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)

Phase Propagation Season

- Direction ~-

17rom Hodograph

-- - - -- ~-

Zonal Meridional Zonal Meridional Rolatiun Vertical wavelength - . - ~~

Direccior. of wii;d v i ~ i o i - -. .- - (rn) ~-

Aut. Eqx Downward Downward 3 3

z CT.

Winter Constant Phase Downward .-. 5

Clockwise

Anticlockwise

Ver. Eqx Downward Downward 5 6 Clockwise 5

Summer Downward Constant Phase 5 --.- Antlclockwise 6

Table 5.4

Observed vertical propagation characteristics of diurnal tides over Gadanki (13.5"N, 79.2"E), in the upper troposphere (above 14 km)

From Phase Profile ~ - -~ ~~ - - ~ ~

Phase Propagation Season Vertical W;~velength ( k ~ n )

Direction ~~.~ ~ ~ ~~ ~~ ~~ ~

From Hodograph

- - .-

Zonal Meridional Zonal Meridional Rotation [>irecri~fi of t.y:nd -ec;or

Vertical wavelength (km) P . . -

Aut. Eqx Downward Downward 5 6 Clockwise 9

Winter Downward Downward 7 6 Clockwise 9

Ver.Eqx Upward Downward ... 3 Anticlockwise 4

Summer Downward Downward 3 3 Ciockw~se 4

on the depth and shape of the heating rate. A heating rate that is very shallow will

not efficiently excite tidal modes with large vertical wavelength, where as heating

rates that are deep, in comparison can efficiently excite longer wavelength tidal

modes (Williams and Avety, 1996a). If the depth of heating is "h" kilometres and

the shape of the heating profile is a half-sine wave then the mode with a vertical

wavelength of "2h" kilometres will be the one, most efficiently excited since there is

a perfect matching between the heating profile and the vertical wavelength. For the

same depth of heating "h" kilometres if the shape of the heating profile will be a

combination of the heating profile is a full sine wave then the mode with a vertical

wavelength of "h" kilometre!; will be the most efficiently excited oscillation. But in

practice, for diurnal heating sources such as deep convective clouds, the shape of

half and full sine waves arid one can expect excitation of modes with vertical

wavelength centred around 'h" and "2h" kilometres. For diurnal heating sources

such as planetary boundary layer heat flux the vertical heating will be a half-sine

wave and excitation of modes with vertical wavelength of "2h" kilometres will be

having maximum efficiency.

The heating rates due to diurnal heating of water vapour and latent heat

release in convective clouds extend throughout the troposphere and will be mainly

exciting tidal modes with long vertical wavelength. Short vertical wavelength modes

will also be excited. but they will undergo destructive interference within the source

region, resulting in very small amplitude. But the heating rate due to sensible heat

flux near the surface extends only through the planetary boundary layer whose

vertical extent is 1-2 km anti which will be efficiently exciting diurnal tidal modes

with vertical wavelength '2-4 km.

Assuming that the diurnal tidal fields in the tropospherellower stratosphere

are generated by the boundary layer sensible heat flux, diurnal solar heating of

water vapour and latent heal: release, the dominance of shorter vertical wavelength

in the height region below 10 km and longer vertical wavelength above may be

explained as follows. Shorter vertical wavelength modes will be generated more

efficiently because of the shallowness of the source region. Near the source region

one may expect amplitudes of shorter wavelength modes to be larger than those of

longer wavelength modes. As these different modes propagate upwards from the

source, shorter wavelength modes will be radiatively damped and longer wavelength

modes will dominate. This process will take place only at stratospheric altitudes,

(above 30 km) and is not important in the troposphere. Hence the observed tidal

mode characteristics need sorne other mechanism to be operative. One possibility is

the efficient generation of lorrger vertical wavelength modes by diurnal heating due

to latent heat release in the troposphere. It is known that vertical extent of this heat

source is deeper (-14 km) in comparison with that in the planetary boundary layer

(Mapes, 1993; Williams. 1994). With this value of the depth of the vertical heating

profile one can expect excitation of modes with vertical wavelength centred around

14 and 28 km, if this profile shape is a combination of half- and full- sine waves.

From the observed phase profile, it can be seen that there appears to be a

boundary layer signal in the diurnal winds in the lower troposphere. This signal is

not always observable in both zonal and meridional wind components [e.g. winter

(zonal) and summer (merid:ional)]. The vertical wavelength also has seasonal

variability in the lower atmosphere. The change in phase in the lower altitudes

suggests a boundary layer forcing that has seasonal dependence and is different from

the phase of solar absorption of water vapour forcing used in the tidal model

(FG82). 'The change in vertical wavelength is due to seasonal variation in the depth

and shape of heating rate of planetary boundary layer forcing.

From 8 to 14 km, the phase of the diurnal variation is constant. This may be

a probable source region, where the largest amplitude is observed and the phase

appears constant with altitude. Above 14 km the phase slope is negative suggestive

of upward energy propagation except for vernal equinox season (zonal). This zonal

wind variation in the vernal equinox may be the result of a forcing either above the

tropopause level with energy propagating downward or a forcing distributed through

the troposphere. A thin heating source near the tropopause could be caused by the

solar radiation absorption by cloud tops and/or cirrus clouds produced by the deep

convective clouds. The vertically distributed heating source may be the latent heat

release from precipitating cl~ouds.

[n almost every season the observed diurnal tidal winds in the lower

troposphere were different than the winds observed in the upper troposphere. This

difference consisted of a change in phase and vertical wavelength with season. This

change in structure suggests a lower atmosphere process that may be decoupled

from the upper troposphere. Modelling of heating sources need to be done to

determine the contribution of each forcing to the observed winds.

5.5. Discussion

The similarities and differences between the observed winds and the

theoretical FG82 model values will shed light on whether the oscillations are locally

forced or globally forced by solar absorption of water vapour. The amplitude values

observed for diurnal tides for all the four seasons, is 1-2 m s-I. It is clearly seen that

observed diurnal tidal amplitudes are, in general by an order of magnitude larger

than the corresponding theoretical FG82 model values. 'The horizontal wind

amplitudes are having a small-scale height structure. The vertical wavelength

observed from phase profiles are -5 km. These phase profiles show significant

deviations from the theoretical one. The theoretical vertical wavelength for the

dominant migrating diurnal tide is 25-30 km, which is much larger than the

observed ones. The numerical simulation of nonmigrating diurnal tides by Tsuda

and Kato (1989) shows that similar large diurnal wind amplitudes and short vertical

wavelengths can be expecred in the tropical troposphere and lower stratosphere

which are produced by diurnally varying heat fluxes in the planetary boundary layer

over land. The present observations are also consistent with radar observations of

diurnal tidal characteristics at .4recibo (Fukao er al., 1980). The present observed

amplitude values are matching with those obtained by Tsuda er al. (1994, 1997) in

the observation of diurnal tides below 20 km using radiosondes over Indonesia (6.4

"S). The height structures of amplitudes and phases suggest that they are probably

produced by the interference of weak global migrating diurnal tidal mode and the

locally generated strong nonmigrating tidal modes. A simple simulation of the

interference in the vertical. between a strong nomigrating mode (amplitude 5 m s",

vertical wavelength. 6 krn) and migrating mode (amplitude 1 m s-', vertical

wavelength 30 km) shows that successive amplitude maxima (minima) are separated

by 6 km. The vert~cal wavelength calculated from the simulated height profile of

phase is 6 km corresponding to the nonmigrating mode. Thus the vertical

wavelength obtained can be mken as that of the stronger nonmigrating tidal mode.

It may be mentioned. here that Williams and Avery (1996b) have reported

diurnal tidal amplitude peak of -1.5 m s-' in meridional winds at an altitude of -14

km over Biak ( 1 5 , l36"E) and Christmas Island (2ON, 151°W). The diurnal tidal

phase showed a constant value around 14 km and downward phase propagation

above 14 km and upward phase propagation below. Similar amplitude and phase

structure of diurnal meridional winds is seen over Gadanki during winter and

summer seasons (figures 5.1 l and 5.17). Williams and Avery (1996b) have

suggested a probable source near 14 km where the largest wind amplitude is

observed and the phase appears to be constant with altitude. According to them the

solar radiation heating of cloud tops and the cirrus clouds distributed by deep

convection in the tropics is a source of tidal excitation.

The major sources for diurnal nonmigrating tides in the tropical atmosphere

are solar radiative heating of water vapour, latent heating due to deep convection

and eddy thermal conduction heating in the planetary boundary layer. Nonmigrating

tidal fields have been numerically modelled using these sources together or singly

(e.g., Tsuda and Karo. 1989; Lieberman and Leovy. 1995; Ekanayake et al., 1997).

Both eastward and westward propagating modes with different zonal wavenumbers

were considered in these num~:rical studies of nomigrating tidal fields. The study

by Tsuda and Kato (1989) shows that nonrnigrating components in horizontal winds

in the troposphere and lower stratosphere are characterised by short vertical

wavelength (2-5 km) and fluctuating (with height) large amplitudes (1-3 m s-I) which

are entirely produced by diurnally varying upward sensible heat flux in the planetary

boundary layer. Similar results are obtained by Liebennan and Leovy (1995) but

with smaller horizontal wind aniplitudes and slightly larger vertical wavelength.

It is possible that the nonmigrating tidal modes excited in the lower

troposphere are associated with the eddy heat flux in the planetary boundary layer

and that excited in the upper ~iroposphere are associated with some other independent

diurnal heat source located in that region. Diurnal heating due to solar radiation

absorption by cloud tops andlor cirrus clouds produced by the deep convection

could also be responsible for the diurnal tidal oscillation in the upper troposphere in

the tropics (e.g., Pilewskie and' Valero. 1995; Williams and Avery , 1996a). So the

heating of clouds (cloud tops andlor cirrus clouds) in the upper troposphere by solar

short-wave radiation is a pote:ntial source for the generation of nonmigrating diurnal

tides. A recent study of earth's annual global mean energy budget by Kiehl and

Trenberrh (1997) indicated that that short-wave radiation absorption by clouds has to

be increased from a previously estimated value of -7 Wm" to -25 Wm.'. This new

estimate of the solar radia1:ion absorption by clouds shows that it is equally

important as the turbulent sensible heat flux into the atmosphere from the planetary

layer (-24 Wm2) in the clin~atological sense. The persistence of subvisible c h s

clouds in the upper troposphere in the tropics for several days and the zonal

asymmetry of these clouds (~:.g., Jensen et a l . , 1996) reinforces the idea that the

heating of these clouds along with cloud tops could act as a diurnal heat source for

the generation of nonmigrating diurnal tidal modes. However, the vertical extent of

this heat source may be comparable to or more than the planetary boundary layer

heat source extent. The nomligrating tidal modes excited in the upper troposphere

over Gadanki may be associated with this heat source and this can be ascertained

only by simulating the tidal fields generated by solar short wave heating of the

clouds.

5.6. Conclusion

The vertical characteristics of diurnal oscillations in the horizontal winds

measured by Indian MST radar in the troposphere and lower stratosphere over

Gadanki are studied for autumn equinox, winter, vernal and summer seasons. The

vertical profile of the observed diurnal amplitudes shows small-scale vertical

structures in the 3-20 km altitude region in all the four seasons. It is observed that

the tropical region is dominated by diurnal tides with amplitudes of 1-2 ms-' and

vertical wavelengths - 5 km, during all the four seasons. A comparison of these tidal

amplitudes and phases with those of the global migrating tides (Forbes and Gillene,

1982) shows that diurnal oscillations with large amplitude and short vertical

wavelengths are probably produced by locally generated nonrnigrating tides. It may

be mentioned here that the observed amplitudes and vertical wavelengths, in the

lower uoposphere, are very similar to those predicted in the numerical simulations

of nonrnigrating tides (Tsuda and Karo, 1989; Lieberman und Leov, 1995). The

sources of these nonmigrating tidal oscillations may be the diurnally varying

planetary boundary layer heat flux, diurnal heating due to water vapour and latent

heat release, and diurnal heating of cloud tops in the upper troposphere. The present

study shows that though the seasonal variation of the diurnal tidal amplitudes in

zonal and meridional wincis is not so strong, vertical phase propagation

characteristics show significant seasonal variation. The vertical profile of diurnal

phase shows downward propagation in some height regions and upward propagation

in some other height regions. The seasonal variations of the tidal characteristics may

be due to the seasonal variation of the above mentioned heat sources that excite the

tidal oscillations. The nonrnigrating tidal modes excited in the upper troposphere

over Gadanki may be associated with these heat sources and this can be ascertained

only by simulating the tidal fields generated by these heat sources.