Annular Mode Variability of the Atmospheric Meridional Energy Transport and Circulation

Transcription

1 27 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 72 Annular Mode Variability of the Atmospheric Meridional Enery Transport and Circulation RAY YAMADA Courant Institute of Mathematical Sciences, New York University, New York, New York OLIVIER PAULUIS Courant Institute of Mathematical Sciences, New York University, New York, New York, and NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates (Manuscript received 27 July 214, in final form 6 January 215) ABSTRACT Month-to-month variability in the meridional atmospheric enery transport is analyzed in the Modern-Era Retrospective Analysis for Research and Applications (MERRA) reanalysis for The meridional transport of moist static enery (MSE) is composited onto the hih and low phases of the northern and southern annular modes (NAM and SAM). While the hih phase of the NAM and SAM is known to involve a poleward shift in the midlatitude storm track and jet, it is shown here that the distribution of poleward MSE transport shifts equatorward. This chane is explained by examinin the variability of the underlyin meridional circulation. In particular, chanes in the mass transport averaed on dry and moist static enery levels are considered. These circulations have an advantae over the conventional Eulerian circulation for explainin the total enery transport. They are computed usin the statistical transformed Eulerian-mean (STEM) formulation, which provides a decomposition of the circulation into Eulerian-mean and eddy-driven components. The equatorward shift in the MSE transport is larely explained by a poleward shift of the Ferrel cell, while chanes in the eddydriven circulation have a comparatively small effect on the enery transport. The chanes in the residual circulation and jet are shown to be consistent throuh momentum balance aruments. Mean-eddy feedback mechanisms that drive and sustain the annular modes are discussed at the end as a possible explanation for why the chanes in the eddy-driven circulation are weak compared to the chanes in the Eulerian circulation. 1. Introduction Midlatitude storms make up an essential part of the climatoloical atmospheric circulation. They are responsible for most of the poleward transport of enery and water and maintain the surface westerlies aainst friction (e.., Peixoto and Oort 1992; Vallis 26). Understandin their variability is important for assessin how the distribution of wind, temperature, water, and other atmospheric tracers may chane over time. The impact of their variability on the lare-scale climate is typically captured by an empirical orthoonal function (EOF) analysis of the extratropical eopotential heiht or zonal wind fields. The leadin EOF in both hemispheres Correspondin author address: Ray Yamada, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY yamada@cims.nyu.edu is nearly zonally symmetric and is referred to as the northern and southern annular modes, or NAM and SAM, respectively (Limpasuvan and Hartmann 1999; Thompson and Wallace 2). The annular mode is associated with north south vacillations of the eddy-driven jet about its mean position (e.., Hartmann and Lo 1998; Eichelberer and Hartmann 27), where, by convention, the jet is displaced anomalously poleward (equatorward) when the annular mode is in its positive (neative) phase. Althouh the natural variability in the atmosphere arises predominantly from synoptic storms spannin a few days, the annular modes vary on much loner intraseasonal time scales. This has led to the idea that the zonal wind anomalies persist from a mean-eddy feedback, in which a meridionally displaced jet is supported by the chanes it induces in the storm track and eddy forcin. A potential feedback mechanism is proposed in Robinson (2): anomalously stron westerlies, with vertical shear induced by surface dra, reside over a reion of enhanced DOI: /JAS-D Ó 215 American Meteoroloical Society

2 MAY 215 Y A M A D A A N D P A U L U I S 271 baroclinicity from thermal wind balance. The increase in baroclinicity facilitates the eneration of baroclinic eddies, which propaate away from and convere momentum into the jet, thereby strenthenin the oriinal westerly anomaly. In the case of the annular modes, this feedback would imply that a shift of the jet will lead to a shift in the baroclinicity and reion of baroclinic wave eneration. The baroclinicity must shift with the jet from thermal wind balance, but as Robinson points out, this feedback mechanism depends on the assumption that an increase in baroclinicity strenthens the source of wave activity. Lorenz and Hartmann (21, 23) use time la reression to show that, in response to both the NAM and SAM, the source of synoptic waves shifts with the baroclinicity and that the chane in the synoptic eddy forcin supports the zonal wind anomaly. These results indicate that, at least for synoptic eddies, the feedback mechanism appears robust. The importance of the feedback mechanism has been debated however, as for example, Feldstein and Lee (1998) show that a positive feedback is supported by synoptic eddies, but the total eddy contribution does not appear to increase the persistence of the jet anomaly. The 2D barotropic model study by Vallis et al. (24) uses a stochastic eddy forcin, which produces lowfrequency variability without any mean feedback on the eddy forcin. Whether the low-frequency variability of the jet is due to a positive feedback or is simply forced at onset (Feldstein and Lee 1998), the lon-term (e.., monthly averaed) zonal momentum balance requires that the eddy forcin supports the jet anomaly. That is, for the barotropic wind anomaly to withstand a proloned shift aainst surface dra, a sufficient chane in the eddy momentum flux converence must take place within the averain period. Such coherent chanes between the jet and eddy forcin been observed in various observational (Lau 1988; Karoly 199; Hartmann and Lo 1998; Limpasuvan and Hartmann 2) and model studies (Robinson 1991; Yu and Hartmann 1993; Limpasuvan and Hartmann 1999, 2). The aforementioned studies have larely focused on understandin the dynamics between the zonal jet and its eddy forcin. Moreover, the mean-eddy dynamics are often studied usin vertically interated (e.., Feldstein and Lee 1998; Lorenz and Hartmann 21, 23) or stochastically forced 2D barotropic (Vallis et al. 24) dynamics. In such cases, the zonal jet is coupled to only the eddy momentum fluxes. In fully 3D dynamics, both the eddy fluxes of heat and momentum and the meridional circulation are important for momentum balance (Andrews and McIntyre 1976; Edmon et al. 198). Hence, a systematic chane in the storm track should be tied to a chane in the meridional mass transport. This would consequently impact the poleward transport of heat, water, and other atmospheric tracers in the larescale circulation. Understandin the internal variability of the meridional circulation associated with the annular modes is the primary oal of this work. In this study, we first examine the monthly annular mode variability of the meridional transport of atmospheric enery. Our results are based on the MERRA reanalysis dataset from 1979 to 212. The atmospheric enery transport includes the contribution from the sensible heat and eopotential enery, which toether are referred to as the dry static enery (DSE), the latent heat (LH), and to a lesser extent the kinetic enery. The moist static enery (MSE) is defined to be the sum of the DSE and LH, and its transport ives a close approximation of the total atmospheric enery transport (e.., Peixoto and Oort 1992). The poleward advection of MSE by the circulation is essential for maintainin lobal thermal equilibrium by compensatin radiative imbalances at the top of the atmosphere. Anomalies from the annual cycle for the monthly averaed transports of MSE, DSE, and LH are composited onto the low and hih phases of the NAM and SAM. Since MSE is primarily advected poleward by midlatitude eddies (e.., Peixoto and Oort 1992), it miht seem that the distribution of poleward MSE transport would shift toether with the midlatitude storm track and jet. But, to the contrary, we find that it shifts in the opposite direction of the jet in both hemispheres. Namely, in the positive phase of the NAM and SAM, the distribution of poleward MSE transport shifts equatorward as the jet shifts poleward, and similarly for the DSE transport. The chane in the enery transports reflects a chane in the underlyin meridional mass transport. We show that the equatorward shifts of the DSE and MSE transports are larely explained by the chane in the Eulerian circulation. However, the Eulerian circulation does not include the eddy contribution to the enery transport. To understand how the total enery transport is affected by the meridional circulation, we consider the mass transport averaed on surfaces of constant DSE and MSE (Czaja and Marshall 26; Döös and Nilsson 211). The circulations that result are similar to the circulations on dry and moist isentropes (Pauluis et al. 28, 21) and include contributions from both the Hadley circulation in the tropics and synoptic-scale eddies in the midlatitudes. They offer a better approximation to the mean Laranian trajectories of air parcels, since static enery is almost conserved for adiabatic processes. The chane in the circulation determines the chane in the total enery transport and also has implications for the variability of other atmospheric tracer transports. Additionally, it

3 272 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 72 connects the chane in the enery transport to the chane in the jet, as the circulation and jet are related throuh the zonal momentum budet. The section overview for the paper is as follows. Details about the dataset and the annular modes can be found in section 2. The results for the annular mode variability of the enery transports are presented in section 3. Section 4 beins with a discussion of the meridional circulation computed on surfaces of constant enery and its relationship to the enery transport. The annular mode variability of the circulation is then presented. The chane in the circulation is shown to be dynamically consistent with the jet shift throuh an analysis of the zonal momentum budet. We then discuss mean-eddy feedbacks for the annular modes and a possible explanation for why the chane in the enery transport driven by the eddies is relatively weak compared to the chane driven by the Eulerian-mean circulation. We conclude with a summary and discussion in section Dataset and annular modes a. Dataset The results in this study are based on monthly and zonally averaed quantities from the MERRA reanalysis dataset from 1979 to 212 (Rienecker et al. 211). The MERRA data are output 83 daily(every3hfrom UTC) on a 1: :258 latitude lonitude rid at 42 pressure levels. Zonal averaes are first computed at 83 daily resolution and then monthly averaes are taken. The monthly and zonal averae of a field X will be denoted by X. The deviation from X will be denoted by X. The anomaly of X will refer to the departure of X from its annual cycle, where the annual cycle is computed as the climatoloical averae of X for each calendar month. b. Annular modes The NAM and SAM were computed as the leadin EOF of zonally and monthly averaed eopotential heiht anomaly at 85 hpa from 28 to 88 in their respective hemisphere. The anomaly was first weihted by the square root of the cosine of latitude to weiht each point by its spatial area. The NAM and SAM account for 58% and 73%, respectively, of the total variance in the monthly- and zonal-mean 85-hPa heiht anomaly. The annular mode index is taken to be the standardized (i.e., taken to have unit variance and zero mean) first principal component (PC) time series from the EOF calculation. The index is defined to be hih (low) when its value lies above (below) 1.25 standard deviations. Between 1979 and 212 (48 months) there were 33 (4) NAM hih (low) events and 42 (41) SAM hih (low) events that were used for compositin. The variance of the NAM is reatest in the winter, with the months of December February (DJF) accountin for 67% (5%) of the hih (low) events. The seasonality of the SAM is less pronounced, as JJA accounts for only 26% (32%) of the hih (low) events. When computin the hih (low) annular mode composite of a field, we first remove the field s annual cycle to subtract out seasonal variability. The resultin anomaly field is then averaed over the months when the annular mode index is hih (low). The hih and low composites are based on the anomaly field, rather than the full field, and reflect chanes associated with extreme annular mode events without confoundin the effects of seasonality. When plottin the hih or low composite, we add back the field s annual mean to visualize the effect of the annular mode on the full field. Note that addin back the annual mean does not affect the hih minus low composite difference. The hih minus low composite differences of the zonalmean zonal winds onto the SAM (left) and NAM (riht) are shown in shadin in Fi. 1. The annual-mean jet profile is drawn in black contours for comparison. In both hemispheres, the composite difference consists of an equivalent barotropic dipole. The dipole is centered about the midlatitude jet maximum and results from a poleward (equatorward) shift of the midlatitude jet from its mean position durin the hih (low) phase of the annular mode. This is more clearly seen in the Southern Hemisphere, where the subtropical and midlatitude jets are clearly separated. In the Northern Hemisphere, the jets in the Atlantic are well separated, but in the Pacific the jets are more closely collocated (Eichelberer and Hartmann 27). The lack of separation throuhout the Northern Hemisphere is apparent in the annual-mean jet profile, but the variability described by the NAM is still stronly dipolar about the approximate midlatitude jet position. The dashed, black, vertical lines mark the positive and neative centers of the dipole in the lower troposphere and will be drawn in later fiures for reference. They are located at 578 and 38 in the Northern Hemisphere and at 68 and 378 in the Southern Hemisphere. The positive (neative) center position is computed as the averae of the latitudes of maximum (minimum) values in the composite difference for pressure levels reater than 6 hpa. Lower-level winds were used to track the chanes in the eddy-driven jet since they are less affected by the subtropical jet. 3. Variability of the enery transport a. Enery transport climatoloy The MSE is equal to the sum of the DSE and LH, where the DSE equals c p T 1 Z and the LH equals L y Q.Here

4 MAY 215 Y A M A D A A N D P A U L U I S 273 FIG. 1. The hih minus low composite differences of the zonal-mean zonal wind onto the (left) SAM and (riht) NAM (shadin). The positive and neative centers of the composite differences are marked by black, dashed vertical lines. The annual-mean climatoloy of the jet is drawn with ray contours with positive (neative) values denoted by the solid (dotted) lines. The contours are drawn at [21, 25,..., 25, 3] m s 21, excludin zero. the specific heat at constant pressure, c p ;thelatent heat of vaporization, L y ; and the ravitational acceleration,, are taken to be constants (c p 5 14 J K 21 k 21, L y 5 2: Jk 21, 5 9:8ms 22 ). The variables T, Z, and Q are the temperature, eopotential heiht, and specific humidity, respectively. Let j(l, f, p) represent the MSE, DSE, or LH, and y(l, f, p) be the meridional velocity, where j and y vary over lonitude l, latitude f, and pressure p. The total transport of j across latitude f computed for each month is iven by ð 2pa cosf psfc M j (f) 5 yj(f, p) dp, where a the radius of the earth and p sfc the surface pressure. The quantity M j is the zonally and vertically interated meridional flux of j at f and can be decomposed into the sum of the j transport by the mean flow and the eddies where M j 5 M j,mean 1 M j,eddy, (1) ð 2pa cosf psfc M j,mean (f) 5 y j dp and ð 2pa cosf psfc M j,eddy (f) 5 y j dp. We will refer to M j as the total j transport, M j,mean as the mean-flow j transport, and M j,eddy as the eddy j transport. Fiure 2 shows the climatoloical annual mean for the MSE (top), DSE (middle), and LH (bottom) transports in the reanalysis. The enery transports are decomposed into the total (solid line), mean-flow (dashed line), and eddy (dotted line) transports. Since northward fluxes are taken to be positive by convention, a poleward enery transport by the circulation is positive in the Northern Hemisphere and neative in the Southern Hemisphere. The total MSE transport is poleward at all latitudes and attains a maximum poleward transport of around 4 petawatts (PW) near 48 in both hemispheres. Most of the poleward enery transport is accomplished by the eddies alon the midlatitude storm track, where the maximums are attained in the three eddy enery transports (the LH transport peak occurs further equatorward where there is a hiher moisture concentration). The MSE transport by the mean flow is small in comparison to the eddy MSE transport and exhibits a tripolar structure with a poleward transport at low and hih latitudes and an equatorward transport in the midlatitudes. The mean-flow DSE and LH transports are also tripolar but are out of phase, unlike their eddy transports, which weakens the overall MSE transport. The tripolar structure can be explained by understandin how mass is advected by the Eulerian-mean circulation, which is computed from the time and zonally averaed meridional mass transport on pressure surfaces. An Eulerian streamfunction, denoted by C p,wheresubscript p desinates that the mass flow is isobarically averaed, is defined as

5 274 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 72 FIG. 2. The annual-mean climatoloy of the total, mean-flow, and eddy enery transports (solid, dashed, and dotted lines, respectively) for the (top) MSE, (middle) DSE, and (bottom) LH. 2pa cosf C p (f, p) 5 ð p y(f, ~p) d~p (2) and consists of three cells: the tropical Hadley cell, the midlatitude Ferrel cell, and the polar cell (Fi. 3). Positive (neative) values of the circulation denote anticlockwise (clockwise) rotation in the fiure. 1 While eddies transport enery throuh quasi-horizontal mixin of hih- and lowenery air parcels, the Eulerian circulation transports enery throuh overturnin cells. In the time mean, the cells have no net meridional mass transport but do yield a net poleward enery transport. Since DSE increases with heiht, the net transport of DSE is in the direction of the upper branch of the cell. Similarly, moisture is concentrated in the lower troposphere and so the direction of LH advection is determined by the lower branch. The DSE transport by the circulation is reater than the LH transport and so the overall MSE transport is in the same direction as the DSE. The Hadley and polar cells are therefore thermally direct (i.e., they provide a net 1 Since pressure decreases with heiht, its vertical axis is typically plotted in reverse. For this reason, we plot 2C p, rather than C p,to maintain the sin convention. poleward enery transport by brinin hih-enery parcels to hiher latitudes where they lose enery throuh radiative coolin), whereas the Ferrel cell is thermally indirect. The alternatin sins in the cells of the streamfunction explain the tripole structure that was observed in the mean-flow enery transport in Fi. 2. b. Observed chanes in the enery transport The total, mean-flow, and eddy enery transports (M MSE, M MSE,mean, M MSE,eddy ; M DSE, M DSE,mean, M DSE,eddy ; M LH, M LH,mean, M LH,eddy ) were composited onto the hih and low phases of the NAM in the Northern Hemisphere and SAM in the Southern Hemisphere. The hih minus low composite differences are shown in Fi. 4 for NAM (riht column) and the SAM (left column). The chanes in the MSE (black), DSE (teal), and LH (maenta) transports are broken down into the total (top row), mean-flow (middle row), and eddy (bottom row) contributions. The composites were qualitatively similar when just the first or second half of the time series was used instead of the full time series. The extratropical response to the annular modes is qualitatively symmetric between the two hemispheres, althouh there are considerable differences in the tropics. In the extratropics, the chanes in the total enery

6 MAY 215 Y A M A D A A N D P A U L U I S 275 FIG. 3. The annual-mean climatoloy of the Eulerian circulation. Positive (neative) values indicate anticlockwise (clockwise) circulation. transports (top row of Fi. 4) are dipolar and are centered about a nodal latitude near 368 in the Northern Hemisphere and 448 in the Southern Hemisphere. On the poleward (equatorward) side of the node, there is a decrease (increase) in the total poleward transport of DSE. The chane in the total LH transport are similarly dipolar but of opposite sin. The dipolar chane in the DSE transport acts to shift the distribution of the total poleward MSE transport from Fi. 2 equatorward, while the LH transport chane acts to shift it poleward. Equatorward of the node, the chanes in the DSE and LH transports larely compensate each other, such that the net chane of the total MSE transport is small. Poleward of the node, the chane in the MSE transport is dominated by the chane in the DSE transport and reaches a maximum reduction of around.3 PW near 478N and.25 PW near 568S. The dipole structure indicates that the annular mode variability of the midlatitude poleward enery transports are described by north south vacillations, similar to the eddy-driven jet (the dotted vertical lines mark the jet dipole axes as in Fi. 1). However, while the jet shifts poleward in the hih annular mode phase, the distributions of the poleward DSE and MSE transport shift equatorward. The equatorward shift in the DSE transport is characterized by a dipolar anomaly, whereas in the case of the MSE, the chane occurs mainly on the poleward flank owin to the latent heat compensation in the subtropics. Since MSE is primarily transported poleward by midlatitude eddies (Fi. 2), an equatorward shift in the total MSE transport appears at odds with a poleward shift in the storm track and eddy-driven jet. To explain these apparently inconruous chanes, we first decompose the chane in the total enery transport into its mean-flow and eddy components. Comparin the panels in Fi. 4, the annular mode variability of the total MSE, DSE, and LH transports are noticeably dominated by the chane in their mean-flow components, except near 68 where the eddy chanes are comparable. The mean-flow chanes are similarly dipolar and reflect a chane in the Eulerian circulation. Fiure 5 shows in shadin the hih minus low composites of the Eulerian circulation onto the NAM (Fi. 5b) and SAM (Fi. 5a). The black contours show the annualmean Eulerian circulation for comparison. From the low to the hih phase, there is a noticeable poleward shift of the Ferrel cell in both hemispheres. This is indicated by a dipolar anomaly, centered rouhly about the mean position of the Ferrel cell, that consists of two anomalous circulation cells: a thermally direct cell in the subtropics and an indirect cell at hiher latitudes. The Eulerian circulation dipole alins well with the mean-flow DSE and LH transport dipoles from Fi. 4 (middle row). The chanes in the mean-flow enery transports reflect the enery advected by the anomalous circulation cells. The anomalous direct cell transports DSE poleward and LH equatorward in similar amounts, such that there is a small chane in the MSE transport equatorward of around 48 in both hemispheres. The anomalous indirect cell is located at hiher latitudes, where there is less moisture, and its net MSE transport is composed mostly of an equatorward DSE transport. This anomalous equatorward MSE transport is equivalent to a decrease in the overall poleward MSE transport. A poleward shift of the Ferrel cell in the hih annular mode phase therefore induces an equatorward shift in the midlatitude transports of DSE and MSE. As has been noted in past studies (Limpasuvan and Hartmann 1999; Thompson and Wallace 2), the annular mode chanes in the midlatitude Eulerian circulation

7 276 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 72 FIG. 4. Hih minus low composite differences for the MSE (black), DSE (teal), and the LH (maenta) for the (top) total, (middle) mean-flow, and (bottom) eddy enery transports. Composites for the (riht) Northern [(left) Southern] Hemisphere onto the NAM [(left) SAM]. The dotted vertical lines mark the positive and neative centers from the zonal wind composite in Fi. 1. are consistent with the poleward shift of the jet. There is anomalous warmin (coolin) on the equatorward (poleward) side of the anomalous indirect cell, as can be seen in the composite difference of the temperature field (bottom row of Fi. 5). These temperature anomalies arise from the adiabatic warmin and coolin of air advected by the modified mean flow. The chane in the Eulerian circulation adjusts the backround baroclinicity to restore thermal wind balance with the vacillatin zonal jet. It should be noted that the jet dipole (denoted by the dashed vertical lines) is not in exact alinment with the Eulerian circulation dipole, especially for the equatorward node. This is because, in addition to the Ferrel cell shift, the chane in the Eulerian circulation also involves sinificant strenthenin of the Hadley circulation, which extends the equatorward dipole node farther equatorward. The composite differences for the eddy enery transports are shown in the bottom row of Fi. 4. The most sinificant chanes are described by a monopolar increase in the poleward eddy enery transport around 68 in both hemispheres but are noticeably stroner in the Northern Hemisphere than in the Southern Hemisphere. Except near the center of the monopole, the responses of the eddy enery transports to the annular modes are small in comparison to those of the mean flow. This is in sharp contrast to the climatoloical enery transports in Fi. 2, in which the eddies dominated the mean flow. The annular modes clearly do not describe a uniform poleward shift of the midlatitude circulation. For if this were the case, then the equatorward shift in the mean-flow enery transport would be compensated by a poleward shift of the eddy enery transport. The chane in the eddy enery transport is markedly different from the chane in the eddy momentum flux converence of the upper troposphere, which has a stron dipolar response that is coherent with the jet shift [e.., Limpasuvan and Hartmann (2) and discussed next].

8 MAY 215 Y A M A D A A N D P A U L U I S 277 FIG. 5. (top) The hih minus low composite difference for the Eulerian circulation (shadin) for the Northern Hemisphere onto the (riht) NAM and Southern Hemisphere onto (left) the SAM. The annual-mean Eulerian circulation is drawn in black contours for reference, with contours drawn at [24, 2,...,6,8]3 1 1 k s 21, excludin zero. The dotted vertical lines mark the positive and neative centers from the zonal wind composite in Fi. 1. (bottom) The composite difference of the temperature field (shadin). The black contours show the composite difference of the Eulerian circulation from the panels above. Solid (dashed) contours represent positive (neative) values. 4. Variability of the dry and moist circulations While the jet shifts poleward in the hih annular mode phase, the DSE and MSE tranports shift equatorward. To reconcile these rather counterintuitive chanes, it is important to understand the variability of the meridional circulation. On the one hand, the circulation determines the enery transport, while on the other hand, the variability of the circulation and jet are related throuh momentum balance constraints. In this section, we first discuss the connection between the total enery transport and the circulation, and then we examine the annular mode composites of the circulation. We show that the chanes in the jet and circulation are dynamically consistent by considerin the momentum budet. At the end, we discuss mean-eddy feedbacks, which may explain why the chane in the Eulerian circulation is more pronounced than the chane in the eddy-driven circulation in the monthly composites. a. Relationship between the meridional circulation and enery transport The chanes observed in the Eulerian circulation in the previous section helped explain the chanes in the meanflow enery transport. However, the Eulerian circulation does not account for the total enery transport, especially in the midlatitudes where eddies dominate the circulation. The indirect overturnin implied by the Ferrel cell ives a strikinly misleadin impression of the midlatitude circulation, which is actually thermally direct (Fi. 2) and larely comprises quasi-horizontal eddy transports of heat and moisture. To understand the variability in the meridional transport of enery and other tracers, it is necessary to consider a more complete description of the meridional circulation that accounts for both the Eulerian-mean and eddy transports. One alternative description of the circulation, which better captures the total midlatitude enery transport, relies on usin a quasi-laranian vertical coordinate, such as entropy or static enery, instead of pressure. We consider the circulation averaed on the latter surfaces of constant DSE and MSE and will refer to these as the dry and moist circulations. The motivation here is twofold. First, as static enery is almost conserved for reversible adiabatic processes, averain the flow on surfaces of constant static enery offers a better approximation of the Laranian trajectories than an averae on pressure surfaces. The streamfunctions that result consist of a sinle thermally direct cell that extends from equator to pole in both hemispheres (Czaja and Marshall 26; Döös and Nilsson 211). Second, in such framework, the mean circulation accounts for the total enery transport

9 278 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 72 without any eddy contribution (as by definition, there is no fluctuation of enery content on surfaces of constant static enery). A streamfunction for the mass transport interated on levels of constant j canbecomputedas follows (e.., Pauluis et al. 28; Döös and Nilsson 211): C j (f, j )5 ð 2p ð psfc H[j 2j(l, f, p)šy(l, f, p)acosf dp dl, (3) where H(x) denotes the Heaviside function, defined H(x) 5 1 for x $ and H(x) 5 for x,. The zonally interated meridional mass transport at latitude f between j and j 1 dj is iven by C j / jdj. The total transport of j across latitude f can then be computed as M j (f) 5 j C j dj 52 j C j dj, (4) where the second equality is obtained usin interation by parts and the fact that C j vanishes at infinity. Hence, the total transport of DSE and MSE is iven by the neative of the interal over enery of the dry and moist streamfunctions, respectively. Computin the streamfunction as in (3) requires daily and zonally varyin data. Instead, we compute the dry and moist streamfunctions usin the statistical transformed Eulerian-mean (STEM) approximation (Pauluis et al. 211). The STEM streamfunction is a statistical eneralization of the transformed Eulerian-mean (TEM) streamfunction (Andrews and McIntyre 1976; Edmon et al. 198) that can be applied to an arbitrary, unstratified, vertical coordinate usin only zonal- and monthly-mean statistics output on pressure. It is based on the assumption that the joint probability density function of the meridional velocity, y, and the vertical coordinate, j, is approximately bivariate Gaussian. The STEM streamfunction only requires knowlede of the first- and second-order moments: y, j, j 2, and y j. Moreover, analoous to TEM, STEM provides a decomposition of the total streamfunction, C STEM,j (C j for short), into an Eulerian-mean and eddy-driven streamfunction iven by where C j (f, j) 5C j,mean (f, j) 1C j,eddy (f, j), (5) ð 2pa cosf j y C j,mean (f, j) 5 pffiffiffiffiffiffi 2p ð 2pa cosf j C j,eddy (f, j) 5 exp 1/2 j 2 y j ( ~ j 2 j) pffiffiffiffiffiffi 2p j 2 3/2 exp (~ j 2 j) 2 5 dp d ~ j and (6) 2j (~ j 2 j) 2 5 dp d ~ j. (7) 2j 2 The relationship between the enery transport and streamfunction (4) also holds for STEM (derivations are iven in appendix A). Additionally, the STEM decomposition (5) allows for the mean-flow and eddy enery transports to be related to their respective components of the STEM circulation: M j (f) 52 C j (f, j) dj, (8) M j,mean (f) 52 C j,mean (f, j) dj, and (9) M j,eddy (f) 52 C j,eddy (f, j) dj. (1) For example, the connection between the chanes in the mean-flow enery transport and those in the Eulerian circulation, discussed in section 3, can be made explicit by analyzin the chane in the mean-flow component of the streamfunction (9). Fiure 6 shows the annual-mean climatoloy of the dry and moist streamfunctions computed from (5), (6), and (7) with j taken to be the DSE (left column) and MSE (riht column). The total streamfunction (Fis. 6a,b) is iven by the sum of a three-celled Eulerian-mean circulation (Fis. 6c,d) and an eddydriven circulation (Fis. 6e,f). In both the dry and moist cases, the total circulation consists of a sinle thermally direct cell. The Eulerian-mean circulation has a three-celled structure as before, but in the total circulation the indirect Ferrel cell is dominated by a direct eddy-driven circulation. The dry circulation has two distinct cores, arisin from a stron Hadley circulation in the tropics and an eddy-driven circulation in the midlatitudes. In contrast, the moist circulation has a sinle core with a stroner extratropical circulation than that of the dry. These differences are due, in part, to the fact

10 MAY 215 Y A M A D A A N D P A U L U I S 279 FIG. 6. (a),(b) The annual-mean climatoloy of the STEM streamfunctions on (left) DSE and (riht) MSE, alon with the correspondin (c),(d) Eulerian-mean circulations and (e),(f) eddy-driven circulations. that the overturnin cells of the Eulerian streamfunction are weaker in the moist case than in the dry case (compare Fis. 6c and 6d). The upper and lower branches of the circulation represent the mass flow of hih- and low-enery parcels, respectively. In the moist case, since low-level air parcels can carry enery in the form of latent heat, hih enery does not necessarily reflect hih altitude. Consequently, there is more cancellation between the upper and lower branches in the moist representation of the Eulerian circulation than in the dry. This is especially true for the Hadley cell, since in the tropical troposphere MSE is well mixed by convection (Xu and Emanuel 1989; Czaja and Marshall 26). The stroner extratropical core in the moist circulation can also be attributed to an increase in the eddy mass transport on MSE levels as compared to that on DSE levels (Fis. 6e and 6f). Pauluis et al. (28, 21) show that this additional mass flux on moist isentropes arises from a low-level flow of warm moist air parcels that are advected from the subtropics into the storm track by midlatitude eddies. b. Observed chanes in the dry and moist circulations The dry and moist circulations (C DSE, C MSE ) and their mean-flow (C DSE,mean, C MSE,mean ) and eddy-driven (C DSE,eddy, C MSE,eddy ) components were composited onto the hih and low phases of the NAM and SAM. The total, mean-flow, and eddy-driven circulation composite differences are shown in Fis. 7 and 8 for the dry and moist circulations, respectively. The results were aain robust when just the first or second half of the time series was used instead of the full time series. First we will discuss the chanes in the dry circulation. The annular mode chanes in the extratropical dry circulation (Fis. 7a,b) are dipolar in both hemispheres, with strenthenin near the subtropics and weakenin in the midlatitude core. This dipole indicates an equatorward shift within the dry circulation durin the hih phase. The subtropical strenthenin of the circulation, centered near 258N and 38S, occurs near the joint connectin the subtropical and midlatitude cores. In the hih phase, the circulation is more uniformly distributed

11 28 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 72 FIG. 7. The hih minus low composite differences onto the (left) SAM and (riht) NAM for the dry circulation (top) C DSE, (middle) C DSE,mean,and(bottom)C DSE,eddy. The annual-mean climatoloies of the circulations are drawn in black contours at [26, 4,...,6,8]3 1 1 k s 21 for the total and eddy-driven circulations and at [25, 23,...,5,7]3 1 1 k s 21 for the Eulerian-mean circulation. Zero contours are not drawn. Solid (dashed) contours represent positive (neative) values. from equator to pole, whereas in the low phase, the circulation is more clearly separated into two distinct cores. From relationship (8), the dry circulation dipole corresponds to the dipole observed in the total DSE transport (Fi. 4, top row). Since the chanes in the streamfunction are for the most part equivalent barotropic, there is little cancellation when the streamfunction is interated in the vertical. Hence, latitudes at which the dry circulation is stroner (weaker) correspond to locations at which the total DSE transport is reater (smaller). The chanes in the total dry circulation can be decomposed into the individual chanes in the Eulerianmean and eddy-driven circulations usin the STEM decomposition (5). The composite difference for the Eulerian circulation is shown in the middle row of Fi. 7. The chanes are qualitatively the same as those discussed in section 3 and involve a poleward shift of the Ferrel cell in the hih annular mode phase. Since the Ferrel cell is thermally indirect, this induces an equatorward shift within the total dry circulation. The low-to-hih chanes in the eddy-driven circulation are shown in the bottom row of Fi. 7. The eddy-driven circulation was computed usin the contributions from both the transient and stationary eddies. Despite the sinificant contrast in the land sea distribution between the two hemispheres, there is a clear symmetry in the response of the eddy-driven circulations. The chanes in the eddy-driven cell are marked by three centers: two centers of opposite sins between the jet dipole axes and a third center just poleward of 68. The two centers between the jet dipole axes form a vertical dipole and are indicative of an upward shift (i.e., to hiher enery) in the eddy-driven circulation. The upper branch of the

12 MAY 215 Y A M A D A A N D P A U L U I S 281 FIG. 8. As in Fi. 7, but for the moist circulation. The contours for the annual-mean circulations are drawn at [21, 26,..., 6, 1] k s 21 for the total and eddy-driven circulations and at [23, 22,...,2,3]3 1 1 k s 21 for the Eulerian-mean circulation. Zero contours are not drawn. eddy-driven circulation is more intense, while the lower branch is weaker. This chane in sin in the vertical results in stron cancellation when the interal is taken in (1). Hence, there is little chane in the eddy DSE transport between the jet dipole axes. The center poleward of 68 accounts for the monopolar intensification of the eddy DSE transport that was seen in Fi. 4. The upward shift in the eddy-driven circulation between the jet dipole axes is consistent with the anomalous warmin that occurs at the same latitudes in the hih annular mode phase (Fi. 5). In a warmer backround state, the transport of eddy enery occurs relative to a hiher mean enery. Similarly, the center located poleward of 68 is in a reion of anomalous coolin. Althouh a vertical dipole is not observed here (except for the Southern Hemisphere in the moist case), the sin of the center is consistent with a strenthenin of the lower branch that would be induced by a downward shift in the circulation. The steepenin of the temperature radient (increase in baroclinicity) about the poleward jet dipole axis increases the tilt of the eddy-driven circulation but does not lead to a stron increase in the poleward eddy enery transport. Even near 68N, where the increase in poleward eddy enery transport is larest, the chane in the eddy enery transport is mostly compensated by a decrease in the mean-flow enery transport. In the case of the moist circulation (Fi. 8), the chanes are qualitatively similar to the dry case in that the Ferrel cell is observed to shift poleward and the eddy-driven cell is more steeply tilted in the hih phase. However, the extratropical chanes in the total circulation are rather tripolar instead of dipolar. The midlatitude chanes in the eddy-driven circulation are comparable in manitude and spatial scale to the chanes in the Eulerian circulation. In comparison to the dry case, the dipolar anomaly arisin from shift of the Ferrel cell is not as pronounced and the response of the eddy-driven circulation is also stroner. As discussed earlier, this is larely because the inclusion

13 282 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 72 of latent heat accounts for the mass transport of low-level moist air parcels, which weakens the overturnin cells of the Eulerian circulation and strenthens the eddy-driven circulation. c. Momentum balance in annular mode composites To relate the poleward shift of the jet to the equatorward shift within the dry circulation, we turn here to an analysis of the zonal momentum budet, which under quasieostrophic scalin (e.., Peixoto and Oort 1992) can be written as follows: u t 5 f y 1 1 a cos 2 f f (2u y cos 2 f) 1 D. (11) The forcin terms on the riht-hand side are the Coriolis force on the Eulerian-mean flow, eddy momentum flux converence, and friction, respectively, where f denotes the Coriolis parameter. For studyin the dynamics of the dry circulation, it is more useful to consider the TEM formulation of (11) as in Edmon et al. (198): u t 5 f y* 1 1 $ F 1 D. (12) a cosf Here the eddy forcin is iven by the diverence of the Eliassen Palm (EP) flux vector F, where 1 F cosfu y, fa cosf y u A and u is the potential temperature. The subscript p denotes the partial derivative with respect to pressure. The Coriolis force is determined by the residual meridional velocity, y* 5 y 2 (y u /u p )/ p, rather than the Eulerianmean velocity y. The residual circulation represents the mean meridional circulation driven by diabatic heatin and coolin and approximates the isentropic circulation (e.., Haynes and McInyre 1987; McIntosh and McDouall 1996). Its streamfunction, referred to as the TEM streamfunction, is defined as the interated mass flux by the residual velocity in pressure: ð 2pa cosf p C TEM (f, p) 5 y*(f, ~p) d~p. (13) The residual circulation is closely related to the STEM circulation on DSE used earlier, as Pauluis et al. (211) have shown that the STEM streamfunction converes toward the TEM streamfunction in the limit of vanishin variance. It is also shown in appendix B that the use of DSE rather than potential temperature does not affect the result. The primary advantae of usin the TEM u p circulation here lies in the explicit formulation of the momentum balance (12). Above the boundary layer and on monthly time scales, the dominant balance in (12) is between the Coriolis force actin on the residual circulation and the eddy forcin: f y* 1 1 $ F. (14) a cosf The hih minus low composite difference of the eddy forcin (shadin) and of the zonal wind (contours) are shown in the middle row of Fi. 9. The chane in the eddy forcin consists of an upper-tropospheric dipole that is nearly coincident with the jet dipole, as has been observed by Hartmann and Lo (1998), Limpasuvan and Hartmann (2), and others. This suests that the eddy forcin anomaly acts to drive and sustain the jet anomalies. Equation (14) indicates that a positive anomaly in the eddy forcin must be balanced by an easterly Coriolis force and, hence, an equatorward anomaly in the residual velocity. From mass conservation, there must be a poleward anomaly in the residual velocity below, which provides a westerly Coriolis force that supports the surface westerlies aainst friction (Limpasuvan and Hartmann 2; Thompson and Wallace 2). Hence, a positive anomaly in the eddy forcin aloft induces an anomalous indirect circulation. Similarly, a neative anomaly in the eddy forcin induces an anomalous direct circulation. The poleward shift of the jet and eddy forcin must therefore induce an equatorward shift within the residual circulation. This can be seen in the bottom row of Fi. 9, which shows the composite difference of the residual circulation. The balance in (14) can be written explicitly in terms of the residual streamfunction by dividin by the Coriolis parameter and the ravitational constant and then zonally and vertically interatin the expression C TEM 2 2p ð p $ F d~p. f The composite difference shows the approximate chane in the circulation that would be induced by the chane in the eddy forcin. Note that we are plottin the neative of the residual streamfunction (see earlier footnote). The chane in the residual circulation reflects the chane in the Eulerian circulation to the deree in which the eddy forcin in (12) is driven by the chanes in the eddy momentum fluxes. From the momentum balance written as in (11), a chane in the eddy momentum flux converence must be balanced by a chane in the Eulerian circulation. The top row of Fi. 9 shows the chane in the momentum flux converence in

14 MAY 215 Y A M A D A A N D P A U L U I S 283 FIG. 9. (top) The hih minus low composite differences for the eddy momentum flux converence term in (11) (shadin) and zonal wind (contours) of the (riht) Northern Hemisphere onto the NAM and (left) Southern Hemisphere onto the SAM. Zonal wind contours are drawn at [24, 25,..., 8, 1] ms 21, excludin zero. Solid (dashed) contours represent positive (neative) values. (middle) Similar to (top) but for the eddy forcin in (12), which is equivalent to the eddy PV flux. (bottom) The hih minus low composite difference of the residual circulation. The annual-mean circulation is drawn in black contours at [27, 25,..., 11] k s 21, excludin zero. shadin. As compared with the eddy forcin (middle row), the eddy momentum fluxes larely explain the meridional shift in the eddy forcin. The part of the eddy forcin driven by the eddy heat fluxes [not shown; see Limpasuvan and Hartmann (2)] accounts for the vertical tilt in the eddy forcin. d. Feedback between the chanes in the mean flow and eddies A stron poleward shift in the eddy forcin aloft may seem to suest that the reion of baroclinic eddy eneration near the surface should also shift poleward in the hih annular mode phase. Fiure 1 shows the hih minus low composite difference of the EP flux vectors [arrows, plotted as in Edmon et al. (198)], which indicate the chane in the propaation of wave activity. In climatoloy, the EP flux vectors are larest near the lower boundary where they point vertically upward and indicate a stron poleward flux of DSE by the eddies; that is, y DSE is positive (neative) in the Northern (Southern) Hemisphere (shown in black contours). The composite difference for the eddy DSE flux (shadin) indicates that there is some poleward shift in the source of wave activity. Where there is a stron (weak) anomaly in the poleward eddy DSE flux, the anomalous EP flux vectors tend to point upward (downward). However, the most sinificant chanes in the EP flux vectors occur in the upper troposphere in the horizontal direction and are related to chanes in the eddy momentum fluxes. This suests that the reion of eddy eneration has not shifted very much in the monthly composites. Moreover, a stron shift in the source of wave activity would imply a stron shift in the poleward eddy DSE transport. This is not the case, as we showed earlier that the response

15 284 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 72 FIG. 1. The hih minus low composite differences for y DSE, the zonally averaed meridional eddy flux of DSE (shadin), and EP flux vectors (arrows). The contours show the annual-mean climatoloy of the zonal-mean-eddy DSE flux, drawn at [22, 215,...,15]3 1 1 m 3 s 23, excludin zero. The EP flux vectors are plotted as in Edmon et al. (198) and have units of m 3 and m 3 Pa for the horizontal and vertical components, respectively. (left) The horizontal arrow scale is shown in the bottom riht corner. A vertical arrow of the same lenth corresponds to m 3 Pa. of the eddy-driven circulation mainly involves tiltin of the eddy-driven cell, which has little effect on the poleward eddy enery transport. The most sinificant chane in the eddy DSE transport occurred in the Northern Hemisphere near 68N but was not lare enouh in manitude and spatial extent to shift the total DSE transport poleward. This raises the question, why is there a stron shift in the eddyforcinaloftwhenthesourceofwaveactivityhasnot shifted very much? Equivalently, why does the Eulerian circulation respond more stronly to the annular modes than the eddy-driven circulation?part of the answer lies in the fact that monthly composites conflate the chanes in both the buildup and decay phase of the annular mode anomalies. In the studies by Lorenz and Hartmann (21, 23) usin daily reanalysis, they show that the eddy forcin anomaly supports the zonal wind anomaly at both positive and neative las (where positive la means that the mean flow leads the eddy forcin). This indicates that while the eddy forcin anomaly at first drives the buildup of the jet anomaly, it is further sustained as the mean-flow anomaly tends to reinforce the eddy momentum fluxes. At positive las, their results support the feedback described in the introduction; that is, a poleward shift of the jet leads to a poleward shift of the baroclinicity and wave activity source. This feedback miht explain the poleward shift in the wave activity source observed in Fi. 1 and accounts for part of the chanes in the eddy forcin in Fi. 9. At neative las there is also a stron chane in the eddy momentum fluxes, which drives the jet shift and makes up the bulk of the chanes observed in Fi. 9. The feedback mechanism described in Robinson (2) does not apply before the rowth of the zonal wind anomaly and so a lare shift in the wave activity source would not be expected at neative las. This may explain why the chanes in the vertical component of the EP flux vectors are relatively weak compared to those in the horizontal component in the monthly composites in Fi. 1. While the initial eddy forcin anomaly may be stochastically driven, it continues to row from as much as 3 days prior to the maximum wind anomaly [e.., Fi. 5 in both Lorenz and Hartmann (21, 23)]. This suests that the eddy momentum fluxes are oranized by another feedback durin the rowth stae of the zonal wind anomalies that is independent of a shift in the source of wave activity. It is this stron initial rowth in the eddy forcin that drives the bulk of the chanes in the Eulerian circulation and enery transport. Here we consider a feedback mechanism based on ideas behind jet formation. The eddy forcin term in (12) can be interpreted in terms of potential vorticity (PV) mixin, since the EP flux diverence can be rewritten in terms of the quasieostrophic eddy flux of PV, $ F 5 a cosfy q, where q denotes PV. In climatoloy, the eddy PV flux is downradient (neative) and indicates reions of irreversible mixin from Rossby wave breakin. Eddy mixin is stronest on the flanks of the jet and attenuated near the core of the jet in the upper troposphere and lower stratosphere (Haynes and Shuckburh 2). Inhomoeneous PV mixin creates persistent jets throuh a positive feedback mechanism [e.., see the review paper by Dritschel and McIntyre 28)]. Rossby waves are less likely to break near the core of the jet, since

16 MAY 215 Y A M A D A A N D P A U L U I S 285 FIG. 11. (left) (top) Hih and (bottom) low composites for the residual streamfunction (shadin) and zonal wind (thick contours) onto the NAM. (riht) The hih and low composites for the eddy PV flux (shadin) onto the NAM are similarly displayed. The contours for the annual-mean climatoloical streamfunction (thin black contours) are drawn for reference at [27, 25,...,1]3 1 1 k s 21, excludin zero. The thick black contours show the composites for the zonal-mean zonal wind. The contours are drawn at [5, 1,..., 25] m s 21. their phase speed is much less than the mean flow (Andrews et al. 1987; Randel and Held 1991). The waves propaate meridionally away from the jet before eventually breakin near critical latitudes on the flanks of the jet, thereby converin momentum into the jet reion and deceleratin the mean-flow and mixin PV on the sides of the jet. This further sharpens the jet and steepens the PV radient in the jet reion. In this manner, the jet acts as an eddy mixin barrier in the upper troposphere, which reinforces itself as waves are forced to propaate outside the jet reion before breakin. The above feedback mechanism provides a possible explanation for the rowth of the annular mode jet anomalies. The shift of the jet corresponds to a shift of the uppertropospheric mixin barrier, which then leads to a shift in the reion of wave breakin. This supports the rowin jet anomalies, as there is more wave propaation out of the reion of anomalous westerlies and more wave breakin in the reion of anomalous easterlies. This mechanism does not require a sinificant shift in the source of wave activity for there to be a shift in the eddy forcin aloft. The path of wave enery propaation from the existin wave source is sufficiently modified by the chanes in the mean flow. This mechanism is supported by the observed shift in the eddy forcin (i.e., the eddy PV flux) in the middle row of Fi. 9. In the reion where the jet is anomalously stron, there is a positive anomaly in the eddy PV flux, which indicates less mixin. This suests that the anomalous westerlies strenthen the mixin barrier, which reduces the wave dra on the jet in this reion and therefore reinforces the oriinal westerly anomaly. Similarly, where the jet is anomalously weak, there is a neative eddy PV flux anomaly, which corresponds to a reion of enhanced wave breakin and further deceleration of the mean flow. As the jet is shifted poleward in the hih phase, the waves must propaate farther equatorward before breakin. This can be seen by the arrows in Fi. 1, in which equatorward propaation is noticeably stroner in the hih phase an observation that was also noted in Hartmann and Lo (1998) and Limpasuvan and Hartmann (2). This is also consistent with the index of refraction aruments used in Limpasuvan and Hartmann (2) and Lorenz and Hartmann (23) for Northern Hemisphere stationary waves, in which they show that more wave activity is absorbed at hih latitudes when the jet is shifted equatorward durin the low phase of the NAM. The riht column of Fi. 11 shows the individual NAM hih and low composites for the eddy PV flux and jet. The results for the SAM are not shown but are qualitatively similar. In the low phase (Fi. 11d), the jet core is centered about 358N and 2 hpa and flanked on both sides by stirrin reions, as indicated by downradient eddy PV fluxes. In the hih phase (Fi. 11b), since the midlatitude jet shifts poleward away from the subtropical jet, the jet core is less intense and mixin is strenthened in the reion near 358N and 2 hpa as compared to the low phase.