Chapter V SEASONAL VARIATION OF DIURNAL TIDES IN THE TROPICAL LOWER ATMOSPHERE 5.1. Introduction In this chapter the results of an observational study of atmospheric tides in the lower atmosphere are presented. The observational data used for this study are collected from Indian MST radar, Gadanki (13.5"N, 79.2"E). Some interesting features of the amplitude and phase of the diurnal tides in the horizontal wind components over Gadanki are brought out and possible physical processes responsible for them are discussed. A comparison of these observed characteristics with theoretically expected global migrating diurnal tidal amplitudes and phases obtained for 12"N is made Seasonal variation of the vertical characteristics is examined. 5.2. Data and Method of Analysis The radar wind data obtained from the Indian MST radar is used for the study of diurnal tides over tropical lower aunosphere. The diurnal experiment, using Indian MST radar. was conducted for 18 diurnal cycles covering four season from September 1995 to August 1996 yielding Doppler spectra in the height range 3-20 km with a vertical resolution of 150 m for six beams (two vertical beams and four oblique beams in the north, south, east and west directions). There are three diurnal cycles of data for autumnal equinox season, seven for winter, three for vernal equinox and five for summe]:. Details of the period of observation of the diurnal cycles are given in Table 5 . 1 E,ach diurnal cycles started from 10 00 hrs and ended up at 09 00 hrs next day. Tht: measurements were made every 1 hour for 24 hours, each measurements lasting for -10 minutes, obtaining four samples of the spectra corresponding to each beam. 'These four spectra were incoherently averaged to obtain single spectra in every range bin. This incoherent averaging improves the detectability of the true Doppler peak by a factor of 2. The noise level in each range
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Chapter V
SEASONAL VARIATION OF DIURNAL TIDES IN THE
TROPICAL LOWER ATMOSPHERE
5.1. Introduction
In this chapter the results of an observational study of atmospheric tides in
the lower atmosphere are presented. The observational data used for this study are
collected from Indian MST radar, Gadanki (13.5"N, 79.2"E). Some interesting
features of the amplitude and phase of the diurnal tides in the horizontal wind
components over Gadanki are brought out and possible physical processes
responsible for them are discussed. A comparison of these observed characteristics
with theoretically expected global migrating diurnal tidal amplitudes and phases
obtained for 12"N is made Seasonal variation of the vertical characteristics is
examined.
5.2. Data and Method of Analysis
The radar wind data obtained from the Indian MST radar is used for the
study of diurnal tides over tropical lower aunosphere. The diurnal experiment, using
Indian MST radar. was conducted for 18 diurnal cycles covering four season from
September 1995 to August 1996 yielding Doppler spectra in the height range 3-20
km with a vertical resolution of 150 m for six beams (two vertical beams and four
oblique beams in the north, south, east and west directions). There are three diurnal
cycles of data for autumnal equinox season, seven for winter, three for vernal
equinox and five for summe]:. Details of the period of observation of the diurnal
cycles are given in Table 5 . 1 E,ach diurnal cycles started from 10 00 hrs and ended
up at 09 00 hrs next day. Tht: measurements were made every 1 hour for 24 hours,
each measurements lasting for -10 minutes, obtaining four samples of the spectra
corresponding to each beam. 'These four spectra were incoherently averaged to
obtain single spectra in every range bin. This incoherent averaging improves the
detectability of the true Doppler peak by a factor of 2. The noise level in each range
bin was objectively determined adopting the method developed by Hildebrand and
Sekhon (1974). Then the largest spectral peak in each range bin was determined and
taken as the true Doppler peak corresponding to the atmospheric motion if the peak
is 8 dB above the noise lev'cl. This condition is satisfied in most of the range bins.
Then the hourly vector wind components, namely westerly (u), southerly (v) and
vertical (w). were obtained in each range bin from the six line of sight (LOS)
velocities usins a least squares method as discussed in section 3.4.6. Thus the time
series of u, L' and w were obtained for the 24 hour period with a time resolution of
one hour and height resolution of 150 m.
Table 5.1
Period of observation of diurnal cycles
Season - Period of observation
Autumnal Equinox
Winter
Vernal Equinox
13-14 September 1995 26-27 September 1995
10-11 October 1995
06-07 December 1995
21-22 December 1995
04-05 January 1996
08-09 January 1996
16-17 January 1996 3 1 Jan - 01 Feb 1996
15-16 February 1996
12-13 March 1996
28-29 March 1996
21-22 April 1997
10-11 June 1996
27-28 June 1996
23-24 July 1996 06-07 August 1996
For the present study the horizontal components of the wind in the 3-20 km
height region is utilised. The height profiles of u and v were subjected to five-point
running mean with weights 0.125, 0.125, 0.5, 0.125 and 0.125. This process limits
very large fluctuations of u and v with height, which may be partly due to real wind
shear with small scales. The:n the time series in each range bin was examined for the
presence of any wild point, which may be a true outlier or produced by short-period
large-amplitude gravity waves. This was achieved by calculating the mean and the
standard deviation (u) in e:ach range bin and the wind value was considered an
outlier if it exceeded 1 . 7 ~ from the mean. These outliers were replaced by
interpolated values from adjacent hourly bins. In practice, occurrence of such
outliers were absent below about 14 km height and were 1 or 2 at higher heights.
The time series of u and v is detrended to remove any long-term variations. To have
a better representative picture over a particular season, the velocity values during all
diurnal cycles in a particular season were averaged on an hour to hour basis.
Fourier analysis of the averaged hourly zonal and meridional winds for each season,
in the 3-20 km region could provide the altitude structure of amplitudes and phases
of different tidal components.
5.3. Vertical Structure of .4tmospheric Tides
Vertical structure of atmospheric tides observed over Gadanki is presented
here for each season during 1995-1996. The diurnal component is found to be
prominent for all the four seasons.
5.3.1. Autumnal Equinox
The time series of u and v at 8.02 and 16.05 km heights during September
13-14, 1995. are shown in figure 5.1. Diurnal oscillation in winds is clearly seen in
the time variation shown in this figure. At the higher altitude short-period
fluctuations with a period of 3-4 hours are seen which may be a manifestation of
short-period gravity waves. However, the present study is confined to the diurnal
cycles.
( a ) 8.02 km (b ) 16.05 knr
h
d
I 4 n
E Y
% O 0) a V1
a .s -4 B
-8 u ' ' ' ' ~ ~ ~ 4 ~
24 4 8 12 16 20 24 4 8 12 16 20 Time (hrs LT) Time (hrs LT)
Figure 5.1, Time variations (after removing the mean) of zonal (triangles) and meridional (crosses) components of the horizontal winds at Gadanki (13.5N. 79.2E) during September 13-14, 1995: (a) at 8.02 krn and (b) at 16.05 krn
Figure 5.2 and 5.3 gives a typical plot of vertical profile of amplitude and
phase of u and v of single diurnal cycle (for September 13-14, 1995). Amplitudes
and phases are plotted at 150 m height intervals. The phase values in these figures
represent time of maximum westerly (eastward) winds and southerly (northward)
winds for the zonal and rneridional components, respectively. Theoretically
expected diurnal tidal amplitudes and phases obtained for 12"N by Forbes and
Gillene (1982) (hereinafter 1:his will be referred to as FG82) are also shown in these
figures.
It may be mentioned here that the diurnal amplitudes and phases shown in
figures 5.2 and 5.3 could be possibly affected by the presence of inertia gravity
wave (IGW) with periods around 24 hours. However, local inertial period at a
latitude of 13 .SON is -51.1 'hours. A strong easterly jet is present in the upper
troposphere over the Indian subcontinent during southwest monsoon period
(approximately from June to September) with core of the jet located just below the
tropopause height in the 9" N - 13" N latitude region and is known as tropical
easterly jet. In principle, this strong jet can generate IGWs having different periods.
If the tropical easterly jet is acting as a source (by geostrophic adjustment process)
for the generation of IGWs, then the majority of gravity wave energy will be
occurring near the inertial period (e.g., Fritrs and Luo, 1992). Thus one can
reasonably expect that most of the energy of the observed 24 hour oscillation at
13.5"N latitude could be due to tidal oscillations. Nevertheless, there may be a small
contamination of the amplitudes and phases of the diurnal tidal oscillation of the
horizontal winds by the IGWs with period close to 24 hours. Another source of
contamination of the comput:ed diurnal amplitudes and phases is the presence of
short-period gravity waves which are present at some height regions as was shown
in figure 5.1. But the effect of these waves on the diurnal amplitudes and phases
determined from the hourly data is small as this will appear as random errors
because of their relative temporal incoherence for a period of 24 hours when
compared to the coherent dliurnal tidal oscillations.
Figure 5.2. Amplitudes and phases of diurnal oscillation in zonal winds at Gadanki during September 13-14, 1995. The FG82 values for 12"N are shown by triangles joined by solid lines ; observed values are shown by circles
Figure 5 . 3 Amplitudes and phases of diurnal oscillation in meridional winds at GadaAi during September 13- 14, 1995. The FG82 values for 12'N are shown by triangles joined by solid lines ; observed values are shown by circles
It is seen from figures 5.2 and 5.3 that diurnal tidal oscillations attain large
amplitudes of 2-3 m s ~ ' both in the troposphere and lower stratosphere. A condensed
version of these tidal fields in FG82 had been presented by Forbes (1982a). These
theoretical values are obtained by considering the thermal excitation of tides due to
solar radiation absorption by water vapour in the troposphere and ozone in the
middle atmosphere both of which have zonally symmetric distribution and as such
these values represent cha~:acteristics of migrating tides. It is clearly seen that
observed diurnal tidal amplitudes are, in general, larger (by an order of magnitude)
than the corresponding theoretical values. It is also found that both zonal and
meridional wind amplitudes are having a height structure with small scales. The
observed phase profile shows significant departures from the theoretical one. The
theoretical vertical wavelength for the dominant migrating diurnal tide is 25-30 km,
whereas the observed ones inferred from the phase profile are much shorter with
values 3-6 km.
The results shown in figures 5.2 and 5.3 are based on the radar observed
winds for only one diurnal cycle during September 13-14, 1995. The diurnal wind
amplitudes and phases computed from the radar data obtained during September 26-
27, and October 10-11, 1995, also show very similar large amplitudes and short
wavelength. This similarity of amplitude and phase structure for the three cycles
arise from the coherence of these diurnal tidal oscillation (both migrating and
nonmigrating) during a panicular season (September-October). Since these three
diurnal cycles belong to auturmlal equinox season, a better representative picture of
diurnal tidal characteristics during autumnal equinox season can be obtained by
averaging the data for the ]:bee diurnal cycles. This has the twin advantage of
smoothing out any random variations in the radar winds produced by the shon-
period gravity waves and building up the coherent tidal oscillations. Since the time
separations between the three: diurnal cycles are -15 days, any inertia gravity wave
with period near 24 hours, if present, will also get smoothed out because of the
incoherence of such waves occurring with a large gap of time. Thus the data for the
three cycles were averaged on an hour-to-hour basis to obtain a composite cycle,
and the hourly wind values were subjected to harmonic analysis for getting the
diurnal amplitudes and phases in the troposphere and lower stratosphere for the
autumnal equinox season. The results are shown for the zonal and meridional winds
in figures 5.4 and 5.5, respectively. The theoretical values of migrating tidal
amplitudes and phases obtained by FG82 are also shown in these figures. Both
amplitude and phase profiles appear to be smoother when compared to those
obtained by analysing only one diurnal cycle of data. However, the following points
may be noted by comparir~g the amplirude and phase profiles of the zonal and
meridional wind components in figures 5.2 and 5.4 and figures 5.3 and 5.5,
respectively. The amplitude values become smaller in the case of results for the
composite day, especially for the meridional wind component (figures 5.3 and 5.5).
The number of large-amplitude peaks is also reduced for the composite day and
many of the smaller amplitudes lie around the FG82 values. The height structure of
the phase becomes relatively smoother and well defined for the zonal and meridional
components as can be seen figures 5.4 and 5.5. respectively.
The r.m.s. errors (on and op) in the amplitudes and phases are shown as
error bars (?on and +op) at selected altitudes and are calculated using the following
methods. First. the r.m.s. error in every hourly mean wind value (which is the
mean of three hourly values in three different diurnal cycles) is computed under the
assumption that the differences between the mean and the individual diurnal cycle
values arises due to random errors. Even if the differences occur due to gravity
waves, for diurnal tidal oscillation they will appear as random errors because of the
lack of coherence of the gravity waves for an interval of nearly 2 weeks, (which is
the period between the individual diurnal cycles). The r.m.s values of these
differences are taken as r.m.s error in the hourly mean wind values. The r.m.s error
at every 300 m are shown i n figures 5.6(a) and 5.7(a) as scatterplots for hourly
zonal and meridional winds, respectively. From these hourly values mean r.m.s
errors are computed and are shown in figures 5.6@) and 5.7(b) for the two
horizontal wind components, respectively. It is seen that below about 8 km altitude
both zonal and meridional winds have mean r.m.s errors of less than 1 m s-'. The
r.m.s. error is between 1 and 2 m s ~ ' in the height range of 8 km - 19 krn. These
mean r.m.s errors (standard deviations) shown in figures 5.6b and 5.7b are used for
Figure 5.4. Amplitudes and phases of diurnal oscillation in zonal winds, obtained from the Fourier analysis of time series averaged over the t h m cycles during autumnal equimx season The r .m.s errors at selected altitudes are shown as error bars FG82 values for 12.N during auhmnal equinox wason are shown by triangles joined by solid lines; observed values are shown by circles
Figure 5.5. Amplitudes and phases of diurnal oscillation in meridional winds, obtained from the Fourier analysis of time series averaged over the three cycles during autumnal equinox season. The r.m.s. errors at selected altitudes are shown as error bars. FG82 values for 12"N during autumnal equinox season are shown by triangles joined by solid lines; observed values are shown by circles
Figure 5 . 6 The r.m.s. errors in the zonal wind values detived from the three diurnal cycles of dah during autumnal equinox season. (a) The scatterplots at each height are obtained by plotting the r.m.s differences between mean (over three diurnal cycles) hourly wind values and individual hourly wind values in each diurnal cycle, and (b) the mean values of the r.m.s. errors obtained from the scatterplots shown in Figure 6. 6 (a).
Figure 5 7 The r m . S errors in the meridional wind values derived from the three diurnal cycles of data during auhmnal equinox season. (a) The scatterplols at each height are obtained by plotting the r.m.s differences between mean (over three diurnal cycles) hourly wind values and individual hourly wind values in each diurnal cycle, and (b) the mean values of the r.m,s. errors obtained from the scatterplots shown in Figure 6.7 (a).
computing the r.m.s errors (q, and a,) in the tidal amplitudes and phases by making
use of error propagation fclrn~ulae following Whitfaker and Robinson (1965). tcr,
and to, are shown as error bars in figures 5.4 and 5.5. 'The r.m.s errors in the
amplitudes and phases are determined in the following way. After removing the
trend and the steady component, the time series of wind values are expressed as
x,,(t) = ~ c o s ( w , t - y) (5.1)
where
XR residual value of wind at time t
A amplitude of the 24-hour component
V phase of the 24-hour component
01 ZnID,. where D, = 24 hour
Equation (5.1) can be rewritten in the fonn
SF, =bcosw,f+dsinw,f
where
b = Acos~+/ and d = Asinty
It follows that
where b and d are rhe Fourier coefficients
It can be shown that (under the assumption of q,= q,, where u,, and a,,
are the standard deviations in b and d respectively) the r.m.s. errors in A and y a r e
given by the following equatior~s
a,, can be shown to be approxirnately given by
where q = r.m.s error in X(t,l , n , = the number of data points, o,, and 4, are oo
and a, respectively.
'The r.m.s. errors of the hourly winds (both zonal and meridional components)
for different seasons are calculated and are shown in figure 5.8. It is seen that the
r.m.s. errors are less than 2 m s-l in all the height regions with smaller ( i l m s")
values occurring in the lower troposphere and higher values in the upper troposphere
and lower stratosphere. For the summer season the meridional wind shows larger
r.m.s. errors (>2 m s- I ) in the height region above 14 km. It may be noted that during
the summer season tropical easterly jet is present in this height region with its core
around 15 km height. The enhanced r.m.s. errors seen during this season may be due
to large amplitude gravity waves generated in the jet region and propagating upwards
and downwards.
A detailed exmination of figures 5.4 and 5.5 shows that the observed
diurnal tidal amplitudes are not increasing monotonically with height. The diurnal
amplitudes of both the zonal and meridional wind components fluctuate with height
creating a complex height structure. In many height regions the observed diurnal
amplitudes of the zonal and n~eridional winds are consistent with those predicted by
migrating tidal model of FG82. However, at some altitude regions observed
amplitude profiles show significantly larger amplitudes when compared to FG82
profile. Two such large-amplitude peaks can be seen for both zonal and meridional
wind profiles. For zonal winds these occur at -17 krn and -11 km and meridional
winds at -14 and -10 km. respectively. The amplitude peaks have a value of 1-2 m
s ~ ' . One or two smaller peaks are also seen for both the horizontal wind components.
The height profiles of phases also show some interesting features. For example, in
figure 5.4 it can be seen thal: small vertical scale (-3 km) structure exists in the
observed phase values for diurnal variations in the zonal wind in the 4 to 10 krn
height region. There is a sunilar small vertical scale ( -3 km) structure in the
amplitude profile in the same height region, with the heights of amplitude peaks
coinciding with those of phase rninima and those of amplitude minima coinciding
with phase maxima. A very similar amplitude and phase variation with height for
- autumnal equinox - - - - vernal equinox
Figure 5.8. Vertical profiles of' rms errors in hourly averaged meridional (left panel) and zonal winds (right panel) for autumn equinox (thin line), winter (thick dashed line), vernal equinox (thin dashed line) and summer (thick line) seasons.
zonal winds (figure 5.4) can be seen in the 10-20 krn height region, but with a
vertical scale of -6 km. The height profiles of amplitude and phase of diurnal tidal
oscillation in meridional winds also show very similar relationship between the
amplitude and phase fluctuations with height (figure 5.5). For example, the vertical
wavelength inferred from the vertical separation between successive
maxima/minima of amplitude values in the 13-17 km height region is -4 km. The
vertical wavelength calculated from the rate of phase propagation is -6 km.
Similarly, in the 6-10 km region a vertical wavelength of -3 km is inferred from the
amplitude peaks shown in figure 5.5. The vertical wavelength calculated from the
rate of phase propagation gives a value of - 3 km in the 6-10 km height region.
Thus the results shown in figures 5.4 and 5.5 clearly indicate diurnal tidal
propagation characteristics with amplitude of 1-2 m s-' and vertical wavelength of 3-
6 km, the lower region sho'wing smaller vertical wavelength. To investigate the
vertical propagation of the tidal oscillations further, hodographs of the tidal
perturbation velocity (horizon~al:~ were constructed using the time series of zonal and
meridional components obtalmed from diurnal tidal amplitudes and phases at
different heights. Such hodog'aphs are shown in figures 5.9(a) and 5.9(b) for two
height regions at the local rime 23 00 hrs. It is seen that the perturbation wind vector
rotates clockwise with height. indicating upward energy propagation. Further the
dominance of short vertical wavelength at lower height region and larger vertical
wavelength at upper height region can also be seen. The vertical wavelength
inferred from the hodographs are -3.5 km and 6-9 km for the lower and upper
height regions, respectively. These values are somewhat consistent with those
calculated from the successive amplitude maxima/minima and rate of phase
propagation in different height regions.
5.3.2. Winter
There are seven cycles of diurnal data during winter season. The average
value of zonal and mer~dional wind components of these seven cycles are obtained
for 24 hours at each height level with a height interval of 150 m. The time series of
Figure 5.9. Hodographs of diurnal winds for selected time (2300 hours) at heights from -3 to -15 krn during autumnal equinox season. (a) 3.40 - 7.87 km (b) 8.76- 15.01 km. The winds are computed from the amplitudes and phases of the zonal and meridional components. The lowest heights are indicated by open circles, and the tips of the wind vector at successive altitudes (represented by solid circles) are joined together. The direction of rotation with increasing height is shown by arrows.
u and v are subjected to Fourier analysis to extract tidal components. Diurnal wind
oscillation is found to be prominent in the time series.
The diurnal amplitude and phase profile of zonal (u) and meridional (v)
winds are shown in figures 5.10 and 5.11 respectively. The amplitudes are not
increasing monotonically. Tlie diurnal amplitudes of both the zonal and meridional
wind components fluctuate with height. The FG82 values for winter season is also
shown in these figures. The number of amplitude peaks is minimum during winter
season. Two prominent large amplitude peaks are obtained for both zonal and
meridional winds. The two peaks appear in the 8-14 km altitude region for zonal
winds (figure 5.10). For meridional winds one peak appear at -10 km region and
the other above 14 km altitude (figure 5.11). A small amplitude peak is also
observed near 7 km for meridional wind. Meridional wind amplitudes are larger
than zonal wind amplitude. The amplitude peak of zonal wind has a value of 1 m s-'
but that of meridional wind is; 2 m s-'. The phase values also fluctuate about FG82
phase values (figures 5.10 and 5.11). For zonal wind, the phase shows downward
propagation above 8 km, with small vertical structure. The vertical wavelength
observed in the 8-14 km region is -5 km. In the amplitude profile also small vertical
scale structure is observed in this height region (figure 5.10). Above 14 km also
phase shows downward propagation with a vertical wavelength of -4 km for zonal
winds. For meridional wind phase shows downward propagation in the lower
troposphere i.e. below 8 km. .4bove 14 km also a downward phase propagation is
observed for meridional winds. In both these regions the vertical wavelength
obtained from the phase profile is -5 km. In the amplitude profile, it can be seen
that the two amplitude maxima are separated by a distance of -6 km. The vertical
wavelength obtained from successive maximum amplitude maxima and vertical
wavelength calculated from the rate of phase propagation are very much matching.
The amplitude and phase profiles shown in figures 5.10 and 5.11 indicates
diurnal tidal propagation, characteristics with amplitude of 1-2 m s ~ ' and vertical
wavelength of '5 krn. The vertical propagation of the tidal oscillations are
investigated further, using hodographs of the tidal perturbation velocities, using the
20
- E I4 3 -> - Qi w I
5 - C 8
2
Amplitude (m s-' ) Phase (hrs LT)
Figure 5.10. Amplitudes and phases of diurnal oscillation in zonal winds, obtained from the Fourier analysis of time series averaged over the seven cycles during winter season. The r.m.s. errors at selected altitudes are shown as error bars. FG82 values for 12"N during winter season are shown by triangles joined by solid lines; observed values are shown by circles.
Figure 5.11. Amplitudes and phases of diurnal oscillation in meridional winds, obtained from the Fourier analysis of time series averaged over the seven cycles during winter season. The r.m.s. errors at selected altitudes are shown as error bars. FG82 values for 12ON during winter season are shown by triangles joined by solid lines; observed values are shown by circles
time series of zonal and meridional components obtained from diurnal tidal
amplitudes and phases at different heights. Figures 5.12 (a & b) gives the
hodographs at 04 00 hrs at two altitude regions, one below 10 km altitude and the
other above 10 h. From the hodographs 5.12(a), it is observed that the
perturbation wind vector rotates anticlockwise in the lower troposphere. In the phase
profile (figure 5.10) in the lower tropospheric region, phase does not show
downward propagation for zonal winds. But meridional wind shows downward
phase propagation in the lower tropospheric region (figure 5.11). By examining the
hodograph above 10 h (figure 5.12 h) it can be seen that wind vector rotates
clockwise with a vertical wavelength greater than 8 km. Above 8 km, both zonal
and meridional winds show downward phase propagation (figures 5.10 & 5.11).
5.3.3. Vernal Equinox
There are three cycles of diurnal data for the vernal equinox season. The
amplitude and phase profiles of diurnal component of zonal and meridional winds
are shown in figures 5.13 and. 5.14 respectively. Multiple peaks are observed in the
amplitude profile. Throughour the altitude region of observation, the values deviate
from the FG82 values. For zonal wind, there are three prominent peaks, two of
them, in the 8-14 krn altitude region and one above 14 km are observed. The
maximum amplitude observed is 1.5 m s ~ ' . A prominent amplitude peak of 2.5 m s-'
is observed for meridional winds, in the 8-14 km altitude region. The phase profile
of zonal wind shows a downward propagation below 8 km, with a short vertical
wavelength of -5 km (figure 5.13). In the upper troposphere i.e. above 8 krn, the
phase has a constant value for zonal winds. The meridional wind shows downward
phase propagation both in the lower and upper troposphere. The vertical wavelength
of meridional wind observed are ' 6 km and - 3 km in the lower and upper
troposphere respectively (figure 5.14).
The hodographs of the tidal perturbation velocity (horizontal) were
constructed using the tlme series of zonal and meridional components obtained from
diurnal tidal amplitudes and phases at different heights. Two such hodographs are
shown in figure 5.15, one below 8 km and the other above 8 km. Below 8 km, the
Figure 5.12. Hodographs of diurnal winds for selected time (0400 hours) at heights from -3 to -20 km during winter season. (a) 3.40 - 9.65 km (b) 10.55- 18.59 km. The winds are computed from the amplitudes and phases of the zonal and meridional components. The lowest heights are indicated by open circles, and the tips of the wind vector at successive altitudes (represented by solid circles) are joined together. The direction of rotation with increasing height is shown by arrows.
Figure 5.13. Amplitudes and phases of diurnal oscillation in zonal winds, obtained from the Fourier analysis of time series averaged over the three cycles during vernal equinox season. The r.m.s. errors at selected altitudes are shown as error bars. FG82 values for 12"N during vernal equinox season are shown by triangles joined by solid lines; observed values are shown by circles
Figure 5.14. Amplitudes and phases of diurnal oscillation in meridional winds, obtained from the Fourier analysis of time series averaged over the three cycles during vernal equinox season. The r.m.s. errors at selected altitudes are shown as error bars. FG82 values for 12"N during vernal equinox season are shown by triangles joined by solid lines; observed values are shown by circles
Figure 5.15. Hodographs of diurnal winds for selected time (0100 hours) at heights from - 3 to -20 km during vernal equinox season. (a) 3.40 - 7.87 krn (b) 8.76 - 18.59 krn. The winds are computed from the amplitudes and phases of the zonal and meridional components. The lowest heights are indicated by open circles, and the tips of the wind vector at successive altitudes (represented by solid circles) are joined together. The direction of rotation with increasing height is shown by arrows.
wind vector shows clockwise: rotation. with a vertical wavelength of -5 km. From 8
to 19 km, the wind vector shows anticlockwise rotation, completing two cycles,
with a vertical wavelength of -5 km each. In the phase profile also phase
propagation is downward for both zonal and meridional components below 8 km
(figures 5.13 and 5.14). Above 8 km, the meridional wind shows downward phase
propagation but zonal wind propagates with constant phase.
5.3.4. Summer
For the summer season five diurnal cycles of data are available. The
amplitude and phase profiles of zonal wind are given in figure 5.16. Figure 5.17
shows the amplitude and phase profiles of meridional wind. The amplitude values do
not increase monotonically. There are multiple peaks observed in amplitude profile
of both zonal and meridional winds. Meridional wind amplitude profile is smoother
than that of zonal wind. At most of the altitude region the observed amplitude values
deviate from the FG82 values. The largest peak is observed between 14 and 20 km
for both zonal and meridional wind. The maximum amplitude is -2 m s-'. The phase
values also show large deviation from FG82 values. The phase shows downward
propagation, both in lower and upper troposphere for zonal winds (figure 5.16). The
vertical wavelength of zonal wind in the lower troposphere is -6 km and in the
upper troposphere is - 5 km. For the meridional winds (figure 5.17) the phase shows
downward propagation near the tropopause region only. The meridional wind
oscillations show very small vertical wavelength near the tropopause level, i.e a
vertical wavelength of - 2 km. IN the lower and middle troposphere meridional wind
oscillates with almost constant phase.
The vertical characteristics are studied using amplirude and phase profiles.
To have a further understanding of the vertical propagation characteristics,
hodographs are plotted with zonal and meridional winds of diurnal component.
Typical hodographs are shown in figure 5.18 for 12 00 hrs. Hodographs are plotted
at two height regions i.e. 3.4 -9.65 km region and 10.55-18.59 km region. In the
hodographs, below 10 km, t ie wind vector rotates anticlockwise. In the phase
profile also meridional wind does not show any downward propagation in the lower
Figure5.16 Amplitudes and phases of diurnal oscillation in zonal winds, obtained from the Fourier analysis of time series averaged over the five cycles during sunlnler season. The r.m.s. errors at selected altitudes are shown as error bars. FG82 values for 12.N during summer season are shown by triangles joined by solid lines; observed values are shown by circles
Figure 5.17. Amplitudes and phases of diurnal oscillation in meridional winds, obtained from the Fourier analysis of time series averaged over the five cycles during summer season. The r.m.s. errors at selected altitudes are shown as error bars. FG82 values for 12"N during summer season are shown by triangles joined by solid lines; observed values are shown by circles
I r:: Figure 5.18. Hodographs of diurnal winds for selected time (1200 hours) at heights from -3 to -15 km during
summer season. (a) 3.40 - 9.65 km (b) 10.55- 15.01 km. The winds are computed from the amplitudes and phases of the zonal and meridional components. The lowest heights are indicated by open circles, and the tips of the wind vector at successive altitudes (represented by solid circles) are joined together. The direction of rotation with increasing height is shown by arrows.
troposphere. The wind vector rotates clockwise, completing two cycles, with a
vertical wavelength of -5 lun each. above 10 km. This indicates the upward
propagation of diurnal tides in this region. In the phase profile also both zonal and
meridional wind show downward phase propagation near the tropopause.
5.4. Seasonal Variation of Vertical Structure of Diurnal Tides
Seasonal variation of vertical structure of tides occurs mainly due to seasonal
variation in the sources that excite these tidal oscillations. The amplitude values of
both zonal and meridional wind do not increase monotonically for all the four
seasons. The amplitude profile exhibit small-scale height structures. Multiple peaks
are observed in the amplitude profile, except for winter season. For winter season
two amplitude peaks are observed for zonal wind and three peaks for meridional
wind. At 11 km an amplitude peak is observed for all four seasons for zonal wind.
An amplitude maximum is observed at 10 km for all the four seasons for meridional
wind. The maximum amplitude obtained for both zonal and meridional wind lie
between 1 to 2 m s ~ ' . Table 5.2 gives the details of vertical structure of amplitudes.
Table 5.2
Seasonal variation of vertical structure of amplitudes of diurnal tides
Number of Peaks Maximum Am~litude (m s-') Season
Zonal Meridional Zonal Meridional
Autumnal Equ~nox Four Three 2 1.5
Winter Two Three 1 2
Vernal Equinox F ~ v e Five 1.5 2
Summer Four Five 1.5 2
The phase profile is having a complicated structure for both zonal and
meridional winds. Phase va~lues decreases with altitude at some heights and
increases with altitude at sow: other heights, showing both upward and downward
energy propagation. In the lower troposphere (below 8 km) phase propagates
downward for all the seasons except for winter season for zonal wind. Zonal wind
shows downward phase propagation in the upper troposphere (above 16 km) for all
the four seasons except for vernal equinox. The meridional wind shows downward
phase propagation in the lower troposphere (below 8 km) for all the seasons except
for summer season. In the upper troposphere (above 15 km) meridional wind shows
downward phase propagatioi~ for all the four seasons. Between 8-14 km both zonal
and meridional wind propagates with constant phase, indicating a source region
here. The phase propagation characteristics and vertical wavelengths obtained for
horizontal components of diurnal tide are given in Table 5.3 and 5.4 for lower and
upper troposphere respectively
There is not much seasonal variation in the amplitude values for both zonal
and meridional winds. The phase propagation and vertical wavelength of the
horizontal wind components of diurnal tide show seasonal variation both in the
lower troposphere and upper troposphere. A wave with a negative (positive) phase
slope in a source free region of the atmosphere indicates upward (downward)
propagation of energy away from a source that is below (above) the region of
observation. In the source acrive region of the atmosphere the negative or positive
slope of the phase profile does not exclusively indicate energy propagation direction
but results from the phase and vertical structure of the active source.
In the lower troposphere the vertical wavelength observed during autumnal
equinox is 3 km and during other three seasons viz., winter, vernal equinox and
summer it is -5 km. In this r'tgion planetary boundary layer heat flux is the main
heat source for tidal forcing. The observations indicate that there is a seasonal
change in the planetary boundary layer heat flux that varies from autumnal equinox
to other three seasons. In the upper troposphere the vertical wavelength of -9 km
(from hodograph) is obtained during autumnal equinox and winter. During vernal
equinox and summer a vertical wnvelength of -4 km is obtained (from hodographs).
In the upper troposphere the latent heat release in clouds and cloud forcings are
probable heat sources. The observation shows that there is seasonal variation in the
forcing due to these sources from autumnal equinox and winter to vernal equinox
and summer. The efficiency of exciting a particular diurnal tidal mode is dependent
Table 5.3
Observed vertical propagation characteristics of diurnal tides over Gadanki (13SoN, 79.2"E), in the lower troposphere (below 8 km)