Ann. Geophys., 26, 3731–3739, 2008
www.ann-geophys.net/26/3731/2008/
© European Geosciences Union 2008
Annales
Geophysicae
Influence of gravity waves and tides on mesospheric temperature
inversion layers: simultaneous Rayleigh lidar and MF radar
observations
S. Sridharan1 , S. Sathishkumar2 , and S. Gurubaran2
1 National
Atmospheric Research Laboratory, Gadanki-517 112, Pakala Mandal, Chittoor, India
Geophysical Research Laboratory, Indian Institute of Geomagnetism, Krishnapuram, Tirunelveli-627 011, India
2 Equatorial
Received: 24 March 2008 – Revised: 20 October 2008 – Accepted: 21 October 2008 – Published: 25 November 2008
Abstract. Three nights of simultaneous Rayleigh lidar
temperature measurements over Gadanki (13.5◦ N, 79.2◦ E)
and medium frequency (MF) radar wind measurements over
Tirunelveli (8.7◦ N, 77.8◦ E) have been analyzed to illustrate
the possible effects due to tidal-gravity wave interactions on
upper mesospheric inversion layers. The occurrence of tidal
gravity wave interaction is investigated using MF radar wind
measurements in the altitude region 86–90 km. Of the three
nights, it is found that tidal gravity wave interaction occurred
in two nights. In the third night, diurnal tidal amplitude is
found to be significantly larger. As suggested in Sica et al.
(2007), mesospheric temperature inversion seems to be a signature of wave saturation in the mesosphere, since the temperature inversion occurs at heights, when the lapse rate is
less than half the dry adiabatic lapse rate.
Keywords. Atmospheric composition and structure (Pressure, density, and temperature) – Meteorology and atmospheric dynamics (Middle atmosphere dynamics; Waves and
tides)
1
Introduction
Temperature inversions have been ubiquitous features in the
mesosphere and lower thermosphere (MLT) region. They
have been studied by several authors in the past few decades
and most of the important findings are recently reviewed by
Meriwether and Gardner (2000) and Meriwether and Gerrard (2004). They are found to occur more frequently in
winter months at mid-latitudes (Leblanc and Hauchecorne,
1997) and in equinox months in low-latitudes (Siva Kumar
et al., 2001). The mid-latitude observations show that they
are longitudinally extended phenomena and are not local.
Correspondence to: S. Sridharan
(ssri dhar@rediffmail.com)
There are different schools of thought on how these inversions are formed. Whiteway (1995) suggested that the inversions could be formed due to turbulent mixing. Hauchecorne
et al. (1987) suggested that the inversions were due to gravity waves breaking within the inversion region for extended
periods. The peak altitudes of mesospheric inversion layer
(MIL) events will often show a downward phase progression
typical of the diurnal tide. States and Gardner (2000) showed
that the inversion layer could not be observed in the 24-h averaged sodium resonance lidar observations suggesting the
role of diurnal tide or its sub harmonics. However, the amplitude of mesospheric inversion is considerably greater than
tidal model predictions attributed to migrating tidal waves
alone. Both the NCAR general circulation model and the
Global Scale Wave Model predicted similar and smaller amplitudes than the observed. Meriwether et al. (1998) suggested that the enhancement of the MIL amplitude to temperatures considerably elevated above that represented by the
tidal structure alone may be indicative of dynamical forcing.
A possible source for this was suggested to be gravity waves
interacting with tidal wave activity. Liu et al. (2000)’s model
calculations showed that the breaking of a gravity wave with
a 50 km horizontal wavelength and a horizontal phase speed
of 30 ms−1 could cause downward propagating MIL. The
other possible mechanism for the occurrences of these inversions with large amplitudes could be due to chemical heating
through exothermic reactions as reported by Meriwether and
Mlynczak (1995).
Using coincident measurements with the MF radar and lidar at Western Ontario (42.9◦ N, 81.4◦ W), Sica et al. (2002)
observed that there are two type of inversions. The first type,
which persists for many hours, is associated with increased
gravity wave variance, as the magnitude of westward tide decreases. The second type of inversion persists for less than
2 h, but the increase in temperature, is much greater than
that expected from tidal dissipation. Using Canadian Middle
Published by Copernicus Publications on behalf of the European Geosciences Union.
3732
S. Sridharan et al.: Influence of gravity waves and tides on mesospheric inversion layers
atmosphere Model (CMAM), Sica et al. (2007) predicted that
the environmental lapse rate must be less than half the adiabatic lapse rate for an inversion to form, and it predicts the
ratio of the inversion amplitude and thickness as a function
of environmental lapse rate.
Though there have been a lot of studies on mesospheric
inversions (see review article by Meriwether and Gerrard,
2004), the formation mechanisms of the mesospheric inversions have not yet been understood. In the present
study, three nights of simultaneous measurements with the
MF radar zonal wind observations over Tirunelveli (8.7◦ N,
77.8◦ E) and Rayleigh lidar temperature observations over
Gadanki (13.5◦ N, 79.2◦ E) are presented and discussed to
illustrate the possible effects due to tidal-gravity wave interactions on upper mesospheric inversion layers. As suggested
by Sica et al. (2007), the mean temperature profiles are compared with the dry adiabatic lapse rate profiles to see whether
the condition “environmental lapse rate less than dry adiabatic lapse rate” is satisfied for the formation of mesospheric
inversion.
2
2.1
Data analysis
Rayleigh lidar temperature measurements
The Rayleigh lidar system at National Atmospheric Research Laboratory, Gadanki employs the second harmonic
of Nd:YAG pulsed laser at 532 nm with an energy of about
550 mJ at a pulse repetition rate of 20 Hz and a pulse width
of 7 ns. The Rayleigh lidar technique involves range resolved detection of molecular backscattered laser radiation
from altitudes above 30 km, where the atmosphere is free
from aerosols. The Rayleigh receiver employs a Newtonian
telescope of diameter 750 mm, detected by photo multiplier
and counted sequentially into successive 300-m range bins.
More details of this instrument and method of analysis can
be had from Siva Kumar et al. (2003). The four minute averaged photon count profiles were averaged for 30 min and
temperature and its standard error are determined using the
method given by Hauchecorne and Chanin (1980).
The relative density is calculated from the number of photons backscattered (N(z)), by a layer of thickness 1z at altitude z assuming (i) the scattering due to aerosols is negligible
compared to molecular scattering, (ii) the atmospheric transmission is constant throughout the entire zone and (iii) the
telescope field of view is large enough to include the entire
volume of the scattered beam, using the following relation
(Keckhut et al., 1993)
ρ(z) =
C(z − zo )2 N(z)
,
1z
where C is the normalizing constant, which is altitude independent and 1z is the vertical spatial resolution (300 m). The
constant C is determined by taking CIRA 86 model density
Ann. Geophys., 26, 3731–3739, 2008
values at 40 km and the absolute density profile is derived.
The uncertainty on the density profile is assumed to be equal
to the statistical standard error
|N (z) + Nm |1/2
δρ(z)
=
ρ(z)
N (z)
where δρ(z) is the standard deviation of atmospheric density and Nm is the background noise. All subsequent quantities are derived from the density profile and the corresponding error bars are calculated from Gaussian error propagation
(Schöch, 2007; Schöch et al., 2008).
The pressure profile is computed from the density profile
assuming the atmosphere to be in hydrostatic equilibrium.
The temperature profile T (zi ) is derived from pressure and
density profile assuming that the atmosphere obeys ideal gas
law and is expressed as:.
T (zi ) =
Mg(zi )1z
,
RLog(1 + X)
where
X=
ρ(zi )g(zi )1z
P (zi + 1z/2)
The statistical standard error on the temperature is
δ Log(1 + X)
δT (zi )
δX
=
=
T (zi )
Log(1 + X)
(1 + X)Log(1 + X)
with
2
δρ(zi )
δX
=
X
ρ(zi )
δP (zi +1z/2)2 =
2
+
n
X
2
δP (zi + 1z/2)
P (zi + 1z/2)
2
g(zj )δρ(zj )1z + |δPm (zn +1z/2)|2
j =i+1
P (zi + 1z/2) =
n
X
g(zj )ρ(zj )1z + Pm (zn + 1z/2),
j =i+1
where P (zi +1z/2) is the pressure at the top of the i-th layer
and Pm is the pressure of the topmost layer upto which density profile is calculated (90 km). The value of Pm is taken
from CIRA 86 model atmosphere.
The temperatures determined for every 30 min are averaged for the entire night and are further smoothed vertically
by 10 points (3 km) to obtain a mean temperature profile. Atmospheric internal gravity waves are observed in profiles of
fractional temperature perturbation, T ′ (z)/To (z), Perturbations, T ′ (z)=T (z)−To (z), are extracted from half-hour average temperature profiles by approximating an unperturbed
background state (Whiteway et al., 1995).
Profiles of mean square perturbations and available potential energy density are determined from the variance of temperature fluctuations. As done by Tsuda et al. (2000), the
variance T ′ (z)2 of the temperature fluctuations is calculated
from the series of half-hour averaged temperature profiles
obtained on a given night as
Z Z max
1
′
T 2 dz
T ′ (z)2 =
Zmax − Zmin Z min
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S. Sridharan et al.: Influence of gravity waves and tides on mesospheric inversion layers
3733
Fig. 1. (a) Sequence of altitude profiles of temperature (top left), (b) temperature profiles averaged for the first and second half of the
observation period (bottom left), (c) contour plot showing temperature perturbations from the night mean profile (top right) and (d) time
variation of potential energy averaged for 60–70 km, 70–80 km and 60–80 km for 21–22 October 1998 (bottom right).
As suggested in Whiteway et al. (1995), the computed variance may have a component due to noise fluctuations in the
photon counting process and is subtracted to obtain an accurate measure of the associated available potential energy,
which is given by
1
Ep(z) =
2
g
N (z)
2
T ′ (z)
T0 (z)
!2
within a layer with top and bottom layer heights Zmax and
Zmin respectively (Tsuda et al., 2000). The variance at a
given altitude is determined for a layer of 3 km thick, by
sliding both top and bottom height of the layer with a step
of 300 m. The brunt-Vaisala frequency squared, N 2 is calculated by differentiating the mean temperature profile with
adjacent three heights (Tsuda et al., 2000). The error in the
estimation of brunt-Vaisala frequency squared and potential
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energy per unit volume is below 10% at heights below 50 km.
It increases to 10–30% at heights 60–75 km and to even 50%
at heights above 80 km. The available potential energy per
unit volume is determined by multiplying the above equation
by the mean density profiles of the entire observation period
on the night.
2.2
MF radar measurements
The MF radar (1.98 MHz) at Tirunelveli (8.7◦ N, 77.8◦ E)
has been installed and operated by Indian Institute of Geomagnetism since November 1992 (Rajaram and Gurubaran,
1998). It provides horizontal wind information in the altitude
region 68–98 km for every 2 km height interval and 2 min
time interval. The pulse width of 30 µs limits the height resolution to 4.5 km. The raw winds are available every 2 min.
Ann. Geophys., 26, 3731–3739, 2008
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S. Sridharan et al.: Influence of gravity waves and tides on mesospheric inversion layers
Fig. 2. Same as Fig. 1 except that it is for 25–26 January 1999.
For the present study, the zonal wind data for a bandwidth
of 4 days centred on the days cosidered for Rayleigh temperature measurements are chosen. These four day data set
are fitted with 24 h, 12 h and 8 h components and the time
variation of each tidal components are obtained. The raw
measurements in the 86–90 km height range at 2 km intervals are used to obtain wind fluctuations variances in each
1 h and they are correlated with the time variation of tidal
components. This method is similar to the one described in
Thayaparan et al. (1995).
Ann. Geophys., 26, 3731–3739, 2008
3
Results
3.1
3.1.1
Mesospheric temperature inversion
21–22 October 1998
The left panels of Fig. 1 show sequence of temperature profiles (top panel) and the temperature profile averaged for first
and second halves of the observation period (bottom panel)
for the night of 21–22 October 1998 and for the altitude region 40–90 km. An upper mesospheric inversion layer is evident in the second half of the night (dashed line in the bottom figure). Below this region the lapse rates in both first
and second halves are much steeper than the value expected
from CIRA-86 model values (plotted as thin line). The top
right panel of Fig. 1 shows the temperature variations from
the mean changes in temperature as a function of height and
time. The mesospheric inversion occurs during the second
half of the measurement period, where between 78 and 82 km
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S. Sridharan et al.: Influence of gravity waves and tides on mesospheric inversion layers
3735
Fig. 3. Same as Fig. 1 except that it is for 11–12 February 1999.
the average temperature is 15–30 K higher when compared to
the first half. Above the region of warming, there is a significant cooling of similar magnitude (15–30 K).
The total gravity wave potential energy density for the upper mesosphere is shown in the right bottom panel of Fig. 1.
After 2230 h, the mesospheric potential energy densities in
the altitude region (60–70 km) increase in concert with the
temperature in the inversion region. They show larger values
during the time (20:00–22:00 IST) of extended cooling also.
3.1.2
25–26 January 1999
In this case, temperature inversion occurs for a shorter time in
the first half of the observation period (Fig. 2). In the second
half of the observation period, the inversion occurs at lower
height. Though the averaged temperature profile shows that
the temperature inversion amplitude is smaller in the first
half than in the second half, the time variation of temperature from the mean shows the inversion occurred for a shorter
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time in the first half, but with a warming greater than 40 K.
Below this warming, there is a cooling greater than 20 K.
After 2500 h, warming prevails, however, with smaller amplitude than in the first half of the observation period, till the
end of the observation period. Above the region of extended
warming, cooling is observed.
The potential energy density per unit volume for the height
region 60–70 km shows larger values in the beginning and
end of the observation period, when the inversion amplitude
is larger. The total gravity wave kinetic energy density is
weaker from 2530 h to the end of the observation period.
3.1.3
11–12 February 1999
In this case, temperature inversion occurred during 2200–
2500 h just above 80 km. There exists cooling by about 20 K
just below 80 km (Fig. 3). However, after 2500 h, the inversion occurs at still lower region. During the entire observation period, the maximum amplitude of the inversion
Ann. Geophys., 26, 3731–3739, 2008
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S. Sridharan et al.: Influence of gravity waves and tides on mesospheric inversion layers
Fig. 4. Correlation coefficient between tidal components and gravity wave variances in zonal winds at 86–90 km.
occurred around 2600 h. Though the gravity wave potential
energy density for the height region 60–70 km shows larger
values for the temperature inversion occurred just above 80
km during 2200–2500 h, it shows minimum values from
2530 h to the end of the observation period.
3.2
Gravity wave tidal interaction
As mentioned in Sect. 2.2, the raw wind measurements
(2 min) in the 86–94 km height range at 2 km intervals observed by MF radar at Tirunelveli are used to obtain wind
fluctuations in each 1 h and they are correlated with the time
variation of tidal components. Figure 4 shows the cross
correlation coefficient between gravity wave variance and
tidal components for 24–27 January 1999 (left panels), 10–
13 February 1999 (middle panels) and 20–23 October 1998
(right panels). From the right panels of the figure, it can be
Ann. Geophys., 26, 3731–3739, 2008
inferred that the tidal components are not correlated with the
gravity wave variance for 21–22 October 1998, as the correlation coefficient is nearly zero at zero lag. This suggests
that the gravity wave tidal interaction does not occur. However, it may be noted that the diurnal tidal amplitude is significantly larger (40 m/s). Recently, Liu et al. (2007) found
that when diurnal and semi-diurnal tidal amplitudes increase
by factors of 2–3, a strong temperature inversion was observed around 90 km. The authors suggested that the temperature inversions occurring in a global scale were probably
as a consequence of tidal planetary wave interaction. The
nightly variations of three tidal components (diurnal, semidiurnal and ter-diurnal) at 86 km are shown in the top (25–
26 January 1999), middle (21–22 October 1999) and bottom
(11–12 February 1999) panels of Fig. 5. On 21–22 October
1998, the semi diurnal (12 h) tide is positive (eastward) at the
time extended cooling and crosses zero, when temperature is
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S. Sridharan et al.: Influence of gravity waves and tides on mesospheric inversion layers
3737
around zero and reaches negative maxima (westward), when
temperature shows larger warming. As the semi-diurnal tides
are having large vertical wavelengths, we can assume that
almost similar time variation is prevailing at the height of
temperature inversions also. It suggests that the temperature
change in the inversion region could be correlated with the
semidiurnal tidal variation.
For the case of 24–27 January 1999, there exists anticorrelation between tidal components and gravity wave variances (left panels of Fig. 4). The correlation coefficient between these two is between −0.3– −0.4 at heights 88–94 km.
On 10–13 February 1999, the correlation analysis between
gravity wave variances and tidal components at upper mesospheric heights show the correlation coefficient of −0.5 at
heights 90 and 92 km (middle panels of Fig. 4). It is interesting to note that ter-diurnal tidal amplitude is larger than
semi-diurnal tidal amplitude. The comparison between the
occurrence of MIL with the time variation of tidal components shows that the zero crossing of semi-diurnal tide coincides with the transition of cooling to warming at heights just
below 90 km (middle panel of Fig. 5).
3.3
Relation between mesospheric inversion and dry adiabatic lapse rate
Recently, Sica et al. (2007) suggested that mesospheric temperature inversions can be formed, if the environmental lapse
rate is less than half of the adiabatic lapse rate. We tested
this condition on the mean temperature profiles for the nights
21–22 October 1998, 25–26 January 1999 and 11–12 February 1999. Figure 6 shows altitude variation of temperature
lapse rate and mean temperature. The standard deviation
of the lapse rate is below 2–3 km/h at heights below 70 km.
In the height region 70–85 km, it increased from 3 km/h to
7 km/h with height. The adiabatic lapse rate is approximately
9.8 K/km and the half of it is 4.9 K/km. On 21–22 October
1998, mean temperature begins to decrease from the height
76 km to 80 km. It is nearly constant between 80 and 82 km.
Again, it increases with height above 82 km. The background
lapse rate (Ŵ) is much less the half of the adiabatic lapse rate
(Ŵa /2) between the heights 72 km to 82 km to enable the inversion to be formed. On 25–26 January 1999, the mean
temperature increases from about 73 km to 78 km. Again,
coinciding with the rise in temperature, the Ŵ is much less
than Ŵa /2 from 74 to 78 km. On 11–12 February 1999 also,
coinciding with the increase in mean temperature, Ŵ is less
than Ŵa /2. Inversions come back to normal at 82 km (11–12
February 1999) and 84 km (25–26 January 1999), when the
lapse rate increases above half of the adiabatic lapse rate. If
the background lapse rate is too large, then a saturated wave
does not lead to an inversion. If it is less than half of dry
adiabatic lapse rate, then a saturated wave may result in an
inversion layer (Sica et al., 2007).
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Fig. 5. Time variation of tidal components at 86 km on 25–26 January 1999 (top panel), 11–12 February 1999 (middle panel) and
21–22 October 1998 (bottom panel).
4
Discussion and conclusion
Simultaneous observations with the MF radar and Rayleigh
lidar on three nights are presented to show the occurrence
of mesospheric temperature inversions in the mesosphere region. Our observations do not always suggest direct relationship between inversion layers and gravity wave potential energy computed from temperature perturbations at or
below the temperature inversion heights. The temperature
variation seems to be correlated with that of the semi-diurnal
tide. Since the semi-diurnal tide has large vertical wavelength, direct comparison between 90 km and lower mesospheric heights (80 km) is reasonable. The results shown
in the present study reveals that there is an evidence for
the occurrence of gravity wave-tidal interaction. A notable
anti-correlation between the gravity wave variance and the
amplitude of the diurnal tidal motion is clearly apparent for
Ann. Geophys., 26, 3731–3739, 2008
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S. Sridharan et al.: Influence of gravity waves and tides on mesospheric inversion layers
Fig. 6. The altitude variations of local environmental lapse rate (left panels) and mean temperature (right panels) over Gadanki. The
uncertainties in the estimations are shown as error bars.
the zonal component. It occurs in phase at all four adjacent
heights between 86–90 km, with similar correlation values.
The gravity wave variance shows positive correlation with
semi-diurnal tide. These observations showed that propagating gravity waves with periods less than 1 h can significantly modulate the tidal amplitudes, and the reverse is also
true. Thayaparan et al. (1995) observed positive (negative)
correlation between diurnal tidal amplitude and gravity wave
variance in winter (summer) and observed no correlation between semidiurnal tidal amplitude and gravity wave variance.
Sica et al. (2002) found positive correlation between semidiurnal tide and gravity wave variance. These observations
suggest that gravity wave tidal interaction occurred.
Ann. Geophys., 26, 3731–3739, 2008
Our observations show that cooling is observed above
or below the warming region. During gravity wave breaking, heating rates are determined by wave advection, turbulent diffusion, and turbulence dissipative heating. Liu
et al. (2000), through a series of numerical experiments,
showed that the total heating rates could be large and could
cause large local temperature changes. The wave advection
could cause dynamical cooling in most of the wave breaking
region. The simulation results showed that the large temperature changes in this process could form temperature inversion
layers progressing downward with a speed similar to that of
a diurnal tide phase speed, which clearly suggested the tidal
modulation of the gravity wave and mean flow interactions.
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S. Sridharan et al.: Influence of gravity waves and tides on mesospheric inversion layers
Such a process is dependent on season and latitude, because
the background state stability varies with season and latitude.
The development of the temperature inversion is also affected
by the gravity wave characteristics. Our observations show
that the tidal-gravity wave interactions seem to occur in two
of the three nights, as there is a correlation between gravity wave variance and diurnal tidal oscillation. In the other
event, diurnal tidal amplitude is significantly larger. Liu et
al. (2007) found when diurnal and semi-diurnal tidal amplitudes increase by factors of 2–3, a strong temperature inversion was observed around 90 km. The authors suggested that
the temperature inversions occurring in a global scale are
probably as a consequence of tidal planetary wave interaction.
Sica et al. (2007) suggested that mesospheric temperature
inversions could be formed, if environmental lapse rate is
less than half the adiabatic lapse rate. Our observations show
that when there is an increase in temperature, the background
lapse rate is much less than half the adiabatic lapse rate. The
mean temperature decreases, whenever there is a large deviation from the dry adiabatic lapse rate. These results suggest
that the mesospheric temperature inversion is a signature of
wave saturation and the saturated wave can be gravity waves,
tides or planetary waves.
Acknowledgements. This work is supported by Department of
Space, Government of India. The authors would like to acknowledge the support of the operating staff in conducting Nd:YAG lidar
experiments at NARL, Gadanki. The MF radar at Tirunelveli has
been installed and operated by Indian Institute of Geomagnetism.
The authors would like to thank the Topical Editor and the two
anonymous referees for their critical evaluation of the manuscript.
Topical Editor U.-P. Hoppe thanks J. Meriwether and another
anonymous referee for their help in evaluating this paper.
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