To investigate gravity wave (GW) perturbations in the
midlatitude mesopause region during boreal equinox, 433 h of continuous
Na lidar full diurnal cycle temperature measurements in September between
2011 and 2015 are utilized to derive the monthly profiles of GW-induced
temperature variance,

Gravity wave (GW) forcing and its associated spatial and temporal spectrum within the mesosphere/lower thermosphere (MLT) are the key parameters for understanding the energy and momentum transfers between the lower and upper atmosphere GWs (Fritts and Alexander, 2003). GWs also play critical roles in various coupling processes between neutral atmosphere and the ionosphere (Vadas and Liu, 2013; Liu and Vadas, 2013). Mainly generated in the troposphere by orography, convection, and jet-front systems, the GWs propagate upward and horizontally throughout the atmosphere. Due to conservation of wave energy density, the wave amplitudes increase as they propagate into higher altitudes to compensate for the decreasing air density, until they become unstable and break mostly in MLT region.

Based on Ern et al. (2004), GW potential energy density (PED) is directly
related to the GW momentum flux (MF) and the associated body forcing on the
mean flow. Indeed, Yuan et al. (2016) successfully derived the momentum flux
of a GW packet through this approach by using the coordinated observations
from the Na lidar and a co-located mesospheric temperature mapper (Pautet et
al., 2014). The calculation of PED requires precise measurements of both
slow varying background temperature modulated by large-scale tidal waves and
the GW-induced temperature perturbations through carefully de-trending of
the data. So far, experimental investigations on GW perturbations and
dynamics have mostly focused on nocturnal small-scale individual events with short
periods (Bossert et al., 2015; Fritts et al., 2014; Cai et al., 2014; Yuan
et al., 2016). Except for a few studies in the polar region, long-period
large-scale GWs, especially inertia GWs, which play critical roles in MLT
dynamics, are not well studied, leaving contributions from most of these
waves unchecked. The ground-based experimental studies on climatological GW
perturbations (Gardner and Liu, 2007; Rauthe et al., 2006, 2008) have been
limited to nocturnal observations as well with various de-trending
algorithms developed, trying to remove tidal biases from the measurements.
At the same time, several bandpass filter techniques are also be attempted
and utilized in similar GW investigations. However, it is quite difficult to
set the frequency range to cover the whole GW temporal spectrum, because
some inertia GWs can have quite low frequencies that are close to those of
tidal waves (diurnal tide excluded). For example, the GW inertial period is
18.44 h at Utah State University (USU) based on the inertial frequency

In this paper, we utilize the full diurnal cycle temperature observations (a total of 433 h) in the month of September between 2011 and 2015, taken by the USU Na lidar, to calculate the monthly temperature variance and PED during boreal autumnal equinox in the midlatitude mesopause region. Here we develop a new algorithm to de-trend and remove the tidal bias in the lidar temperature measurements. To evaluate this new algorithm, we introduce the latest Whole Atmosphere Community Climate Model (WACCM) mesoscale simulation results (Liu et al., 2014), which generate global distribution and variations in GW. This new and unique study covers the GW spectrum up to inertia period, providing the most comprehensive large-scale GW results from ground-based observations. As the only investigation of this kind based on full diurnal cycle observations, these results could be utilized to evaluate the current effort of GWs simulations from all whole-atmosphere general circulation models, such as WACCM (Garcia et al., 2007), that can simulate GW impacts and evolution from the surface up to the lower thermosphere.

The USU Na lidar is a narrowband resonance fluorescence Doppler lidar system
operating at the Na D

WACCM is a comprehensive numerical model covering the altitude range between the surface and thermosphere. It uses the National Center for Atmosphere Research (NCAR) Community Earth System Model (CESM) as a common numerical framework (Garcia et al., 2007). Liu et al. (2014 and the references within) developed a high-resolution WACCM run based on the framework of WACCM version 5 and simulated GW activity in mesoscale globally from the troposphere to the lower thermosphere.

The lidar data are first processed with 1 h temporal resolution and
smoothed vertically through a moving 2 km FWHM
Hanning window. The temperature measurements with uncertainty equal or
larger than 15 K are treated as bad data. There are a total of 433 h of
continuous full diurnal cycle lidar data at USU involved in this study.
These September data include 116 h in 2011; 73 h in 2012, with one gap
of less than a day; 64 h in 2013; 89 h in 2014; and 91 h in 2015.
The WACCM temperature simulations included in this study are from 1 to 10 September at 41

From Ern et al. (2004), the PED can be calculated as follows:

To calculate GW-induced temperature perturbations at each lidar-measured
altitude, the slowly varying background temperature,

Figure 1 shows an example of this new method of determining the GW-induced
temperature perturbations based on a Na lidar campaign from UT day of year
(DOY) 252 to 255 (9 to 12 September) in 2015. Figure 1a is the
comparison between the hourly lidar temperature measurements and the
reconstructed slow varying background temperature,

Figure 2 indicates the monthly averaged temperature variance profiles (Fig. 2a)
and PED profiles (Fig. 2b) derived from this LSF algorithm. On the other
hand, to investigate the differences between these full diurnal cycle
results and those based solely upon nocturnal lidar measurements, we
reprocess the USU Na lidar nighttime data between 02:00 and 12:00 UT by
following the algorithm presented by Gardner and Liu (2007). In this
algorithm, the lidar-measured temperature variations at each lidar altitude
during the whole night are linearly fitted to a straight line to calculate
the background temperatures,

The 5-year USU Na lidar September monthly climatology of

WACCM results of

Lomb spectra power of the lidar-measured temperature perturbations during each of the six lidar campaigns in September between 2011 and 2015. The DOY of each campaign is listed in the parentheses. Only components with significant level larger than 50 % are plotted.

To evaluate this new LSF algorithm described above and see whether the
deduced GW perturbations can precisely represent those of the whole large-scale GW temporal spectrum, we introduce the latest high-resolution WACCM
simulations in September that are able to simulate global GW distribution
and variations. Here the WACCM data are processed in two completely
different approaches and two sets of GW perturbation results are generated.
The first approach is to process WACCM's high-resolution outputs at the USU
location with the same LSF tidal fitting algorithm discussed above,
generating background

As shown in Fig. 2a and b, the derived lidar temperature variance and PED
profiles for September share very similar vertical structure within the
mesopause region between 84 and 99 km. The errors represent the averaged
goodness of fit (chi-square divided by the difference between the numbers of
sampling and fitting parameters) in the temperature variance,

Although

Compared to the LSF results with those based on nocturnal data using NLF
algorithm, there are considerable differences below around 90 km in the
lidar results, shown in Fig. 2. For example, near 86 km, the results deduced
from NLF are

To validate the new LSF algorithm and the associated GW results above, we
present the two kinds of profiles derived from WACCM data using the two
completely different algorithms mentioned in the previous Section. Figure 3a
shows the mean temperature

Figure 4 illustrates the Lomb spectrum power for the temperature
perturbations during each of the lidar campaigns in September between 2011
and 2015. The lidar temperature perturbations are derived from the
aforementioned LSF tidal removal algorithm. Here, only modulations with
significance level larger than 50 % are shown. The figure shows the
dominance of long-period large-scale GWs' modulations in the mesopause
region with periods between 3 and 5 h during almost all of the six
campaigns, except the campaign during DOY 251 and 253 in 2012. This
indicates that the GW perturbations in the mesopause region are mostly generated
by this part of the GW spectrum during autumnal equinox around midlatitudes. To
confirm this conclusion, we re-analyzed the lidar data with 15 min
resolution and conducted the same LSF algorithm. This extends the highest GW
frequency in this study from the current 0.5 to 2 h

By applying a newly developed LSF tidal removal algorithm to the unique full
diurnal cycle Na lidar observations at USU in September between 2011 and
2015, the monthly averaged profiles of temperature variance and the
associated PED induced by the large-scale GWs are derived in the mesopause
region during the boreal autumnal equinox near midlatitudes. The study
covers the GW spectrum from 2 h up to the inertia period, providing the
most comprehensive large-scale GWs results in MLT. It reveals a “node”
structure near the middle of mesopause region in both profiles, decreasing
GW modulations between 84 and 90 km, but a reversed trend above 90 km,
where temperature variance increases from its minimum of less than 20 K

To validate this new algorithm for de-trending lidar measurements, the
latest high-resolution simulation results from NCAR WACCM are introduced.
Besides applying the same LSF tidal removal approach on the WACCM data at the
USU location, we also apply a spatial zonal wavenumber removal algorithm
to the WACCM data of all longitudes at 41

The lidar data of this study are available at the CRRL Madrigal database (2017) at

The authors declare that they have no conflict of interest.

This study was performed as part of a collaborative research program supported under the Consortium of Resonance and Rayleigh Lidars (CRRL), National Science Foundation (NSF) grant AGS-1135882. Han-Li Liu's effort is partially supported by NSF grant AGS-1138784. The National Center for Atmospheric Research is sponsored by the National Science Foundation. The topical editor, K. Hosokawa, thanks one anonymous referee for help in evaluating this paper.