Stratospheric Transport

Journal of the Meteorological Society of Japan, Vol. 80, No. 4B, pp. 793--809, 2002 793

R. Alan PLUMB

Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

(Manuscript received 3 July 2001, in revised form 15 February 2002)

Abstract

Improvements in our understanding of transport processes in the stratosphere have progressed hand in hand with advances in understanding of stratospheric dynamics and with accumulating remote and in situ observations of the distributions of, and relationships between, stratospheric tracers. It is conve- nient to regard the stratosphere as being separated into four regions: the summer hemisphere, the tropics, the wintertime midlatitude ‘‘surf zone’’, and the winter polar vortex. Stratospheric transport is dominated by mean diabatic advection (upwelling in the tropics, downwelling in the surf zone and the vortex) and, especially, by rapid isentropic stirring within the surf zone. These characteristics determine the global-scale distributions of tracers, and their mutual relationships. Despite our much-improved understanding of these processes, many chemical transport models still appear to exhibit signiﬁcant shortcomings in simulating stratospheric transport, as is evidenced by their tendency to underestimate the age of stratospheric air.

1. Introduction have opposite large-scale gradients (HF has a stratospheric source and tropospheric sink, It has long been recognized that strato- CH a tropospheric source and stratospheric spheric trace gases with sufficiently weak 4 sink); nevertheless, the shapes of their iso- chemical sources and sinks have similar global pleths are very similar, with isopleths bulging distributions, in the sense that their isopleths upward in the tropics and poleward/downward (surfaces of constant mixing ratio) have similar slopes in the extratropics. Especially in the spatial shapes. This was evident from some winter or spring hemisphere, there are strong of the earliest global observations of CH and 4 horizontal gradients in the subtropics, rela- N O from the SAMS instrument on the Nimbus 2 tively flat isopleths in middle latitudes, and 6 satellite (Jones and Pyle 1984) and has been strong gradients again near 60 latitude in the confirmed (albeit with some reservations, as we winter hemisphere. The similarity of structure shall discuss below) in subsequent observations between two chemically unrelated tracers is and modeling studies of many such tracers. strong evidence that these characteristics are Examples of these characteristic shapes are determined by transport, and thus by strato- shown in Fig. 1 for monthly mean distributions spheric (and mesospheric) dynamics. around the equinoxes. The two tracers shown Comprehensive perspectives of the global- scale dynamics of the stratospheric circulation Corresponding author: R. Alan Plumb, Depart- have been given elsewhere (e.g., Holton et al. ment of Earth, Atmospheric and Planetary 1995, to which the reader is referred for details Sciences Massachusetts Institute of Technology, and for original references). For present pur- Cambridge, MA 02139, USA. E-mail: [email protected] poses, we will just summarize the main points ( 2002, Meteorological Society of Japan that are relevant to trace gas transport. 794 Journal of the Meteorological Society of Japan Vol. 80, No. 4B

Fig. 2. Schematic of the residual mean meridional circulation in the atmosphere. The heavy ellipse denotes the thermally-driven Hadley circulation of the troposphere. The shaded regions (labelled ‘‘S’’, ‘‘P’’, and ‘‘G’’) denote regions of breaking waves (synoptic- and planetary-scale waves, and gravity waves, respectively), responsible for driving branches of the stratospheric and mesospheric circulation. Fig. 1. Monthly mean meridional distributions of (left two panels) HF (parts per billion by volume) and of (right two served distributions of temperature and radia- panels) CH4 (parts per million by volume) during March (top) and Septem- tively active constituents (Rosenlof 1995; ber (bottom), from measurements by Eluszkiewicz et al. 1996), provided one inter- the HALOE instrument (Russell et al. prets ‘‘mean circulation’’ as ‘‘residual mean cir- 1993a) on the Upper Atmosphere culation’’, rather than the straightforward Research Satellite. Calculation of the Eulerian mean (it is the residual mean that is monthly mean distributions for these relevant to tracer transport (e.g., Andrews et al. data is described in Randel et al. (1998). 1987)). A schematic of the residual circulation of the atmosphere (up to the mesopause) is depicted in Fig. 2. In the tropical troposphere, 2. Overview of stratospheric circulation the well-known Hadley circulation can be and transport understood, at least in its simplest form, as a 2.1 The stratospheric circulation nonlinear circulation driven by latitudinal gra- The meridional circulation of the strato- dients in thermal forcing (Held and Hou 1980). sphere, known as the ‘‘Brewer-Dobson’’ circula- Despite the temptation to interpret the appar- tion, after the pioneering deductions of Brewer ently thermally-direct circulation of the strato- (1949) and Dobson (1956) from observations sphere in the same way, it is clear that other of stratospheric water vapor and ozone, respec- processes must be involved, since air following tively, comprises a two-cell structure in the the circulation must lose angular momentum lower stratosphere, with upwelling in the trop- as it moves poleward. The direct, large-scale, ics and subsidence in middle and high lat- effects of friction being utterly negligible in the itudes, and a single cell from the tropics into stratosphere, such loss of angular momentum the winter hemisphere at higher altitudes. can only be ascribed to the impact of waves: the These characteristics have been conﬁrmed from presence of wave drag is thus crucial to the modern radiation calculations based on ob- stratospheric circulation. August 2002 R.A. PLUMB 795

In contrast to the much more quiescent sum- yond the surf zone, deep into the tropics and mer hemisphere, the wintertime stratosphere even across the equator: issues involved in ex- is dominated by large-amplitude, planetary- plaining this behavior are discussed in Plumb scale Rossby waves propagating upward from and Eluszkiewicz (1999). At least a component the troposphere. Intermittently, these waves of the tropical circulation may be a nonlinear, break, stirring air more or less isentropically thermally driven circulation, analogous to the across large distances of the winter strato- tropospheric Hadley cell (Dunkerton 1989; Se- sphere within a region that has become known meniuk and Shepherd 2001a,b). The compo- as the ‘‘surf zone’’ (McIntyre and Palmer 1983), nent driven by wave drag may also extend into bounded by sharp gradients of potential vor- the tropics, either via a similar nonlinear ticity (PV) and of tracers in the winter sub- mechanism or through the effects of other wave tropics and at the edge of the polar vortex. motions within the tropics (Plumb and Elusz- Apart from the direct effects of this stirring on kiewicz 1999; Scott 2002). At the vortex edge, tracers, it has an indirect effect through the theoretical arguments lead us to expect little meridional circulation induced by the stirring penetration of the steady circulation into the of PV. For adiabatic, inviscid flow, and assum- vortex, even under nonadiabatic conditions ing steady state (i.e., solstice conditions), the (Bu¨ hler and Haynes 1999; Sobel and Plumb zonal mean momentum budget can be written 1999), despite the observational evidence there (e.g., Andrews et al. 1987) of strong descent of tracer isopleths (such as in Fig. 1). vP ¼ v^P^ ; ð1Þ In the lower stratosphere, the effects of syn- where P is Ertel PV, v is northward velocity, optic-scale tropospheric disturbances, present the notation v denotes the mass-weighted throughout the year, are probably responsible zonal mean of v along isentropic surfaces, and for driving the strong two-cell circulation there v^ ¼ v v the departure from that mean. Eq. and in the upper troposphere, through the (1) simply states the need for zero net flux of same Rossby wave pumping mechanism (the PV in a conservative steady mean state: mean local dynamics of these waves, away from their and eddy fluxes must cancel. Therefore, a non- baroclinic sources, being just Rossby wave zero eddy flux of PV—which will be present dynamics). Near the surface, these same bar- whenever waves are breaking, unless there is oclinic disturbances drive an equatorward re- no background PV gradient—requires a non- turn flow (Held and Schneider 2000; Koh 2001) zero mean circulation in steady state. In fact, in in the form of cold air outbreaks. the usual case of northward mean PV gradient The mesosphere is dominated by a strong and downgradient eddy flux, v^P^ < 0, and (1) global circulation (with v of several ms1) from implies a poleward circulation (since the sign summer pole to winter pole, which manifests of P has the same sign as latitude, except per- itself in the dramatic reversal of pole-to-pole haps very close to the equator). Thus, the wave temperature gradient in the upper mesosphere. drag drives the flow poleward, through a mech- This circulation is believed to be driven pri- anism we will here refer to as the ‘‘Rossby wave marily by upward propagating inertia-gravity pump’’1, providing an explanation for the pole- waves. Unlike Rossby waves, inertia-gravity ward flow in the winter stratosphere (for a waves can propagate through both mean east- thorough discussion, see Haynes et al. 1991; erlies and westerlies, and their effects on the Holton et al. 1995). There are outstanding is- mean zonal flow can be of either sign, depend- sues, however, in our understanding of the lat- ing on their phase velocities. Because of selec- itudinal extent of the circulation. In the tropics, tive dissipation of these waves in the strato- the observed circulation clearly extends far be- spheric winds, it turns out that their effect on the mesosphere—through what we here call the ‘‘gravity wave pump’’—is such as to drive 1 We prefer to avoid the nomenclature ‘‘extra- the flow generally equatorward in summer and tropical pump’’ proposed by Holton et al. (1985); poleward in winter, as observed. While the as (1) implies, for a given PV flux, the mechanism becomes more efficient closer to the equator, mesosphere itself is not our prime concern where P is small. here, this mechanism is strong enough to pump 796 Journal of the Meteorological Society of Japan Vol. 80, No. 4B significant descent of mesospheric air deep into parable with the Earth radius, but is weak the stratosphere, as we shall see below. enough that there is little tendency toward ho- mogenization of PV within it; then DP @ P, and 2.2 Rapid stirring in the surf zone the two contributions to the tracer budget are Within the surf zone of the midlatitude win- comparable. However, the real stratospheric ter stratosphere, tracers are subjected to both surf zone has weak PV gradients—a conse- isentropic stirring and diabatic advection. If the quence of strong stirring (Juckes and McIntyre eddy motions are almost adiabatic, then, for a 1987)—such that DP f P, implying that isen- tracer with mixing ratio w, tropic stirring dominates the tracer budgets qw qw qw 1 q within the surf zone. This fact, which is simply þ v þ y_ ¼ ðsv^w^ Þ; ð2Þ qt qy qy s qy a consequence of the decreasing efficiency of the Rossby wave pump under strong stirring, where y is potential temperature and s ¼ has important consequences for stratospheric g1qp=qy is the isentropic density2. Now, transport. in (1), we saw that the dynamical balance is such that eddy and mean transport of PV are of 3. Tracer-tracer relationships the same magnitude: is the same true of trac- 3.1 Equilibrium slopes and compact ers? Suppose that the eddy fluxes (of PV and relationships tracers) are such as to destroy the gross mean The most immediate consequence of the gradient across the surf zone in a characteristic dominance within the surf zone of isentropic time scale t, so that the eddy flux of PV is stirring is that, for ‘‘long-lived’’ tracers for DP which the effects of local chemical sources and v^P^ @ L; t sinks, and of entrainment from outside the surf zone, are negligible on the time scale t, hori- where L is the surf zone width, and DP the zontal mean tracer gradients are almost, but gross mPV gradient across the surf zone. Then, importantly not quite, eliminated. This implies from (1), that tracer isopleths (surfaces of constant mix- DP L ing ratio) have shallow slopes, and in this re- v @ ; P t gime the slope is determined by a balance be- where P is a typical value of PV in the surf tween the flattening effect of isentropic stirring zone. Therefore the time scale T for mean trac- and mixing, and the steepening effect of dia- er advection horizontally across the surf zone, batic advection (Plumb and Ko 1992; Plumb or vertically across a density scale height H,is 1996, 2002; Sparling et al. 1997; Thuburn and McIntyre 1997), implying that the isopleths are H L P T @ @ @ t : in the ‘‘slope equilibrium’’ regime described by w v DP Holton (1985) and Mahlman et al. (1985). In Hence the ratio of eddy to mean tracer trans- this regime, the shapes of the tracer isopleths port time scales is are determined solely by this kinematic balance, and so the isopleths of all sufficiently t DP @ : long-lived tracers exhibit the same shape, in T P agreement with the observed characteristics Now, suppose the surf zone has width com- discussed in Section 1. Moreover, Plumb and Ko (1992) argued that this in turn implies that a plot of one such tracer versus another would 2 The reader may wonder (as a reviewer did) about the self-consistency of retaining diabatic terms in form a ‘‘compact’’ relationship, as illustrated in (2) while neglecting them in (1). The neglected Fig. 3. This deduction remains true whether terms in the latter represent diabatic advection of variations in mixing ratio are from temporal momentum, which is small under reasonable assumptions (such as near-geostrophic conditions) or spatial (vertical or horizontal) sampling, in because of the modest vertical gradient of the agreement with observational findings (e.g., zonal flow. In the tracer budget (2), however, dia- Ehhalt 1983; Fahey et al. 1990). From a theo- batic advection remains important, even when the diabatic flow is weak, since then the mean retical viewpoint, the tracer-tracer relationship vertical gradient qw=qy becomes very large. can never be precisely compact in the presence August 2002 R.A. PLUMB 797

reproducibility of tracer-tracer plots makes for a more concise and useful form of data presen- tation than, say, time series or spatial proﬁles of tracer mixing ratios, which will usually differ from one proﬁle to another simply because of air movement between samples. More importantly, the robustness of tracer-tracer relationships allows for the empirical determination of a ‘‘canonical’’ relationship for each long-lived tracer pair that can be used as a reference to isolate anomalous or otherwise noteworthy characteristics of tracer measurements. Inter- pretation of such relationships is not always easy, as most of our understanding of tracer characteristics is based on the spatial structure of transport, and hence of the tracer structures themselves. In order to utilize tracer-tracer plots to the full, there is a need to be able to think in tracer-tracer space. As yet, the body of theory that would allow us to do that is incom- plete, but some important results are known, of which some will be discussed in the following.

3.2 Tropical isolation (and non-isolation) The subtropical edge to the winter surf zone is evident, like the vortex edge, as a region of strong local gradient in tracer distributions, as seen in Fig. 1, for example, on the global scale. Its sharpness also shows up clearly in in situ Fig. 3. Illustrating compact relationships aircraft data, as a near-discontinuity in local within the surf zone (schematic). The upper ﬁgure shows isopleths of mixing mixing ratios (e.g., Murphy et al. 1993). In fact, as Fig. 1 illustrates, there are regions of strong ratio w1 for one tracer in the winter hemisphere; the isopleth slope is weak subtropical gradient on both sides of the equa- within the surf zone (the middle region) tor, which persist throughout the year. Figure 4 but may be steep at the surf zone edges. shows their seasonal evolution at several stra- The dashed contour is an isopleth mix- tospheric altitudes, as determined from six ing ratio w2 of a second tracer: within years of HALOE observations of CH4 (Neu, the surf zone, the isopleth is almost the 2000). The edge locations are remarkably con- same shape as one of w1. This implies sistent from year to year. The ‘‘tropical region’’ that whenever w1 has a certain value (i.e., the region bounded by the subtropical within the surf zone, w always has a 2 edges) migrates, most markedly at higher alti- ﬁxed value, so that a plot of w2 vs. w1 is compact, as shown in the lower curve. tudes, into the summer hemisphere, qualitatively similar to the migration of maximum upwelling (Rosenlof 1995; Eluszkiewicz et al. of mixing unless the relationship is linear 1996). However, the location of the winter edge (Plumb 2002) but, in practice, scatter is often in fact corresponds more closely with the zero weak, unless (as we shall see) data are included wind line than with the transition from up- from outside the surf zone. welling to downwelling (Neu 2000; Neu et al. The practice of presenting measurements of 2002). This is consistent with calculations of long-lived tracers by plotting against a refer- ‘‘effective diffusivity’’ (Nakamura 1996) which ence tracer (frequently N2OorCH4) has be- show high values within the surf zone, de- come widespread. Amongst other things, the creasing sharply at the vortex and subtropical 798 Journal of the Meteorological Society of Japan Vol. 80, No. 4B

Fig. 4. Seasonal evolution of the subtropical edges, as determined from HALOE observations of CH4 during the period 1993 through 1998. Each line shows the location of the edge through a HALOE observing period. (After Neu 2000.)

edges, with much smaller values throughout several other lines of evidence (such as the year- the tropical easterlies (Haynes and Shuck- long persistence of successive phases of the burgh 2000; Allen and Nakamura 2001). Taken quasi-biennial oscillation), perhaps the most together with the observed equatorward mi- visual is the now-famous ‘‘tape recorder’’ signa- gration of the subtropical edge in early winter, ture in the tropical lower stratosphere (Mote such evidence suggests that the wintertime et al. 1996): the annual cycle of temperature at subtropical edge, like the vortex edge, is pro- the tropical tropopause imprints a similar cycle duced and sharpened by entrainment of edge on water vapor which, in turn, is converted by air into the surf zone, associated with surf zone mean upwelling into a cyclic vertical structure. stirring. On the summer side of the equator, About one complete wavelength is visible: since where such processes are at best weak (except there is little annual cycle in extratropical at low altitudes), the situation is not so clear. water vapor, this implies that the time scale for However, it appears that the summer subtropi- injection of extratropical air into the tropics is cal edge is not merely a survivor of wintertime of the order of a year. While this is long enough formation, but is actively sustained by diabatic to ensure that the tropical region is distinct processes, especially at higher altitudes (Neu from the surf zone, with its much shorter mix- 2000). ing time scales, it is not so short as to be unim- Evidence that the subtropical edges act in portant in tracer budgets within the tropics, some sense as transport barriers, at least where the competing transport process (mean partly isolating the tropics from the vigorous vertical advection) is very slow (tropical up- stirring of the surf zone, comes from the obser- welling velocities in the lower stratosphere are vation that tracer-tracer relationships in the typically around 1 km per month). Thus, it is tropics are distinct from those of the surf zone not accurate to regard the tropical region as (e.g., Plumb 1996; Volk et al. 1996). Among being completely isolated. Indeed, many studies August 2002 R.A. PLUMB 799 have deduced similar time scales (most in the range 1–1.5 yr) for detrainment of surf zone air into the tropical lower stratosphere, on the basis of the observed budgets of chemical tracers (e.g., Avallone and Prather 1996; Volk et al. 1996; Hermann et al. 1998) or of age (Hall and Waugh 1997; Neu and Plumb 1999). Indeed, Hall and Waugh (1997) used simultaneous analysis of observations of age and of the tape recorder to make independent determinations of all components of transport in the region, which amongst other things allowed them to conﬁrm that the effects of vertical diffusion are negligible (as had previously been assumed).

3.3 The formation of tracer relationships in the surf zone As a first step toward understanding what makes surf zone tracer relationships they way they are, consider a simple, hypothetical stratosphere comprising two regions: a tropical region in which there is upwelling, and a surf zone with rapid isentropic stirring and net mean downwelling, as illustrated in Fig. 5. (This case Fig. 5. Schematic showing the develop- is considered more explicitly in Plumb 2002.) ment of tracer-tracer relationships in The net mass flux associated with the upwell- the stratospheric ‘‘surf zone’’. Upper ing and downwelling decreases with height, so figure shows a schematic latitude/po- there must be entrainment of air into the surf tential temperature cross section, with zone across the subtropical edge separating the upwelling in the tropics and down- two regions. As we have seen, there may also be welling in the surf zone. Lower figure shows the relationship between the detrainment into the tropics; we will consider mixing ratios of two tracers in the trop- its influence later. ics (curve ‘‘T’’) and in the surf zone Now suppose, also for simplicity, that photo- (curve ‘‘S’’). See text for discussion and chemical sources and sinks are confined to the for explanation of other symbols. (After tropics; the tracers of interest are conserved Plumb 2002.) within the surf zone. To be specific, we consider two tracers with tropospheric sources, and whose tropospheric mixing ratios can be con- that does not matter greatly for our present sidered fixed, with stratospheric sinks. Tracer arguments. At sufficiently high altitudes the 1 is supposed to have a longer lifetime than mixing ratios of both tracers will be close to tracer 2 (so the pair could be, e.g., N2O and zero, corresponding to the point labeled ‘‘m1’’ on CFC-11). Within the tropics, their mixing ratios the curve. Let us now follow this air into the w1 and w2 decrease with height, w2 the faster, surf zone, where it will begin to descend to as it has the shorter lifetime. Therefore the some lower altitude. In the absence of any local w2 : w1 relationship will look something like that entrainment of air from the tropics, the mixing shown in the curve marked ‘‘T’’ on Fig. 5; mov- ratios will be preserved and so, in tracer-tracer ing up in altitude corresponds to sliding down space, the air is still at point m1. However, at the curve T from upper right to lower left. In the the same potential temperature, the tropical simplest case, this curve will be purely photo- mixing ratios are located at point t1, where chemically controlled. In general, however, the both are greater than at m1. If there is now curve may not be compact—we know little entrainment of tropical air, which is then as- about mixing processes within the tropics—but similated into the surf zone at the same y,the 800 Journal of the Meteorological Society of Japan Vol. 80, No. 4B resulting air mass will now lie at point m2, of surf zone air is likely to reduce the gross somewhere along the line joining m1 and t1 curvature of T. The nature of the tracer-tracer (Waugh et al. 1997), exactly where depending relationships in this case can be revealed by on the relative masses of air being mixed to- iterating the above arguments, allowing for gether. Subsequently, as shown on Fig. 5, one modification of the tropical tracer profiles, but can imagine a sequence of similar events of the end result is qualitatively unchanged: the descent followed by entrainment and mixing, surf zone curve lies on the concave side of the such that m2 mixes with t2, to produce m3, tropical curve, because the central fact that which mixes with t3 to produce m4, and so on. surf zone air comprises a mixture of tropical air If we imagine this sequence of discrete events is unaffected by the existence of detrainment being replaced by a continuous interplay of into the tropics. descent and mixing, the resulting surf zone tracer-tracer relationship will be the curve 3.4 Tracers in the vortex ‘‘M’’ on Fig. 5, which is distinct from the It is clear from evidence such as that shown photochemically-determined tropical relation- in Fig. 1 that tracer isopleths are depressed ship. Note that the surf zone relationship lies substantially within the polar vortex. While on the concave side of the tropical one; we can this is frequently interpreted as being indica- now see that this simply results from the fact tive of greater mean diabatic descent within that surf zone air at any altitude is a mixture of the vortex than outside, this is not necessarily tropical air from all higher altitudes. Note also so. Determinations of mean residual or diabatic that the separation of the two relationships de- velocity (Rosenfield et al. 1994; Rosenlof 1995; pends on nonlinearity of the tropical curve: if it Eluszkiewicz et al. 1996) frequently show broad were linear, a mixture would always lie on the regions of descent in midwinter throughout same line, and M would overlie T. high and middle latitudes, not necessarily con- If the tracer-tracer curve within the tropics centrated within the vortex. Rather, the differ- were not compact (but still exhibited the gen- ence lies in the differing climatologies of stir- eral tendency of curve T ), one would expect ring in the vortex and surf zone. Within the little difference in the predicted curve M. Surf surf zone, rapid stirring ensures that a typical zone mixing would still guarantee the compact- trace particle, while it may be subjected to ness of M, and the precise shape of M would strong diabatic cooling when it is near the vor- depend on the particular mix of tropical air tex edge, does not remain there for long enough that is entrained into it. to undergo a substantial downward displace- A complete separation between M and T, ment. Over seasonal time scales, as noted ear- manifested by the tracer-tracer scatterplot com- lier, air is stirred throughout the surf zone and prising these two curves only, presumes that thus responds to the net diabatic descent assimilation of tropical air into the surf zone (averaged over the surf zone), rather than to occurs completely and instantaneously. During the much stronger local descent in high lat- the time mixing actually occurs, however, in- itudes. By contrast, vortex air remains within termediate mixing ratios will be formed and the vortex for long periods and is thus sub- so, at any instant in time, or averaged over jected to sustained diabatic cooling. Thus, vor- time, the scatterplot will include a smaller tex air is characterized by ‘‘unmixed descent’’, population of air intermediate between M and in the words of Russell et al. (1993b), although, T (including discrete mixing lines if individ- as we shall see below, this should be qualified ual entrainment/mixing events are captured). to ‘‘relatively unmixed descent’’. All this is just (This is discussed in more detail in Plumb another way of saying that the strong tracer 2002.) gradients at the vortex edge are produced by We saw earlier that there is evidence for a differential isentropic stirring, rather than by significant amount of detrainment of surf zone differential diabatic descent. air into the tropics. Thus the assumption we That said, there is some degree of mystery as made earlier in this Section, that the tropical to the dynamical origins of the high latitude tracer-tracer curve is purely photochemically descent. There are theoretical grounds to ex- determined, is likely to be invalid. Inclusion pect Rossby wave pumping in the surf zone to August 2002 R.A. PLUMB 801 produce most descent at the vortex edge, rather than deep within, and the sustained vortex descent through the winter, evident in calculations based on radiation codes and in tracer measurements, is difficult to explain on the basis of the transient circulation produced by fall cooling and the concomitant setting up of the polar night jet. Rather, there is growing evidence of a substantial contribution to vortex descent, all the way down to the lower stratosphere, from the ‘‘gravity wave pump’’ of the mesosphere. Estimates of the mean poleward velocities within the mesosphere are sufficient to flush the entire mesosphere over the course of a single winter season, much of that air reaching the lower stratosphere by late winter. Direct evidence of this degree of descent has come from observations made during the SOLVE campaign; in March 2000, markers of mesospheric air (anomalous apparent SF6- based ‘‘age’’ (Moore et al. 2002), and CO, of upper mesospheric origin) were observed and modeled in the lower stratospheric vortex (Plumb et al. 2002). Just as we have discovered for the tropics, it Fig. 6. As Fig. 5, but adding the polar is now recognized that the vortex edge, though vortex. Upper figure is a schematic clearly impermeable to a first approximation, showing a latitude/potential tempera- is not a perfect barrier to transport. The most ture depiction of transport in the three compelling evidence of this comes from obser- regions. The lower figure shows the vations of anomalous vortex relationships be- relationship between tracer 1 and 2, tween certain pairs of long-lived tracers (Mi- the curves ‘‘T’’, ‘‘M’’, and ‘‘V’’ represent- chelson et al. 1998; Kondo 1999; Plumb et al. ing the relationships in the tropics, surf 2000; Rex et al. 2000), whose only apparent ex- zone, and vortex, respectively. (After planation is that surf zone air is being mixed Plumb 2002). into the vortex. Indeed, it now appears that distinct compact relationships were established zone air that is assimilated into the vortex re- within the Arctic vortex by late winter of 2000 lationship gets there by being transported (Ray et al. 2002), implying also the presence of across the vortex edge during winter, rather rapid mixing within (in addition to possible than simply being caught up in the vortex at weak mixing into) the vortex. In some ways, the the time of its formation in fall (cf., the remarks development of compact vortex relationships, of Ray et al. 2002). through the mixing of surf zone air, parallels Such development of distinct vortex relation- the discussion of Section 6, and we might ships undermines attempts to use anomalous replace Fig. 5 with Fig. 6, in which we add a tracer-tracer relationships as a means of quan- vortex to the system, and in which a compact tifying chemical losses of ozone (e.g., Proffitt et relationship is established within the vortex al. 1990; Mu¨ ller et al. 1996) or sedimentation through vortex descent and assimilation of surf of NOy (e.g., Fahey et al. 1990). Use of mixing zone air, in just the same way as we discussed line arguments (Rex et al. 2000) to remove in Section 6 for development of the surf zone transport effects are unlikely to be reliable in relationship. One key difference, however, is general, since it is necessary to assume a that the vortex edge is a transient phenome- single mixing event (Plumb et al. 2000) and the non, and it is not clear to what extent the surf production of a compact vortex relationship 802 Journal of the Meteorological Society of Japan Vol. 80, No. 4B requires many such events. One promising growth of CO2 is contaminated by the annual approach, proposed by Esler and Waugh (2002), cycle transported from the troposphere (Boer- is to use a linear combination of independent ing et al. 1996), and SF6 has a mesospheric tracers that exhibit a near-linear canonical re- sink, which corrupts determinations of age in lationship with a reference tracer; since this air (such as air in the polar vortices, as we linear relationship is unaffected by mixing, noted in Section 7) that has been in the meso- anomalies can arise only though anomalous sphere (Hall and Waugh 1998; Moore et al. sources and sinks. 2001). Nevertheless, ages can be determined from SF in ‘‘young’’ lower stratospheric air 4. Quantification of transport: age 6 (where CO2 is influenced by the annual cycle), 4.1 Definition of age from CO2 in ‘‘old’’ air within the polar vortices All long-lived tracers carry information about (where SF6 is influenced by its mesospheric transport in their distributions. As we have sink), and from either in the considerable re- seen, their surfaces of constant mixing ratio are gion of overlap where both species are good determined entirely by a balance between com- tracers of age [see Waugh and Hall (2002) and peting effects of transport. However, their gra- references therein]. Thus, between the two spe- dients normal to such surfaces are dependent cies, we can obtain reliable determinations of on chemical sources and sinks, and so they mean age from observations throughout the cannot be used to make unambiguous deduc- stratosphere. tions about transport. It is difficult, for example, to determine whether errors in model sim- 4.2 Modeling of stratospheric mean age ulations of tracer distributions result from Observations of age provide us with a ref- errors in transport or in the specification of erence against which the transport character- sources and sinks. Identification of transport istics of stratospheric chemical transport effects are more easily made on the basis of the models (CTMs) can be assessed. In the inter- distributions of temporal tracers, those which comparison project ‘‘Models and Measurements have known, time-dependent, mixing ratio II’’ (Park et al. 1999), many CTMs (both 2-D wTðtÞ in the troposphere, and negligible internal and 3-D) were used to simulate age. The results stratospheric sinks (or sources). A special case of this exercise are discussed in detail in Hall et of such tracers (or, rather, a derivative of them) al. (1999). Nearly all of the models seriously is ‘‘age’’. (See Waugh and Hall (2002) for an underestimated age throughout the strato- up-to-date comprehensive review of the theory sphere, including in the tropical lower strato- and applications of the concept of ‘‘age’’ in the sphere where the air has only recently entered stratosphere.) In it simplest form, one might be from the troposphere. Moreover, as a demon- tempted to define age GðxÞ at location x as the stration of the relevance of the simulation of time lag between local and tropospheric con- age to the proper simulation of stratospheric centrations, i.e., chemistry, the modeled abundances of real tracers, including the crucial chemical families wðx; tÞ¼wT½t GðxÞ: ð3Þ of total inorganic chlorine and total reactive However, because of the dominance of stirring nitrogen, were shown to correlate strongly with and mixing in stratospheric transport, one age simulations. It appears that the current must think of age not as a simple time lag, but generation of stratospheric CTMs exaggerate as a statistical distribution of lag times (the stratospheric transport, which raises concerns ‘‘age spectrum’’), as emphasized by Hall and about their ability to generate an accurate sim- Plumb (1994). Eq. (3) is valid, for linearly ulation of stratospheric chemistry. Recent ex- growing tracers only, if G is equated with the periments (Mahowald et al. 2002; W.A. Norton, ‘‘mean age’’—the first moment of the age spec- private communication) have shown that use trum. Fortunately, we have at least two strato- of isentropic coordinates greatly improves the spheric tracers, SF6 and CO2, which approxi- simulation of stratospheric age (and therefore mately meet the criteria of negligible sinks and of transport). Use of these coordinates guaran- of linear growth, though neither does so tees the crucial connection between diabatic exactly: in the lower stratosphere, the secular processes and vertical transport. Mahowald August 2002 R.A. PLUMB 803 et al. (2002) showed such improvement, using globe, Plumb and Ko (1992) argued that the net the same input winds to off-line pressure- global fluxes of two long-lived tracers across a coordinate and isentropic-coordinate models, surface of constant mixing ratio are in a ratio and ascribed much of the improvement to a equal to the slope of the compact curve relating better simulation of slow vertical transport in the two tracers. This result follows directly the equatorial lower stratosphere. from the fact that the net flux through such a surface is, under assumptions of rapid mixing, 4.3 Flux of age diffusive, so that the flux of each species F z Age is itself a tracer; if we write the general n qw =qy. Since w ¼ w ðw Þ, it then follows that tracer transport equation as n 2 2 1 F dw q 2 ¼ 2 : ð6Þ r1 ðrwÞþ‘ Á F ¼ S; F dw qt w 1 1 One can, alternatively, frame (6) as a ratio of where r is air density and F the advective- w atmospheric lifetimes. Plumb (1996) showed diffusive flux of w, then given (3) for a linearly that this result remains valid for fluxes across growing tracer in steady transport, it is easy to the tropopause even when allowance is made show that G satisfies the equation for different tracer-tracer relationships be- 1 r ‘ Á FG ¼ 1; ð4Þ tween surf zone and tropics, provided the surf zone relationship is used to determine the subject to the tropospheric boundary condition slope. We can understand this result using a GT ¼ 0. Thus, age is the steady state solution simpler, but more general, argument which to a tracer budget with unit source (air ages also illustrates some possible limitations. Con- by one year per year). Waugh and Hall (2002) sider Fig. 7. We separate exchange of air across call age defined by (4) ‘‘ideal age’’. Therefore, the tropopause into upward events, with net age can be treated like other long-lived tracers mass flux m , and downward events, with net (provided it is borne in mind that age has a u mass flux m . Adopting the tropopause as the source everywhere) and, for example, it ex- d reference surface allows a powerful simplifica- hibits compact relationships with other tracers tion, namely that for tracers that are long-lived such as N O (Boering et al. 1994, 1996). 2 in the troposphere as well as in the strato- One consequence of (4) that proves to be use- sphere, tropospheric gradients are very weak ful is that the flux of age through any surface and so it is a good approximation to assume can be easily determined (Neu and Plumb 1999). If we integrate (4) with respect to mass over the entire atmospheric region R above a global surface S, then ð ð

FG:n dA ¼ dm ¼MR; ð5Þ S R where n is the upward unit normal at S, and MR is just the mass of the atmosphere in R: the net downward ﬂux of age through S simply equals the air mass above S. If we take S to be the tropopause, the ﬂux of age into the troposphere equals the mass of the stratosphere, which is of course known (to the accuracy with which we know the mean pressure on the tropopause).

5. Stratosphere-troposphere exchange

5.1 Net tracer ﬂuxes Fig. 7. Schematic showing transport On the basis of an analysis in which a single across the tropopause. See text for dis- surf zone was assumed to encompass the entire cussion. 804 Journal of the Meteorological Society of Japan Vol. 80, No. 4B that the tropospheric mixing ratio, wT, is uni- or lifetime of a particular species, it is neces- form. Then the net upward tracer ﬂux is just sary to know that of a second species. However,

T S as we saw in Section 8, we do know the flux F ¼ muw mdw ; of age, at least to the accuracy with which we where wS is the mass-weighted average mixing know the mass of the stratosphere, and this can ratio of air entering the troposphere. Note that be used as the reference tracer, as done by Volk wS may be quite different from wT in vigorous et al. (1997). (They actually used the budget of cross-tropopause stirring events in which air is SF6, rather than of age itself, but the approach taken from deep in the stratosphere. However, is equivalent to using age directly.) However, since such events are likely to be largely adia- unlike many tracers, age does have an effective batic, the air will come from within the ‘‘lower- source everywhere, including the lowermost most stratosphere’’—the shaded region on Fig. stratosphere, and so its relationship with other 7—lying below the isentrope (about 380 K) that long-lived tracers will not usually be linear, as skims the highest point on the tropopause. Volk et al. found, a fact that presents some dif- Now, if we average over a year and neglect in- ficulties in applying (7) directly. terannual variability, the net flux of mass into the stratospheric must vanish, so m ¼ m . Then 5.2 Dehydration and transport through the u d tropical tropopause T S F ¼ mdðw w Þ; Stratospheric dryness was explained in the classic study of Brewer (1949) as a consequence from which we obtain, for two species, the flux of the passage of air through the cold tropical ratio tropopause. While important details, such as T S the question of whether the large-scale tropical F2 w2 w2 ¼ T S : ð7Þ tropopause temperatures are quite cold enough F1 w w 1 1 to explain the observed dryness, remain a This relation is obviously similar to (6), but the matter of active debate, the key element of local slope in the latter is replaced by a ratio of Brewer’s suggestion—the ‘‘freeze drying’’ of air finite differences. In fact, the mutual relation- as it passes through the tropical ‘‘cold trap’’— ship between pairs of tracers that have no local remains at the center of conventional wisdom. sources or sinks within the lowermost strato- The details of the drying mechanisms lie be- sphere should be linear there (Plumb 2002), as yond the scope of this review; however, we take observations seem to confirm; for such pairs of the opportunity to note something that until tracers, we recover (6). We can also see why it very recently appears to have been overlooked, is the surf zone relationship that is relevant namely the likely partial analogy between here: it is the region from which air entering transport through the tropical tropopause and the troposphere originates that matters. Air in the winter surf zone. Mean upwelling, as cannot cross the tropopause adiabatically from noted above, is no more than about 1 km per the tropical stratosphere, even if it enters the month in the tropopause region and so vertical tropical upper troposphere, nor from the polar advection is much slower than probable hori- vortex, which disappears as a distinct entity zontal (isentropic) transport. Thus, just as in below about 400 K (McIntyre 1995). Air does, of the surf zone, a typical trace particle will act as course, enter the tropopause in the summer an integrator of diabatic motion across a wide hemisphere: it is assumed here that the surf horizontal domain, responding to the mean up- zone relationships established in the previous welling across the domain rather than to local winter are preserved in the midlatitude sum- values. Thus, for example, the mean motion of mertime lower stratosphere, as observations Lagrangian tracers may be even slower than appear to suggest. 1 km per month. These considerations are like- The result (6) has been exploited to deter- ly to be important, given that the cold trap is mine net ozone fluxes through the tropopause geographically local, both in latitude and longi- (Murphy and Fahey 1994) and to calculate life- tude. Moreover, such a scenario implies that all times of a range of species (Volk et al. 1997). In air will sample a wide horizontal domain dur- order to utilize the result to determine the flux ing ascent, and may pass through the cold trap August 2002 R.A. PLUMB 805 even if local diabatic motion is downward there. (The same point has been made by Holton and Gettleman 2001.) To illustrate this consider the following simple illustration. We assume a two-dimensional ( y; z) system (so that y represents either the zonal or latitudinal direction, or both) of width L, in which the temperature Tðy; zÞ is specified to be 220 K everywhere, except in a region LCT =2 < y < LCT=2, and HCT=2 < z < HCT=2 within which "# Fig. 8. Schematic of the cold trap calculation. See text for discussion. 2y 2 Tðy; zÞ¼220 30 1 LCT p 1 Â sin z þ HCT ; ð8Þ HCT 2 so the minimum temperature at the center of the ‘‘cold trap’’ is 190 K. Air moves vertically through this entire region with specified velocity y wðyÞ¼W 1 þ a cos 2p ð9Þ 0 L where W0 > 0—mean motion is upward—but the motion is not upward everywhere if jaj > 1. In y, horizontal stirring is represented by having air parcels perform a random walk yðtÞ!yðt þ dtÞ at each time step dt, where pffiffiffiffiffiffiffiffiffiffiffi yðt þ dtÞ¼yðtÞþr 2Kdt; ð10Þ where r is a random number between 0 and 1, and K is the diffusivity corresponding to the random walk. The key parameters of the prob- lem are b ¼ LCT=L, the fractional area occupied 2 by the cold trap, and o ¼ W0L =ðKHCTÞ, the ratio of horizontal dispersion time (across the entire region) to vertical advection time (through the cold trap). We consider a case with a ¼2 and b ¼ 0:2; in this case local vertical velocities are downward everywhere within the cold trap, as shown in Fig. 8. Trace particles were initialized every time step at a random horizontal posi- Fig. 9. PðTminÞ, the equilibrium fraction tion, a distance HCT below the bottom of the cold trap, and the minimum temperature, T , of parcels that have experienced a min- min imum temperature of T (in 1 K bins, they experience during upwelling was recorded. min except that the last bin contains all Eventually, the probability distribution of Tmin Tmin > 210 K) during passage through in air that has moved to altitudes above the the altitudes of the cold trap. Each cold trap reaches equilibrium: these equilib- frame is labeled at its top right with the rium values of Tmin are shown in Fig. 9, for dif- value of o. 806 Journal of the Meteorological Society of Japan Vol. 80, No. 4B ferent values of o. Even though the cold trap versations or correspondence with Kristie Boer- occupies only 20 percent of the horizontal area, ing, Janusz Eluszkiewicz, Gavin Esler, Tim for o < 0:4 all air parcels pass through the cold Hall, Peter Haynes, Jim Holton, Malcolm Ko, trap, and for o < 0:1 more than 90 percent of Jerry Mahlman, Michael McIntyre, Noboru parcels experience temperatures within 1 K of Nakamura, Jessica Neu, Warwick Norton, Bill the minimum temperature. As expected, there- Randel, Emily Shuckburgh, Adam Sobel, Dar- fore, in the limit of small o (rapid horizontal ryn Waugh, and Steve Wofsy. This work is stirring) parcels sample the entire horizontal supported by NASA. domain during their mean ascent. Only when References o b 0:5 does a significant fraction of particles avoid passing through the cold trap, even Allen, D.R. and N. Nakamura, 2001: A seasonal cli- though all upwelling takes place outside the matology of effective diffusivity in the strato- cold trap. sphere. J. Geophys. 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