Nonlinear forcing mechanisms of the terdiurnal solar tide and their impact on the zonal mean circulation

. We investigate the forcing mechanisms of the terdiurnal solar tide in the middle atmosphere using a mechanistic global circulation model. In order to quantify their individual contributions, we perform several model experiments and separate each forcing mechanism by switching off the remaining sources. We ﬁnd that the primary excitation is owing to the terdiurnal component of solar radiation absorption in the troposphere and stratosphere. Secondar y Secondary sources are nonlinear tide-tide interactions and gravity wave-tide interactions. Thus, although the solar heating clearly dominates the terdiurnal forcing 5 in our simulations, we ﬁnd that nonlinear tidal and gravity wave interactions contribute in certain seasons and altitudes. By slightly enhancing the different excitation sources, we test the sensitivity of the background circulation on these changes of the dynamics. As a result, the increase of terdiurnal gravity wave drag can strongly affect the middle and upper atmosphere dynamics, including an irregular change of the terdiurnal amplitude, a weakening of neutral winds in the thermosphere, and a signiﬁcant temperature change in the thermosphere, depending on the strength of the forcing. On the contrary, the inﬂuence of 10 nonlinear tidal interactions on the middle atmosphere background dynamics is rather small. the increased simulation numerical

1. The model does not generate non-migrating tides in the current configuration as described in section 2. Please add "migrating" before "terdiurnal solar tide" in the title.
We adjusted the title, accordingly.
2. "In order to reduce the time of computation for the simulations with enhanced forcing mechanisms, only the January runs are performed as an ensemble. The other months represent the conditions for the year 2000, only". Please discuss the potential difference or evaluate the influence of these two kinds of processing methods.
In the meantime, we can provide an update with ensemble means for the 5% enhanced simulations, too. This should be more consistent than using only one single year. The present Figs. 2-4 and related descriptions have been updated, accordingly (note that former Fig. 1 was removed following the suggestion of reviewer #1). 3. Figure 1 and Page 5 Line 1: "This is due to the fact that MUAM tends to underestimate tides in general, which is frequently seen in other models, too". Page 5 Line 14: There are differences in the seasonal variation of the TDT from different models. What's the reason behind these phenomena? Besides, would you please demonstrate why you present the seasonal cycle of TDT at 109 km?
There is no general agreement on the cause of tidal underestimation in models, but it has to be connected with strong damping in the mesosphere region, for example due to gravity waves. The Lindzen-type parameterization used in MUAM tends to damp tides relatively strongly, while other parameterizations can lead to slightly stronger tides (e.g. the one after Hines or Yigit). Neverless, as we mainly focus on relative amplitude changes, our results are not significantly influenced by this underestimation.
Please note that our statement about the different seasonal cycles (page 5 line 14 of the discussion manuscript) only refers to the pure nonlinear TDT, not to the total TDT (which could be compared to observations). The reason is most likely based on the different tidal forcing mechanisms, but also on different methods to determine the nonlinear TDT contribution. For example, Smith and Ortland (2001) used a model with explicit lower boundary forcing of the diurnal (DT) and semidiurnal tides (SDT), while all tides in MUAM are forced in-situ by absorption of solar radiation without lower boundary forcing. The latitudinal distribution of the tides by Smith and Ortland (2001) is therefore already prescribed to a certain degree and possible nonlinear interactions may appear at different latitudes and altitudes than in our model. For Fig. 1, the altitude of 109km was chosen to be able to compare the REF results with satellite measurements which are not available further above. Below that altitude, MUAM produces relatively small amplitudes which might be connected with large uncertainties. Therefore, we think that 109km is the best choice as a compromise between large amplitudes and comparability. Note, however, that according to the suggestions of reviewer #1 we removed this figure in the revised version, as it shows similar results as already presented by Lilienthal et al. (2018). Instead, we added a supplement, where it can still be found. Figure 3 and Page 7 Line 4: ". . . in the forcing locally amounts to +500% . . . and to . . . +1800% . . ..". The +500% and +1800% cannot be tell in Figure 3b and Figure Figure 3 (b, d, f, and h).

4.
In order to improve the visibility of maximum values of Fig. 2 (former Fig. 3), we used a logarithmic scale instead of a linear one and included colors that are easier to distinguish. We believe that additional contour lines had been rather confusing in these plots.

You can simply illustrate the limit of the standard deviations. Only the interval of the standard deviations in Figures 1, 2, and 4 can not demonstrate the exact values.
We now provide the maximum values of the standard deviations and amplitude differences (contour lines) in the panels of Figs. 1 and 3.
6. Page 7 Line 30: ". . .becomes instable for some months." The results of which months in Figure  6 are unstable?
For the months June, July and August, Figure 6c and 6d do not show any data for an enhancement factor of 1.10. These are the simulations that became unstable. We added a brief note in the revised version (P8, L7-8).   Figure 5 shows the horizontal mean (over all latitudes/longitudes) vertical mean (80-160km) amplitudes of the TDT. Figure 6 presents the horizontal and vertical mean of zonal mean wind/temperature differences, respectively. Therefore, "global mean" was here associated with "horizontal mean vertical mean". In the revised version, it has been substituted to avoid confusion.

List of relevant changes
for the article "Nonlinear forcing mechanisms of the migrating terdiurnal solar tide and their impact on the zonal mean circulation" by F. Lilienthal and Ch. Jacobi Text: -Section 3.1 has been shortened and adjusted because of removed figures.
-Grammatical and Spelling issues have been addressed. a supplement has been added to show also April, July and October conditions for Figs. 1-4 the removed former Fig. 1 has also been added for zonal wind and temperature parameters in the supplement.

Introduction
The middle atmosphere dynamics are mainly determined by waves that are excited in the troposphere or stratosphere and propagate to the upper atmosphere (see, e.g., reviews by Forbes, 1995;Yiǧit and Medvedev, 2015). These waves can be either global scale like atmospheric solar tides, or small scale like the internal gravity waves (GW :::: GWs). GWs are generated in the 15 lower atmosphere due to orography :::::::: geography, convective instabilities, wind shears, jet streams, spontaneous adjustment, or wave-wave interactions (Fritts and Alexander, 2003). Due to wave breaking and momentum deposition they are mainly responsible for the wind reversal in the mesosphere and lower thermosphere (MLT) region. However, GWs also play an important role in the thermosphere where they can damp or enhance tides (e.g., Yiǧit et al., 2008;Yigit and Medvedev, 2017), and may also transport wave signatures to the thermosphere (e.g., Eckermann et al., 1997;Meyer, 1999;Hoffmann et al., 2012). 20 Atmospheric solar tides are global scale waves owing to the diurnal variation of solar radiation. Therefore, they have periods of a solar day and its harmonics. They are primarily excited in the water vapor and ozone heating region (Chapman and Lindzen, 1970;Andrews et al., 1987). Due to decreasing density with increasing height, tides reveal their maximum amplitudes in the MLT region. Above, in the thermosphere, they are damped, e.g. by increasing molecular diffusion and thermal conduction.
Amplitudes of diurnal tides (DTs) and semidiurnal tides (SDTs) are generally larger than those related to higher harmonics and wavenumbers such as the terdiurnal tide (TDT). However, during some seasons the TDT amplitudes may locally become comparable to those of the DT (Cevolani and Bonelli, 1985;Reddi et al., 1993;Thayaparan, 1997;Younger et al., 2002). For ex-5 ample, radar measurements at midlatitudes show large TDT amplitudes in autumn and early winter (Beldon et al., 2006;Jacobi and Fytterer, 2012;Jacobi, 2012), and also in spring (Thayaparan, 1997). Global observations of the TDT have been presented by Smith (2000), Moudden and Forbes (2013), Pancheva et al. (2013) and Yue et al. (2013). Yue et al. (2013) obtained TDT amplitudes of more than 16 m s −1 at 50 • N/S above 100 km from observations using the Thermosphere Ionosphere Mesosphere Energetics and Dynamics Doppler Interferometer (TIMED/TIDI). They reported another maximum in the meridional wind at 10 about 82 km at lower northern latitudes. For 90 km altitude, based on Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) data, Moudden and Forbes (2013) observed large amplitudes over the equator during equinoxes (6 − 8 K), and also at 60 • during spring.
While the excitation mechanism is relatively well known for the DT and SDT, those of the TDT are still under debate (e.g., Lilienthal et al., 2018, and references therein). Besides the direct solar forcing, higher harmonics are also subject of :: to 15 nonlinear tidal interaction (e.g., Glass and Fellous, 1975;Teitelbaum et al., 1989;Teitelbaum and Vial, 1991). For example, the interaction between DT and SDT can lead to a secondary TDT. On the other hand, interactions between GWs and tides can also produce a secondary TDT (Miyahara and Forbes, 1991). Ribstein and Achatz (2016) have shown that such interactions strongly depend on model physics but they did not include the TDT in their analysis.
The excitation mechanisms of the TDT have been investigated by several model studies (Akmaev, 2001;Smith and Ortland, 20 2001; Huang et al., 2007;Du and Ward, 2010;Lilienthal et al., 2018) but with partly inconclusive results. This is most likely caused by different models and analysis techniques, e.g. Akmaev (2001) and Smith and Ortland (2001) use models with explicit lower boundary forcing of DT and SDT while the simulations of Du and Ward (2010) and Lilienthal et al. (2018) are based on fully self-consistent tides. Furthermore, the authors partly focused on different latitudes and altitudes which cannot be easily compared. 25 The majority of these publications agrees that the direct solar forcing is the most dominant, although not the only, excitation mechanism of the TDT (Akmaev, 2001;Smith and Ortland, 2001;Du and Ward, 2010;Lilienthal et al., 2018). For example, Huang et al. (2007) found significant nonlinear TDT amplitudes above 90 km, especially during equinoxes, which agrees with the simulations by Akmaev (2001). Lilienthal et al. (2018) found that the solar forcing is the primary excitation mechanism, but nonlinear tide-tide interactions and also GW-tide interactions play a role. They analyzed the phase relations of differently 30 forced TDTs and found destructive interferences between them. This suggests that different excitation mechanisms can also counteract, partly leading to a reduced and not an enhanced TDT.
To extend the work of Lilienthal et al. (2018) and in order to further investigate the nonlinear mechanisms of TDT forcing, we now present model simulations, which are each restricted to only one terdiurnal forcing mechanism, i.e. either the solar heating absorption, or nonlinear tidal interactions, or GW-tide interactions. The remainder of this paper is organized as follows.
In section 2, the model and experimental setup is described, and in section 3 the results of the model runs are discussed with respect to TDT zonal wind amplitudes (section 3.1). In section 3.2 a sensitivity study with modified forcings is presented and their effect on the mean flow is analyzed. Section 4 concludes the paper.

Model Description and Experimental Setup
In the following analysis we use the Middle and Upper Atmosphere Model (MUAM) in the same configuration as described 5 in detail by Lilienthal et al. (2017Lilienthal et al. ( , 2018. In short, MUAM is a mechanistic primitive equation global circulation model that reaches from the troposphere to the thermosphere, i.e. to about 160 km in logarithmic pressure height, given a constant scale height of 7 km. The horizontal resolution is 5 × 5.625 : 5 • There are three main sources of atmospheric tides in the model. The primary source is the absorption of solar radiation which creates tides self-consistently. The solar heating is parameterized according to Strobel (1978) and considers heating due to all important gases for tidal forcing such as water vapor and ozone in the troposphere and stratosphere, as well as oxygen and 15 nitrogen in the thermosphere. For more details, see Lilienthal et al. (2018).
Nonlinear interactions between different tides and between GWs and tides can generate a secondary TDT as described above. : in :::::::: section 1. : The interactions related to GWs can be realized within the GW parameterization of the model. This is a coupled parameterization based on an updated linear scheme for the lower and middle atmosphere (Lindzen, 1981;Jakobs et al., 1986;Fröhlich et al., 2003;Jacobi et al., 2006) and an adjusted nonlinear scheme according to Yiǧit et al. (2008Yiǧit et al. ( , 2009), 20 see also Lilienthal et al. (2017Lilienthal et al. ( , 2018, for the thermosphere. Even though both schemes are coupled through the eddy diffusion coefficient, which is transfered from the linear scheme to the nonlinear scheme, both parameterizations are almost independent from each other, because they handle a different range of phase speeds without overlap, i.e. the linear scheme is responsible for slowly traveling GWs which mainly break in the middle atmosphere while the nonlinear scheme is responsible for fast traveling GWs that reach the lower thermosphere. 25 Nonlinear interactions are a rather dynamic feature of the tendency equations of the model. They are, mathematically, to a certain degree hidden in the product of non-zonal parameters of the model equations. In particular, they are included in the advection terms and in the adiabatic heating component (see also Lilienthal et al., 2018). Further interactions, i.e. further products of non-zonal parameters, are possible within the parameterizations of eddy diffusion, molecular conduction, and in the Coriolis terms. However, these terms are comparatively small and their separation and extraction, partly leads to numerical instabilities. Therefore, these terms are neglected in the following. To summarize, the main three forcing mechanisms of TDTs in MUAM are the direct solar forcing, nonlinear tidal interactions and GW-tide interactions.
In order to quantify the relevance of these three mechanisms, Lilienthal et al. (2018) performed model runs, each of them with removing one of these mechanisms in order to determine the change in tidal amplitude due to this forcing. Following Lilienthal et al. (2018) and extending the analysis, we now go the other way around and remove all forcing mechanisms except for the respective one of interest. The procedure to remove the nonlinear terms is technically the same as the one used by Lilienthal et al. (2018). A Fast Fourier transform according to Danielson and Lanczos (1942) is used to extract the wavenumber 3 pattern in each time step of the model. Due to the fact that the model, in the current configuration, does not generate nonmigrating tides, this is the simplest way to remove the whole TDT structure. In contrast to Lilienthal et al. (2018), this is not only applied to one of the forcing terms, but to two of them in parallel. The remaining amplitudes can be directly attributed to the respective third and remaining forcing. Thereby we produce a reference simulation with all forcing mechanisms included, and three further simulations:

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-REF: reference run. This is the same one that has been shown by (Lilienthal et al., 2018)  All of these simulations are performed as ensembles as described above.
On an average, the amplitudes of the GWF simulation ( Fig. ?? : 1d) are smaller than those of the NLIN simulationbut they maximize during summer near 60N where they can be even larger than those due to the nonlinear forcing.Near the equator, they are close to zero. ::::::::: However, :: in ::::: other ::::::: seasons ::: and ::: in :::::: certain ::::::: altitudes :: it :::: can :: be :::::::: different :::: (see :::: Fig. ::: S2). When the GWF 25 amplitudes maximize, they reach a similar magnitude like those obtained by Miyahara and Forbes (1991). In the following, we present the vertical structure of the TDT for different forcing terms and each season (Fig. 1). Background colors denote ensemble means of the latitude-altitude distribution, according to the 11 ensemble members, and contour lines represent their standard deviations. January and July reveal a similar amplitude distribution, considering that the hemispheric structure is reversed due to the reversed circulation patterns. April and October are similar, too. Standard deviations are generally small 30 with respect to the ensemble means, and they tend to be larger in July (October) compared to January (April). Furthermore, the latitudinal structure of TDT amplitudes changes in the lower thermosphere (approximately above 120 km) for most experiments and seasons, e.g. the triple peak structure of REF and SOL in the MLT during equinoxes turns into a double peak structure above 140 km. In the following analyses, we restrict ourselves to the months January and April to show typical solstice and equinox conditions, respectively. In this section we analyze the effect of each different forcing on the TDT as well as the background atmosphere. Therefore, the simulations SOL, NLIN and GWF now serve as a reference for the TDT amplitudes and the respective background circulation.
In each of these simulations, we enhance the active forcing mechanism (tendency term) in each time step and for each latitude/altitude by 5% of the respective original value, i.e. the solar forcing is enhanced in SOL, the nonlinear forcing is enhanced 5 in NLIN and the GW forcing is enhanced in GWF. These enhanced simulations are called SOL5, NL5 and GW5. Figure 2 shows the observed amplitude change of the respective terdiurnal forcing terms for January (top) and April (bottom) in the thermal (a,b,e,f) and dynamical (c,d,g,h) parameters ::: (for :::: July :::: and ::::::: October ::::::::: conditions ::: see ::: Fig. :::: S3). Thereby, the data at each grid point are normalized by their value in the respective reference simulation. For example, the terdiurnal nonlinear forcing of NL5 is normalized by the terdiurnal nonlinear forcing of the NLIN simulation. The solar forcing term of the SOL5 10 simulation is not shown in Fig. 2 because the effect is nearly linear, i.e. the strength of enhancement almost shows the expected value of +5% with a maximum deviation between +4.6% to +5.3% during solstices. Figure 2 demonstrates that the observed nonlinear (NL5) and GW tendency terms (GW5) can strongly deviate from +5% compared to NLIN and GWF, respectively.
The nonlinear forcing terms (temperature advection and zonal wind acceleration; Fig. 2a,c,e,g) show a change in the terdiurnal forcing between roughly −8% to +22%. However, as indicated by the shaded areas, these are rather exceptional cases, and 15 usually the forcing enhancement varies between 4.5 to 5.5%. The GW forcing terms are more extreme, ranging from −92% to +500% in the heating component (Fig. 2b,f) and from −93% to almost +1800% in the component of zonal wind drag ( Fig. 2d,h). The shading for the enhanced GW forcing covers a range between 0 to 10%, but shaded areas are rather small, indicating that these large numbers are not only outliers.
A possible reason for these large discrepancies are feedback mechanisms within the model. It is widely known (e.g., Lindzen,20 1981; Holton, 1982) that GWs strongly influence the background circulation, being responsible for the wind reversal in the mesosphere due to wave breaking and momentum deposition. Therefore, a change in the terdiurnal component of GW drag may also influence the background circulation, leading to altered propagation condition for tides, which again affects the terdiurnal component of GW drag. Such a mechanism is very difficult to control within a nonlinear model. Before we go into detail with the analysis of the background circulation, we first have a look at the amplitude of the TDT due to the increased forcing.  The simulation NL5 (Fig. 3a) looks equal :::::: similar to NLIN ( Fig. 1 first row, third column), because the enhancement of 5% is ::::: mostly : too small to be visible in the chosen color scheme. The variability between the different seasons (Fig. 3a, profiles) is small for all altitudes, and the zonal wind amplitudes in NL5 are approximately 4% to 6% larger than in NLIN. The temperature amplitude (Fig. 3b) shows a similar behavior below 130 km but above, the horizontal mean TDT amplitudes roughly vary between 0% and +8% compared to the original forcing. During April (light blue line), the amplitude does even slightly decrease near 150 km, i.e. the change is negative.
The zonal wind TDT amplitudes due to a 5% increased GW forcing (Fig. 3c) are drastically increased in comparison to the GWF amplitudes in Fig. 1 (first row, last column). This is mainly an effect of the increased GW forcing terms. They do not only influence the zonal wind amplitude (Fig. 3c) but also the temperature tide (Fig. 3d). Below 100 km, the amplitudes are approximately doubled (+100%). This factor further increases up to an altitude of 140 km reaching a maximum increase 10 by more than 800% :::: 600% : (zonal wind) and almost 600% :::: about ::::: 500% : (temperature), respectively. These maxima are found during : in : August/September for both parameters ::::: (zonal ::::: wind) :::: and ::::::::::::::: October/November :::::::::::: (temperature). The change in amplitude is enormous, considering that the GW forcing was only increased by 5% in each time step. However, the overall change in the forcing locally amounts to +500% (in the heating due to GWs, see Fig.2b) and to almost +1800% (in the zonal GW drag, see Fig.2h), which is possibly due to feedback mechanisms within the model that also influence the background conditions 15 and GW propagation conditions. Therefore, the dramatic increase in TDT amplitude can be partly explained by the strongly enhanced GW forcing. Furthermore, the TDT amplitude changes are considerably strong above 100 km, which coincides with the fact that the terdiurnal zonal GW drag maximizes in the thermosphere (Fig.2).
The differences of the zonal mean zonal wind and zonal mean temperature are shown in Fig. 4, each for January and April conditions ::: (for :::: July :::: and ::::::: October ::::::::: conditions ::: see :::: Fig. ::: S5). We only show the differences between GW5 and GWF, and 20 not between NL5 and NLIN because the latter ones are small. It can be seen in Fig. 4 that the terdiurnal GW forcing only affects the thermosphere. Below 130 km, the thermosphere experiences a cooling and above that height, there is a warming : , :: in :::::::: particular :::::: during :::: April : (Fig. 4b,d). This respective cooling and warming is larger in April than in January. The zonal wind during January (Fig. 4a) is mainly accelerated in the eastward direction, with a maximum at low and middle latitudes of the NH above 130 km. As a result, the westerly winds in that region are slightly enhanced by about +4 :: +3 m s −1 . During April, 25 the zonal wind in the thermosphere is generally small. The enhanced GW forcing leads to an alternating pattern of eastward and westward directed acceleration with a magnitude of about ±5 m s −1 , again with maxima in the NH. The magnitude of the cooling/warming of the thermosphere strongly depends on the strength of the terdiurnal GW forcing, i.e. it becomes stronger for stronger enhancements (not shown here). Figure 5 shows the behavior of TDT amplitudes depending on different factors of forcing enhancements where a factor 30 of 1.05 refers to an increase by 5%. Figure 5a,b refer to an increase of the terdiurnal nonlinear forcing in steps of 10% enhancement, and Fig. 5c,d refer to an increase of the terdiurnal GW forcing in steps of 1%. The amplitude response is shown for the temperature (Fig. 5, top row) and the zonal wind component (Fig. 5, bottom row). The different colors refer to different months of the year 2000 and the relative amplitude change is globally averaged ::::::::: (horizontal ::::: mean :::::: vertical :::::: mean) for a height range of 80 to 160 km.

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7 For the increased nonlinear forcing (Fig. 5a,b), a linear fit is added where each fit has a squared correlation coefficient R 2 > 0.99 and the respective slopes :: (s) are given in the legend. They are close to 1, suggesting that the amplitude is directly correlated with the factor of increase in the nonlinear forcing. However, this does not mean that the total observed amplitude in the REF simulation is increased by the same factor. The increase in amplitude only refers to the pure nonlinear part of the TDT. Due to the fact that the nonlinear TDT is much weaker than the solar TDT, its overall impact is rather small.

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Instead of the slopes, we show the correlation coefficients for the linear fits in the legend of Fig. 6a,b. These are close to one for most of the months, except for June to August (for zonal mean temperature) and for June to September (for zonal mean zonal wind). However, the overall impact of nonlinear forcing mechanisms on the background circulation is small as global mean differences amount to less than 0.5K and 0.5 m s −1 , respectively.
Again, the response is much more relevant, when the GW forcing is increased (Fig. 6c,d). The temperature reveals an 15 exponential-like increase in absolute temperature change where an increase by 10% can change the zonal mean temperature above 80 km by more than 50 K on a global average and the zonal mean zonal wind by about 2 to 6 m s −1 . The maximum temperature change is found in the thermosphere as shown in Fig. 4. To give an example, an increase of the GW forcing by 10% in January leads to a temperature decrease of about 10 K in the mesosphere (about 110 km altitude). The patterns of the differences are in this case similar to those shown in Fig. 4. In the thermosphere, the temperature is drastically increased by up 20 to 140 K near the upper boundary of the model.

Conclusions
Based on the experiments by Lilienthal et al. (2018), we performed extended simulations of the terdiurnal solar tide using a mechanistic global circulation model. Besides the primary forcing, which is the absorption of solar radiation in the lower atmosphere (Chapman and Lindzen, 1970;Andrews et al., 1987), further possible sources of atmospheric tides are nonlinear 25 tidal interactions (e.g., Glass and Fellous, 1975;Teitelbaum et al., 1989) and gravity wave-tide interactions (e.g., Miyahara and Forbes, 1991;Ribstein and Achatz, 2016).
In order to separate the forcing mechanisms, we performed simulations in which we kept only one of these forcings and removed the other sources. As a result, these simulations allowed us to show the amplitudes of the TDT based on each excitation mechanism, separately, and we found that the global structure of the simulated TDT (REF simulation) is in good 30 accordance with measurements in the MLT. Furthermore, the pure solar forcing (SOL simulation) explains most of the TDT global structure. This, in combination with the small TDT amplitudes of NLIN and GWF, indicates that the direct solar heating is the most important excitation mechanism of the TDT. Nonlinear tidal interactions only play a role during local winter at midlatitudes above 100 km and during equinoxes above 140 km. GW-tide interactions mainly appear in the thermosphere with maxima during NH summer and during equinoxes above the equator.
The influence of the nonlinear tidal and GW-tide interactions on TDT amplitudes and on the zonal mean circulation was investigated based on a sensitivity study with enhanced terdiurnal forcing terms. Each simulation represented a certain factor of increase and we focused on the 5% increased simulation which was the best compromise between significant changes in the 5 atmosphere and numerical stability of the simulations. Our main results are the following: -There is a direct and linear relationship between the nonlinear tidal forcing and the TDT amplitudes, but its influence on the zonal mean circulation is small.
-The influence of GW-tide interactions is more irregular with respect to the TDT amplitude, indicating that GW can play an important role for TDT forcing when the conditions for GW-tide interactions are favorable, especially in the 10 thermosphere (e.g. Yiǧit et al., 2008). Lilienthal et al. (2018) have shown that terdiurnal zonal GW drag is large in the thermosphere and this may also cause the large TDT amplitudes.

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To conclude, modifications of terdiurnal forcing mechanisms do not only have an effect on TDT amplitudes but they may also influence the background circulation, especially with respect to the terdiurnal GW drag. Since tidal forcing in a real atmosphere is not as regular as in our model, such interactions may play an important role for the vertical coupling of the atmosphere. Our simulations also demonstrate the importance of GW-tide interactions and their consideration in global circulation models.