This study evaluates commonly used methods of extracting gravity-wave-induced temperature perturbations from lidar measurements. The spectral response of these methods is characterized with the help of a synthetic data set with known temperature perturbations added to a realistic background temperature profile. The simulations are carried out with the background temperature being either constant or varying in time to evaluate the sensitivity to temperature perturbations not caused by gravity waves. The different methods are applied to lidar measurements over New Zealand, and the performance of the algorithms is evaluated. We find that the Butterworth filter performs best if gravity waves over a wide range of periods are to be extracted from lidar temperature measurements. The running mean method gives good results if only gravity waves with short periods are to be analyzed.

Atmospheric gravity waves are well known to have a strong impact on
the middle-atmospheric circulation

Lidar technology has been used to study gravity waves in the
middle atmosphere for the last 3 decades

Gravity waves are usually determined from lidar measurements
by separating an estimated background temperature (density)
profile from the measured profiles in order to derive
temperature (density) perturbation profiles. Several methods
have been developed and used over the last decades. For
example

All of these methods are most sensitive to different parts of
the gravity wave spectrum. Thus, results from different lidar
studies become hardly comparable because one cannot
distinguish between variations that are caused by a different
methodology and variations that are geophysically
induced.

To our knowledge, no literature is yet available which
characterizes and evaluates the most commonly used methods to
extract information on gravity waves from lidar
profiles. Thus, we will evaluate and compare four methods in
detail: subtraction of the nightly mean profile, subtraction
of temporal running mean profiles, the sliding polynomial fit
method proposed by

This paper is structured as follows: the four methods are
described in detail in Sect.

Lidar systems used for studies of the middle atmosphere measure the
Rayleigh backscatter signal which is proportional to atmospheric
density after range correction. The temperature is commonly retrieved by
integration assuming hydrostatic equilibrium

The combination with a resonance lidar system extends the altitude
range of temperature measurements up to

Lidar studies usually determine wave-induced temperature perturbations

The frequency range of gravity waves which may be present in

A widely applied method is the use of the nightly mean temperature
profile as a background temperature profile

Another common method is to determine background temperature
profiles by means of a running mean over a time window which is
typically on the order of 3 h

The sliding polynomial fit method was designed to produce
a background temperature profile which contains all perturbations
with vertical scales larger than 15 km. For each measured
temperature profile

Here

In this study the following set of parameters is used: a fit length

Another method which can be applied to vertical profiles is
spectral filtering

In this study we use a 5th-order Butterworth high-pass filter with
a cutoff wavelength

In order to characterize the different methods regarding their
ability to extract temperature perturbations from middle-atmospheric
temperature profiles, we apply them to a synthetic
data set with known temperature perturbations. These perturbations
are added to a fixed, realistic background temperature profile

Sinusoidal temperature perturbations with exponentially increasing
amplitude were added to the background temperature profile according to

For each method, the spectral response

All simulations conducted for this study use the realistic set of
parameters

As a first step, simulations were carried out with a constant
background temperature profile

Spectral response of different methods of determining temperature
perturbations as a function of vertical wavelength

The nightly mean method (Fig.

Same as Fig.

Figure

In the first simulation setup the vertical wavelength

Same as Fig.

While in the previous section the simulated background temperature
was kept constant, we now examine the influence of a time-dependent
variation of the background temperature on the different
methods. Slow variations of the form

Filter characteristics are shown for a varying vertical wavelength
in Fig.

The filters exhibit similar characteristics if the gravity wave
period is varied instead of the vertical wavelength. The nightly
mean method (Fig.

Rayleigh lidar measurements at Lauder, New Zealand,
(45.0

A detailed analysis with the four different methods of extracting
temperature perturbations is shown for the data set obtained on
23 July 2014 in Fig.

The main features of the mean temperature profile
(Fig.

The temperature perturbations as determined by the nightly mean
method (Fig.

The 3 h running mean method on the other hand
(Fig.

Same as Fig.

Temperature

The sliding polynomial fit method (Fig.

A quantity often used as a proxy for gravity wave activity is the
GWPED per mass:

From TELMA observations above New Zealand over the period 1 July
to 30 September 2014 we determined the mean GWPED per mass
using the four methods of gravity wave extraction discussed in this
study (Fig.

Mean gravity wave potential energy density (GWPED) per mass over
Lauder, New Zealand, (45.0

The nightly mean method has been applied in many studies

In practice measurement periods vary typically in length between
a few hours up to a whole night as weather conditions can change
rapidly during an observational period. Moreover, there is
a seasonal dependency because most middle-atmospheric lidars are
capable of measuring in darkness only. This results in shorter
measurement periods in summer and longer measurement periods in
winter. Hence, the nightly mean method is sensitive to different
parts of the gravity wave spectrum depending on weather conditions
as well as season. For example,

The use of the nightly mean method in gravity wave analysis is
further complicated by the fact that there are processes besides
gravity waves which occur on similar timescales. For example tides
with periods of 8, 12 and 24 h are within the sensitivity
range of this method. In the analysis of radar data, the removal of
tidal signals is a standard procedure

The running mean method

The beginning and the end of the measurement period pose an additional problem for the application of the running mean method. At the beginning of the measurement period, a centered running mean of 3 h lacks the first 1.5 h of observations necessary for determining the background temperature. Thus, if in the beginning of the measurement only 1.5 h of data are available for averaging, the spectral response differs at the beginning of the measurement period compared to later times when 3 h of measurements are available. The same is true at the end of the measurement period as well as in the presence of measurement gaps. Thus, when requiring the same spectral response at all times, the “spin-up” time of the running mean method would have to be discarded. However, this would result in a significantly reduced data set because one window width of data would have to be discarded from each measurement period, in addition to another window width for each measurement gap.

Note that the resolved high-frequency range of the gravity wave spectrum is limited by the sampling frequency of the lidar system which ranges typically between 10 min and 1 h, depending on lidar performance. This is a fundamental limitation to the extractable part of the gravity wave spectrum which affects all methods of extracting gravity-wave-induced temperature perturbations in the same way. The same holds true for the effective vertical resolution of the temperature profiles.

Filtering in the spatial domain, by using either the sliding
polynomial fit or the Butterworth filter, has the advantage that
the spectral response in the time domain is independent of the
length of the measurement period and the presence of measurement
gaps. This makes it possible to derive temperature perturbations
associated with gravity waves from observational periods which are
too short to yield meaningful results if temporal filtering methods
are applied. In addition, both spatial filtering methods are
capable of detecting waves with periods larger than 12 h
(Fig.

The sliding polynomial fit has been applied in several studies

The sliding polynomial fit method is sensitive to large changes of the temperature gradient and may falsely overestimate temperature perturbations for example in the presence of mesospheric inversion layers (not shown). The Butterworth filter tends to overestimate sudden changes in the temperature gradient of the measured temperature profile as well. However, the magnitude of the overestimation is generally lower than for the sliding polynomial fit method. Furthermore, the Butterworth filter has the advantage that it can be easily adjusted if a different cutoff wavelength is desired.

All the previously discussed characteristics influence the gravity
wave spectrum which is extracted from lidar temperature
measurements. This becomes visible if the mean GWPED of a set of
measurements is computed using different methods as shown in
Fig.

The fact that the Butterworth filter exhibits a lower growth rate
of GWPED compared to the running mean method (Fig.

We evaluated four commonly used methods of extracting gravity-wave-induced temperature perturbations from lidar measurements. A widely used method – the nightly mean method – relies on filtering in time by subtraction of the nightly mean temperature. Thus, it is sensitive to all temperature changes occurring on the timescale of the measurement period, including temperature changes induced by planetary waves and tides. Because measurement periods can vary substantially in length and the spectral response of the nightly mean method depends on the length of the measurement period, the extracted gravity wave spectrum can vary from observation to observation. This makes the nightly mean method an improper choice for compiling gravity wave statistics if a data set with a varying length of observational periods is analyzed.

The second method which relies on filtering in time, the running mean method, provides a more stable spectral response with regard to a varying length of the measurement period. However, it extracts only a small fraction of the gravity wave spectrum, with long-period waves being strongly suppressed. Moreover, the running mean method exhibits a variation in the spectral response at the beginning and end of a measurement period as well as in the presence of measurement gaps.

The sliding polynomial fit method is not only capable of extracting waves over a broad range of temporal scales but also suppresses tides and planetary waves due to their large vertical wavelengths. In addition, it is unaffected by measurement gaps. However, the parameters used for the sliding polynomial fit need to be adjusted to the altitude resolution of the measured temperature profiles in order to provide a flat spectral response in the passband.

The Butterworth filter provides an alternative to the sliding polynomial fit method which is not only easy to implement but also easily adjustable to a desired cutoff wavelength. Also, the filter is largely independent of the altitude resolution while providing all the advantages of the sliding polynomial fit method. Furthermore, sudden changes in the background temperature gradient affect the Butterworth filter less than the sliding polynomial fit method.

Based on the results presented here, two methods are recommended for gravity wave extraction from lidar temperature measurements covering a large altitude range: the running mean method is the most suitable method if the analysis is focused on short-period gravity waves with large vertical wavelengths. On the other hand, if a broad passband is desired which covers a large part of the gravity wave spectrum, the Butterworth filter is the method of choice. Additional advantages are the insensitivity to measurement gaps, a varying length of observational periods and the altitude resolution of the measured temperature profile.

We thank the NIWA personnel at Lauder station for their support during the DEEPWAVE measurement campaign. This work was supported by the project “Processes and Climatology of Gravity Waves” (PACOG) in the framework of the research unit “Mesoscale Dynamics of Gravity Waves” (MS-GWaves) funded by the German Research Foundation. The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association. Edited by: L. Hoffmann