Modelling the residual mean meridional circulation at different stages of stratospheric warming events

Ensemble simulation of the general atmospheric circulation of the middle and upper atmosphere up to the lower thermosphere is performed using the 3-D nonlinear mechanistic numerical model MUAM. Residual mean meridional circulation (RMC) in terms of the Transformed Eulerian Mean is calculated for the boreal winter and changes in its vertical 10 and meridional velocity components during different phases of simulated composite stratospheric warming (SW) events are studied. The simulation results show general decrease in RMC velocity components up to 30% during and after SW in the mesosphere and lower thermosphere of the Northern Hemisphere. There are also increases in the downward and northward velocities at altitudes 50-70 km at the northern high latitudes. Associated changes in adiabatic heating/cooling rates can contribute to heating the stratosphere and cooling the mesosphere during the composite SW. The changes in the transport of 15 conservative species (like ozone) during SWs are estimated. Weakening of ozone fluxes at the middle latitudes of the Northern Hemisphere may reach 30% during SWs and 30 – 40% after the events at the altitudes of stratospheric maximum of ozone concentration. Such statistically confident simulations of RMC reactions on SWs at altitudes up to the lower thermosphere are performed for the first time. The study of the residual meridional circulation is useful for effective analysis of wave impacts on the mean flow and for diagnostics of the transport of atmospheric gas species in the atmosphere. 20


Introduction
The circulating transport of trace gases in the middle and upper atmosphere affects the overall distribution of ozone and other atmospheric gas components. The main mechanism for the global transport of trace gases (e.g., Fishman and Crutzen, 1978) between the stratosphere and troposphere is the Brewer-Dobson meridional circulation (Dobson et al., 1929;Dobson, 25 mesoscale wave disturbances (Pogoreltsev et al., 2014, Gavrilov et al., 20152018) as well as atmospheric tides (Suvorova 80 and Pogoreltsev, 2011). The amplitudes of stationary planetary waves (SPWs) at the lower boundary are calculated from the geopotential height distributions in the lower atmosphere obtained from reanalysis of meteorological information UK Met Office (UKMO, Swinbank and O'Neill, 1994). In addition, the MUAM includes a parameterization of the westward travelling atmospheric normal modes with zonal wave numbers m = 1 -3 and periods from 2 to 16 days (Pogoreltsev et al., 2009). The model also includes parameterizations of the dynamic and thermal effects of stationary orographic gravity waves 85 developed by Gavrilov and Koval (2013) and of nonorographic gravity waves (GWs), which is similar to those developed by Lindzen (1981) and Yigit and Medvedev (2009). Estimations by Pogoreltsev et al. (2007) and Gavrilov el al. (2015) showed that the MUAM satisfactorily reproduces the structure of atmospheric circulation up to altitudes of the lower thermosphere.
To improve the statistical significance and smooth out the interannual variability in the MUAM, an ensemble of 19 model runs was obtained, containing major or minor SSW events during model runs for January-February conditions. Different 90 MUAM runs correspond to different phases of vacillations between the mean wind and SPWs in the middle atmosphere.
These phases in the MUAM are controlled by changing of the inclusion date of daily variations in the solar heating and generation of normal atmospheric modes in different ensemble members of model runs (Pogoreltsev et al., 2007(Pogoreltsev et al., , 2009).
The model dates or simulated SSWs were obtained using the definition by Charlton and Polvani (2007). However zonal wind reversals at every MUAM run were detected not only at pressure level of 10 hPa (near 30 km altitude), but also at 95 higher altitudes up to 50 km (Savenkova et al., 2017;Gavrilov et al., 2018). To differentiate these phenomena from traditionally considered SSWs near 10 hPa pressure level, we call them simply as "stratospheric warmings" (SWs). Types of SW events may be different for different model runs. Examples of temperature and wind variations during SW events simulated with the MUAM runs one can see in Figure 1 of the papers by Koval et al. (2019) and Gavrilov et al. (2018).
The changes of thermodynamic fields in different MUAM runs could be considered as variability corresponding to different 100 phases of stratospheric vacillations in different years. For each simulated SW event, its onset date was determined and three 11-day consecutive intervals were selected before, during and after the SW. After averaging over all simulated SWs, this approach allowed us to obtain average characteristics for a composite SW event statistically relevant to the SW climatology obtained by analyzing processing multi-year reanalysis data and described, for instance, by Savenkova et al. (2017).

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Residual circulation in this study is understood in the context of the transformed Eulerian mean approach (Andrews et al., 1987). The meridional and vertical components of the RMC can be calculated by the following formulas (Andrews et al., 1987;Butchart, 2014): where the overbars denote the zonal-mean values, the dashes mark the deviations of hydrodynamic quantities from their zonal-mean values; v and w are the meridional and vertical components of wind; ρ is background atmospheric density; z is vertical log-isobaric coordinate; θ is potential temperature; φ is latitude; a is the Earth's radius.
Introducing deviations from the mean zonal components of the wind velocity and potential temperature as one can obtain the following equations used in this study for calculating the meridional and vertical 115 components of the residual mean circulation from the wind and temperature fields simulated with the MUAM: https://doi.org/10.5194/angeo-2020-71 Preprint. Discussion started: 23 October 2020 c Author(s) 2020. CC BY 4.0 License.
In contrast to the conventional mean Eulerian circulation (having velocity components v and w ) the residual vertical velocity * w is proportional to the rate of diabatic heating. It roughly represents a diabatic circulation in the meridional 120 plane (Shepherd, 2007), i.e., when the heating of ascending air parcels and the cooling of descending air take place, while their potential temperature adapts to the local environment. Thus, the time-averaged RMC approximates the average movement of air masses and, therefore, it can be observed as the average movements of conservative gas components.  Figure 1 is also in agreement with that obtained by Gille et al. (1987) and Kobayashi and Iwasaki (2016). The latter study presents the RMC fields for winter in the Northern Hemisphere obtained with the data from the Limb Infrared Monitor of the Stratosphere on the Nimbus-7 140 satellite and from the JRA-55 reanalysis data (Kobayashi et al., 2015).

Residual circulation at the different SW stages
In this section, we study the changes in RMC at an altitude of 0 -100 km during different stages of the composite SW event (averaged over 19 model runs) simulated with the MUAM. In addition, we estimate changes in meridional fluxes such relatively conservative gas species as ozone caused by simulated changes in the RMC. Residual wind components are 145 calculated applying Eq. (3) and (4) to the wind and temperature fields obtained with the MUAM. Then these characteristics are averaged over 19 model runs, separately, for 11-day intervals "before", "during" and "after" SW (see section 2).  Global atmospheric meridional circulation is the most important transport mechanism for atmospheric gas species (Fishman and Crutzen, 1978). Vertical transport of air particles under the influence of the residual circulation of the atmosphere produces fluxes of gas species, which could be important for the climate changes. In the present study, we made diagnostics 215 of simulated RMC fluxes of gas species using the example of ozone, which for short time intervals may be considered as conservative gas at heights of the lower and middle atmosphere. The MUAM includes a 3D ozone distribution Pogoreltsev, 2011, Suvorova et al., 2017), which takes into account long-term climatic longitudinal variability. This distribution was compared by Suvorova and Pogoreltsev (2011) with the ozone empirical model by Randel and Wu (2007) and with databases by Hassler et al. (2008) and Cionni et al. (2011). The meridional, Fx, and vertical, Fz, components of gas 220 RMC fluxes are estimated by multiplying the gas concentration by the residual vertical and meridional velocities, respectively. Therefore, at each grid node, we have the following formulae for the components of RNC ozone fluxes: where v* i are the zonal-and monthly-mean meridional (i=x) and vertical (i=z) residual velocity components, ρ0 is the surface atmospheric density, XO3 is the zonal-mean ozone mixing ratio in ppm, NA is the Avogadro number.

Conclusion
In the present study, estimations of the mean residual meridional circulation are performed, using temperature and wind Hemisphere may reach 30% during SW and 30 -40% after this event at the altitudes of stratospheric ozone layer maximum.
The approach used in this work within the framework of the transformed Eulerian mean circulation allows obtaining the residual wind components, which effectively take into account wave effects on transport of atmospheric quantities and gas species in the meridional plane.  https://doi.org/10.5194/angeo-2020-71 Preprint. Discussion started: 23 October 2020 c Author(s) 2020. CC BY 4.0 License.