Is our dynamical understanding of the circulation changes associated with the Antarctic ozone hole sensitive to the choice of reanalysis dataset?

Abstract. This study quantifies differences among four widely used
atmospheric reanalysis datasets (ERA5, JRA-55, MERRA-2, and CFSR) in their
representation of the dynamical changes induced by springtime polar
stratospheric ozone depletion in the Southern Hemisphere from 1980 to 2001.
The intercomparison is undertaken as part of the SPARC
(Stratosphere–troposphere Processes and their Role in Climate) Reanalysis
Intercomparison Project (S-RIP). The reanalyses are generally in good
agreement in their representation of the strengthening of the lower
stratospheric polar vortex during the austral spring–summer season,
associated with reduced radiative heating due to ozone loss, as well as the
descent of anomalously strong westerly winds into the troposphere during
summer and the subsequent poleward displacement and intensification of the
polar front jet. Differences in the trends in zonal wind between the
reanalyses are generally small compared to the mean trends. The exception is
CFSR, which exhibits greater disagreement compared to the other three
reanalysis datasets, with stronger westerly winds in the lower stratosphere
in spring and a larger poleward displacement of the tropospheric westerly
jet in summer. The dynamical changes associated with the ozone hole are examined by
investigating the momentum budget and then the eddy heat and momentum
fluxes in terms of planetary- and synoptic-scale Rossby wave contributions.
The dynamical changes are consistently represented across the reanalyses
and support our dynamical understanding of the response of the coupled
stratosphere–troposphere system to the ozone hole. Although our results
suggest a high degree of consistency across the four reanalysis datasets in
the representation of these dynamical changes, there are larger differences
in the wave forcing, residual circulation, and eddy propagation changes compared to the zonal wind trends. In particular, there is a noticeable
disparity in these trends in CFSR compared to the other three reanalyses,
while the best agreement is found between ERA5 and JRA-55. Greater
uncertainty in the components of the momentum budget, as opposed to mean
circulation, suggests that the zonal wind is better constrained by the
assimilation of observations compared to the wave forcing, residual
circulation, and eddy momentum and heat fluxes, which are more dependent on
the model-based forecasts that can differ between reanalyses. Looking
forward, however, these findings give us confidence that reanalysis datasets
can be used to assess changes associated with the ongoing recovery of
stratospheric ozone.


they have their own biases throughout the atmosphere. Therefore, reanalysis datasets do not necessarily agree on how the SH circulation responds to the ozone hole, possibly making the results reanalysis dependent. This is perhaps especially an issue in 90 the stratosphere, as compared to the troposphere this region is characterised by smaller volumes of observational data available for assimilation and larger biases in observational data (Fujiwara et al., 2017), implying a greater reliance on the performance of the forecast model and its representation of dynamical processes (e.g., Orr et al., 2010). The representation of the underlying dynamics in reanalyses is therefore an additional concern, which has not been examined for the SH despite showing nonnegligible differences for some diagnostics in the Northern Hemisphere (e.g., Bengtsson et al., 2006;Lu et al., 2015;95 Martineau et al., 201695 Martineau et al., , 2018bChemke and Polvani, 2020).
The primary aim of this study is to compare trends in the SH circulation over the 1980 to 2001 period associated with the ozone hole in four widely-used reanalyses, and to analyse their connection to changes in various dynamical quantities to establish whether they consistently support the proposed mechanisms associated with the ozone hole. The four reanalyses datasets examined are JRA-55 (Kobayashi et al. 2015), MERRA-2 (Gelaro et al., 2017), CFSR (Saha et al., 2010(Saha et al., , 2014, and 100 ERA5 (Hersbach et al., 2020). stratospheric temperature from 2000 to 2006 due to the use of inappropriate background error covariances (Simmons et al., 2020). This issue was fixed in a new set of ERA5 reanalysis from 2000 to 2006, termed ERA5.1 (Simmons et al., 2020), which 120 we used instead of ERA5 for this period (hereinafter this combined dataset is referred to as ERA5 for simplicity).
The key variables examined in this study are the zonally averaged zonal wind �, the eddy momentum flux ′ ′ ������ , and the eddy heat flux ′ ′ ������ . Here is the temperature, u the zonal wind, v the meridional wind, overbars denote zonal averages, and primes denote deviations from the zonal average. Additionally, the wave forcing is diagnosed using the quasi-geostrophic form of the TEM momentum equation (Edmon et al., 1980). This is expressed as 125 where is the quasi-geostrophic Eliassen-Palm (EP) flux, which takes the form with the wave forcing represented by the EP flux divergence (EPFD) term, which is the second term on the right-hand-side of Eq.
(1). The first term on the right-hand-side of Eq. (1) is the Coriolis torque. Here is the Coriolis frequency, ̅ * is the residual 130 meridional circulation, is the mean radius of the Earth, is the latitude, represents any residual tendencies (unresolved waves, diffusion, ageostrophic effects), is the potential temperature, and is pressure (Martineau et al., 2018c).
We examine the momentum flux and heat flux instead of the EP flux components � , � as the latter requires the vertical derivative of temperature or static stability, resulting in noisy wave driving and EP fluxes (Lu et al., 2014). The eddy heat fluxes play a key role in the vertical component of EP flux � �, which is a measure of the upward fluxes of Rossby wave 135 activity (Edmon et al., 1980) (Banerjee et al., 2020). It also provides a clean case study for reanalysis data inter-comparison in terms of atmospheric trends and the associated dynamical connection between the troposphere and the stratosphere in the SH. descent to the tropopause, iii) weakening of the anomalously strong westerly winds in the lower stratosphere from December to January and descent of the winds to the surface, and iv) a continued weakening of the anomalously strong stratospheric winds from December to February, consistent with a delayed breakup of the vortex in summer. According to Orr et al. (2012), these four stages refer respectively to the 'onset', 'growth', 'decline', and 'decay' stages of the lifecycle of the zonal wind 180 response to the ozone hole.
The results for ERA5, JRA-55, and MERRA-2 are again largely in good agreement (with differences not exceeding ±0.6 m s −1 dec −1 ). The largest differences among the reanalyses are again associated with CFSR, which shows much stronger stratospheric winds than ERA5 between September and November (i.e., 'onset' and 'growth' stages), suggesting the initial strengthening of the winds occurs earlier in CFSR. Furthermore, the four reanalyses generally show a similar delayed breakup of the polar 185 vortex. The final warming date for all reanalyses occurs around 0.9 days later per year or around 19 days later over the period 1980 to 2001 (not shown).
In ERA5 the corresponding time-height cross-section of trends in zonally averaged temperature ( Figure A1) demonstrates that the stratospheric cooling associated with the ozone hole lasts from October to January, with a peak of -4 K dec -1 in November.
This agrees with radiosonde observations from Antarctica (Thomson and Solomon, 2002), and is also in agreement with 190 MERRA-2 and JRA-55 results. However, CFSR again contrasts with the other three reanalyses in terms of the temperature trend, evident by both an earlier onset to the cooling (beginning from September) and enhanced cooling between 300 and 100 hPa (by ~-1 K dec −1 ) throughout September to February.
To further investigate the response of the tropospheric polar front jet during DJF, Figure 3 shows the latitudinal profile of the trend and climatology of the 500 hPa zonally averaged zonal wind for the four reanalyses. The climatologies are nearly 195 identical except poleward of ~70°S and show that the peak winds associated with the jet occur around 50°S. The lack of agreement poleward of ~70°S may be due to a lack of observations over the continent and/or the increase in uncertainty of zonal mean quantities near the pole, an effect of spherical geometry. Positive trends (~1.5 m s -1 dec -1 ) are found on the poleward flank of the jet while negative trends (~-0.8 m s -1 dec -1 ) occur at ~38°S, which is consistent with the results of Figure 1, i.e. a strengthened and poleward shift of the polar front jet in the troposphere. In comparison with other reanalyses, there is a clear 200 poleward shift of ~4° for the CFSR trend, which is also consistent with the stronger poleward shift in the jet shown in Figure   1. The good agreement between the climatological results suggests that the differences in the trends are not due to biases/differences in the climatological strength or location of the tropospheric westerly jet.

A dynamical analysis of trends: EP flux divergence
To study the spread among the four reanalyses in terms of wave driving, Figure 4 (a,d,g,j) shows time-height cross-sections of 205 the trend in EPFD (averaged over 40-80°S) from September to February. For ERA5, in the lower stratosphere the EPFD shows https://doi.org/10.5194/acp-2020-1288 Preprint. Discussion started: 23 December 2020 c Author(s) 2020. CC BY 4.0 License. a positive trend during November (i.e., weaker wave drag, coinciding with the 'growth' stage and the peak increase in stratospheric winds), followed by a negative trend during DJF (i.e. stronger wave drag, coinciding with the 'decay' and 'decline' stages and a weakening of the strengthened vortex and a delay in its breakdown). This is in dynamical agreement with the temporal evolution of the zonal wind trends in Figure 2 but does not necessarily indicate causality. The total zonal wind 210 acceleration (in the absence of e.g. unresolved small-scale forcing) is largely a balance between the Coriolis torque on the residual meridional circulation and the wave drag on these time scales (Eq. 1). For September and October, the trend in lower stratospheric EPFD is largely negligible, suggesting that the circulation response during this time is primarily radiatively controlled. Both positive and negative trends in EPFD descend from 30 hPa to 300 hPa, indicating a downward influence from the stratosphere. In the lower stratosphere the trend in EPFD shows little difference among the four reanalyses. 215 Orr et al. (2012) also describe a switch from weaker (in November) to stronger (in DJF) wave drag in response to the ozone hole. They emphasize two factors, (i) a positive feedback process whereby an initial strengthening of the polar vortex winds in response to radiative cooling (during the 'onset' phase) plays an important role in conditioning the polar vortex so that that fewer planetary waves can propagate up from the troposphere into the stratosphere, resulting in reduced wave drag (during the 'growth' phase): this agrees with the conclusion of Chen and Robinson (1992) that enhanced vertical wind shear at the 220 tropopause is key to reducing the propagation of planetary wave activity into the stratosphere. And (ii), a negative feedback process whereby the prolonged existence of the westerly winds due to the delayed breakdown of the stratospheric vortex permits increased upward wave propagation into the stratosphere, resulting in stronger wave drag (during the 'decline' and 'decay' stages): this is consistent with a larger positive refractive index "cavity" in this region (wave activity tends to propagate towards more positive refractive index values). 225 In the troposphere, EPFD shows bands of negative (positive) trends in the upper (middle) troposphere for ERA5 from September through to February (cf. Figure 4a). The agreement among the four reanalyses is poor, with the discrepancies relative to ERA5 marked by alternating negative and positive horizontal stripes, which can be greater in amplitude than the mean trends, and are most prominent for CFSR (e.g., during October). However, the rather large spread in the tropospheric EPFD trends (Figure 4 (a,d,g,j)) are accompanied by relatively small differences in the tropospheric wind trends ( Figure 2). 230 There is also no evidence of vertically alternating differences in the wind trend.
These results suggest that in the troposphere the resolved EPFD trend is not directly linked to the trends in the zonal wind; the latter is more linked to direct observation, while the former is more forecast model dependent. In addition, the tropospheric circulation is relatively more constrained by observational input in comparison to the stratospheric circulation (Martineau et al., 2016). Lu et al. (2014) found similar alternating stripes in the EPFD when they compared wave driving between ERA-235 Interim and ERA-40 reanalyses. They showed that one of the main contributors to the EPFD differences was the vertical derivative of the temperature. Note that interpolation from model levels to standard pressure surfaces could also play a role in discrepancies of the EPFD term, as derivatives are very sensitive to interpolation. Differences in trends in the upward https://doi.org/10.5194/acp-2020-1288 Preprint. Discussion started: 23 December 2020 c Author(s) 2020. CC BY 4.0 License. component of the EP flux (Eq. 2), which also includes the vertical derivative of temperature, also characterized by alternating negative and positive horizontal stripes (not shown). 240  Figure 2 shows that this period is also contemporaneous with the descent of 245 the anomalously strong westerly winds / increased vertical wind shear to the tropopause. For DJF, the ERA5 results show a negative trend in the lower stratosphere signifying enhanced poleward eddy heat flux / upward propagating wave activity into the stratosphere, which corresponds to negative trends in EPFD, i.e., increased EP flux convergence. For September and October, the trend in lower stratospheric eddy heat flux is much smaller and noisier. This corresponds to the switch from weaker (in November, during the 'growth' stage) to stronger (in DJF, during the 'decline' and 'decay' stages) wave activity 250

A dynamical analysis of trends: Eddy heat and mome ntum fluxes
propagating into the lower stratosphere described by Orr et al. (2012). The other reanalyses exhibit minor differences compared to ERA5, except for CSFR, which exhibits a stronger negative trend of the eddy heat flux in DJF (and September and October) and a weaker positive trend in November. Additionally, in ERA5 the region of positive trend in heat flux in November appears to start from around the tropopause and extends upward quickly in time, while this effect is less apparent or more barotropic in the other three reanalyses. Negligible trends in the heat flux can be detected in the troposphere, confirming that changes in 255 the upward propagating waves are confined in the stratosphere (Orr et al., 2012). In the troposphere, in ERA5 the trend in eddy momentum flux is marked by persistent negative values from December to February, indicating enhanced poleward momentum transfer. This occurs at the same time as the poleward displacement of 265 the polar front jet and anomalously strong westerlies in the troposphere (Figures 1 and 2). This negative trend in eddy momentum flux in the troposphere is evident for all four reanalyses products, although JRA-55, MERRA-2, and CFSR have weaker trends than ERA5. Orr et al. (2012) similarly describe strengthened equatorward synoptic-scale wave propagation in the troposphere in response to the ozone hole during the 'decline' and 'decay' stages. They show that this coincides with https://doi.org/10.5194/acp-2020-1288 Preprint. Discussion started: 23 December 2020 c Author(s) 2020. CC BY 4.0 License. enhanced baroclinity at the surface (i.e., an increase in upward synoptic-scale waves) at the same latitude as the strengthened 270 polar front jet. This suggests that the circulation trends are the result of the interactions between the zonal-mean flow and the eddies, which maintain anomalies in the polar front jet / tropospheric annular mode. The fluxes of momentum into the jet (convergence) balances anomalous surface wind stress associated with the shift (see also Hartmann et al., 2000).
The analysis in the next two sub-sections further explores the differences in the trends in eddy heat and momentum fluxes for November ( Figures 5 and 6) and DJF (Figures 7 and 8). The reason for focusing on these two periods is to further examine the 275 switch from weaker (in November) to stronger (in DJF) wave activity propagating into the lower stratosphere, as well as the strengthening and poleward-displacement of the polar front jet in the troposphere (in DJF). Figure 5a shows the latitude-height profile of the zonally averaged eddy heat flux ′ ′ climatology from ERA5 for November, which is dominated by negative values from 45-80°S in the lower stratosphere, consistent with upward propagating waves 280 along the polar vortex edge. Quantitatively similar results can be obtained from the other three reanalyses (not shown). Figure   5 (c,e,g,i) shows the trend in eddy heat flux for November, which for all four reanalyses is marked by positive values in the lower stratosphere at 40-80°S, so in agreement with Figure 4 and confirming the reduction of poleward eddy heat flux / upward wave activity flux from the troposphere into the lower stratosphere. Overall, in terms of both magnitude and location, the best agreement is found between ERA5 and JRA-55, while the positive trend in CFSR is around half that of ERA5, indicating a 285 much weaker reduction in upward wave activity from below for CFSR. This is despite CFSR showing stronger positive wind trends in the lower stratosphere compared to the other reanalyses in November (Figure 2), which is dynamically inconsistent as this would be expected to be associated with a relative stronger (rather than weaker) reduction in upward wave activity.   Figure 5 (d,f,h,j) shows the trend in eddy momentum flux, which for all four reanalyses at around 50-80°S is marked by negative values at ~100 hPa, so in agreement with Figure 4 and confirming enhanced poleward eddy momentum flux / equatorward propagation of wave activity. All four reanalyses show this feature, except that the magnitude of the trend is larger in MERRA-2 and even larger and more poleward in CFSR. Note that there are also positive trends at ~300 hPa, which are also apparent in Figure 4. Figure 6 (b,d,f) shows that the negative lower stratospheric trends displayed in   Figure 8 (a,c,e) shows that the eddy heat flux trend from 30-300 hPa due to all waves is dominated by negative values at 45-80°S, which is poleward of the climatological values at 30-70°S (cf. Figure 7). In agreement with Orr et al. (2012), these trends are dominated by planetary waves at 55-80°S (Orr et al., 2012), while synoptic waves also have some role at 45-70°S. 320

A dynamical analysis of trends: Nove mber
As the climatological tropopause height is above 300 hPa equatorward of 60°S (Figure 7(a,b)), some of the synoptic waves in this region are actually in the upper troposphere and not the lower stratosphere. Again, ERA5 and JRA-55 are in good agreement, while the MERRA-2 and CFSR trends are both stronger and more poleward. can be obtained from the other three reanalyses with differences of no more than 4 m -2 s -2 at a few locations within the positive and negative regions shown for ERA5. Figure 7(d,f,h,j) shows DJF trends in momentum flux derived from ERA5, JRA-55, MERRA-2, and CFSR. The trends are marked by negative values reaching -5 m -2 s -2 dec -1 in the troposphere at 40-70°S, so consistent with Figure 4 and confirming the importance of enhanced poleward eddy momentum fluxes at the core of the climatological polar front jet in the troposphere (Orr et al., 2012). All four reanalyses capture this feature, except that the 330 magnitude of the trend is largest in ERA5. The other three reanalyses produce the effect with a slightly more poleward shift. https://doi.org/10.5194/acp-2020-1288 Preprint. Discussion started: 23 December 2020 c Author(s) 2020. CC BY 4.0 License. Figure 8 (b,d,f) shows vertically integrated results for DJF from 100-500 hPa for the eddy momentum flux. The trends in eddy momentum fluxes due to all waves are also dominated by negative values centered at 40-70°S (cf. Figure 7), which is poleward of the climatological minimum values and also dominated by the contribution from synoptic-scale waves. This is again in agreement with Orr et al. (2012). The four reanalyses, however, exhibt more considerable disagreement in the trends that are 335 more pronounced than the differences in their climatological values.

Sensitivity of the trends to time period
To assess the statistical robustness of the trends, we explore the impact of small shifts in the time period of the analysis on the trend. Figure 9 shows time-height cross-sections of the trends in zonally averaged zonal wind for the reanalyses from September to February for three different 20-year periods (1980 to 1999, 1981 to 2000, and 1982

Discussion and summary 350
Differences in the formulation of reanalysis systems and their observational inputs can lead to significant differences in their representation of the atmosphere, particularly for variables that are not directly observed (Fujiwara et al., 2017). Given the relatively limited observations over Antarctica, there is greater potential for spread in their representation of the SH circulation response to the ozone hole. Our results suggest that that there is nonetheless a high degree of consistency across the four reanalysis datasets in the representation of the dynamical changes associated with ozone depletion. This conclusion is based 355 on a thorough assessment of trends in the zonally averaged zonal wind, eddy heat flux, eddy momentum flux, and wave forcing (EPFD).
The expected strengthening of the lower stratospheric polar vortex during the austral spring-summer season and poleward shift of the polar front jet in the troposphere during summer is apparent in all four reanalyses. The differences in the trends in zonal wind between ERA5, JRA-55 and MERRA-2 is generally small in both the lower stratosphere and troposphere, with the largest 360 differences of the order 0.2 m s -1 dec -1 , which is small compared to the size of the reanalysis ensemble mean trends (up to 5 m https://doi.org/10.5194/acp-2020-1288 Preprint. Discussion started: 23 December 2020 c Author(s) 2020. CC BY 4.0 License. s -1 dec -1 in the stratosphere and 2 m s -1 dec -1 in the troposphere). CSFR, however, shows greater disagreement compared to the other three reanalyses, evident by a relatively stronger wind increase in the lower stratosphere in spring and a larger poleward displacement of the polar front jet in summer (resulting in differences in the troposphere of up to 1 m s -1 dec -1 ).
The good agreement between ERA5 and JRA-55 circulation trends is perhaps because they both employ a 4D-VAR 365 assimilation scheme, which is more sophisticated than the 3D-FGAT scheme employed by MERRA-2 and the 3D-VAR scheme employed by CSFR. However, examination of the timeseries of lower stratosphere temperatures for spring (Craig Long, personal communication) showed that CSFR was warmer than the other three reanalyses in the 1980s, which explains why its springtime temperature trends in the lower stratosphere are more negative than the others. The reason for this is that CFSR is initialized by NCEP-NCAR Reanalysis 1 (Kistler et al., 2001), which is also too warm in the 1980s in spring and the 370 lower stratosphere (Carig Long, personal communication). Disagreements between the reanalyses could also depend on the observations that they assimilate (Manney et al., 2005;Lawrence et al., 2015). Long et al. (2017) shows that disagreements between reanalyses in the lower stratosphere temperature at SH high-latitudes are greater during the period 1979 to 1998 (corresponding to the assimilation of TIROS Operational Vertical Sounder (TOVS) data), which largely corresponds to the period examined in this study, and less afterwards during the ATOVS (Advanced TOVS) period from 1999 to 2014. The ability 375 of each reanalysis to transition seamlessly between different satellite and other data sources at different times is also an issue, with more recent reanalysis having fewer discontinuities (Long et al., 2017). How the reanalysis systems include ozone and treat its radiative feedback also varies widely between reanalysis and might be an additional factor (Davies et al., 2017).
The circulation changes are consistent with our dynamical understanding of the stratosphere-troposphere system and are explainable in terms of four stages, which are apparent in all four reanalyses. An initial strengthening of the circulation in 380 response to radiative cooling during the 'onset' stage plays an important role in conditioning the polar vortex so that fewer planetary waves can propagate into the stratosphere from the troposphere. The strengthening of stratospheric vortex winds in spring (mainly November) during the 'growth' stage is associated with a positive trend in EPFD. This coincides with reduced upward planetary wave activity fluxes at high latitudes from the troposphere into the lower stratosphere, causing a reduction in the wave-driven deceleration of the polar vortex. The weakening of the strengthened vortex in summer during the 'decline' 385 and 'decay' stages is associated with a negative trend in EPFD. This coincides with increased upward planetary wave activity fluxes from the troposphere into the lower stratosphere at high latitudes due to the delayed breakdown of the stratospheric vortex, causing an increase in the wave-driven deceleration of the polar vortex. Both positive and negative trends in EPFD descend towards the tropopause, indicating a feedback between the strength of the vortex and the propagation of planetary waves (Chen and Robinson, 1992). The strengthening and poleward-displacement of the polar front jet in the troposphere 390 during the 'decline' and 'decay' stages are associated with changes to the synoptic-scale eddy fluxes of momentum and heat that drive the tropospheric annular modes, which is evident by enhanced poleward eddy momentum fluxes into the jet. These changes in wave forcing and wave propagation are described by Orr et al. (2012Orr et al. ( , 2013, as well as other studies such as https://doi.org/10.5194/acp-2020-1288 Preprint. Discussion started: 23 December 2020 c Author(s) 2020. CC BY 4.0 License. Hartmann et al. (2000), McLandress et al. (2010), and Hu et al. (2015. They agree with the temporal evolution of the zonal wind trends, although this does not necessarily indicate causality. 395 It is found that although the circulation trends are generally similar from one reanalysis to the next (with the exception of CSFR), significant discrepancies in the EPFD trends in the troposphere among the four reanalyses show up as alternating negative and positive horizontal stripes, which can be greater than the size of the mean trends across all reanalyses. Lu et al.
(2014) suggest that the main contributor for such discrepancies are differences in the vertical derivative of the temperature, 400 which are related to known issues with temperature increments caused by systematic biases in the assimilation of satellite measurements (e.g., Kobayashi et al., 2009). An additional factor could also be that derivatives are sensitive to interpolation from model levels to standard pressure levels. However, as there are no vertically alternating differences in the tropospheric wind trend, this suggests that this potential issue is relatively well constrained by analysis increments during data assimilation, while the EPFD is more model dependent. In the lower stratosphere, the trend in EPFD shows little difference among the four 405 reanalyses.
The disparity between the size of the differences in wind trend and differences in eddy fluxes is also apparent. There are significant discrepancies in the associated trends in the eddy heat flux during the 'growth' stage (in November) and the 'decline' and 'decay' stages (in DJF) in the lower stratosphere, and the eddy momentum flux during the 'decline' and 'decay' stages in the troposphere. For CSFR, the positive trend in eddy heat flux during November is around half that of ERA5, indicating a 410 much weaker reduction in upward wave activity / smaller reduction in wave-driven deceleration, despite it showing stronger positive wind trends in the lower stratosphere compared to the other reanalyses, which is dynamically inconsistent. This suggests that the eddy fluxes are also less constrained by the assimilation of observations, and that reanalysis temperature increments are able to cancel out differences in wave forcing, so that ultimately the impact on the large-scale circulation is small. Generally, across the four reanalyses, there is a large amount of disagreement in the CFSR wave forcing / propagation 415 trends compared to the other three reanalyses, while the best agreement is found between ERA5 and JRA-55.
Another important source of possible dynamical inconsistency could stem from Coriolis torque on the residual meridional circulation and unresolved smaller scale forcing (Martineau et al., 2016), which although not considered in this study are both terms of the momentum budget (Eq. 1). Orr et al. (2012) investigated the role of the mean meridional circulation in the ozone hole momentum budget. They showed that the sum of the wave driving (EPFD) and Coriolis torque agreed well with the zonal 420 wind tendency. They further showed that the magnitude of the Coriolis torque was typically the same as the wave driving term, offsetting each other as expected under quasi-geostrophic scaling. Orr et al. (2012Orr et al. ( , 2013 also stress that the circulation changes caused by the ozone hole are the result of both wave and radiative driving, although differences in radiative driving between the reanalyses are also not considered in this study. https://doi.org/10.5194/acp-2020-1288 Preprint. Discussion started: 23 December 2020 c Author(s) 2020. CC BY 4.0 License.
To summarize, we show that all four modern reanalysis datasets provide a consistent estimate of the circulation changes due 425 to the ozone hole, and that the discrepancies between the datasets are comparatively small. While our results show broad agreement on dynamical trends (eddy heat and momentum fluxes), there are non-trivial differences between reanalysis products, indicating that there is still room for improvement in our characterization of the atmosphere. Despite the consistency across reanalyses, it is possible that changes in the observational network over time could lead to spurious trends across them all; they share the vast majority of the same input data. We have greater confidence in the trends in the circulation precisely 430 because the changes can be explained by robust dynamical mechanisms. The reanalyses are both consistent with each other and self-consistent with our dynamical understanding of stratosphere-troposphere interactions. Looking forward, these findings will give us confidence that reanalysis datasets can be used to rigourously assess changes associated with the recovery of stratospheric ozone (Solomon et al., 2016;Banerjee et al., 2020), which is projected to return to 1980 levels within the next few decades (Iglesias-Suarez et al., 2016). 435

Author contribution 450
AO prepared all the figures, with advice from HL. AO wrote the text, with advice from all co-authors.