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. Secondary sources are nonlinear tide–tide interactions and gravity wave–tide interactions. Thus, although the solar heating clearly dominates the terdiurnal forcing in our simulations, we find that nonlinear tidal and gravity wave interactions contribute in certain seasons and at certain altitudes. By slightly enhancing the different excitation sources, we test the sensitivity of the background circulation to 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 nonlinear tidal interactions on the middle atmosphere background dynamics is rather small.

The middle atmosphere dynamics are mainly determined by waves that are excited in the troposphere or stratosphere and propagate to the upper atmosphere

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

Amplitudes of diurnal tides (DTs) and semidiurnal tides (SDTs) are generally larger than those related to higher harmonics and wave numbers such as the terdiurnal tide (TDT).
However, during some seasons the TDT amplitudes may locally become comparable to those of the DT

While the excitation mechanism is relatively well known for the DT and SDT, those of the TDT are still under debate

The excitation mechanisms of the TDT have been investigated by several model studies

The majority of these publications agrees that the direct solar forcing is the most dominant, although not the only, excitation mechanism of the TDT

To extend the work of

In the following analysis we use the Middle and Upper Atmosphere Model (MUAM) in the same configuration as described in detail by

There are three main sources of atmospheric tides in the model.
The primary source is the absorption of solar radiation which creates tides in a self-consistent manner.
The solar heating is parameterized according to

Nonlinear interactions between different tides and between GWs and tides can generate a secondary TDT as described in Sect. 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

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

In order to quantify the relevance of these three mechanisms,

REF: reference run – this is the same simulation as that shown by

SOL: no nonlinear and GW forcing – TDT amplitudes are only owing to the absorption of solar radiation;

NLIN: no solar and GW forcing – TDT amplitudes are only owing to nonlinear tidal interactions;

GWF: no solar and nonlinear forcing – TDT amplitudes are only owing to GW–tide interactions.

In order to investigate the impact of these forcing mechanisms on the background circulation, we also enhance the respective remaining forcing in the SOL, NLIN, and GWF simulations, stepwise.
Therefore, each simulation represents a certain factor of enhancement.
Technically, this is the same procedure as that for the removal of terdiurnal forcing terms, except that the respective wave number

We present the latitudinal and vertical structure of the TDT for different forcing mechanisms (Fig.

Latitude–altitude distribution of January mean TDT amplitudes owing to different forcing mechanisms.

It is obvious that the SOL simulation (Fig.

The nonlinearly excited TDT (Fig.

On average, the amplitudes of the GWF simulation (Fig.

In this section we analyze the effect of each different forcing on the TDT as well as the background atmosphere. Therefore, the SOL, NLIN, and GWF simulations 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 in NLIN, and the GW forcing is enhanced in GWF. These respective enhanced simulations are called SOL5, NL5, and GW5.

Figure

Relative change of terdiurnal forcing terms for an implemented increase of

A possible reason for these large discrepancies are feedback mechanisms within the model.
It is widely known

Figure

Color plots: latitude–altitude distribution of TDT zonal wind

Contour lines: latitude–altitude distribution of zonal mean zonal wind

The zonal wind TDT amplitudes due to a

Normalized, horizontal mean vertical mean (80–160 km height range) TDT amplitudes for temperature

The differences of the zonal mean zonal wind and zonal mean temperature are shown in Fig.

Figure

For the increased nonlinear forcing (Fig.

The dependence of TDT amplitudes on the GW forcing (Fig.

Horizontal mean vertical mean (80–160 km height range) absolute change of zonal mean temperature

Again, the response is much more relevant, when the GW forcing is increased (Fig.

Based on the experiments by

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 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

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

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 GWs can play an important role for TDT forcing when the conditions for GW–tide interactions are favorable, especially in the thermosphere

There is an exponential-like relationship between the strength of terdiurnal GW–tide interactions and the zonal mean circulation in the thermosphere, which is cooled below

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. As 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.

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

The supplement related to this article is available online at:

FL designed and performed the MUAM model runs. FL and CJ wrote the first version of the text and discussed the results.

Christoph Jacobi is one of the editors in chief of

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.

SPARC global ozone fields are provided by William J. Randel (NCAR) at

This research has been supported by the Deutsche Forschungsgemeinschaft (grant no. JA 836/30-1).

This paper was edited by Petra Koucka Knizova and reviewed by two anonymous referees.