To investigate the effects of the gravity wave (GW) drag on the general circulation in the thermosphere, a nonlinear GW parameterization that estimates the GW drag in the whole-atmosphere system is implemented in a whole-atmosphere general circulation model (GCM). Comparing the simulation results obtained with the whole-atmosphere scheme with the ones obtained with a conventional linear scheme, we study the GW effects on the thermospheric dynamics for solstice conditions. The GW drag significantly decelerates the mean zonal wind in the thermosphere. The GWs attenuate the migrating semidiurnal solar-tide (SW2) amplitude in the lower thermosphere and modify the latitudinal structure of the SW2 above a 150 km height. The SW2 simulated by the GCM based on the nonlinear whole-atmosphere scheme agrees well with the observed SW2. The GW drag in the lower thermosphere has zonal wavenumber 2 and semidiurnal variation, while the GW drag above a 150 km height is enhanced in high latitude. The GW drag in the thermosphere is a significant dynamical factor and plays an important role in the momentum budget of the thermosphere. Therefore, a GW parameterization accounting for thermospheric processes is essential for coarse-grid whole-atmosphere GCMs in order to more realistically simulate the atmosphere–ionosphere system.
It has been widely recognized that internal atmospheric waves from the lower atmosphere, such as planetary waves, solar tides, and gravity waves (GWs), propagate into the upper atmosphere and affect the circulation in the thermosphere–ionosphere system (Yiğit and Medvedev, 2015, and references therein). In this study, we focus our attention on the impact of GWs of lower-atmospheric origin on the thermospheric circulation and solar tides. While middle-atmospheric effects of GWs have been extensively studied, GW effects in the upper atmosphere above the turbopause have been studied to a much lesser extent due to a combination of observational and modeling challenges. On one hand, due to insufficient observations of the neutral winds in the thermosphere, the behavior of GWs in the thermosphere has not been sufficiently known. On the other hand, whole-atmosphere models, which can study GW propagation continuously in different layers of the atmosphere, has been developed only in recent times. Middle-atmosphere models had upper boundaries somewhere in the upper mesosphere, while thermosphere–ionosphere models had lower boundaries around the lower thermosphere. Additionally, the vast majority of the existing GWs focused on the middle-atmosphere dynamics and thus were not designed to represent GW processes in the upper atmosphere. Developments and challenges in the parameterization of gravity waves in the whole-atmosphere region have been discussed in detail in the work by Yiğit and Medvedev (2013). Briefly, gravity waves propagating from the lower atmosphere into the thermosphere are subject to additional dissipation processes that are characteristic of the thermosphere–ionosphere system, as documented for the first time in the context of a parameterization in the work by Yiğit et al. (2008). These wave-damping mechanisms are molecular diffusion and thermal conduction and ion drag in addition to nonlinear interactions. Therefore, in order to realistically simulate GW dynamics in the thermosphere, these processes have to be taken into account. The majority of the conventional GW schemes were not designed for the upper atmosphere in the first place.
Recently, an increasing number of numerical studies have revealed direct upward propagation of GWs from the lower atmosphere into the thermosphere and demonstrated significant GW effects on the thermospheric circulation (e.g., Yiğit et al., 2014; Heale et al., 2014; Gavrilov and Kshevetskii, 2015). Earlier, using a regional model and ray-tracing method, Vadas and Fritts (2004) showed that GWs generated by cumulus convection can propagate into the thermosphere and produce large GW drag in the thermosphere. GWs with high frequency (large vertical wavelength) can penetrate into the thermosphere (Vadas and Fritts, 2005). Yiğit et al. (2008) developed a nonlinear whole-atmosphere GW parameterization and succeeded in the implementation and application of their GW parameterization in the Coupled Middle Atmosphere Thermosphere-2 (CMAT2) general circulation model (GCM). Yiğit et al. (2009) showed that the dynamical effects of gravity waves in the thermosphere are comparable with the ion-drag effects up to ionospheric F2-region altitudes. Later, based on the similar modeling framework, Yiğit and Medvedev (2009) showed for the first time that GW thermal effects are very important globally in the thermosphere, competing with joule heating, and ultimately cool the thermosphere. More recently, Yiğit and Medvedev (2017) demonstrated that the small-scale GWs impact the amplitude of the diurnal tide in the low-latitude middle atmosphere and in the high-latitude thermosphere. Using the first-generation CMAT model with two different older GW parameterizations, England et al. (2006) investigated effects of the GW drag on the diurnal tide and green-line airglow emissions during equinox in the equatorial mesosphere and lower thermosphere (MLT). Based on idealized numerical simulations with the Yiğit et al. (2008) scheme, Medvedev et al. (2017) have discovered that the magnetic field configuration can significantly influence the propagation and dissipation of lower-atmospheric GWs in the thermosphere via the ion-drag force.
GW effects can also be studied using high-resolution GCMs. Models are increasingly capable of implementing higher resolutions, which can capture smaller-scale physics. Using a GW-resolving (i.e., high horizontal resolution) GCM, Miyoshi and Fujiwara (2008) and Miyoshi et al. (2014, 2015) investigated upward propagation of GWs and the GW drag in the thermosphere. They indicated that the GW drag in the thermosphere is much larger than that in the mesopause region. The GW activity in the thermosphere is stronger in winter than in summer and is correlated with the strength of the strato-mesospheric jet. Using a GW-resolving Whole Atmosphere Community Climate Model (WACCM), Liu et al. (2014) also studied upward propagation of GWs excited by tropical convection up to a 105 km height. Overall, high-resolution simulations supported the finding that the mean GW effects in the thermosphere can be adequately represented by physics-based GW parameterizations, such as the one developed in the work by Yiğit et al. (2008).
Previous numerical studies indicated that the GW drag plays an important role in maintaining the momentum and energy balance in the thermosphere. Both GW parameterizations and high-resolution simulations provide various advantages as well as some limitations. While the mean global structure of GW effects is well represented by GW parameterizations extending into the thermosphere, high-resolution simulations can more self-consistently simulate GW processes probably in more detail; for example, smaller-scale variability in GWs can be better captured. This implies overall that a GW-resolving GCM is necessary in order to simulate thermospheric circulation more accurately. However, numerical diffusion schemes (e.g., hyperdiffusivity) may excessively damp smaller-scale GWs. Often, GW sources and their generations are still parameterized in high-resolution simulations. Also, conducting numerical simulations with a GW-resolving GCM requires high-performance computer systems and overall needs much more computational time and data storage. Therefore, long-term simulations using a GW-resolving GCM are unpractical. Therefore, a low-resolution GCM based on a physics-based whole-atmosphere GW parameterization is strongly required. However, there are only a few studies concerning GW drag parameterization for the thermosphere, and there are various aspects of GW effects in the thermosphere that are still unexplored. One such unexplored territory that is the focus of this paper is the interaction of GWs with the semidiurnal migrating tide (SW2) in the upper atmosphere. Simultaneously, this work serves as the first study with the whole-atmosphere GCM by Miyoshi and Fujiwara (2003) implementing the whole-atmosphere GW parameterization by Yiğit et al. (2008). Thus, we will also study and revisit the mean GW effects on the thermosphere and solar tides.
The descriptions of the GCM, the GW parameterization, and numerical simulations are presented in Sect. 2. Results and discussions are presented in Sect. 3. Concluding remarks follow in Sect. 4.
The model used in this study is a whole-atmosphere GCM as shown in Miyoshi (2006) and Miyoshi
and Fujiwara (2003, 2008). This model is a thermospheric extension of
the middle-atmosphere model developed at Kyushu University (Miyahara et al.,
1993; Miyoshi, 1999). The GCM is a global spectral model with a horizontal
grid spacing of 2.8
The GCM incorporates schemes for a hydrological cycle, a boundary layer, moist convection, and infrared and solar radiations (Miyoshi and Fujiwara, 2003; Miyoshi, 2006). Effects of mountains and land–sea contrast are also taken into account. The GCM was nudged by Japanese Meteorological Agency reanalysis data (JRA-55; Kobayashi et al., 2015) up to a 40 km height to simulate realistic temporal variations in the lower atmosphere (Jin et al., 2012). In the thermosphere, the GCM has schemes for molecular diffusion, thermal conductivity, joule heating, ion-drag force, and auroral precipitation heating. To estimate joule heating, ion-drag force, and auroral precipitation heating, the electron density is prescribed using an empirical ionosphere model. The global electron density distribution produced by the solar radiation is represented by Chiu's empirical model (Chiu, 1975). Electrons produced by auroral particles are estimated by Fuller-Rowell and Evans (1987). We use a coarse grid in this study, which provides computational efficiency, and represent GWs that are not explicitly resolved by the model with orographic and nonorographic GW parameterizations. The GW parameterization developed by McFarlane (1987) is used for orographic GWs. The previous standard version of the GCM includes a linear nonorographic GW parameterization developed by Lindzen (1981). However, the GW drag estimated by these GW parameterizations is taken into account only below a 100 km height. Thus, note that no GW effects are calculated in the thermosphere above a 100 km height in this configuration. This setup mimics the traditional approach of accounting for GWs only in the middle atmosphere, which is essentially what low-top middle-atmosphere models used to do. The numerical simulation using this original GCM is called EXP1. This standard version is described in detail in previous publications (Miyoshi and Fujiwara, 2003; Miyoshi, 2006; Miyoshi et al., 2009).
To assess impacts of GW drag on the general circulation in the thermosphere
as well as in the lower and middle atmosphere, we need a GW scheme that
extends into the thermosphere. Therefore, the GW parameterization developed
in the work by Yiğit et al. (2008) has been implemented in the GCM
developed by Miyoshi and Fujiwara (2003). Yiğit's GW parameterization
can estimate the GW effects in the whole-atmosphere system from the
troposphere to the upper thermosphere. The GW spectrum is specified in terms
of momentum fluxes as a function of horizontal phase speeds. The phase
speeds of GWs used in GW calculations range from 2 to 80 m s
To exclude influences from temporal variations in solar UV and EUV fluxes and
geomagnetic activity, we performed the numerical simulations under solar
minimum and geomagnetically quiet conditions. The 10.7 cm solar radio flux
(F10.7) was fixed at
Impacts of GWs on the zonal-mean zonal wind are examined first. Figure 1a
shows the height–latitude section of the zonal-mean and diurnal-mean zonal wind
obtained by the application of the Lindzen scheme (EXP1). Data are averaged
from 1 to 30 June. Note that thermospheric GW effects above a 100 km height are not incorporated in this scheme. Strong jets exist in the
stratosphere and mesosphere. These jets weaken in the upper mesosphere, and
the reversal of the zonal-wind direction occurs at around a 80–100 km height. It
is well known that this reversal of the zonal wind is generated by the GW
drag (e.g., Lindzen, 1981; Matsuno, 1982; Garcia and Solomon, 1985). Again,
the westward and eastward wind appear above a 120 km height in the Northern
Hemisphere (NH) and Southern Hemisphere (SH), respectively. The peak of the
westward wind (48–52 m s
Figure 1b shows the zonal and diurnal-mean zonal-wind distribution obtained
by the application of the Yiğit scheme (EXP2). As shown before,
Yiğit's GW parameterization is implemented in the whole-atmosphere
region. The strato-mesospheric jets weaken in the upper mesosphere, and the
reversal of the zonal-wind direction occurs at a 80–100 km height. The
difference of the zonal-mean zonal wind between EXP2 and EXP1 is shown in
Fig. 1c. There are substantial differences of the magnitudes of the
strato-mesospheric jets between EXP1 and EXP2. The eastward jet in the SH is
stronger in EXP1 than in EXP2. On the other hand, the westward jet in the NH
at 20–50
Figure 2a and b show the height–latitude distribution of the zonal-mean
meridional wind obtained by EXP1 and EXP2, respectively. In both
experiments, southward flow from the summer pole to winter pole is dominant
at a 50–100 km height, whereas northward flow appears between a 100 and 120 km
height. These flows are stronger in EXP2 than in EXP1, which is explained by
the enhanced GW drag in EXP2 as shown later. Above a 130 km height, southward
flow is dominant in both experiments. The magnitude of the southward wind
between a 130 and 250 km height is weaker in EXP2 than that in EXP1 except for
southward of 30
Figure 3a and b show the height–latitude distribution of the zonal-mean
temperature obtained by EXP1 and EXP2, respectively. At a 80–100 km height,
Cooling and warming occur at 30–90
The impact on the migrating semidiurnal tide (SW2) is examined here. Figure 4a shows the height–latitude distribution of the temperature component of
the SW2 amplitude in June obtained by EXP1. The amplitude maximizes at around a
125 km height. The maxima are 41 K at 15
Figure 4b shows the temperature component of the SW2 amplitude obtained by
EXP2. The SW2 in the lower thermosphere maximizes at 15–20
Figure 5a and b show the zonal-wind component of the SW2 amplitude in EXP1
and EXP2, respectively. Figure 5c shows the amplitude difference between
EXP1 and EXP2. The maximum of the zonal-wind component of the SW2 at a 120 km
height in EXP1 (EXP2) is 68 m s
The SW2 also has significant day-to-day variations. For example, the SW2
amplitude at 20
Figure 6a shows the height–latitude distribution of the temperature
component of the migrating terdiurnal tide (TW3) amplitude in June obtained
by EXP1. The amplitude peak is located at 15
Figure 7a shows the height–latitude section of the zonal and diurnal mean of the zonal GW drag estimated by Lindzen's parameterization (EXP1). Eastward (westward) acceleration exists in the NH (SH) and attenuates the mesospheric jet. Figure 7b shows the zonal and diurnal mean of the zonal GW drag estimated by Yiğit's parameterization (EXP2). The differences of the GW drag below a 100 km height are substantial. The magnitude of the GW drag in EXP1 below a 100 km height is similar to that in EXP2. However, the peak of the GW drag in EXP1 is located around 60–70 km, whereas that in EXP2 is located around a 90–100 km height. These differences of the GW drag below a 100 km height produce the differences of the strato-mesospheric jets. The GW drag in EXP2 extends to a 300 km height. It is noteworthy that the magnitude of the GW drag in a 150–300 km height is comparable to that in the MLT.
In the previous sections, we investigate zonal and diurnal mean of the GW
drag. Longitudinal and diurnal variabilities in the winds are significant in
the thermosphere, so longitudinal and diurnal variability of the GW drag is
examined next. Figure 8a shows the height–longitude distribution of the zonal GW
drag at 35
The zonal and diurnal mean of the zonal GW drag at 35
Figure 9a and b show the global distribution of the zonal GW drag at 120 km
at two representative times, 00:00–01:00 and 06:00–07:00 UT, respectively. The
GW drag in low and middle latitudes has zonal wavenumber 2 structure. The
magnitude of the GW drag sometimes exceeds 150 m s
In this section, the relationship between the GW drag and the zonal wind in
high latitudes, where the diurnal variation of the zonal wind is the
largest, is investigated. Figure 10a shows the height–longitude section of the
zonal GW drag in EXP2 at 65
To investigate the impact of the GW drag on the zonal-wind variation, the
zonal-wind distribution obtained by EXP1 is shown in Fig. 10c. In EXP1,
the westward (eastward) wind prevails in the 0–180
The global distribution of the zonal GW drag at a 200 km height is examined
here. Figure 11a and b show the zonal GW drag distribution in 00:00–01:00
and 06:00–07:00 UT, respectively. In both figures, the GW drag is significant at
high latitudes. For example, in 00:00–01:00 UT, westward acceleration of 1500 m s
Figure 11c and d show the horizontal wind distribution at a 200 km height in 00:00–01:00 and 06:00–07:00 UT, respectively. Colored shading in Fig. 11a and b shows the zonal-wind distribution. The enhanced zonal GW drag is located at the regions where the strong zonal wind appears. The strong zonal winds in high latitudes are mainly generated by the convective electric fields of magnetospheric origin, auroral energy precipitation, and ion-neutral coupling processes such as ion-drag force and joule heating (e.g., Yiğit and Ridley, 2011). The enhanced eastward (westward) wind is favorable for upward propagation of westward-moving (eastward-moving) GWs from the lower atmosphere. The westward (eastward) acceleration due to the dissipation and/or breaking of westward-moving (eastward-moving) GWs occurs in the eastward (westward) wind region. This is the reason why the GW drag is enhanced at high latitudes. These results indicated that the GW drag plays an important role in the momentum budget in high latitudes at around a 200 km height. Using a GW-resolving GCM, Miyoshi et al. (2014) showed the enhancement of the GW drag in the polar region at a 200 km height. Their result is in good agreement with the results presented here.
General circulation models (GCMs) provide a powerful methodology for
studying the global effects of gravity waves (GWs) in the atmosphere. One
strength is the continuous coverage of atmospheric layers; thus interaction
processes between different layers can be studied. However, they have
limited resolutions, so physical parameterizations are crucial. Nowadays,
atmospheric models are gradually being converted into whole-atmosphere
models, which can provide a framework in which atmospheric wave propagation
can be studied from the lower atmosphere to the upper atmosphere in a more
self-consistent manner (e.g., Miyoshi and Fujiwara, 2003, 2008; Akmaev et
al., 2008). Also, it is increasingly acknowledged that GW parameterizations
must cover the entire atmosphere, following the realization that GWs deposit
their energy and momentum at different layers in the atmosphere, with a
significant portion being deposited in the middle thermosphere. In this
context, we exploit the capability of the whole-atmosphere GW
parameterization of Yiğit et al. (2008). Note that recent studies showed
that lower-atmospheric GWs can directly propagate into the thermosphere and
can dump significant energy and momentum there. For example, the magnitude
of the GW drag in the lower thermosphere sometimes exceeds 150 m s
Using the SABER measurement aboard the TIMED satellite, Pancheva and Mukhtarov (2011) investigated
the behavior of the SW2 in the MLT. There, the typical observed peak values for
the SW2 amplitudes are situated at low latitudes during the June solstice: 25–28 K at 15–30
Using the CHAMP and GRACE accelerometer measurements, Forbes et al. (2011) showed the SW2 amplitude in the upper thermosphere. The GCM without GW drag parameterization in the thermosphere fails to reproduce the observed SW2 in the upper thermosphere, whereas the GCM with the GW parameterization succeeds in reproducing the behavior of the observed SW2 in the upper thermosphere. This result also indicates the importance of the GW effects in the thermosphere.
There are substantial differences between the linear and the nonlinear schemes in the treatment of GW processes, as has been initially discussed in detail in the work by Yiğit et al. (2008). One major difference is that the linear scheme is based on the linear saturation principle, ignoring wave–wave interactions, while the Yiğit scheme takes into account not only nonlinear wave–wave interactions but also dissipation of GWs due to additional processes, such as ion drag, molecular viscosity, and thermal conduction, which are important dissipative processes in the thermosphere–ionosphere system. Any GCM that extends into the thermosphere, including a GW parameterization, must incorporate these effects on GW propagation. While the linear scheme assumes an artificial tuning factor for the GW drag, the nonlinear scheme does not require any artificial tuning parameters. However, GW parameterizations are not devoid of limitations. They all assume a single-column approach and instantaneous response of the flow field to the upward-propagating waves.
The whole-atmosphere GCM uses an empirical ionospheric model. At high latitudes, the behavior of the ionosphere can substantially influence the thermospheric circulation. On the other hand, the background atmosphere is very important for the GW propagation and dissipation. A modeling framework with a self-consistent two-way coupled ionosphere–thermosphere system could provide a more realistic picture of ion-neutral coupling, and GW effects could be evaluated more precisely at high latitudes.
The GW parameterization developed by Yiğit et al. (2008) has been
implemented in the Japanese Kyushu University whole-atmosphere GCM (Miyoshi
and Fujiwara, 2008), and the impact of small-scale GWs on the migrating
semidiurnal tide as well as the GW effects on the general circulation of the
thermosphere have been studied. We obtained the following results.
The GW drag attenuates the magnitude of the zonal-mean and diurnal-mean zonal wind
in the thermosphere. The GW drag modifies the zonal-mean meridional and
temperature distributions in the thermosphere. The GW drag attenuates the SW2 amplitude in the lower thermosphere and
modifies the latitudinal structure of the SW2 above a 150 km height. The GW
drag also attenuates the TW3 amplitude in the thermosphere. The GW drag in the lower thermosphere has zonal wavenumber 2 structure
and has semidiurnal variation. The GW drag above a 150 km height is enhanced in high latitudes. The
maximum value sometimes exceeds 1000 m s
The whole-atmosphere GCM used in this study uses an empirical ionosphere.
Therefore, impacts of the GW drag on the ionospheric variability have not
been investigated in this study. In the next step, implementation of GW drag
parameterization in an atmosphere–ionosphere coupled model, such as GAIA
(Jin et al., 2012), is strongly required. Using an atmosphere–ionosphere
coupled model with GW drag, we will investigate impacts of the GW drag on
the ionospheric variability.
Upon request, the data used for the publication of this study are available from Yasunobu Miyoshi (y.miyoshi.527@m.kyushu-u.ac.jp).
YM performed the simulation and wrote a substantial portion of the paper. EY provided the whole-atmosphere GW parameterization scheme and significantly contributed to writing and discussion of results.
Erdal Yiğit is one of the editors of this special issue. The authors declare that they have no conflict of interest.
This article is part of the special issue “Vertical coupling in the atmosphere–ionosphere system”. It is a result of the 7th Vertical coupling workshop, Potsdam, Germany, 2–6 July 2018.
The GFD Dennou library was used to produce the figures. The numerical simulation was performed using the computer system at the Research Institute for Information Technology of Kyushu University and at the National Institute of Information and Communication Technology, Japan. Erdal Yiğit was partially funded by the National Science Foundation (NSF) grant AGS 1452137.
This research has been supported by the JSPS, Japan (grant no. 15H03733); the JSPS, Japan (grant no. 18H04447); and the National Science Foundation, USA (grant no. AGS 1452137).
This paper was edited by Kathrin Baumgarten and reviewed by two anonymous referees.