Diagnostic results are presented indicating that during the Arctic oscillation surface climate variations are directly forced by changes in the strength of the stratospheric polar vortex. To be specific, large-scale potential vorticity anomalies in the lower stratosphere induce zonally symmetric zonal wind perturbations extending downward to the earth's surface. This represents a large-scale annular stirring of the troposphere from above. During discrete events, this influence is manifested as a downward transient pulse initially emanating from the midstratosphere and ultimately altering surface weather. It is suggested that this mechanism may help to explain several observed stratospheric influences upon surface climate, including the effects of volcanic eruptions, the solar cycle, ozone depletion, and greenhouse gases.
It is becoming increasingly evident that longitudinally symmetric (or annular) modes of atmospheric variability, such as the Arctic oscillation (AO), strongly influence surface climate variability at mid- and high latitudes (Thompson and Wallace 1998; Kerr 1999; Hartmann et al. 2000). In particular, the AO accounts for a large fraction of recent decadal climate trends in the northern high latitudes (Hurrell 1995; Thompson et al. 2000). Thus, a thorough understanding of extratropical climate variability requires improved knowledge of the dynamical mechanisms responsible for the annular modes. During winter, the AO signature appears in both the troposphere and stratosphere (Thompson and Wallace 1998, 2000). This is evident in Fig. 1a, which displays the longitudinal average structure of the zonal wind perturbations associated with the AO during Northern Hemisphere winter. In addition, distinct stratospheric precursors to AO events have been observed (Baldwin and Dunkerton 1999). Although the mechanistic nature of a downward stratospheric influence during the AO is unresolved (Wallace 2000), recent studies postulate an indirect mechanism in which the stratosphere alters the vertical propagation characteristics of tropospheric waves (Kuroda and Kodera 1999; Shindell et al. 1999a). I present evidence that, in fact, a direct downward forcing mechanism (Hartley et al. 1998) induces a substantial portion of the zonal-mean surface climate signature associated with the AO. The stratosphere is thereby directly implicated in contributing to recent surface climate trends in the Northern Hemisphere.
The physical basis for the approach draws from the analogy between electric charge and atmospheric potential vorticity (PV) anomalies (Bishop and Thorpe 1994). In this paradigm, localized PV anomalies induce wind fields that have a nonlocal component, qualitatively similar to the relationship between electric charge and electric field. The implementation of our approach involves performing so-called piecewise PV inversions, in which wind fields attributed to specified subsets of a given atmospheric PV anomaly distribution are deduced (Davis 1992). In this case, the contribution of stratospheric PV anomalies toward the tropospheric wind field is diagnosed by applying quasigeostrophic piecewise PV inversions. The diagnostic approach of Hartley et al. (1998) is followed. For quasigeostrophic flow on a sphere (e.g., Matsuno 1970; Black 1998) the balance condition relating PV anomalies to geopotential anomalies is given by
Here, q is the quasigeostrophic pseudopotential vorticity (hereinafter referred to simply as potential vorticity), f is the latitudinally varying Coriolis parameter, Φ is geopotential, and σ is a horizontally invariant static stability measure (proportional to N2, where N is the buoyancy frequency). Because this relation is linear, piecewise PV inversions can be performed unambiguously and one can linearly superpose the individual contributions of separate pieces of the three-dimensional PV anomaly distribution.
Because of the elliptic nature of (1), the “response” (Φ′) to a localized anomaly of PV is a field that decays vertically with a scale H = fL/N, where L is the horizontal scale of the motion. Thus, the circulation “induced” by PV anomalies contained within the stratosphere may extend into the troposphere. In fact, the associated circulation anomalies at these lower altitudes have been found to be substantial, particularly in cases of major distortions of the stratospheric polar vortex (e.g., Hartley et al. 1998).
To complete the specification of the boundary-value PV inversion problem, boundary conditions on the geopotential must be specified. These consist of a Neumann condition on horizontal (upper and lower) boundaries:
where θ is potential temperature. To perform piecewise inversion of PV, (1) is solved with (2) applied on the upper and lower boundaries and a lateral boundary condition of Φ′ = 0 at 5°N. To assess nonlocal influences, one first defines a reference level at which a downward (or upward influence) is evaluated. The PV anomalies above and below the reference level can be inverted individually and linearly combined to assess the influence of PV over any vertical span of levels upon the flow at the reference level.
For inversions of PV anomalies interior to the atmosphere, the condition on the lower boundary is homogeneous; that is, the lower-boundary potential temperature perturbations associated with interior PV anomalies are assumed to be zero. This approach is physically equivalent to assuming an infinite subterranean vertical stratification (Bishop and Thorpe 1994) and has been used successfully in numerous diagnostic studies of atmospheric phenomena (e.g., Davis and Emanuel 1991; Black and Dole 1993; Nielsen-Gammon and LeFevre 1996; Hartley et al. 1998). In this approach, lower-boundary potential temperature (surface theta) anomalies are treated as a distinct part of the PV distribution (Bretherton 1966) and are inverted separately from interior PV anomalies (subject to a homogeneous interior balance equation). Note that alternate approaches have been put forth in the literature (e.g., Hakim et al. 1996). A salient question regarding the current approach is the degree to which the surface theta anomalies depend upon the interior PV anomalies. This question is addressed in section 3b by assessing upper bounds on the influence of surface theta anomalies.
The approach implements a horizontally averaged vertical temperature stratification that is a function of pressure only. Figure 2, which displays a pressure–latitude cross section of the square of the buoyancy frequency, illustrates that the vertical stratification, in fact, exhibits a pronounced latitudinal variation near the tropopause. Most of this variation is concentrated in the region extending from 20° to 40°N, resulting in distinct tropical and extratropical stratification “regimes.” Recognizing that the choice of stratification parameter may impact the results, here σ is calculated as an average over extratropical latitudes (north of 40°). This represents a conservative choice because high values of vertical stratification limit the effective downward influence of stratospheric PV anomalies. Also, as the results of section 3a show, these are the latitudes in which a downward stratospheric influence is most evident. I will further examine the impact of vertical stratification upon the results in section 3b.
I focus on AO structures occurring during wintertime for which the stratospheric AO signature is strongest (Thompson and Wallace 2000). The study uses the 40 years of meteorological data produced jointly by the National Centers for Environmental Prediction and National Center for Atmospheric Research (NCEP–NCAR; Kalnay et al. 1996). Characteristic AO perturbation structures are obtained by performing linear regressions using daily and monthly annular mode indices (Baldwin and Dunkerton 1999; Thompson and Wallace 2000). For consistency with Thompson and Wallace (2000), the AO patterns presented in Figs. 1–5 are derived using the monthly annular mode indices for the winter period of January–March. The results presented in Figs. 6–7 are derived from daily indices for the months of December–February (as in Baldwin and Dunkerton 1999). As discussed in Baldwin and Dunkerton, the results are insensitive to the precise winter time period chosen. Regressed perturbation structures have amplitudes corresponding to 1 standard deviation in the index time series. Although the perturbation sign is arbitrary, here the sign is chosen to be consistent with observed decadal trends in the AO (Thompson et al. 2000).
3. Monthly AO structure
a. Basic results
The longitudinal (zonal) average structure of the zonal wind perturbations associated with the monthly AO index is presented in Fig. 1a. Deep vertically coherent westerly (easterly) wind patterns are observed at higher (lower) latitudes. High-latitude westerly wind anomalies extend from the surface well into the stratosphere, achieving largest amplitudes at stratospheric levels. This pattern is also characterized by a northward perturbation tilt with height at lower altitudes.
The corresponding zonal-average PV anomaly field for the AO is presented in Fig. 1b. The most striking aspect of this field is the modest pool of anomalously high PV found at high latitudes within the stratosphere. This is accompanied by broad oppositely signed PV anomaly patterns located to the south and just below. Potential vorticity anomalies of much smaller scale are found at lower-tropospheric levels. Considering the known variation of the tropopause with latitude, the PV anomaly field is partitioned using the World Meteorological Organization thermal tropopause definition (e.g., Lewis 1991). Using this definition, the stratosphere closely corresponds to the lightly shaded region in Fig. 2 (noting that the anomaly magnitudes are not large enough to significantly alter the location of the tropopause). The surface theta anomalies are included as part of the tropospheric PV distribution. Note that in the region extending from 70° to 90°N it is not evident that the broad negative PV anomaly centered at 400 hPa in the upper troposphere is distinct in structure from the oppositely signed feature located directly above in the stratosphere. Thus, there is some ambiguity regarding the independence of this tropospheric feature from its stratospheric counterpart above. In the following sections, the impact of this feature upon the tropospheric circulation is considered.
I next contrast the horizontal structure of the stratospheric, 50 hPa, PV anomaly field associated with the AO (Fig. 3a) to the long-term winter-average PV field. Figure 3b illustrates the horizontal PV structure of the winter-average stratospheric polar vortex. Although the correspondence is by no means perfect, both fields describe a similar large-scale spatial pattern and lend credence to the idea that the AO acts to modulate the strength of the stratospheric polar vortex (Thompson and Wallace 1998). According to the PV invertibility principle, PV anomaly fields having the largest magnitudes and spatial scales will induce the strongest remote circulations (Hoskins et al. 1985). In this sense, Fig. 3a illustrates that the AO represents an optimal candidate for providing a downward influence from the stratosphere, because the stratospheric PV anomaly pattern has a very large spatial scale.
Inversions of the PV anomaly field displayed in Fig. 1b are performed next. Figure 4a displays the zonal wind field that is obtained when the entire PV anomaly field is inverted. It is reassuring that the PV inversion process retrieves much of the original pattern of zonal winds displayed in Fig. 1a (except for quantitative discrepancies at subtropical latitudes influenced by the lateral boundary condition applied at 5°N). This provides an important consistency check for the analysis.
I next partition the PV anomaly field into its respective stratospheric and tropospheric parts (as discussed above) and apply piecewise PV inversions to deduce the zonal wind field induced by each component (shown in Figs. 4b and 4c, respectively). It is evident from Fig. 4 that a large part of the total zonal-average zonal wind pattern observed during the AO (Fig. 1a) is attributable to stratospheric PV anomalies, which induce substantial westerly winds at high latitudes that extend downward through the troposphere to the earth's surface. This represents a direct downward influence upon surface climate by the stratosphere. At low latitudes (<40°N), the stratospheric PV anomalies induce weak easterly winds that are primarily confined to the stratosphere, providing little downward influence into the troposphere. Further partitioning of the stratospheric PV anomalies (not shown) indicates that only PV anomalies in the lower stratosphere (below 30 hPa) contribute significantly to the observed tropospheric westerly wind anomalies. The reason for this result is the cumulative shielding effect of high vertical temperature stratification in the stratosphere, which limits the downward penetration of wind anomalies induced by PV anomaly structures located at higher vertical levels (Hoskins et al. 1985). This interestingly implies that detailed information regarding the mid- and upper stratosphere is not necessary to diagnose the net direct influence of stratospheric PV anomalies upon the troposphere. On the other hand, because lower-stratospheric processes are strongly coupled to processes occurring at higher stratospheric levels (Andrews et al. 1987), the results imply that a proper simulation of AO behavior requires an atmospheric model that, at the very least, adequately represents the net dynamical feedback of the mid-to-upper stratosphere upon the lower stratosphere. This idea helps to explain the results of recent modeling studies (Shindell et al. 1999a; Ruosteenoja 1999) that indicate a tropospheric sensitivity to varying model representations of the stratosphere.
Last, I note that the tropospheric PV anomalies (including the contribution of surface theta anomalies) induce a tripole pattern in the zonal wind field (Fig. 4c) that contributes toward 1) the northward tilting structure in the high-latitude westerly wind field and 2) the tropospheric part of the low-latitude easterly wind field (Fig. 1a). This pattern is consistent with the north–south PV anomaly dipole observed in the upper troposphere at midlatitudes (Fig. 1b). To the extent that the results discussed below (Fig. 6) indicate that the midlatitude tropospheric PV anomaly signature lags its stratospheric counterpart, one might interpret the zonal wind field in Fig. 4c as representing a tropospheric “adjustment” to the initial stratospheric forcing.
b. Sensitivity analyses
It was earlier noted that the vertical temperature stratification is observed to increase quickly with respect to latitude from 20° to 40°N near the tropopause. Here, the sensitivity of the results to the choice of vertical stratification parameter is examined. As discussed earlier, higher values of vertical stratification will reduce the effective downward penetration of the circulation anomalies induced by stratospheric PV anomalies. The results presented in Fig. 4 are based upon stratification parameter values that are representative of extratropical latitudes (>40°N). To assess this sensitivity, once again the stratospheric PV anomaly distribution is inverted, but this time I use a vertical temperature stratification that is calculated as an average over the latitudes 5°N and higher (the PV inversion domain). The resulting zonal wind pattern is shown in Fig. 5a. In contrast with Fig. 4b, it is found that, although the qualitative pattern in the troposphere remains unchanged, the magnitude of the tropospheric anomalies in Fig. 5a is systematically larger in the extratropics [about 25% (0.5 m s−1) greater at the surface near 65°N]. Thus, varying the vertical stratification parameter provides little qualitative change in the basic conclusion regarding a downward stratospheric influence. However, because in both situations the primary tropospheric anomalies are located in the extratropics, it seems most appropriate to choose stratification parameter values that are representative of extratropical latitudes. As a consequence, this convention is retained for the remaining analyses presented in the paper.
The boundary condition used implicitly presumes that the lower-boundary potential temperature (surface theta) anomalies are independent of the stratospheric PV anomaly field. Here I test the impact of this assumption by conversely assuming the surface theta anomaly distribution to be entirely dependent upon the stratospheric PV anomaly field. In this case, the surface theta anomalies are formally included as part of the “stratospheric” PV anomaly distribution for the purposes of PV inversion. This is equivalent to implementing an inhomogeneous lower-boundary condition (in terms of surface theta) and provides a useful test of the influence of the boundary condition upon the results.
The results of such a test are shown in Fig. 5b, which displays the zonal wind anomaly pattern obtained by inverting the combined field of stratospheric PV and surface theta anomalies. In contrast to Fig. 4b, it is found that a net westerly wind anomaly pattern extends downward to the surface but 1) is weaker in magnitude in the troposphere and 2) tilts northward with height in the troposphere. Thus, the zonal winds induced by the surface theta anomalies do act to partially oppose the downward tropospheric influence of the stratospheric PV anomalies. The results also indicate, however, that even if the entire surface theta anomaly distribution is considered to be dynamically linked to the stratospheric PV anomaly field, this dependence is insufficient to alter the basic conclusions about a downward stratospheric influence upon tropospheric climate. Furthermore, it is unlikely that stratospheric dynamical processes alone determine the distribution of surface theta anomalies. Thus, this test represents an upper bound on the potential indirect impact of stratosphere dynamics via the surface theta field. Further research will be required to refine this delineation.
The role of the broad negative PV anomaly located at high latitudes (>70°N) in the upper troposphere (∼400 hPa) is also considered. As discussed earlier, given its structure and location, it is unclear whether this tropospheric feature is independent of the positive stratospheric PV anomaly feature located directly above. this issue is studied in a similar manner to the lower-boundary condition test discussed above (Fig. 5b), by considering the tropospheric feature as part of the stratospheric PV anomaly field. The tropospheric PV anomaly feature is first spatially isolated by selecting a bounding box that extends from 600 to 300 hPa in the vertical and from 70° to 90°N in latitude (inclusive). The PV anomalies in this region are then grouped with the stratospheric PV anomalies, and this repartitioned PV is then inverted (Fig. 5c). By contrasting Figs. 4b and 5c, it is clear that the tropospheric feature primarily acts to reduce the magnitude of the induced extratropical tropospheric response with a slight pattern shift toward lower latitudes. Similar to the surface theta test, I conclude that even if this feature is regarded as somehow dynamically linked to the stratospheric PV anomaly distribution, the basic result of a substantial net downward influence from the stratosphere is retained. This issue emerges again in the following section. In summary, several different diagnostic tests all confirm the basic conclusions regarding the existence of a direct downward stratospheric influence upon the tropospheric circulation.
4. Intraseasonal time evolution
Additional support for the existence of downward stratospheric forcing during the AO is provided by analyzing the time evolution of the AO on short timescales. Analyses of daily meteorological data indicate that in some cases AO signals first appear in the midstratosphere (near 10 hPa) and then descend through the lower stratosphere and troposphere over a 3-week period (Baldwin and Dunkerton 1999), providing evidence of stratospheric precursors to certain tropospheric AO events.
Here daily AO indices derived for each of the 17 NCEP–NCAR pressure levels (the “signature” time series of Baldwin and Dunkerton) are used to construct regressed three-dimensional perturbation structures representing the typical flow anomaly patterns that would be observed at zero lag for the pressure level in question. Beginning with the highest pressure level (10 hPa) and proceeding downward, the sequence of 17 three-dimensional anomaly patterns thus represents the typical flow evolution occurring during the 3-week descent of the AO. These perturbation structures are then mapped into discrete time lags based upon the results presented in Fig. 5 of Baldwin and Dunkerton. Thus, for each time lag, a three-dimensional perturbation structure is obtained that is then analyzed in the same manner as the time-mean AO structure.
In Fig. 6 I present time–pressure slices of zonal-mean PV anomalies at 80° (Fig. 6a) and 60°N (Fig. 6b). The former cuts through the primary stratospheric pool of anomalously high PV as well as the underlying tropospheric feature of opposite sign. The latter isolates the development of the tropospheric lobe of PV centered at 60°N in Fig. 1b [a second lobe centered at 45°N exhibits a similar evolution (not shown)]. The positive PV anomaly signature in the lower stratosphere increases in magnitude during the first 5 days, remains steady until about day +13, and then quickly decays thereafter (Fig. 6a). The midlatitude tropospheric PV lobe develops after day +10, reaching peak amplitudes toward the end of the 3-week period (Fig. 6b). Thus, Fig. 6 illustrates how the primary stratospheric PV anomaly signature tends to precede the appearance of the major midlatitude tropospheric PV anomaly features later on in the AO evolution. On the other hand, Fig. 6a also shows that the high-latitude negative PV anomaly in the upper troposphere is a preexisting flow feature that weakens after the first few days. This reinforces the idea that this feature may not be dynamically distinct from its oppositely signed stratospheric counterpart located directly above.
A time–pressure slice of the zonal wind field induced at 60°N by stratospheric PV anomalies during the 3-week time period is shown in Fig. 7a. Although it is clear that the strongest zonal wind signature is confined to stratospheric altitudes, it is also evident that the stratospheric PV anomalies induce a downward influence into the lower troposphere that is here maximized about 8 days into the evolution. The results thus indicate that the earth's surface does not feel the strongest downward forcing until the AO signal descends into the lower stratosphere. The tropospheric signal rapidly weakens after about 2 weeks in concert with the stratospheric PV anomaly evolution (Fig. 6a).
One unexpected aspect of Fig. 7a is that a substantial downward influence appears to exist at day 0 in the evolution, at which time the AO signal is strongest at upper levels. This is where the upper-tropospheric PV anomalies come into play. As discussed above, at day 0 there is a pronounced negative PV anomaly feature located in the upper troposphere at high latitudes. As illustrated by the tests performed in section 3b, this feature acts to counter the downward influence of the positive PV anomalies in the stratosphere. This is confirmed by repeating the PV inversion analysis of Fig. 7a but using the PV-anomaly partitioning scheme that is applied in Fig. 5c (i.e., grouping the high-latitude, upper-tropospheric PV anomalies along with the stratospheric PV anomaly field).
The results of this calculation are shown in Fig. 7b, which sheds light on the how the downward stratospheric influence is communicated to the troposphere. In this case, the net downward influence appears as a well-defined pulse into the troposphere that is maximized at the surface about 2 weeks into the evolution. Also, the surface signature at day 0 is considerably reduced (to less than 1 m s−1). It appears that the negative PV anomaly feature at high latitudes in the upper troposphere effectively acts to delay the downward communication of the stratospheric PV feature into the troposphere by initially opposing the downward stratospheric influence. In summary, the PV evolution during the first few days appears to poise the stratosphere to produce a downward influence while the decay of the underlying tropospheric PV anomaly feature provides a release mechanism that allows the stratospheric influence to extend downward into the troposphere. Further study will be necessary to ascertain the dynamical linkages that exist between these two PV features during the early evolution.
Considering Figs. 6 and 7 together, it is evident that the midlatitude tropospheric PV anomaly features (e.g., Fig. 6b) develop after the downward stratospheric pulse reaches the lower troposphere (Fig. 7b). The picture emerging from these diagnostic analyses is that the troposphere experiences a dynamical adjustment to the downward stratospheric forcing. It is possible that the midlatitude tropospheric PV anomaly features displayed in Fig. 1b [and their associated zonal wind signature (Fig. 4c)] may be excited in different ways. For example, it may be that in some cases local tropospheric dynamics may be sufficient to produce this pattern. This helps to explain Baldwin and Dunkerton's (1999) result that not every tropospheric AO event is connected to a precursor stratospheric signal. Our results also suggest that the effectiveness of this type of downward stratospheric influence will likely depend upon the structure and magnitude of preexisting tropospheric zonal flow anomalies.
5. Discussion and concluding remarks
It is well known that the troposphere provides a strong dynamical forcing to the stratosphere via the vertical propagation of planetary-scale Rossby waves. The concept that the stratosphere can dynamically influence the troposphere is less commonly accepted in atmospheric science. A number of recent studies (Kuroda and Kodera 1999; Shindell 1999a; Hartmann et al. 2000) provide evidence that variations in the stratospheric polar vortex can indirectly impact the troposphere by altering the propagation characteristics of tropospheric planetary waves, which themselves provide a feedback to the zonal-mean flow in both the stratosphere and troposphere. Here evidence is provided that variations in the winter stratospheric polar vortex can directly impact surface climate during the AO.
The results indicate that large-scale potential vorticity anomalies in the lower stratosphere act to induce an annular pattern of zonal wind perturbations that extends downward through the troposphere to the earth's surface. Diagnostic analyses of regressed daily data show that the intraseasonal time evolution typically begins with a descent of the primary AO signal from the midstratosphere to lower-stratospheric levels. The PV anomalies in the lower stratosphere then induce a downward transient pulse into the troposphere (after a delay due to upper-tropospheric PV anomalies near the Pole). The troposphere thereafter dynamically adjusts to the downward pulse, leading to the creation of a distinct midlatitude tropospheric PV anomaly signature. The sensitivity of the results to variations in vertical stratification and lower-boundary condition specification has been tested. Although further work will be required to better quantify these sensitivities, the tests performed here indicate that they are not large enough to alter the basic conclusions.
These results implicate the stratosphere as a potentially significant contributor toward recent climate trends. I suggest that the indirect mechanism discussed above likely plays a key role in moving the AO signal from the midstratosphere to the lower stratosphere, after which time the direct forcing mechanism discussed here provides the remaining link to surface climate. Both direct and indirect stratospheric influences require initial changes in the stratospheric circulation. This brings up the issue of causality given that it is known that the stratospheric circulation is strongly influenced by the troposphere. The mechanistic interpretation of such downward influences thus depends upon what processes are responsible for producing the initial stratospheric circulation anomalies.
On short intraseasonal timescales, planetary-scale tropospheric Rossby waves are known to propagate upward into the stratosphere and initiate changes in the stratospheric polar vortex (e.g., during stratospheric warming events). This requires nonlinear wave breaking to occur within the stratosphere. In such cases, a subsequent downward stratospheric influence is likely best regarded as a dynamical feedback to the troposphere. On longer timescales, however, local radiative processes play a key role in determining variations in the strength of the polar vortex, suggesting a downward stratospheric forcing rather than a feedback. In either case, it is important to recognize that nonlinear and/or nonconservative processes internal to the stratosphere are essential in providing the downward influence. The implication is that a proper simulation of tropospheric climate requires an adequate representation of stratospheric dynamical and physical processes. This is consistent with the results of recent numerical modeling studies (Shindell 1999a; Ruosteenoja 1999).
The results also have more general implications for stratosphere–climate linkages because this mechanism simply requires a large-scale PV anomaly pattern to exist in the lower stratosphere. Thus, PV anomaly patterns distinct from the AO are also candidates for producing a downward influence. This is likely relevant for helping to explain some elusive stratosphere–climate linkages such as those observed in association with volcanic eruptions, the solar cycle, ozone depletion, and greenhouse gas forcing (Shindell et al. 1999a, 1999b; Volodin and Galin 1999; Robock 2000), all of which can provide large-scale alterations to the structure of the stratospheric polar vortex.
I thank David Thompson and Mark Baldwin for kindly providing the Arctic oscillation indices used in this study. I also thank Dana Hartley for comments on early drafts of this paper. Last, I am greatly appreciative of the comments provided by Brian Hoskins and an anonymous referee, which were instrumental in improving the paper. This work is jointly supported by the NSF Climate Dynamics Program under Grant ATM-0001346 and the NASA Global Modeling and Analysis Program under Grant NAG 5-7471.
Corresponding author address: Dr. Robert X. Black, School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, GA 30332-0340. Email: email@example.com