Using a nonlinear mechanistic global circulation model we analyze the migrating terdiurnal tide in the middle atmosphere with respect to its possible forcing mechanisms, i.e., the absorption of solar radiation in the water vapor and ozone band, nonlinear tidal interactions, and gravity wave–tide interactions. In comparison to the forcing mechanisms of diurnal and semidiurnal tides, these terdiurnal forcings are less well understood and there are contradictory opinions about their respective relevance. In our simulations we remove the wave number 3 pattern for each forcing individually and analyze the remaining tidal wind and temperature fields. We find that the direct solar forcing is dominant and explains most of the migrating terdiurnal tide's amplitude. Nonlinear interactions due to other tides or gravity waves are most important during local winter. Further analyses show that the nonlinear forcings are locally counteracting the solar forcing due to destructive interferences. Therefore, tidal amplitudes can become even larger for simulations with removed nonlinear forcings.

Atmospheric waves such as solar tides play a crucial role in
the dynamics of the mesosphere and lower thermosphere (MLT) region. Tides are
global-scale oscillations with periods of a solar day (

Due to the fact that diurnal tides (DTs) and semidiurnal tides (SDTs) usually
have larger amplitudes than the harmonics of higher wave numbers or higher
frequencies, they have attracted more attention in the past and are therefore
relatively well understood. However, there are observations of terdiurnal
tides (TDTs) showing local amplitudes comparable to those of DTs during some
months of the year

Satellite observations have been used to analyze the TDT on a global scale

Modeling studies of the TDT are mainly concerned with the analysis of forcing
mechanisms

Another possible excitation source is gravity wave–tidal interactions

To summarize, there are only few modeling studies which address the forcing mechanisms of TDTs, and they do not provide a consistent perspective. Nonlinear interactions seem to play a tangible role in TDT forcing but to what extent is heavily under debate. To shed more light on this matter we have used a nonlinear global circulation model to explore this issue. To this end we performed model simulations with simultaneous nonlinear and solar terdiurnal forcing. Additional model experiments were undertaken, each with one of the forcing mechanisms switched off, in order to analyze TDT amplitudes due to each forcing, separately.

The paper is arranged as follows: the model and the numerical experiments are
described in Sect.

We use the nonlinear Middle and Upper Atmosphere Model (MUAM) to investigate
the forcing mechanisms of tides with wave number

The model has a horizontal resolution of

Gravity waves are calculated by an updated Lindzen-type parameterization

MUAM experiments analyzing TDTs have been performed by

In the configuration used here, the model incorporates a spin-up of

Overview on the different simulations.

Within the model there are three mechanisms that may excite TDTs: solar
heating, nonlinear interactions between tides, and gravity wave–tidal
interactions. The first, the diurnal variation of solar heating rates,
creates atmospheric tides self-consistently. This mechanism is known to be
the most important factor for the forcing of DTs and SDTs

In order to separate these different mechanisms we analyze the wave number

Note that the background (monthly mean zonal mean) circulation is not
significantly altered when TDT forcings are removed (not shown here).
Differences amount to not more than the actual standard deviations in the REF
simulation (Fig.

The parameterization of solar heating in the middle atmosphere is calculated
following

In the NO_SOL simulation, the total heating rate of all heating
contributions is analyzed using a Fourier transform to separate the tidal
components. For the analysis of the forcing mechanism we subtract the
wave number

In order to separate the nonlinear forcing we modify the nonlinear terms in
the tendency equations of the model

Linearizing these equations, i.e.,

The simulations NO_SOL and NO_NLIN are very similar to the approach
presented by

As a control simulation (CTRL), the wave number

In the following analysis, we focus on the months January and April to show solstice and equinox conditions. During this time, the TDT in MUAM is most prominent. Results for July and October are similar and therefore they are not shown here.

The REF simulation includes solar, nonlinear and gravity wave forcing for all
wave numbers. Therefore, it serves as a reference for all the experiments. The
following results are given as a mean of the

In Fig.

Comparing the MUAM climatology with empirical climatologies such as CIRA86

Terdiurnal component of thermal tendency terms in the REF simulation
for January conditions

Terdiurnal component of zonal and meridional wind acceleration terms
in the REF simulation for January conditions

We notice that the model produces small year-to-year variations below

Figures

Figure

Figure

Generally, direct solar forcing is weaker during April
(Fig.

Product of DT and SDT amplitudes, scaled by

As described above, the nonlinear terdiurnal forcing is a result of
interactions between the migrating DT and the migrating SDT. These
interactions can only take place if both DT and SDT have a considerable
amplitude. To test this relation between the different harmonics, the product
of DT and SDT amplitudes serves as a proxy for the terdiurnal nonlinear
forcing. Due to the fact that the forcing terms in Figure

Zonal mean TDT amplitudes (colors, REF).

It can be seen that the scaled product of DT and SDT amplitudes exhibits
similar structures to the nonlinear terdiurnal forcing terms in
Figs.

Zonal mean TDT phases (REF).

TDT amplitudes are presented for January (Fig.

However, considering only the maxima does not give a good comparison between
seasons, and the height-latitudinal structure is more important. Especially
in temperature (Fig.

The standard deviation of tidal amplitudes is relatively small, not more than

REF monthly mean TDT amplitudes at an altitude of

The TDT phases are shown in Fig.

Figure

The structure of MUAM temperature amplitudes is generally confirmed by SABER
measurements

Maxima in zonal wind (Fig.

Zonal and meridional amplitudes at midlatitudes (

Some differences between model results and satellite measurements may be explained by the orbit of the satellite passing high latitudes less frequently and leading to larger uncertainties at these latitudes. However, this cannot explain the large discrepancies in the magnitude of the TDT. Smaller model amplitudes may be due to processes that are not included in the simulations such as latent heat release.

As in Fig.

Zonal mean TDT phases (NO_SOL).

In order to determine the effect of each individual forcing on the amplitude
of the TDT we performed the simulations with different forcings switched off,
as listed in Table

Difference of TDT amplitudes between NO_NLIN and REF simulation.
Red colors denote larger NO_NLIN simulation amplitudes and blue colors
denote larger REF simulation amplitudes. Significant areas (

Difference of TDT amplitudes between NO_NLIN and REF simulation,
scaled by

NO_SOL represents a TDT that is only due to nonlinear and gravity wave
effects because wave number 3 direct solar heating is removed in the whole
model domain. Therefore, possible sources of this wave are nonlinear
interactions between other tides, i.e., between the DT and the SDT, and
gravity wave–tide interactions only. The resulting amplitudes and phases are
shown in Figs.

The simulation NO_NLIN only includes direct solar forcing and gravity
wave–tide interactions. Therefore, it does not include nonlinear
interactions. Figure

In April only weak enhancements of about

We do not show the phases of the NO_NLIN simulation and the NO_GW
simulation here because both of these simulations still include the solar
forcing which dominates the other remaining forcing. As a result, the phases
are almost identical to those shown in Fig.

In order to investigate the reason for the positive difference in amplitude
it is useful to compare phase shifts

Figure

Figure

As in Fig.

As in Fig.

The CTRL simulation provides a measure of TDT amplitudes due to effects that
have not been considered in the previous simulations. The presence of regions
of significant amplitude indicates that there still exist other sources in
the model. Figure

The results of our REF simulation present a climatology and structure of the
TDT that generally agrees with observations and earlier model studies. MUAM
produces relatively small amplitudes for the TDT, e.g.,

In contrast to reports by

MUAM simulations show strongest wind amplitudes at midlatitudes
(

The TDT in model simulations by

In order to investigate the different generation mechanisms of the TDT we
present their respective source regions. In addition to the methods used by,
e.g.,

Removing the direct terdiurnal solar heating leads to a significant decrease
in amplitude (see Fig.

Removing the nonlinear tidal interactions leads to an increase in amplitude
for some heights/latitudes during January by up to

Similar results are obtained when the terdiurnal gravity wave–tide interactions are removed but an increase in amplitude in this case is observed for both January and April conditions. Here, the zonal wind component is not affected by this positive amplitude change but temperature and meridional wind are.

This conclusion supports the results of

Finally, a control simulation (CTRL) tested the TDT amplitude when all three
forcings considered here are removed simultaneously to check whether there is
a remaining weak forcing that has not yet been considered. Amplitudes for
that simulation are relatively small (

In the future, it would be interesting to analyze non-migrating tides, as
well. To do this, we would need to include additional sources such as latent
heat release or 3-D ozone and water vapor

The MUAM model code can be obtained from the corresponding author on request.

FL designed and performed the MUAM model runs. CJ together with FL drafted the first version of the text. CJ and CG contributed to the analysis and interpretation of the results.

The authors declare that they have no conflict of interest.

This research has been funded by Deutsche
Forschungsgemeinschaft under grant JA 836/30-1. SPARC global ozone fields
were provided by William J. Randel (NCAR) through