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Stratosphere-Troposphere Coupling: a Method to Diagnose Sources of Annular Mode Timescales

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Stratosphere-Troposphere Coupling: a Method to Diagnose Sources of Annular Mode Timescales 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 ashorizontalZ(x,p,t position)=Z (asx,p a )+temperatureδZ(x,p,t integral). Decomposing from the Earth’s the temperature surface to a andgiven 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 pabove 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 pressureover 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 ofas 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 surfacethe 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.
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