The global overturning diabatic circulation of the stratosphere as a metric for the Brewer-Dobson Circulation

The circulation of the stratosphere, also known as the Brewer-Dobson circulation, transports water vapor and ozone, with implications for radiative forcing and climate. This circulation is typically quantified from model output by calculating the tropical upwelling vertical velocity in the residual circulation framework, and it is estimated from observations by using time series of tropical water vapor to infer a vertical velocity. Recent theory has introduced a method to calculate the global mean diabatic circulation strength through isentropes from satellite measurements of long-lived tracers. In this paper, we explore 5 this global diabatic circulation as it relates to the residual circulation vertical velocity, stratospheric water vapor, and ozone at interannual timescales. We use a comprehensive climate model, three reanalysis data products, and satellite ozone data. The different metrics for the circulation have different properties, especially with regards to the vertical autocorrelation. In the model, the different residual circulation metrics agree closely and are well correlated with the global diabatic circulation, except in the lowermost stratosphere. In the reanalysis products however, there are more differences throughout, indicating the 10 dynamical inconsistencies of these products. The vertical velocity derived from the time series of water vapor in the tropics is significantly correlated with the diabatic circulation, but this relationship is not as strong as that between the diabatic circulation and the residual circulation vertical velocity. We find that the diabatic circulation in the lower to middle stratosphere (up to 500K) is correlated with the total column ozone in the high latitudes and in the tropics. The upper level circulation is also correlated with the total column ozone, primarily in the subtropics, and we show that this is due to the correlation of both the 15 circulation and the ozone with upper level temperatures. Copyright statement. TEXT 1 Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2018-972 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 23 October 2018 c © Author(s) 2018. CC BY 4.0 License.


Introduction
The Brewer-Dobson circulation (BDC) is important for the distribution of gases in the stratosphere (Butchart, 2014) including water vapor, the radiative effects of which have been shown to impact surface climate (Dessler et al., 2013), and ozone, which impacts surface circulation (e.g., Polvani et al., 2011) and human health (e.g.Abarca and Casiccia 2002).In models and reanalysis products, the BDC is frequently quantified by the vertical velocity in the Transformed Eulerian Mean (TEM) framework (Andrews et al., 1987), averaged over the well-mixed tropics (e.g.Butchart et al., 2006;Li et al., 2008;Seviour et al., 2012;Hardiman et al., 2017).In steady state, the total upwelling and downwelling mass fluxes must be equal, and so characterizing the tropics alone is considered sufficient.The TEM framework provides formalism that approximates the Lagrangian-mean mass transport, and in the limit of adiabatic, small-amplitude eddies, the TEM residual mean circulation is equivalent to the density-weighted isentropic mean circulation.The mean and trends of the residual mean circulation average tropical vertical velocity through the 70 hPa level have been used in multimodel comparisons (Butchart et al., 2010) and in comparisons between different reanalysis products (Abalos et al., 2015;Kobayashi and Iwasaki, 2016).The 70 hPa level is consistently within the stratosphere even in climate models that do not accurately simulate tropopause height.As it is in the lower stratosphere, it approximates the mass flux between the troposphere and stratosphere and, as such, is related to the water vapor flux and ozone transport.
The TEM vertical velocity is a useful metric for understanding stratospheric dynamics.However, apart from its theoretical relationship with the Lagrangian-mean mass transport, it is not straightforward to relate the TEM vertical velocity to the tracer transport that is so important to climate due to the presence of other transport processes such as mixing.In contrast, the global average diabatic overturning circulation through isentropes can be theoretically related to observed tracer distributions through the idealized tracer "age" of air (Neu and Plumb, 1999;Linz et al., 2016).This global diabatic circulation has been calculated from two different satellite data products (Linz et al., 2017), thus motivating the use of the global mean overturning diabatic circulation through isentropes as a metric for the BDC strength in addition to the TEM vertical velocity.In this paper, we explore differences between the global diabatic circulation and other calculations for the strength of the circulation in order to understand the relationship of this new constraint to more common metrics.
The calculation of the global diabatic circulation in Linz et al. (2017) is the first of its kind, but not the first observational estimate of the circulation strength.Water vapor is transported into the stratosphere through the cold tropical tropopause, which has a strong seasonal cycle in temperature.The resulting time series of water vapor at the cold-point tropopause similarly has a strong seasonal cycle.By tracking the upward movement of the dry and wet phases over time, the water vapor signal-which is nearly conserved above the cold point tropopause-can be used to calculate an effective velocity (w T R ). "Effective" refers to the aggregated transport, which includes the effects of advection and mixing.As a result, this "water vapor tape recorder" (Mote et al., 1996) method must be used with caution when studying the TTL (Podglajen et al., 2017) and with even more caution when comparing models (Dietmüller et al., 2018).This study minimizes such issues by focusing on the region above the TTL and by using a zonal mean of 10S-10N to reduce the influence of horizontal mixing seen at the edges of the pipe.We will explore the relationship between the vertical velocity derived from water vapor in the deep tropics and the global diabatic circulation strength.
One of the primary motivations for studying the BDC and its variability is its influence on stratospheric ozone.The circulation is known to transport ozone-this is why Dobson proposed it in the first place (Dobson et al., 1929), even if he concluded that this circulation was far-fetched.While the qualitative description of the influence of the circulation on ozone is well established, with it transporting ozone from its primary production location in the middle stratosphere in the tropics to the midlatitudes and poles, quantifying this effect is not simple.We know from observational studies that changes to the dynamics impact polar ozone (Hassler et al., 2011), and that the ozone hole recovery is currently being modulated by the dynamics (Solomon et al., 2016).In the Northern hemisphere, the variability in hemispherically averaged upward Eliassen-Palm (EP) flux at 100 hPa from a reanalysis data product has been shown to explain about 50% of the interannual variability of total column ozone in wintertime (Fusco and Salby, 1999) with the influence of the wave driving dependent on the latitude (Reinsel et al., 2005).These strong relationships are a motivating factor in using the TEM residual mean vertical velocity, which is directly related to the EP flux, as a metric for the BDC strength.The global diabatic overturning circulation on isentropes has been demonstrated to be related to tracer transport more directly, but its relationship with ozone is unknown.This paper serves to explore the diabatic circulation on isentropic levels as a metric for the circulation strength.Section 2 describes the model runs, reanalysis products, satellite data, and regression methods.In Section 3, we provide an explanation of the steps for calculating the global diabatic circulation on isentropes, the necessary model output, and its advantages and disadvantages.In Section 4, we examine three different calculations for the TEM vertical velocity, including the underlying assumptions.Then we compare the total global diabatic circulation on isentropes to the more traditionally used TEM vertical velocity calculated in these three different ways (Abalos et al., 2015) for three different reanalysis products and for the Whole Atmosphere Community Climate Model (WACCM).Thus we determine how the information provided by this new metric compares to the information more typically used.We find close agreement between the diabatic circulation strength and one of the three calculation methods for the TEM vertical velocity for the reanalyses, and close agreement between the diabatic circulation strength and all three calculations for the TEM vertical velocity in the model.In Section 5, we compare the tropical vertical velocity calculated from the water vapor tape recorder (Niwano et al., 2003) from the WACCM model to the total overturning circulation.Similar to the good agreement found for the modeled residual circulation and diabatic circulation, the diabatic circulation strength and the water vapor tape recorder are closely linked in the model, although the correlation is weaker.In Section 6, we examine the relationship between the diabatic overturning circulation and stratospheric ozone, using data, reanalyses, and WACCM.We find that the lower branch of the circulation is important for the polar ozone, while the upper branch is the most important for subtropical ozone.The latter relationship is driven by the temperature dependence of the photochemistry and covariance of temperature and the diabatic circulation.Section 7 summarizes the results and discusses implications and future work.
2 Model, reanalysis products, satellite data, and methods For the model in this study, we use the Whole Atmosphere Community Climate Model (WACCM), a state of the art, chemistryclimate model.This model uses the physical parameterizations and finite-volume dynamical core (Lin, 2004) from the Community Atmosphere Model, version 4 (Neale et al., 2013), with a vertical extent from the surface to the lower thermosphere, and 31 pressure levels from 193 hPa to 0.3 hPa.The WACCM simulation is the first member of an ensemble run based on the Chemistry Climate Model Initiative REF-C1 scenario (Morgenstern et al., 2017), and is forced with prescribed observe sea surface temperatures.This model was shown to have a global diabatic circulation strength that agrees closely with the satellite tracer observations at 460 K (Linz et al., 2017).This study covers the time period from 1980-2014.
Three different renalysis data products are used in this study, following upon the work by Abalos et al. (2015) and Linz et al. (2017).These are the ECMWF Reanalysis Interim (ERA-Interim, Dee et al. 2011), the Modern Era Retrospective analysis for Research and Applications (MERRA, Rienecker et al. 2011), and the Japanese 55-year Reanalysis (JRA 55, Kobayashi et al. 2015).Reanalyses are used for the same time period as WACCM, for consistency in the comparisons.These reanalyses are based on assimilation of different sets of data into three different models and using different assimilation schemes, leading to some significant differences in their output, especially above 10 hPa.However, beneath 10 hPa, the results of Abalos et al. (2015) demonstrated more differences in BDC metrics based on the calculation method than on the reanalysis, concluding that since more uncertainty arose from the method of calculation (except for trends), differences between reanalyses were less significant.We build upon that result here and suggest that because of uncertainties in radiative heating, the reanalyses are not as robust in certain contexts.
Finally, we consider the total column ozone measurements from the Solar Backscatter Ultraviolet Instrument (SBUV) from 1980-2013 from the version 8.6 SBUV ozone data record (McPeters et al., 2013).This data is based on nine recalibrated SBUV instruments with total column ozone measurements that are consistent with ground-based observations of total column ozone to within 1%.We use the total column ozone as it has the least uncertainty for use in long term correlation calculations.
As the primary motivation of this paper is to evaluate relationships between the dynamical and tracer quantities, it utilizes correlations extensively.All correlations are reduced major axis regressions with both variables scaled by their standard distributions.Only results significant at 95% level or greater are reported.Time series are deseasonalized by removing the climatology of each variable.In the stratosphere, correlations might be expected to be driven by the Quasi-Biennial Oscillation (QBO) in addition to the seasonal cycle.Rather than explicitly removing this, we account for it by examining filtered time series and cross-spectra (not shown) and highlight the cases where this is important.Many of the relationships examined are coherent with zero phase lag at all frequencies resolved by the monthly time step for the tracers.

Calculating the diabatic overturning circulation on on isentropes
Why would we need a different metric for the BDC?The residual mean tropical upwelling at 70 hPa has been used for at least a decade (Butchart et al., 2006).However, it is neither directly observable nor easily relatable to observations.A metric for models and reanalyses ideally should be able to be constrained by data.By revisiting the age-circulation relationship in the Tropical Leaky Pipe (Neu and Plumb, 1999), Linz et al. (2016) showed a direct relationship between the idealized age tracer (Hall and Plumb, 1994) and the diabatic circulation through an isentropic surface, demonstrating that the difference between the age of air that is downwelling and the age of air that is upwelling through each isentrope is inversely proportional to the diabatic mass flux through that surface, in steady state and neglecting diabatic diffusion.Thus, the global mean overturning diabatic circulation through an isentrope reflects the total tracer flux and should be considered an additional or alternative metric.
The time-dependent, global, diabatic overturning mass flux through an isentrope is the average of the upwelling and downwelling mass fluxes, as follows.Following Linz et al. (2016), we define the total upwelling mass flux, M u , and the total downwelling mass flux M d , through an isentropic surface: and (1) θ is the total diabatic heating rate, and σ = −g −1 ∂p/∂θ is the isentropic density.The limits of integration are the regions of the isentrope through which air is upwelling ( θ >= 0) and downwelling ( θ < 0) instantaneously.Since the monthly mean is not in equilibrium, some amount of storage may take place, and these two will not necessarily be equal.We therefore define the total overturning circulation as the average: This is an arbitrary but sensible definition.Although one could certainly consider the extratropics or tropics alone, the treatment in (3) accounts for simultaneous variability in the extratropics and in the tropics, thus providing an instantaneous global average overturning circulation strength.Furthermore, it is this quantity that is directly related to the age of air tracer distribution (Linz et al., 2016).
A note about the use of isentropic coordinates: the isentropic framework makes separation of the diabatic and adiabatic components completely natural-they are simply the vertical and horizontal motions, respectively.In the annual mean and in steady state, the circulation on isentropes is much the same as the circulation on pressure surfaces.The seasonal variability of circulation on pressure surfaces and on isentropes differs, however.For example, the isentropes descend at the poles during springtime, which leads to upward motion of the air relative to the isentropes.Such springtime polar upwelling is not visible if pressure surfaces are used instead.Seasonal variability is removed from all time series in this study, and thus we attempt to minimize the effect of this difference on the comparisons.For trends however, the longer-term motion of the isentropes may well be different from the motion of the pressure surfaces, which will naturally be moving up as the tropopause lifts (e.g., Singh and O'Gorman 2012).Thus, we might expect trends to have significantly different results depending on the choice of coordinate system, perhaps as different from trends through pressure surfaces as those calculated relative to the tropopause height (Oberländer-Hayn et al., 2016 To calculate the diabatic circulation from model output or reanalysis, one thus needs the total diabatic heating rate, the temperature, and the pressure.The diabatic heating rate is output differently in different models, but it is straightforward.The diabatic heating rate consists predominantly of two terms, the latent heat flux from phase changes of water and the radiative heating and cooling (Fueglistaler et al., 2009;Wright and Fueglistaler, 2013).For levels wholly within the stratosphere, water vapor concentrations are so low that the former is negligible.Models may output other diabatic terms, such as mixing from parameterized gravity waves; alternatively, they may output a total temperature tendency, which contains all of the necessary information in just one term.Almost all models will output these terms on either pressure or model levels.The diabatic heating rate on those levels must then be interpolated to isentropic levels, for which the temperature and pressure fields are necessary.
The isentropic density can be calculated by finite difference in pressure and then interpolated to isentropes as well.
Since eddies serve to predominantly mix adiabatically, they are, naturally, less important for the diabatic circulation than for the residual circulation.In the conversion from the diabatic vertical velocity on pressure surfaces to the diabatic vertical velocity on isentropes, the covariance of the diabatic vertical velocity and the isentropic levels could nevertheless be important.
However, this covariance is small enough that monthly mean temporal resolution is sufficient to accurately calculate the circulation; specifically, in ERA-Interim using monthly means instead of 6-hourly means results in no bias throughout most of the stratosphere and up to a 10% bias at the poles in wintertime, which, as the pole is a small area of the globe, is a much smaller bias on the total overturning mass flux.While many models do output monthly mean eddy fluxes to calculate the residual circulation, others, especially older model runs, do not.Almost all models output shortwave and longwave radiation, and as these are by far the dominant terms in the total diabatic heating rate, this metric can be calculated using models that did not report the necessary terms or have the necessary temporal resolution for the residual circulation vertical velocity calculation.
The comparatively minimal data requirements for this metric recommend it for intermodel comparisons.
We note that the diabatic circulation strength is a good indication of the integrated eddy forcing on the circulation, but it does not diagnose which eddies are responsible.Thus, models could get the right circulation from the wrong waves, and indeed, there is reason to expect compensation between resolved and parameterized wave driving (Cohen et al., 2013).Because of this compensation, the analysis of different wave forcing contributions to the BDC in the residual mean framework is also potentially problematic.Finding an appropriate way to relate any BDC metric directly to the tropospheric forcing in a way that could inform model development and tuning is an interesting area of research.
The vertical autocorrelation coefficient (r) of the diabatic circulation (with the seasonal variability removed) is shown for WACCM in the first panel of Figure 1.Correlations were performed as described in Section 2. The autocorrelation is relatively narrow in width, so that the variability of the lower level circulation is relatively uncorrelated with that of the upper level circulation.An interesting feature is the weak anticorrelation between lower and upper levels, which can also be seen in the vertical autocorrelation function of the heating rates themselves (in either pressure or isentropic coordinates), and the dynamical reasons for this are the subject of ongoing investigation.
6 The BDC was originally hypothesized to explain tracer measurements (Dobson et al., 1929;Brewer, 1949), and therefore the Lagrangian mean transport is, in some sense, the appropriate formalism to study.The TEM residual circulation is not the same as the Lagrangian mean mass transport, as noted explicitly in Andrews and McIntyre (1976).However, under certain conditions (small amplitude, adiabatic eddies), the Lagrangian mean circulation and the TEM residual circulation are identical.The TEM equations also provide unique insight into the forcing of the mean flow by eddies; when the quasigeostrophic approximation holds, the internal forcing of the mean state by the eddies is encompassed by the divergence of the Eliassen-Palm flux (Edmon et al., 1980).Thus, because of the ready interpretation of the wave-mean flow interactions, the TEM residual mean circulation has been the primary diagnostic for models and observations of the stratosphere.Here, we try to understand differences in the common methods for calculating this diagnostic, and the relationship of the TEM residual circulation vertical velocity with the global diabatic circulation strength.Abalos et al. (2015) performed an extensive reanalysis intercomparison of the trends in the TEM vertical mass flux calculated in multiple ways from ERA-Interim, MERRA, and JRA-55.For this work, the calculations were repeated for the WACCM model output.The three different methods for calculating the mass flux are summarized as follows, and for more details see the original paper.The first method is the residual circulation (Andrews et al., 1987), w * , in which the residual vertical velocity is calculated based on the Eulerian mean vertical velocity and the meridional eddy heat flux.This method, which we will refer to as the "direct" method relies on performing vertical integrals of the velocity fields from reanalyses.The second calculation of the BDC, w * M , is based on the "downward control" principle (Haynes et al., 1991), and is calculated using momentum balance equation, integrating the difference of the divergence of the Eliassen-Palm Flux and the zonal mean zonal wind tendencies on surfaces of constant "angular" momentum (in this case, constant latitude) to derive a streamfunction (Randel et al., 2002) assumption of isolines of angular momentum being equivalent to latitude lines could lead to errors in this estimate.Both of these methods also rely on the applicability of the quasigeostrophic approximation to interpret their results.The final estimate, w * Q , is calculated by iterating the thermodynamic balance and the continuity equation with no net mass flux across a pressure surface (Murgatroyd and Singleton, 1961;Rosenlof, 1995).Any errors in heating rates will be reflected in this calculation.
Because this estimate is also derived from the heating rates, this should be the most closely related to the diabatic overturning circulation.For this study, we use the deseasonalized timeseries of these estimates of the BDC strength integrated over 30 • S-30 • N (Abalos et al. 2015, Figure 8, top panel) at levels throughout the depth of the stratosphere.
The first two of these methods both require at least 4 times daily data, while the thermodynamic w * Q needs only monthly data (Lin et al., 2015).For the purposes of this study, the same frequency of data was used for all three methods and then monthly averages were taken.The interpretations of the results in terms of eddy forcing for both the direct method and the downward control method rely upon quasigeostrophic balance, whereas the thermodynamic method does not.Thus, we might expect that the two quasigeostrophic, high-frequency data derived estimates would be very similar.Butchart et al. (2006) calculated the mean and the trend in the residual vertical velocity using both methods in a variety of models and found that they were generally similar in magnitude and structure, though differences between the two calculations varied more than differences in the interannual variability of each individual calculation.Rosenlof (1995) compared the thermodynamically calculated streamfunction to the downward-control streamfunction and found them to be similar, but with the strongest differences in the lower stratosphere.Abalos et al. (2015) also performed a qualitative comparison between the mean streamfunction for these three estimates, noting that the thermodynamic calculation is larger in the lower stratosphere and with more differences between the downward-control calculation and the other two estimates higher up in the stratosphere at the poles.
In order to understand some of the properties of the different vertical velocity calculations, we examine the vertical autocorrelation of the tropical upwelling velocity for the WACCM model.Note that the "downward control" calculation of w * M includes the gravity wave drag, since this made an important contribution in the model (but not in the reanalyses).Figure 1 shows these autocorrelation coefficients.The "direct" method is shown in b, and the correlation is broader than the equivalent autocorrelation for the diabatic circulation.The "downward control" method is shown in c, and the vertical autocorrelation is even greater.The downward-control theory means that the lower levels are highly correlated with the upper levels, since the momentum deposited at upper levels drives lower levels, and so it is consistent that the spatial autocorrelation of w * M is very broad.Note then that the vertical velocity calculated in this way is essentially a single piece of information for the extent of the stratosphere.Differing variability in the upper and lower branches will be relatively indistinguishable using such a calculation.
Previous results suggest that the upper and lower branches may be distinguished by this metric for subseasonal variability in winter, however (Abalos et al., 2014).The thermodynamic vertical velocity in panel d demonstrates that the vertical covariance is not necessarily a result of the flow itself, since vertical correlation is much narrower in this case.Unlike the diabatic circulation, however, there is little apparent anticorrelation between the upper and lower branches of the circulation.There is an interesting feature in the lower stratosphere for this radiatively determined vertical velocity; beneath 70 hPa, the behavior is much more weakly correlated with upper levels than for the other calculations of vertical velocity.This is consistent with the results of Rosenlof (1995), who speculated that the relatively simple way the radiative heating was calculated was responsible.This different behavior in the lowermost stratosphere was also found by Abalos et al. (2015), and so the true reasons are not clear, since in the more complex model and in the complex reanalyses examined here and by Abalos et al., the same result is seen.These three calculations, often treated as the same, are actually somewhat different, especially with respect to the vertical structure of their interannual variability.
In Figure 2, we show the matrix of correlation coefficients (r) for each version of the residual circulation vertical velocity with each other version from the WACCM model in the top three plots and for one of the reanalyses, ERA-Interim, in the lower three panels.(Behavior is similar for the other two reanalyses.)These correlation coefficients are demonstrating the interchangeability (or lack thereof) of these different calculations for the vertical velocity.The first column shows the correlation between the direct calculation on the y-axis with the downward-control calculation on the x-axis.As expected, the correlation of these two calculations at the same level is very high, with the WACCM correlations appearing very similar to the autocorrelations in Figure 1 and r > 0.9 along the diagonal between 50 and 10 hPa for the reanalysis.We see the evidence of the broad autocorrelation of the w * M as the correlations of the lower level w * with the upper levels of w * M are much higher than the opposite.We note that when the full downward-control calculation-using contours of angular momentum rather than latitude lines-is applied to calculate the w * M , the correlation with w * is actually somewhat worse (r<0.7 along most of the diagonal, not shown), and even lower (r<0.3along the diagonal) when the correlation is calculated with higher frequency data than monthly (c.f. the impact of this calculation on the mean in Ming et al. 2016).The second column shows the correlation of the thermodynamic TEM vertical velocity w * Q with the downward-control calculation w * M .Again the correlations span much deeper along one axis than the other, associated with the broad vertical autocorrelation of the downward control calculation method.Interestingly, at upper levels in the model, this cross-correlation is strongest, while in the reanalysis, the upper levels are where the cross-correlation is weakest.The weak correlation at upper levels in the reanalysis product could be a result of the discontinuities in the heating rates above 5 hPa noted by Abalos et al. (2015).The correlation beneath 70 hPa weak in the model and is not significant in the reanalysis, again consistent with the substantial differences at low levels seen in the mean by both Rosenlof (1995) and Abalos et al. (2015).There are major discrepancies between the lower stratospheric heating rates in different reanalyses, which could explain this feature to some extent (Wright and Fueglistaler, 2013).The third column shows w * on the y-axis and w * Q on the x-axis.These compare more favorably than the middle column, but it is important to note that even in the WACCM model, these are not equivalent beneath 70 hPa.In the reanalysis, the correlation of these is a bit higher than for the comparison in panel e), but again there is limited correlation in the upper stratosphere.Because of their different time evolution, it is not entirely surprising that the trends in the circulation calculated using these different methods disagree with each other for the reanalyses (Abalos et al., 2015).
Next, we seek to answer the question of how the global diabatic circulation on isentropes relates to these metrics.We calculate the correlation of the three different calculations of the TEM vertical velocities with the deseasonalized diabatic circulation strength on each isentrope (as defined above) for each of the three reanalysis data products and for the WACCM model.These twelve correlation coefficient matrices are shown in Figure 3.The highest correlation is found between the diabatic circulation on isentropes and the w * Q , as expected, because these are both calculated from the heating rates for all three reanalyses and the model.In addition, this comparison has the smallest vertical extent, consistent with the narrower extent 9 of vertical autocorrelations seen in Figure 1.The 50 hPa w * Q variability is captured in all three reanalyses by the 450-500 K diabatic overturning.The 10 hPa w * Q variability is captured in all three reanalyses by the diabatic overturning between 800-900 K.These follow relatively closely to the predicted slope of the relationship between potential temperature and pressure, with a slope of -7/2 as shown in the gray dashed line.This is the prediction based on the theoretical relationship between potential temperature and pressure for an ideal gas, but the intercept was defined somewhat arbitrarily.In all three reanalyses and the model, there is some reflection of the anticorrelation of the upper and lower branches of the circulation that is seen in the global diabatic circulation on isentropic surfaces.The relationship with the other TEM vertical velocities is less clear in the reanalyses, though still quite strong in the WACCM model.In the reanalyses, w * at 70 hPa is not strongly correlated with the diabatic circulation strength at any level, with the correlation coefficient only reaching up to r = 0.5 (at 550 K for both JRA55 and MERRA and between 550 and 650 K for ERA-Interim).The momentum derived vertical velocity is the least well correlated, with the lower level diabatic circulation strength having almost no covariability with w * M at any level except in WACCM.We conclude from this comparison that the diabatic circulation through isentropes is very closely related to the TEM vertical velocity calculated using heating rates with less covariation with w * and even less with the momentum derived vertical Q , these results are similar to those found by Abalos et al. (2015) for w * Q .Because of the different coordinate system, however, some differences exist.ERA-I shows an acceleration of the lower branch of the circulation and a deceleration of the upper branch.MERRA shows an acceleration around the midstratosphere, where the upper branch begins, and in the uppermost stratosphere.JRA 55, meanwhile, only has a small region in the midstratosphere where it shows a statistically significant trend.This is also an acceleration.The WACCM simulation for this time period meanwhile, has no statistically significant trend at any level, despite significant trends in the thermal structure.This result of no trend in the WACCM overturning is intriguing-although the isentropic levels are changing location over these decades, the total overturning through each isentrope is not significantly changing.This is perhaps related to the lifting of the circulation described by Oberländer-Hayn et al. (2016).The differences in trends in this metric compared with the "direct" TEM vertical velocity calculation, which show significant positive trends at all levels for MERRA and JRA55, demonstrate that although the diabatic circulation on isentropes varies closely with the other metrics, trends will appear different, considering that changes to the thermal structure as well as the circulation play a role.Note that since the time series of heating rates in reanalyses are somewhat questionable above 800 K, where they are influenced by changes in the observing systems, the trends there are to be treated with caution.As discussed in the introduction, the water vapor tape recorder can be used to calculate an effective velocity (w T R ) by tracking the seasonal cycle as it is moved along by the BDC.We modify previous approaches (Niwano et al., 2003;Schoeberl et al., 2008) by using four levels (instead of two) for a phase-lagged correlation.This modification appears to better capture interannual variability (e.g., QBO) whereas the two-level method is better at capturing the seasonal cycle (Glanville and Birner, 2017).
We correlate monthly data between 3 lower levels (z to z+2) and 3 upper levels (z+1 to z+3) such that the two middle levels overlap.We then calculate the correlation coefficients, shifting the upper level data from +1 to +9 months while holding the lower level still.The lag with the largest correlation coefficient represents the approximate time needed for the tape recorder signal to ascend from the lower levels to the upper levels.The tape recorder speed, assigned to the midpoints between the levels and the time steps, is simply the distance between the levels divided by the time lag.This modified method was tested on various scenarios within a 1-D model and was found to successfully capture variability but underestimate speeds by 5-10%.
It should be noted that methane oxidation acts as a water vapor source, affecting the mean values above 70hPa (∼ 450 K), but with smaller impacts on the interannual variability up to about 10hPa (Kawatani et al., 2014).Depending on the seasonal cycle of the methane and the speed of the BDC, this can result in an apparent slow-down, speed-up, or nothing at all.For example, if oxidation occurs before (after) the wet signal, the effective velocity will appear stronger (weaker).However, if oxidation is concurrent with the wet signal, the velocity calculation will not be affected.
Note that although reanalysis products do output water vapor, the inconsistencies of the water vapor tape recorder with the vertical velocities in reanalysis, likely due to enhanced dispersion from the assimilation process, lead us to omit their analysis (Glanville and Birner, 2017).The results of the water vapor tape recorder comparison to the global diabatic circulation are shown for WACCM at 500 K in the time series in Figure 5.This figure shows the significant correlation between the water vapor tape recorder vertical velocity and the global diabatic circulation strength (r=0.57), and certain features stand out.The Quasi-Biennial Oscillation appears to be related to a significant fraction of the covariation of these two time series, and when examined, the coherence drops off with periods shorter than the seasonal timescale.The water vapor tape recorder vertical velocities also appear to have greater decadal variability than the diabatic circulation.The correlation of these improves upon filtering to remove the higher frequency variability in the diabatic circulation, which the water vapor tape recorder does not capture.The correlation between these two measures of the circulation is not strong enough for them to be considered equivalent, in the way that the WACCM results above suggest near equivalency between the diabatic circulation and the tropical residual circulation vertical velocities for considering interannual variability.w T R results from observations must be understood within this context.
To examine the correlation more broadly, we show the cross correlation between the water vapor tape recorder vertical velocity and the diabatic circulation at every level in the left panel of Figure 6.The correlation is around 0.5-0.6 along the diagonal, with anticorrelation of up to 0.4-0.5 between the upper branch and lower branch (regardless of the metric).
Interestingly, the correlation with the TEM tropical vertical velocity is considerably weaker, as shown in the right panel.that when the correlation between the TEM tropical vertical velocity and the w T R calculated in pressure coordinates, the magnitude of the correlation is the same as with the isentropic coordinates, except between 5-10 hPa where it is much weaker, not shown).This result indicates that although the diabatic circulation is not equivalent to the water vapor tape recorder vertical velocity, it does better reflect the behavior of the water vapor than does the TEM.This may be due to the fact that the effective velocity (w T R ) includes influences from mixing while TEM does not (Glanville and Birner, 2017).The TEM ( w * ) measures only one part of the BDC, whereas the total overturning circulation (M) is a better measure of total transport, neglecting only diabatic diffusion, and therefore correlates more strongly with the water vapor.One motivation for studying the BDC is its influence on radiatively important trace gases, such as water vapor and ozone.Water vapor is a quasi-conserved tracer once it enters the stratosphere (in the absence of the aforementioned methane oxidation), and so its behavior is comparatively straightforward.In contrast, ozone is both produced and destroyed in the stratosphere in chemical processes that are photochemically and temperature dependent.The ozone maximum is around 7 hPa or 800 K in the tropics (e.g.Paul et al., 1998), where photolysis by wavelengths less than 240 nm dissociates molecular oxygen (Chapman, 1930;Seinfeld and Pandis, 2006).As air moves from the tropics, it advects the ozone to mid and high latitudes.Stratospheric ozone absorbs ultraviolet radiation, creating heat, and thereby it influences the thermal structure of the stratosphere (e.g.Andrews et al., 1987) and thus the diabatic heating and transport.As the chemistry itself is temperature dependent, ozone, temperature and the circulation are closely connected.
With this interconnectivity in mind, we examine the total column ozone correlation at every latitude with the the global overturning circulation strength at each level within the stratosphere.The correlation of the deseasonalized time series of the monthly mean total column ozone data from the Solar Backscatter Ultraviolet Instrument (SBUV) from 1980-2013 and the global diabatic circulation strength from the three different reanalyses is shown in Figure 7. Also shown is the correlation of the total column ozone and global diabatic circulation strength from the WACCM model.Generally, there is a consistent pattern across all three reanalyses and the model.The ERA-Interim correlation with the SBUV data is much stronger than the correlations of the other two reanalyses with the SBUV data.Note that ERA-Interim assimilates the SBUV data, where MERRA and JRA55 do not, and this is a likely explanation for the increased correlation.Nevertheless, as the same spatial patterns are visible in the correlations with all three reanalyses and the model, we consider them to be robust and seek to understand them.We will focus on WACCM, as its dynamics are necessarily consistent with the ozone concentrations.
We see that the high latitude total column ozone is correlated with the circulation in the lowermost stratosphere, with the correlation explaining up to 25% of the deseasonalized total column ozone variability in the Northern hemisphere polar region.The total column ozone in the tropics is strongly anticorrelated with the diabatic circulation around 500 K.Both of these are qualitatively consistent with transport being the dominant factor driving the relationship between the ozone and the circulation at these levels.The strong upwelling in the tropics brings up low ozone tropospheric air and is associated with strong downwelling in the extratropics, where the ozone is being transported from the tropics.The correlation is strongest in the Southern hemisphere in the collar region of the polar vortex, around 55 • S, and is weaker at the pole, while in the Northern hemisphere, the correlation is stronger poleward of that, around 70 • N.More air is transported by the diabatic circulation and mixing to the Northern hemisphere pole than the Southern hemisphere pole because the Southern hemisphere polar vortex is a stronger barrier to mixing.The tropical total column ozone is also correlated with the circulation at upper levels, above the ozone maximum (800 K).Some of this correlation can be explained through the anticorrelation of the upper and lower branches of the circulation discussed above, but this is insufficient to explain the correlation, as was the case for water vapor.
The subtropical total column ozone is anticorrelated with the upper level circulation strength, with hemispheric asymmetry in which levels relate to the subtropical ozone in the different hemispheres.This pattern of the total column ozone correlation with 15 At the equator at upper levels, the correlation is high, and the strong subtropical signal we see in Figure 7 is related to the variability of ozone at the uppermost levels and the local ozone concentration on the edge of the tropics in the lower branch.We suggest that two different processes are responsible for these differing behaviors: The upper level local correlations are related to the temperature dependence of the ozone chemistry (which we will demonstrate), and the middle stratosphere local correlations are related to the partitioning of the flow between the upper and lower branches of the circulation (which is the subject of ongoing work).Near, at, and above the ozone maximum, the ozone distribution is determined by chemistry, while at the lower levels the ozone distribution is determined by transport.
The correlation of the upper level circulation with the lower level ozone concentrations on the edges of the tropics is consistent with the anticorrelation of the upper and lower branches of the circulation and different characteristics of the transport.In the lower branch, the stratospheric entry levels are close to the poleward flanks of the tropics (Birner and Bönisch, 2011), and so if the anticorrelation of the upper and lower branches of the circulation is indeed a partitioning between the deep tropical entry latitudes and the more subtropical entry latitudes, the strong upper branch is associated with less upwelling in these flanks and thus less ozone around these turnaround latitudes.This hypothesis of the partitioning of the circulation between upper and lower branches and its relationship with trace gas transport is the subject of further study.ozone and the upper level circulation strength is stronger at short timescales.Ozone variability at the upper levels is dominated by photochemical processes (Perliski et al., 1989), and so we hypothesize that this close correlation is due to the relationship of temperature with both ozone and the circulation strength.When the circulation is stronger in the tropics at these levels, that is associated with cooling and consequently more ozone production.We have therefore plotted the correlation of the temperature with the diabatic circulation at 500 K and 1200 K in Figure 8 (c) and (d).In both (c) and (d), it is evident that at low levels the temperature and ozone respond to the circulation similarly.In (d) in particular, the opposite relationship between the circulation and the temperature is observed to the circulation and the ozone, which indicates that the temperature is driving the chemistry at upper levels.To test this mechanism, we have plotted the natural log of the ozone concentrations against the inverse of temperature at these upper levels and at lower levels, since an exponential dependence on the inverse of temperature is a form that is consistent with the form for many of the reaction rate coefficients for ozone loss processes (Stolarski et al., 2012).These results are shown in Figure 10.Clearly, the upper level and lower level are behaving differently: The lower level depends as much on latitude as on the inverse of temperature; at high latitudes, there is almost no temperature dependence as the ozone is dynamically controlled, and at lower latitudes, where ozone production is expected, the relationship has a negative slope.The upper level has little latitudinal dependence and a positive slope, consistent with the chemical control.When the fit is calculated for 45-50 • S at 1 hPa, as shown in the third panel of Figure 10, the slope agrees to within error with the slope calculated for the Limb Infrared Monitor of the Stratosphere (LIMS) data used by Stolarski et al. (2012).We have taken the opportunity to show the change in the relationship over time using different colors.Calculating the fit for just the earlier years results in a higher value for the "initial" ozone concentration with a slope that is the same to within error.While we do not investigate the cause for this change here, we hypothesize that it is related to the higher mean ozone concentrations being advected to this region during the initial period of the ozone hole.
Stratospheric transport timescales for even the lower branch are around half a year to a year (Orbe et al., 2014), and so instantaneous correlation plots, as in downwelling region simultaneously.Therefore we do not perform lagged regressions to attempt to understand causality.Rather we suggest that the use of frequency dependent correlations, which will have a corresponding phase lag (e.g.Swanson, 2000), will be necessary to look at the causal relationships.However, as we can see from Figure 9, the correlations are in phase at monthly timescales, and so higher frequency records (minimum daily) will be necessary to diagnose the phase (and thus the implied causality) in these relationships.In this study, we have compared the diabatic overturning circulation strength through isentropic levels to the more typically used metrics for the strength of the BDC.In particular, we have examined the residual circulation vertical velocity, the water vapor tape recorder, and total column ozone concentrations.
We find that the three common methods for quantifying the BDC strength from models and reanalysis data products have somewhat different deseasonalized variability, especially in the lower stratosphere.These methods also result in different vertical structures; the calculation based on on the principle of downward control has a much broader vertical autocorrelation than the calculation from diabatic heating rates.Thus, if the separate evolution of the upper and lower branches of the circulation are of interest, the most appropriate metric is one that uses the diabatic heating rates.In the model, the relationship of the different TEM calculation methods are nearly one-to-one above 70 hPa.For the reanalysis products, however, the differences between calculations of the TEM w * are quite distinct, especially at lower levels where they are often analyzed.The comparison between the TEM w * Q with the diabatic overturning circulation is as favorable as the comparison between the TEM w * Q and the w * from the residual circulation method.In general, consistency between methods is better higher up in the stratosphere, while beneath 70 hPa, the differences between the methods is substantial.These results suggest that the method of calculation could significantly affect comparisons between the residual circulation from reanalysis and any other observed stratospheric variable.
Like the thermodynamically constrained w * , which the global diabatic circulation so closely resembles, the global diabatic circulation strength requires only monthly mean heating rates, temperatures, and pressures.Its calculation is simpler than that of w * , which can have complications with convergence.The global diabatic circulation also has an interesting property that the lower and upper branches of the circulation are anticorrelated, so that when the lower branch is stronger, less air is flowing through the upper branch.This is even more curious when one takes into account that the vertical velocity in the lower stratosphere is the sum of both branches.One explanation is that this could be due to a change in index of refraction when there is more total wave activity that causes higher amplitude planetary scale waves to break lower in the stratosphere; we have yet to test this mechanism.Another possibility is that the meridional location of the wave breaking changes such that when the lower branch is stronger, less wave activity can propagate up into the upper stratosphere.Alternatively, there may be an interaction between planetary and gravity waves.The anticorrelation is consistent with the conclusions of both Ray et al. (2010) andStiller et al. (2012), who concluded based on observations that the trends in data were best explained by a strengthening in the lower branch of the circulation and a weakening in the middle and upper stratosphere.The ERA-Interim trends in the global diabatic overturning circulation are consistent with this picture, although the upper-level trends are problematic because of the changes in observing systems.The other two reanalyses do not agree.
The global diabatic circulation is correlated with the water vapor tape recorder vertical velocity, especially at intraseasonal and longer time scales.Perhaps unsurprisingly, given its close theoretical relationship with stratospheric tracers, the global diabatic circulation is a better predictor for the water vapor tape recorder vertical velocity than the residual circulation is.
However, the overall weakness of the correlation, which explains at most <40% of the variability even when both metrics are 20 derived from a model, suggests the inadequacy of using the water vapor tape recorder as a lone observational record of the changing stratospheric circulation.Rather, the water vapor signal should be compared to water vapor in models in order to assess the combined effect of diabatic circulation, diabatic diffusion, and adiabatic mixing.
We analyze the impact of the global diabatic circulation strength on total column ozone using satellite data and the three reanalyses, including examining the dependence of the total column ozone on different vertical levels of the circulation.When we find consistent behavior amongst the three reanalyses, we explore the mechanism using a model which shows the same behavior.We find that the tropical ozone is most correlated with the overturning at 500-550 K, the Southern hemisphere ozone is sensitive to the overturning at around 480 K, and the Northern hemisphere ozone is most sensitive to the overturning at 400-450 K.The subtropics are most sensitive to the midlevel circulation at 800-1000 K, related to dominant role of chemistry at upper levels.
Based on its close relationship with one of the common metrics for the BDC, the ease of calculation, the demonstrated impact on ozone and water vapor, and the constraints provided by tracer observations, we present the global diabatic overturning circulation strength as a metric for the BDC that should be newly considered.Before the community settled on w * , the diabatic circulation was used (Pyle and Rogers, 1980;Rosenfield et al., 1987).Some intuition for the behavior of w * exists, but both Abalos et al. (2015) and this work have demonstrated that the various methods of calculation are not equivalent, especially for renalyses.Thus, although some variety of TEM w * is the most common metric at present, its calculation is not held in common amongst different studies.In order to understand models and reanalyses, consistency is critical.For the purposes of reanalysis evaluation, therefore, we advocate using the diabatic circulation along with a version of the quasigeostrophic TEM w * , since these rely on different assumptions, and the heating rates from reanalysis might be suspect.For the purposes of model evaluation, the global diabatic circulation should be sufficient.
Apart from the brief analysis with ozone, this paper does not directly address causality.It is an investigation of different metrics for the circulation from an empirical perspective, revealing that the significant differences in the behavior of these metrics raises questions about their interchangeability, especially for reanalyses.The inconsistencies reveal the extent to which the reanalyses momentum and energy budgets are not internally consistent.At upper levels, the different vertical velocities are all nearly equivalent, but at lower levels, and especially beneath 70 hPa, the differences are substantial.In particular, using the momentum-based calculation for the residual circulation vertical velocity will mask variability that is not coincident between the upper and lower branches, while the diabatic circulation emphasizes the difference between the upper and lower branch.This work serves as motivation for additional, process-based and theoretical studies that address the causes of these differences between the residual circulation metrics and between tracers and the residual circulation.

Figure 1 .
Figure 1.Correlation coefficient (r) for the autocorrelation of the deseasonalized time series of (a) the diabatic circulation, and of the three different TEM vertical velocities calculated from WACCM: (b) w * , (c) w * M , and (d) w * Q .As the diagonal reflection is redundant, it is not shown.Contours are spaced every 0.1.

Figure 2 .
Figure 2. Correlation coefficients (r) for the deseasonalized time series of the three different TEM vertical velocities calculated from WACCM (a-c) and for ERA-Interim (d-f): (a,d) w * vs. w * M , (b,e) w * Q vs. w * M , and (c,f) w * vs. w * Q .The quantity plotted on the y-axis is listed first.All quantities are averaged between 30 • S-30 • N. Contours are spaced every 0.1.

Figure 3 .
Figure 3.The correlation of the interannual variability of three different estimates of the TEM vertical velocity with the interannual variability of the diabatic circulation M. The first row is the correlation of the diabatic circulation with w * Q ; the second row is the correlation of the diabatic circulation with w * M ; and the third row is the correlation of the diabatic circulation with w * .The first column shows MERRA, the second column shows JRA 55, the third shows ERA-Interim, and the fourth shows WACCM.The gray dashed line shows the theoretical relationship between potential temperature and pressure for an ideal gas.It has a slope of -7/2, with its intercept defined somewhat arbitrarily.All residual circulation velocities are integrated over 30 • S-30 • N. Contours are spaced every 0.1.

Figure 4 .
Figure 4. Trends in diabatic circulation strength at each level calculated from the three reanalysis data products (JRA55: blue; ERA-Interim:yellow; and MERRA: green) and from the WACCM model (black).Dashed lines show the calculated trends that are not significant at the 95% confidence level, while bolded lines are significant.There are no significant trends in the WACCM model run.

Figure 5 .Figure 6 .
Figure 5.Time series of water vapor tape recorder calculated (blue) and the global diabatic overturning circulation strength (black) on 500 K from the WACCM model.Both timeseries have been deseasonalized and scaled by their standard deviations.

Figure 7 .Figure 8 .
Figure 7. Correlation coefficient (r) of the interannual variability of total column ozone at every latitude to the total diabatic overturning circulation strength at every level for (a) ERA-Interim M and SBUV total column ozone, (b) JRA 55 M and SBUV total column ozone, (c) MERRA M and SBUV total column ozone and (d) ozone and M from WACCM.the upper level circulation is not obviously transport related.Although upwelling through the ozone maximum is no longer drawing up low ozone air, stronger circulation still exports ozone to the poles.

Figure 9
Figure 9 shows time series of the local ozone concentrations and total overturning strength based on the maximum correlations shown in Figure 8.(a) shows the tight coupling between the ozone in the Southern hemisphere midlatitudes with the global overturning strength at 500 K.(b) shows the very close correlation of the upper level circulation and the upper level equatorial ozone and the weaker relationship with the upper level midlatitude ozone.The two timeseries in (a) and the equatorial ozone and global overturning in (b) are correlated at all timescales, while the anticorrelation between the the midlatitude

Figure 9 .
Figure 9. Timeseries of monthly mean local ozone concentration and the total overturning circulation strength from WACCM for (a) 62 hPa, 50 • O3 in blue and M at 500 K in black and (b) 2 hPa equatorial O3 in blue, 2 hPa, 50 • O3 in red (multiplied by -1), and M in black.

Figure 10 .
Figure 10.The natural log of the ozone volume mixing ratio (in ppm) and the colocated values of 1000/T for different levels and latitudes in the WACCM model for 1980-2014.a) is at 53 hPa and b) is at 2 hPa, both for all latitudes equatorward of 52 • .c) is at 1 hPa for 45-50 • S only.In a) and b), different colored circles are different latitudes, with the Northern Hemisphere being yellow and the Southern Hemisphere blue.In c), different colors show different years.In b) and c) the best fit lines are also plotted in black with correlation coefficients of r = 0.87 and r = 0.96 respectively.

5
Although the mechanistic relationship between ozone and the diabatic circulation requires more exploration, especially in the middle stratosphere, we have demonstrated the close dependence of ozone variability on the global diabatic circulation variability with data and with a model.The total column ozone at the poles and in the tropics is correlated with transport by the diabatic circulation in the lower stratosphere.19 Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2018-972Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 23 October 2018 c Author(s) 2018.CC BY 4.0 License.