PUBLISHED VERSION
Allen, Simon J.; Vincent, Robert Alan.
Gravity wave activity in the lower atmosphere: Seasonal and latitudinal variations, Journal
of Geophysical Research, 1995; 100 (D1):1327-1350.
Copyright © 1995 American Geophysical Union
http://hdl.handle.net/2440/12556
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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 100, NO. D1, PAGES 1327-1350, JANUARY 20, 1995
Gravity wave activity in the lower atmosphere'
Seasonal and latitudinal variations
Simon J. Allen and Robert A. Vincent
Department of Physics and Mathematical Physics, University of Adelaide, Adelaide, South
Australia
Abstract. A climatology of gravity wave activity in the lower atmosphere based
on high-resolution radiosonde measurements provided by the Australian Bureau of
Meteorology is presented. These data are ideal for investigating gravity wave activity
and its variation with position and time. Observations from 18 meteorological
startions within Australia and Antarctica, covering a latitude range of 12øS - 68øS
and a longitude range of 78øE - 159øE, are discussed. Vertical wavenumber power
spectra of normalized temperature fluctuations are calculated within both the
troposphere and the lower stratosphere and are compared with the predictions of
current gravity wave saturation theories. Estimates of important model parameters
such as the total gravity wave energy per unit mass are also presented. The vertical
wavenumber power spectra are found to remain approximately invariant with time
and geographic location with only one significant exception. Spectral amplitudes
observed within the lower stratosphere are found to be consistent with theoretical
expectations but the amplitudes observed within the troposphere are consistently
larger than expected, often by as much as a factor of about 3. Seasonal variations
of stratospheric wave energy per unit mass are identified with maxima occurring
during the low-latitude wet season and during the midlatitude winter. These
variations do not exceed a factor of about 2. Similar variations are not found in
the troposphere where temperature fluctuations are likely to be contaminated by
convection and inversions. The largest values of wave energy density are typically
found near the tropopause.
1. Introduction
It is now well appreciated that gravity waves play
a crucial role in determining the circulation and mean
state of the atmosphere. If wave effects are to be fully
understood and modeled then more information on the
geographic and seasonal variations of wave activity and
on wave sources is needed.
A wide variety of observational techniques have been
used to study mesoscale fluctuations in the lower and
middle atmospheres and their variations in time and
space. These include balloon soundings [e.g., Fritts et
al., 1988; $idi et al., 1988; Kitamura and Hirota, 1989;
Cot and Barat, 1990; Tsuda et al., 1991], radar observa-
tions [e.g., Tsuda et al., 1989; Fritts et al., 1990], rock-
etsonde measurements [e.g., Dewan et al., 1984; Hamil-
ton, 1991; Eckermann et al., 1994], and lidar studies
[e.g., Wilson et al., 1991; $enfi et al., 1993].
To date, much of our detailed knowledge of wave
sources and effects in the lower atmosphere has come
from ground-based wind-profiling radar studies [e.g.,
Eckermann and Vincent, 1993]. Instrumented corn-
Copyright 1995 by the American Geophysical Union.
Paper number 94JD02688.
0148-0227/95/94J D-02688 $05.00
mercial aircraft observations made in the troposphere
and lower stratosphere during the Global Atmospheric
Sampling Program also provided important information
about wave fluxes over varying terrain and source re-
gions [Nastrom and Fritts, 1992; Fritts and Nastrom,
1992]. While aircraft measurements provide coverage
over both continental and oceanic regions, radar and
lidar observations are primarily confined to land-based
sites, except for a few ship-borne lidar measurements.
Despite the excellent temporal resolution of the ground-
based instruments it is unlikely that there will be suf-
ficient numbers of such instruments deployed to enable
wave climatologies to be established on a global scale,
especially in the southern hemisphere.
Despite the large number of observational studies,
certain theoretical questions remain unresolved. Ini-
tially, the debate was centered upon the relative impor-
tance of gravity waves as compared with two-dimension-
al turbulence in forming the fluctuations observed in
the atmosphere. Dewan [1979] and VanZand! [1982]
argued for a gravity wave interpretation, suggesting
that mesoscale fluctuations are the direct result of a
superposition of many gravity waves. However, Gage
[1979], Lilly [1983], and Gage and Nastrom [1985] ar-
gued that two-dimensionM turbulence is the main cause
of mesoscale fluctuations. It is likely that both waves
and stratified turbulence are present in the atmosphere,
1327
1328 ALLEN AND VINCENT: GRAVITY WAVES IN THE LOWER ATMOSPHERE
although it is now widely accepted that gravity wave
motions are dominant [e.g., Vincent and Eckermann,
19901.
Recently, debate has focused upon the physical pro-
cess apparently acting to limit wave amplitude growth
with height. A common feature of many experimental
studies is approximately invariant vertical wavenumber
and frequency power spectra, despite the exponential
decrease of density with height, and regardless of sea-
son and geographic location. This feature, first recog-
nized by VanZandi [1982] and based on similar stud-
ies of oceanic gravity wave power spectra, led to the
concept of a "universal" spectrum of atmospheric grav-
ity waves with amplitudes constrained to remain below
some fixed value. Several saturation theories have since
emerged [Dewan and Good, 1986; Smith et al., 1987;
Weinstock, 1990; Hines, 1991].
Each theory proposes a physical mechanism thought
to be responsible for limiting wave amplitude growth
and each predicts, approximately, the saturated vertical
wavenumber power spectrum amplitudes that should be
observed. However, due to theoretical uncertainties in
the various proposed mechanisms, it has proven difficult
to distinguish between them on the basis of spectral am-
plitude calculations alone. The question of which phys-
ical mechanism is acting at high vertical wavenumbers
is still, very much, an open one. It seems likely that
the successful theory will best account for some of the
more unusual experimental findings such as recent lidar
measurements within the stratosphere [Hines, 1993].
Very recently, Fritts and VanZandi [1993] and Fritts
and œu [1993] developed a gravity wave parameteriza-
tion scheme which describes the influence of a broad
spectrum of waves on the mean state of the atmosphere.
The scheme is based on the concept of a "universal"
spectrum which is separable in frequency and vertical
wavenumber. Only a few parameters are required to
constrain this model and the scheme links the work of
theorists, who model large-scale motions in the atmo-
sphere, and experimentalists who use convenient ana-
lytical tools such as power spectrum analysis. However,
the extent to which wave activity and influence varies
with height, season, and geographic location is poorly
understood at present. Despite the constraining influ-
ence of the proposed saturation theories there still ex-
ists the possibility for significant variations in the .wave
field, both at low vertical wavenumbers and, in some in-
stances, at high vertical wavenumbers also. Quantifying
these variations is an important experimental problem.
Balloon-borne radiosonde soundings provide one po-
tentially important source of information on gravity
waves and their effects in the troposphere and lower
stratosphere. Early work by, for example, Sawyer [1961]
and Thompson [1978] provided evidence for large-scale
inertial waves in the lower stratosphere and more re-
cently, Kitamura and Hirota [1989] emphasized the im-
portance of radiosonde observations in their study of
inertial-scale disturbances over Japan. Radiosonde sou-
ndings are carried out daily on a world-wide basis, pro-
viding a wealth of information on winds, temperatures,
and humidity. One reason why radiosonde measure-
ments have been little used in wave studies is that mea-
surements are reported and archived at relatively in-
frequent height intervals, leading to poor height reso-
lution. Recently, however, the Australian Bureau of
Meteorology began routinely recording and archiving
high-resolution data from radiosondes, with pressure,
temperature and relative humidity measurements made
every 10 s, or about 50 m in altitude. These data are
ideal for investigations of wave energies and power spec-
tra in the troposphere and lower stratosphere.
The Australian soundings are taken once or twice per
day from stations whose locations vary from the tropics
to the Antarctic. The observations also cover a signifi-
cant spread of longitudes in the Australian sector. By
suitably combining measurements made at a. range of
longitudes in relatively narrow latitude bands it is pos-
sible to build up a climatology of wave activity which
is not biased by localized source effects, such as topog-
raphy. Here we explore the extent to which this ex-
tensive data set of high-resolution radiosonde measure-
ments can contribute to solving some of the problems
described above.
Section 2 of this paper details some background the-
ory as well as discussing the state of current saturation
models of temperature fluctuation spectra. In section 3
the radiosonde data set that was used, the analysis pro-
cedures that were employed, and the possible sources of
measurement errors are described. Vertical wavenum-
ber power spectra of normalized temperature fluctua-
tions are presented in section 4 as are estimates of the
total gravity wave energy density, E0, which is an im-
portant component of the Fritts and VanZandi [1993]
parameterization scheme. A discussion of the results is
given in section 5 followed by the conclusions in sec-
tion 6. The consequences of radiosonde temperature-
sensor response time with regards to measurement ac-
curacy are described in an appendix.
2. Gravity Wave Power Spectra Theory
Fritts and VanZandt [1993] (hereinafter referred to
as FV93) presented a model three-dimensional grav-
ity wave power spectrum which makes use of functional
forms of the one-dimensional vertical wavenumber and
frequency power spectra that are in good agreement
with experimental findings. They assumed a total en-
ergy spectrum that is separable in vertical wavenum-
ber, m, intrinsic frequency, w, and azimuthal direction
of propagation, •b, and is given by
where
E(•,w, O) = EoA(•)B(w)(I)(O) (1)
A(y) = Aoy•/ (1 + y•+t)
(2)
= (a)
and where /• = m/m,, m = 2•r/Az, Az is the vertical
wavelength, m, is the characteristic wavenumber (in
units of radians per second), E0 is the total gravity
ALLEN AND VINCENT: GRAVITY WAVES IN THE LOWER ATMOSPHERE 1329
wave energy per unit mass (energy density), A0 and B0
are defined by the normalization constraints of A(tt)
and B(w), the function (I>(•b) contains the dependence
on wave field anisotropy and the parameters s, t, and p
are to be determined by comparison with the slopes of
observed power spectra.
The quantity E0, an important parameter of the
FV93 formulation, is chosen in this paper as the mea-
sure for gravity wave activity. It is defined by
1
Eo - • + v '• + w '• + N2 (4)
whereu • v • andw •
, , are the zonal, meridional, and ver-
tical components of first-order wind velocity perturba-
tions, respectively, g is the acceleration due to gravity,
N is the Vaisala-Brunt frequency, • - T •/• is the nor-
malized temperature fluctuation, and T and T • are the
background and first-order perturbation of atmosphere
temperature, respectively. Strictly, measurements of
three component wind velocity and temperature are re-
quired to completely define E0. However, it is possible
to estimate this parameter from temperature measure-
ments alone by making use of the appropriate gravity
wave polarization equation and the three-dimensional
v t w t
model spectrum of FV93. This arises since u •, , ,
and • are all coupled to each other through gravity
wave polarization equations.
Consider the equation relating the three-dimensional
power spectrum of normalized temperature fluctuations
to that of total energy,
N •' (1 - f•'/w 2)
E½,(/•,w, 0) - g•. (1 - f2/N •) E(/u,w, O)
(5)
where f is the inertial frequency. This follows from
the equations presented by FV93 which in turn can be
derived from standard textbook formulations of the po-
larization equations, at least those involving the Boussi-
nesq approximation [e.g., Gossard and Hooke, 1975]. By
integrating both sides of (5) with respect to it, w, and •b
using (1), (2), (3), and the normalization condition for
(•(•b), namely, f0 • (•(•b)d•b- 1, the following equation
is derived relating the energy density E0 to the total
normalized temperature variance,
g2 i ½,2 (6)
Eo = N2 BoC•
where
i - fP+•
p + (7)
and where f = f/N, p is the slope of the one-dimension-
al frequency spectrum, and B0 is given by FV93. The
best estimate of p from the literature is 5/3 and this
value will be assumed hereinafter. In obtaining (6),
three assumptions have been made: first, the three-
dimensional energy spectrum is assumed to be separable
in rn, w, and •b; second, the one-dimensional frequency
spectrum is assumed to be of the form B(w) or w -p
where p is 5/3; third, the Boussinesq approximation is
assumed valid since this is used in obtaining (5). The
normalized temperature variance from a given height in-
terval is easily measured, and (6) will be used in a later
section to calculate the gravity wave energy density.
A more typical analysis of radiosonde temperature
measurements involves calculating vertical wavenum-
ber power spectra of normalized temperature fluctua-
tions. These, together with results derived from other
experimental techniques, provide a good picture as to
the nature and shape of vertical wavenumber gravity
wave fluctuation spectra. Generally, a high-wavenum-
her "tail" region, displaying a -3 power law form and
having approximately invariant spectral amplitudes, is
observed and this is separated from the low-wavenum-
her source-dependent region by the so-called charac-
teristic wavenumber m.. Spectral amplitudes in the
low-wavenumber region can increase with height but
must do so in accordance with wave action conserva-
tion. The typical observed shape is well represented by
the modified-Desaubies form, A(•u), first introduced by
VanZandt and Fritts [1989].
The spectral amplitudes of the high wavenumber
"tail" region have been predicted by several authors
on the basis of the physical mechanism thought most
important in causing gravity waves to saturate. When
theoretical uncertainties are taken into consideration,
however, these predictions are difficult to differentiate,
and for the purposes of this paper the saturation limit of
Smith et al. [1987] will be used as a convenient reference.
This limit is given below for the power spectral density
of normalized temperature fluctuations as a function of
inverse vertical wavelength,
N 4 1 1 1
E½,(1/A•) m 6g•. P (27r)-" (1/A•) a (8)
where A• is the vertical wavelength and, as before, p is
the slope of the one-dimensional frequency spectrum. In
their original paper, Smith et al. [1987] derived the sat-
uration limit for the specific case of a one-dimensional
vertical wavenumber power spectrum of total horizontal
wind velocity, which was assumed to take the form de-
fined by (2) with s = 0 and t = 3. Equation (8) follows
from this using a suitable polarization equation and as-
suming that the one-dimensional frequency spectrum is
given by B(w) or w-p [see Fritts et al., 1988].
The purpose of spectral analysis in this paper is not
so much to confirm the agreement between theory and
experiment, something that appears to have been ac-
cepted already, but rather to study how the shape and
amplitudes of vertical wavenumber power spectra can
vary with geographic position and time. The extent of
these variations is not well known at present and the
available data set of high-resolution radiosonde mea-
surements is ideal for addressing the problem. Details
of the experimental data that were used are provided in
the following section.
1330 ALLEN AND VINCENT: GRAVITY WAVES IN THE LOWER ATMOSPHERE
i i 1 •.O'E i 1 ,•OøE i I•O'E i '"'/' 1 ,•OøE i :
Figure 1. The geographic distribution of radiosonde stations used in the study. Davis (69øS,
78 øE), in Antarctica, is not shown.
3. Experimental Data and Analysis
Procedures
Radiosonde Measurements
The Australian Bureau of Meteorology launches one
or two radiosondes per day from 36 meteorological sta-
tions and has recently begun archiving these measure-
ments. Observations from 18 stations have been chosen
for use in this study and these are shown, with the ex-
ception of Davis (69øS, 78øE), in Figure 1. Pressure,
temperature, and relative humidity measurements are
recorded at 10-s intervals which correspond, approxi-
mately, to 50-m altitude intervals. Data were available
for at least a 1-year period (June 1991 to May 1992)
from all but two of the stations, Davis and Willis Is-
land. Only 10 months of data were available from these
sites.
Each meteorological station in Figure 1 makes use of
radiosondes manufactured by Vaisala Oy and the data
obtained were subjected to quality control procedures
developed by that company. These procedures include
removing suspect measurements and replacing them by
linear interpolation. A measurement is deemed to be
suspect if it does not satisfy certain rejection criteria
based on known physical constraints. In addition, the
raw measurements, made at approximately 2-s inter-
vals, are smoothed in order to obtain the 10-s "filtered"
data that are used here.
Temperature measurements are of particular interest
in this study. Figure 2 displays examples of temperature
profiles observed by radiosondes launched from Dar-
win (12øS, 131øE) and Davis (69øS, 78øE) during the
months of January and July. These examples are cho-
sen because of their extreme natures. The tropopause
over Darwin is typically found near 16 km, whereas the
same level over Davis occurs, on average, at about 9 km.
Typical tropopause levels from other locations tend to
fall between these heights. Notice that successive pro-
files, corresponding to a 12-hour delay between sound-
ings, have been displaced by 10øC. The data obtained
from other stations were not always at 12-hour inter-
vals, as indicated by these examples. From many sta-
tions, measurements from only one sounding per day
were available.
Vertical Wavenumber Power Spectrum Analysis
Radiosonde profiles of normalized temperature fluc-
tuations, 2•/, were spectrally analyzed in two altitude
intervals, usually between 2.0 and 9.0 km in the tropo-
sphere and 17.0 and 24.0 km in the stratosphere. How-
ever, at some stations slightly different height ranges
were used and these are listed in Table 1. Notice also
the shaded regions of Figure 2 which correspond to the
particular intervals used for the analysis of observa-
tions made at Davis and Darwin. The principal reason
for choosing these ranges was to ensure a stationary
power spectrum since, according to theory, the verti-
cal wavenumber power spectrum of normalized temper-
ature fluctuations is dependent upon N 4. Therefore
height regions in which the Vaisala-Brunt frequency is
approximately constant should be used.
Data segments for which continuous measurements
were unavailable throughout the entire height interval