A new method of obtaining power spectral distribution of gravity waves as a function of ground-based horizontal phase speed and propagation direction from airglow observations has recently been proposed. To explain gravity wave power spectrum anisotropy, a new gravity wave transmission diagram was developed in this study. Gravity wave transmissivity depends on the existence of critical and turning levels for waves that are determined by background horizontal wind distributions. Gravity wave transmission diagrams for different horizontal wavelengths in simple background horizontal winds with constant vertical shear indicate that the effects of the turning level reflection are significant and strongly dependent on the horizontal wavelength.

An airglow imager is a unique instrument that can detect the horizontal
structures of gravity waves around the mesopause region with high temporal
and horizontal resolutions (i.e.

Matsuda et al. (2014) proposed a new method (hereafter, Matsuda's method) to
obtain a power spectral distribution of gravity waves as a function of
ground-based horizontal phase speed and propagation direction from airglow
data. They applied a three-dimensional (i.e. zonal, meridional and temporal)
fast Fourier transform (3-D FFT) to the airglow emission intensity data at
Syowa Station, Antarctica (69

Gravity waves observed by airglow imagers generally have short horizontal wavelengths (i.e. < 100 km) and propagation times shorter than a few hours from the troposphere up to the mesopause region (e.g. Stockwell and Lowe, 2001). Thus, it is often assumed that the propagation times and horizontal propagation distances of gravity waves during their vertical propagation from a source region up to the mesopause are small such that temporal and horizontal changes of the background horizontal winds can be ignored. Based on this assumption, using a vertical distribution for the background horizontal winds, Taylor et al. (1993) introduced a critical level blocking diagram that represents a restricted region of gravity wave propagation from the source region up to the mesopause due to critical level filtering. Gravity waves with ground-based horizontal phase speeds and propagation directions within this restricted region would encounter the critical level during their upward propagation and thus would be unable to reach the mesopause region. Such blocking diagrams enable assessment of whether the power spectrum anisotropy is due to critical level filtering.

Gravity wave reflection at a turning level has never been considered in previous studies using airglow data. This is probably because the horizontal wavelength of a gravity wave is required to determine its turning level in addition to the background horizontal winds. However, the horizontal wavelength can be obtained using the 3-D FFT in Matsuda's method, which makes it possible to seek the turning level of the wave. A gravity wave transmission diagram, which represents a restricted region of gravity wave propagation due to critical level filtering and turning level reflection, is presented in this article. The relative effects of critical level filtering and turning level reflection on the vertical propagation of gravity waves from their source region to the mesopause are also demonstrated. The effects of additional critical level filtering, which would occur before the intrinsic horizontal phase speed of the wave becomes zero, are also discussed.

The theoretical backgrounds of the critical and turning levels are described in Sect. 2. Section 3 shows how a restricted region of gravity wave propagation due to critical level filtering and turning level reflection could change in relation to the horizontal wavelength of a wave under simple background horizontal wind conditions. The applicability of the gravity wave transmission diagram is discussed in Sect. 4. Concluding remarks are given in Sect. 5.

Vertically propagating gravity waves are absorbed at a critical level at
which the background horizontal wind speed component parallel to a
horizontal wavenumber vector is equal to the ground-based horizontal phase
speed of the wave (Booker and Bretherton, 1967). In other words, the
intrinsic horizontal phase speed of the wave becomes zero at the critical
level. This intrinsic horizontal phase speed is given by

When a vertical distribution of background horizontal winds is given, Eq. (

An intrinsic horizontal phase speed of zero, which is generally used as the
definition of the critical level, corresponds to a zero intrinsic wave
frequency. However, from the dispersion relation of inertia–gravity waves
given by

In linear theory, all waves are absorbed and their vertical wavelengths
become infinitely small at the critical level defined in Sect. 2.2;
however, the waves are totally reflected at the height at which

Matsuda et al. (2014) extracted gravity waves with horizontal wavelengths
(

The buoyancy frequency squared, which is used in the subsequent analysis, is
taken to be

When background horizontal winds and a horizontal wavelength of the wave are
given, gravity wave transmissivity is obtained as follows: first, the
intrinsic horizontal phase speed (

Figure 1a–e show transmission diagrams for gravity waves with

Gravity wave transmission diagrams for gravity waves
propagating to the mesopause region with

The red shaded regions in Fig. 1a–e represent the restricted vertical
propagation of gravity waves due to additional critical level filtering
(outlined in Sect. 2.2). As

The blue shaded regions in Fig. 1a–e represent the restricted vertical
propagation of gravity waves due to turning level reflection (outlined in
Sect. 2.3). Turning level reflection occurs where the magnitude of the
intrinsic phase speed of the wave is larger than the threshold value given
in Eq. (

Same as Fig. 1 except for

Figure 2a–e present transmission diagrams for gravity waves with

Transmission diagrams for gravity waves with

The ground-based horizontal group speed for gravity waves with medium
frequency (i.e.

Gravity wave transmission diagrams in simple background horizontal winds
with constant vertical shear showed the following:

Gravity waves with

Gravity waves with

Gravity waves with

Same as Fig. 1 except for

In principle, the gravity wave transmission diagram can be applied to
gravity waves with long horizontal wavelengths such as

A ray tracing theory has also been used to describe the horizontal and vertical propagation of gravity waves given varying background horizontal winds (Lighthill, 1978). The effects of planetary waves and tides on gravity wave propagation have been studied by Senf and Achatz (2011) and Kalisch et al. (2014) using ray tracing models. As the ray tracing of gravity waves provides accurate and realistic trajectories of the gravity wave packets, it should be explored if possible. However, ray tracing calculations require 3-D horizontal wind and temperature distributions throughout the calculation period. Generally, such data are not available near the mesopause, except in general circulation models. Thus, the gravity wave transmission diagram used in this study remains useful for the interpretation of gravity waves observed by airglow imagers, even if it assumes that the gravity waves only propagate vertically.

Gravity waves with relatively short horizontal wavelengths (i.e. < 100 km) near the mesopause have been studied using airglow imagers. Recently, a new statistical method of obtaining the gravity wave power spectrum as a function of ground-based horizontal phase speed and propagation direction using airglow imager data was proposed (Matsuda et al., 2014). The gravity waves observed around the mesopause generally originate at lower altitudes, and these waves are affected by various processes such as critical level filtering, turning level reflection and turbulent and radiative dissipation during their upward propagation. A critical level blocking diagram, which considers the effects of critical level filtering, has been used to explain the gravity wave statistics observed by airglow imagers (Taylor et al., 1993; Stockwell and Lowe, 2001). However, the effects of turning level reflection have never been considered in such accounts. This report proposed a gravity wave transmission diagram that considers the effects of both critical level filtering and turning level reflection.

Transmission diagrams for gravity waves propagating to the mesopause region
with different horizontal wavelengths and starting heights in simple
background horizontal winds were presented in this study. In previous
studies, critical level filtering has been taken into account for gravity
waves with the same sign for their ground-based and intrinsic horizontal
phase speeds. However, this study demonstrated that gravity waves with
opposite signs for their ground-based and intrinsic horizontal phase speeds
could reach the mesopause region when the gravity waves were emitted in the
stratosphere and mesosphere. Although the effects of additional critical
level filtering at

The effects of turning level reflection on gravity wave transmissivity were
observed to depend considerably on the horizontal wavelength of the gravity
waves. While most gravity waves with

The author thanks T. Nakamura, M. Tsutsumi, M. K. Ejiri, T. Nishiyama
and T. S. Matsuda for their helpful comments. Figures were drawn using
Dennou Club Library (DCL). The author would like to thank Enago
(