrostatic fluid. This is why, for example, global climate models use separate stratosphere30 towards the lower stratosphere over 1-2 weeks. Once30 such anomalies reach • longer decorrelation times in troposphere

-0.9 5 -0.9 Shorter decorrelation 100 0.1 100 -0.5 the lower stratosphere, they rapidly descend throughout the entire troposphere, where like-0.5 -0.1 • increased timescale in upper troposphere -0.5 prognostic0.1 equations for surface pressure5 and temperature.Thisisanimportantcheckonthewhetherthe timescales in stratosphere! signed anomaly300 patterns may exist for upwards of two months. 300 0.1 Decomposition of Coupling Events 0.1 1000 1000 -0.1 d) T/ps correlations! PanelsLonger show decorrelation NAM timescale times and cross correlation timescales

10 0.1 10 0.1 calculatedin troposphere from time series! composed only of years without SSW 0.9 0.5 -0.1 -0.1 For each winter (NDJFM) we define a single weak vortex event as the day with the largest negative 0.9 30 Composite of Warm Vortex Events, 1958-2007, NCEP 30 decomposition (Eq. 5) is reasonable. Level [hPa] Pressure events (a, b) or only of years with SSW events (c,d). The selection NAM index based on the 10 hPa AM time series for the linearized geopotential, yL. criteriaIncrease leads to of non-adjacent timescale yearsin being spliced together. These 10 100 -0.1 100 0.5 -0.5 Composite of warm vortex events splicesupper are aligned troposphere during NH! summer to curtail their effect during the 10 0.5 10 -0.5 0.9 a) -0.1 0.9 -0.1 b)(NDJFM) based on northern 0.5 0.1 -0.1 300 300 -0.1 Figure0.1-0.1 1 illustrates the decompositionNCEP, 1958-2007 at three different prERA40,essure 1961-2001 levels using NCEP reanalysis data Season! active vortex season. hemisphere polar-cap averaged -0.1 0.5 30 a)10 0.9 0.1 -0.1 b) 10 0.9 -0.1 30 30 0.5 0.1 1000 geopotential1000 height anomalies. -0.1 30 30 -0.1 10 Contour10 intervals represent standard -0.1

-0.9 100 100 -0.9 deviations of anomaly indices and -0.5 0.1 0.1 0.5 0.5 100 a)10 -0.5 0.9 0.1 -0.1 b) 10 0.9 -0.1 10030 0.1 are10030 spaced by 0.2. Index -0.5 values 300 0.5 300 0.1 -0.1 -0.1 -0.1 (Kalnay et al. 1996). Fifty years (1958—2007) were used to produce the climatologies.0.1 The agreement 30 30 -0.1 0.5 -0.1 between -0.1 and 0.1 are unshaded. 0.1 1000 1000 Pressure Level [hPa] 100 -0.1 -0.5 100 10010 0.5 0.1 10010 0.1 -0.1 -0.1 Composites for strong vortex events 0.9 -0.5 0.1 -0.1 -0.1 -0.1 300 -0.1 -0.1 0.5 0.5 -0.1 -0.5 0.1 300 are300 similar except for the sign. -0.1 30030 30030 -0.1

-0.1

0.1 300 300 0.1 0.9 0.3 0.1 1000100 1000100 between the-0.1 original geopotential-0.1 -0.5 anomalies and the linear-0.5ization is on order of 1–5%. We find that the 10 0.5 0.1 10 -0.1 0.1 -0.1 10001000 1000 0.9 0.1 Pressure[hPa] Level 1000 1000 300 -0.1 300 -0.1 -60 -40 -20 0 20 40 60 80 -60 -40 -20 0 20 40 60 80 30 30 0.5 1000 1000 0.9 10 10 10010 10010 Event Lag [days]0.5 0.1 0.1 -0.1 -0.1 -0.5 -0.5 0.9 -0.1 -0.1 -0.1 30030 30030 0.1 10 0.5 10 0.9 -0.1 c) d) 0.9 0.5 0.1 -0.5 -0.1 Pressure Level [hPa] Conclusions 0.9 1000100 1000100 -0.1

0.1 -0.1

30 30 -0.1 -0.1 -0.1 30 30 10 10 -0.1 -0.5 300 300 0.3 -0.1 30 -0.1 30 0.3 1000 0.3 10005 0.3

100 100 Pressure Level [hPa] -0.1 0.5 100 100 -60 -40 -20 -0.1 0 20 40 60 80 -60 -40 -20 0 20 40 60 80 100 100 -0.1 We begin by exploring the elementary idea suggested by the mechanistic models -0.1 -0.1 -0.1 -0.5 -0.1 0.1 300 Lag 300 Lag 300 300 -0.1 -0.5 10 0.3 0.5 -0.1 10 The linear decomposition diagnostic we present has several advantageous properties: -0.1 0.3 0.1 0.1 c) d) 0.10.3-0.1 0.9 0.3 -0.1

described above: that AM persistence in stratosphere is related to stratospheric 0.9 -0.1 -0.1 0.1 1000 1000 0.1 0.1 -0.1

30 30 -0.5 1000300 1000300 -60 -40 CMAM-20 LOWERED,0 20 4040 years60 80 -60 -40 -20 0 20 40 60 80 temperature signals while throughout the troposphere it is related to surface 100 100 CMAM HIGH, 40 years 10 10 -0.1 -0.1 0.5 Empirical, relatively easy to do,motivated by basic dynamical ideas 0.5 -0.1 0.1 -0.5 10 0.5 10 -0.1 • c) d) 0.1 0.5 0.5 -0.1 0.9 0.1 -0.1 0.9 0.1 0.1 300 0.9 300

0.1 -0.1 30 30 -0.5 pressure1000 signals. We explicitly decompose AM variability1000 into contributions-0.5 from 30 30 -0.1 1000 1000 • Cleanly separates stratospheric and tropospheric contributions to AM variability 0.9 10010 0.5 10010 surface10 pressure and from temperature fields, based on10 a linearization of the 0.9 0.5 -0.1 -0.5 -0.1 0.9 100 100 0.5 0.5 0.1 0.1 0.1 0.1 30030 30030 -0.5 Quantifies effect of coupling in UTLS on persistence 0.1 -0.1 • -0.1 -0.1 geopotential300 height-0.1 0.1 integral. This decomposition0.1 helps to300 separate stratospheric 1000100 1000100 10 0.5 10 -0.1 30 30 -0.1 0.9 -0.1 -0.1 -0.5 Provides additional views of GCM performance 300 300 0.9 0.5 • 0.1 0.1 and tropospheric1000 AM variability when applied to AM 1000 stratosphere-troposphere 30 30 -0.5 1000 1000

Pressure Level [hPa] 10 10 10010 10010 coupling100 -0.1 events and highlights the role of coupling between100 surface pressure and -0.1 -0.1 -0.1 -0.1 30 30 -0.1 300 300 0.1 30 -0.1 30 -0.1 -0.1 In addition, weak but persistent cross correlations between T and ps suggest dynamical -0.1

Pressure Level [hPa] 1000 1000 temperature signals in determining AM timescales. -0.1 100 100

-0.1 -0.1 -0.1 10 -0.1 10 Pressure Level [hPa] 100 -0.1 100 300 -0.1 300 ideas to test about eddy driving in UTLS. 300 300 -0.1 0.3 30 0.3 30 -0.1 1000 1000 300 300 Pressure Level [hPa] 100-60 -40 -20 0 20 40 60 80 100-60 -40 -20 0 20 40 60 80

-0.1 1000 0.3 1000 -0.1 -0.1 -0.1 300 Lag -0.1 300 Lag 1000 1000 0.3 -60 -40 -20 0 20 40 60 80 -60 -40 -20 0 20 40 60 80 1000 1000 -60 -40 -20 0 20 40 60 80 -60 -40 -20 0 20 40 60 80 -60 -40 -20 0 20 40 60 80 -60 -40 -20 0 20 40 60 80 Lag Lag Lag Lag Lag Lag References Observed Data and Model Output Mudryk, L. R. and Kushner, P. J. (2011), A method to diagnose sources of annular mode time scales, JGR, 116, D14114. c) 10 0.5 d) 10 -0.1 -0.5 Each plot shows composites for warm vortex events for each of the data sets. Within each plot, from top to bottom, panels -0.1 0.9 0.5 0.1 show composites of linearized geopotential, temperature component and surface pressure component, respectively. Contour 1. Thompson, D. W. J and Wallace, J. M., GRL, 25, 1998. 5. Charlton-Perez, A. and O’Neill, A., J. Climate, 23, 2010. Fig. 4. Composite of warm vortex0.9 events0.1 based on northern hemisphere polar-cap averaged geopotential 30 30 intervals are spaced by 0.2. Index values between -0.1 and 0.1 are unshaded. 2. Holton, J.R. and Mass, C., JAS, 33, 1976. 6. Baldwin, M. P., et al., Science, 301, 2003 -0.5 5 Reanalysisheight anomalies. Data Data setsCanadian shown in plots Middle a) through Atmosphere d) are the Model same as(CMAM) Fig. 3. FromData top to bottom the 3. Vallis, G.K. et al., JAS, 61, 2004. 7. Gerber, E. P., et al., GRL, 35, 2008. panels100 show composites of linearized geopotential, temperature100 component and surface pressure component, For both reanalysis data and model runs, the surface pressure component of the 4. Limpasuvan, V. et al., JGR, 110, 2005. NCEP, LOWERED: 41 vertical levels, lid at 10 hPa geopotential height dominates the pattern in the troposphere, while the temperature respectively. Contour intervals are spaced by 0.2. Index values between -0.1 and 0.1 are unshaded.0.1 1958-2007,300 daily resolution HIGH: 71 vertical levels, model300 lid at -0.10.0006 hPa component dominates in the stratosphere. Models display an extended or delayed surface 0.1 0.1 -0.1 -0.1 0.1 ERA40 0.1 0.1both configurations conserve momentum by depositing gravity pressure anomaly compared to observations as well as a stronger warm/positive anomaly in Affiliation 1961-2001,1000 daily resolution wave momentum in the uppermost1000 layer. 10 10 both temperature and surface pressure in the troposphere prior to the stratospheric event. Department of Physics, University of Toronto email: [email protected] 0.5 -0.1 0.1-0.1 -0.5 0.9 0.5

30 30 -0.5

0.9 100 100 300 -0.1 0.1 0.1 300 -0.1 1000 1000 10 10 30 30

Pressure Level [hPa] 100 -0.1 100

-0.1 18 -0.1 300 300

0.3 -0.1 1000 1000 -60 -40 -20 0 20 40 60 80 -60 -40 -20 0 20 40 60 80 Lag Lag

Fig. 4. Composite of warm vortex events based on northern hemisphere polar-cap averaged geopotential height anomalies. Data sets shown in plots a) through d) are the same as Fig. 3. From top to bottom the panels show composites of linearized geopotential, temperature component and surface pressure component, respectively. Contour intervals are spaced by 0.2. Index values between -0.1 and 0.1 are unshaded.

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