Many atmospheric global circulation models have large biases in
predicting meridional and vertical winds and fluxes of gas species
in remote regions such as the middle and upper atmosphere. In this
study, we make sensitivity simulations to recognize the role of
vital processes associated with dynamical coupling between different
atmospheric layers, namely dynamical and thermal impacts of
mesoscale orographic gravity waves (OGWs) generated by the Earth's
topography and changes from the easterly to westerly QBO phases in
the lower equatorial atmosphere. We improved parameterizations of
OGW dynamical and thermal effects and QBO flows and implemented them
into a general circulation model of the middle and upper atmosphere
used in different countries. With this model, we study the
sensitivity of meridional circulation and vertical velocity to
stationary OGWs and to changes in QBO phases at altitudes up to
100

Ozone transfer between the stratosphere and troposphere has an effect on the total ozone distribution in the atmosphere and on its content in the troposphere (Danielsen and Mohnen, 1977; Fishman and Crutzen, 1978). The main supposed mechanism of the global ozone transfer between the troposphere and stratosphere is the ozone ascend at low latitudes and descend at the middle and high latitudes, which is created by the general circulation of the atmosphere (Holton et al., 1995; Holton, 2002). The dynamical and thermal impacts of wave motions can change the general circulation of the atmosphere and thus have an effect on the global ozone transfer.

One of the important factors of dynamical interactions between the lower and upper atmosphere is energy and momentum transfer by internal atmospheric waves. It is also a substantial contributor to space weather developments (Kelley, 1997). For numerical modeling of the general circulation and thermal regime of the middle and upper atmosphere, it is important to take into account accelerations of the mean flow and heating rates produced by dissipating internal waves. One of the major sources of atmospheric waves is the Earth's topography (Gossard and Hooke, 1975). Propagation of the orographic gravity waves (OGWs), generated at the Erath's surface, into the middle and upper atmosphere significantly affects the atmospheric general circulation as well as ozone transport in the middle atmosphere. Simplified algorithms to parameterize thermal and dynamical effects of orographic waves have been developed (e.g., Kim and Arakawa, 1995; Lott and Miller, 1997; Scinocca and McFarlane, 2000; Vosper and Brown, 2007; Catry et al., 2008; Geller et al., 2011). Gavrilov and Koval (2013) developed a parameterization of dynamical and thermal effects of stationary OGWs generated by the surface topography and propagating into the middle and upper atmosphere. They implemented the parameterization into a general circulation atmospheric model (Gavrilov et al., 2013a) and showed that OGWs may produce substantial changes of the general atmospheric circulation in the middle and upper atmosphere.

Gavrilov et al. (2014) performed numerical experiments with a general circulation model of the troposphere and stratosphere and examined the influence of OGWs propagating upward from the Earth's surface on the zonal-mean meridional and vertical velocity. It was shown that dynamical and thermal OGW impacts in the numerical model could change the meridional circulation and ozone fluxes associated with it by up to 20–30 % at heights of the ozone layer maximum. Gavrilov et al. (2014) used for comparison just one-month average meteorology information for January 2004 and two-dimension zonal-mean ozone distribution.

In the present study, we continue these sensitivity experiments using ten-year average meteorological information and three-dimensional ozone distribution, which is a combination of three semiempirical models of ozone mixing ratio (Suvorova and Pogoreltsev, 2011). We focus our experiments on the sensitivity of meridional circulation, vertical velocity, meridional and vertical ozone fluxes in the middle atmosphere to OGW dynamical and thermal effects and changes in QBO phases.

Quasi-biennial changes of the zonal wind direction near equator in the middle atmosphere, the quasi-biennial oscillations (QBO), can affect the general circulation of the atmosphere at middle and high latitudes (e.g. Baldwin et al., 2001). Therefore, we performed numerical experiments for the background and initial conditions typical for the westerly and easterly QBO phases. The sensitivity experiments are essential for better understanding of the roles of different factors in formation of global dynamical processes, in transport and mixing of atmospheric gas components and in dynamical coupling of different layers of the lower, middle and upper atmosphere.

For experiments studying dependencies of the atmospheric dynamics and
ozone fluxes on OGW and QBO phase parameterizations, we use the global
circulation of the

The MUAM is a modification of the COMMA_LIM (Cologne Model of the
Middle Atmosphere – Leipzig Institute for Meteorology, Froehlich
et al., 2003). Both modifications came from the original COMMA model
developed in Cologne University, Germany (Ebel et al., 1995). Gavrilov
et al. (2005) described briefly the main equations and physical
processes of the model. The horizontal grid spacing is 5

The MUAM includes a three-dimensional distribution of the ozone mixing
ratio, which takes into account the climatic (averaged for years
1996–2005) longitudinal ozone inhomogeneities (Suvorova and
Pogoreltsev, 2011). The model combines data from three data sets of
the ozone mixing ratio, namely the ECMWF (European Centre for
Medium_Range Weather Forecasts, project ERA_40) at pressure levels
from 1000 to 30

Previous numerical experiments showed that MUAM can fairly well reproduce climatological mean distributions, but sometimes underestimates seasonal variability. To improve that, a parameterization of the normal atmospheric modes is included into MUAM (Pogoreltsev et al., 2014).

Essential characteristics of the middle atmosphere flows are the
quasi-biennial oscillations of the zonal wind at equatorial latitudes
(Baldwin et al., 2001). The MUAM does not give accurate modeling of
tropospheric dynamics. To parameterize QBOs of zonal wind in the
low-latitude troposphere–stratosphere, Pogoreltsev et al. (2014)
added terms

To determine the easterly and westerly QBO phases, Holton and
Tan (1980), Yamashita et al. (2011), and Inoue et al. (2011) used directions of,
respectively, westward and eastward winds detected in the low-latitude
stratosphere. Huesmann and Hitchman (2001) studied QBOs from the NCEP
reanalysis data and found that average zonal winds and their annual
cycles can give asymmetries in the descent rates of westerly and
easterly QBO wind zones. To reduce such asymmetries, Huesmann and
Hitchman (2001) used the equatorial zonal wind shear anomaly index
representing zonal wind differences at two stratospheric heights. To
diminish asymmetries in the westerly and easterly wind zones,
Pogoreltsev et al. (2014) used the UK Met Office data for January
during years 1992–2011 to analyze signs of deviations of annual-mean
and climatological (averaged for 20

The positive and negative deviations correspond to the westerly and
easterly QBO phases, respectively. Pogoreltsev et al. (2014) found
maximum zonal velocity deviations at altitudes 30–35

Many studies defined QBO phases using wind measurements at lower than
30–35

For studying the OGW influence on atmospheric dynamics, we implemented
the parameterization of dynamical and thermal effects of stationary
OGWs (Gavrilov and Koval, 2013) into the MUAM. To calculate vertical
profiles of the total vertical wave energy flux and the associated
accelerations of the mean horizontal winds by stationary OGWs with
ground-based observed frequencies

In many cases, mesoscale disturbances of atmospheric parameters
produced by air overflowing mountains can be qualified as internal
gravity waves having observed frequencies

The right side of the first equation in Eq. (2) contains the wave
energy dissipation rate and the work of forces caused by nonlinear
wave-mean flow interactions. Assuming nonzero vertical gradient of the
mean wind, Gavrilov (1990, 1997) found approximate analytical
relations between the wave energy dissipation rate and the wave
acceleration and obtained expressions for the total heating rate

To parameterize mesoscale topography, we used a modification of the method developed by Scinocca and McFarlane (2000). This method of the “subgrid orography” takes into account height variations of the Earth's surface with horizontal scales smaller than the horizontal grid spacing of the MUAM. We separated the so-called subgrid topography applying low- and high-frequency numerical filters to the realistic horizontal distributions of the surface (Gavrilov and Koval, 2013). Near each model grid point, we applied an elliptical approximation of the filtered subgrid-scale topography (Lott and Miller, 1997). At the low boundary, we determine OGW amplitudes and effective horizontal wave numbers using the analysis of forces acting on the atmospheric flow moving over the effective elliptical mountain barrier developed by Phillips (1984). These quantities are required for computing the vertical profiles of wave accelerations and heat fluxes, as was described by Gavrilov and Koval (2013). For practical implementation of our OGW parameterization in this study, we used the ETOPO2 (2015) database of the Earth's surface elevations with resolution of two angle minutes along latitude and longitude.

To study influence of described above parameterizations in the MUAM general circulation model we performed standard sensitivity experiments including and excluding the parameterizations and comparing results of simulations. In the present study, we concentrate on the sensitivity of meridional circulation and vertical ozone fluxes to the inclusion of OGW effects and QBO phase parameterizations into the MUAM.

The MUAM vertical grid has equidistant spacing vs. the log-pressure
coordinate

Simulations started from an initial state without wind and with temperature height-latitude structures given by the atmospheric model MSISE (Hedin, 1991) for January. We executed several “adjustment” stages during the first model days. During the first 30 days of simulations, we fixed geopotential heights at the bottom boundary, and do not incorporate the parameterization of OGW effects. After the 30st model day, the empirical changes of the surface geopotential heights and OGW effects are included. The model used the daily mean heating rates in the first 140 model days, and their daily variations are gradually involved after that. A prognostic equation for the geopotential at the Earth's surface was added after the 140st day of simulations. The simulations after the 330 day involved seasonal variations of solar heating. We adjusted starting dates of the simulations so that the 330–390 model days match to January–February.

We used the described above MUAM model with included parameterizations of OGW dynamical and thermal effects (Sect. 2.1) and QBO phases (Sect. 2.1) in numerical experiments simulating the changes in the meridional and vertical velocities in the middle atmosphere. In addition, we studied changes in global-scale ozone fluxes in the middle atmosphere caused by orographic waves generated by the Earth's surface topography and by the changes in QBO phase. In the experiments, the meridional and vertical components of wind velocity were simulated for every set of initial data with and without inclusion of the OGW parameterization for the conditions corresponding to the easterly and westerly QBO phases. The differences in values between these calculations demonstrate respective velocity differences. Their positive or negative values indicate an increase or decrease in the corresponding velocity component due to OGW effects or changes in QBO phases.

Figure 2a presents an example of simulated height-latitude
distribution of the zonal-mean meridional velocity, averaged over
January for the easterly QBO phase without OGW parameterization. Lines
with arrows correspond to schematic zonal averaged streamlines
calculated using the values of vertical velocity

Figure 2b shows simulated meridional velocity differences (MVD) caused
by the inclusion of OGW parameterization into MUAM for the eastern QBO
phase. One can see regions of increases or decreases (positive or
negative MVD) in the meridional velocity after inclusion of the OGW
effects. Hypotheses about nonzero differences in the meridional winds
in Fig. 1b can be verified with the statistical Student's

Simulated MVDs caused by the change from the easterly to westerly QBO
phase without inclusion of the OGW effects are shown in
Fig. 2c. Application of paired

Figure 3a shows the North Pole stereographic projection of the
simulated meridional wind (shaded areas) at altitude 25

The mean vertical ozone flux

Figure 5a presents the simulated altitude-latitude structure of the
zonal-mean vertical ozone flux calculated with Eq. (

The zonal-mean vertical ozone flux differences (OFDs) due to the
inclusion of the OGW parameterization into the MUAM model for January
are plotted in Fig. 5b. One can see regions of positive and negative
OFD values, which correspond to increases or decreases in vertical
ozone fluxes. Figure 5c presents OFDs due to change from the easterly
to the westerly QBO phase and shows substantial differences in
vertical ozone fluxes at altitudes 10–40

Differences in local vertical ozone fluxes in Fig. 5b and c may
change global ozone transfer. Figure 6 gives the January mean vertical
ozone fluxes averaged for different latitude belts 0–30

Dashed lines in Fig. 6a show respective vertical ozone fluxes for the
easterly QBO simulated with the OGW parameterization included into the
MUAM. They show that dynamical and thermal OGW effects substantially
(up to 20–30 %) increase absolute values of ascending and
descending

Figure 7a shows the horizontal distribution of the vertical ozone flux
at altitude 25

Figure 7b and c reveal ozone flux differences caused by OGW effects
for the easterly QBO phase and by changes in QBO phase without
OGWs. There are areas of enhancement or weakening of the ozone flux
corresponding to the regions of positive and negative VVDs in Fig. 4b
and c. Peak differences of the ozone flux in Fig. 7b and c can reach
40–60 % of the flux peak values shown in Fig. 7a. Paired

Results of numerical experiments in Figs. 5–7 expose that global-scale vertical ozone fluxes in the MUAM model are very sensitive to OGW dynamical and thermal effects, as well as to changes in QBO phase. These processes require proper parameterizations and inclusion into the numerical models of atmospheric general circulation for accurate simulations the exchange of optically active gas species between the troposphere and stratosphere. Our experiments also show that the improved parameterizations of OGW and QBO effects advance other MUAM features, getting better the simulation of coupling general circulation, planetary and tidal waves in the lower, middle and upper atmosphere (see Gavrilov et al., 2013a, b).

In the present paper, we described numerical experiments with the MUAM model simulating the general circulation in the middle atmosphere using ten-year average meteorological information and three-dimensional ozone distribution. We focus our experiments on the sensitivity of meridional circulation, vertical velocity and vertical ozone fluxes in the middle atmosphere to inclusions of recently developed parameterizations of OGW dynamical and thermal effects and changes in QBO phases to understand the role of vital processes associated with dynamical coupling between different atmospheric layers in general circulation models. We performed numerical experiments for the background and initial conditions typical for the westerly and easterly QBO phases in the equatorial atmosphere.

Our experiments show that OGW dynamical and heating effects may lead
to changes in zonal-mean meridional circulation fluxes. Maximum
differences of meridional velocity can reach

Simulated absolute peak differences in the zonal-mean vertical ozone
flux values caused by OGW effects and changes in QBO phases in the
Northern Hemisphere can reach 20–50 % of extreme ozone fluxes at
altitudes 10–40

The sensitivity experiments are essential for better understanding of the roles of different factors of general circulation models in formation of global dynamical processes and in transport and mixing of atmospheric gas components. The study shows that global-scale vertical ozone fluxes in the MUAM model are very sensitive to the parameterizations of OGW dynamical and thermal effects and changes in QBO phases. We studied only pure dynamical changes in the ozone fluxes, because MUAM does not simulate changes in atmospheric composition.

The parameterizations of OGW and QBO effects improve other MUAM features, allowing better simulations of coupled general circulation and wave processes in the lower, middle and upper atmosphere.

The MUAM FORTRAN code is based on the COMMA-LIM and MUAM models
described at

This work was partly supported by the Russian Basic Research Foundation and by the Russian Scientific Foundation (grant 14-17-00685).