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Dynamics of the lower stratosphere in the wave number domain in relation to monsoon activity
Ioumalof Atmospheric and TemshiolPhysics.Vol.42. PP. 867-876 PergamonPressLtd. 1980. Printed in Northern Ireland
Dynamics
of the lower stratosphere in the wave number domain in relation to monsoon activity
K. S. RAJA RAO, S. T. AWADE and M. V. HARINDRANATHAN NAIR Indian Institute of Tropical Meteorology, Poona, India (Receiued 7 November 1979;
in reoised
form
8
April 1980)
Abstract-A
study has been made of the dynamics of the lower stratosphere in the wave number domain by spherical harmonic and Fourier analyses of the grid point values of the geopotential heights at the 50 and 30 mb levels for each month of the years 1972 and 1975. Only waves 1, 2 and 3 are dominant. Transports of momentum and of sensible heat in the lower stratosphere, month by month, have been studied by computing the vertical and horizontal tilts of the ridge line. The seasonal variations in the amplitude and in the tilt with height of the ridge line of these waves have been discussed. Weakening of the equator to pole temperature gradient in 1972 and its strengthening in 1975 are striking features. Eddy transports of angular momentum and of sensible heat and energy conversion terms from eddy to zonal kinetic energy and from eddy to zonal available potential energy have been computed for January and July of 1972 and 1975 for the levels 50 and 30 mb and at 30”N and 60”N latitudes and the results have been discussed. Transfer of kinetic energy from eddies to zonal flow in 1975 suggests that the strengthening of the easterlies extends to 30”N and beyond. 1. INTRODUCI’ION
The overall circulation in the stratosphere is maintained by the differential heating due to the net radiation field in which ozone, CO, and Hz0 play an important role. The stratosphere is a region of high static stability, while the troposphere is a region of relatively low static stability. The average equator to pole temperature gradient in the lower stratosphere is opposite to that in the troposphere. Topographical and thermal forcings in the troposphere introduce important non-linear interactions while in the stratosphere, the principal eddies comprise planetary scale waves which can mostly be treated to reasonable accuracy by linear wave dynamics. Many large scale features in the atmosphere become more evident in the stratosphere than in the troposphere, as a number of small perturbations disappear with increase in height. The seasonal nature of the stratosphere is well defined. It is felt that there are significant anomalies in the large scale global circulation pattern before and during the monsoon (June to September) which could be dynamically connected to the behaviour of the monsoon. In order to investigate some of these problems, the present authors have planned to study the lower stratospheric circulation in the wave number domain by the spherical harmonic analysis of the stratospheric parameters. The purpose of the study
is to examine the contrasting features between the stratospheric and tropospheric circulations and the anomaly of the monsoon in the overall stratospheric circulation on a global scale. In the present study we have chosen two years: 1972 and 1975. The year 1972 has been recognised as one of the worst drought years in India and elsewhere (see for example WMO bulletin 1973). Nineteen hundred and seventy-five was a year of good monsoon activity not only over India, but in other parts of Asia. In categorising a year as a “good” or “bad” monsoon year, the June to September rainfall over India is taken as the criterion. The rainfall deviation from normal, over the central parts of India
defines normal
a year as a normal (good) or as below (bad) monsoon year (RAJA RAO and
LAKHOLE, 1977). We have therefore considered 1972 as a typical year of bad monsoon and 1975 a good monsoon year. These two years span a large part of possible range of monsoon activity. As monsoon is a part of general circulation, the contrasting features of the circulations in these two years have been examined. Spherical harmonic analysis is a powerful tool in the study of the dynamics and climatology of the atmosphere, for a large amount of meteorological data can be analysed and the results expressed in a relatively few numbers which represent the global picture on the spherical earth. Spherical harmonics constitute the most natural set of orthogonal functions for the study of planetary scale meteorological 867
K. S. RAJA Fbo, S. T. AWADEand M. V. H~~A~~
868
systems. SCHMIDT (1935) was the pioneer in the application of spherical harmonics to geophysical problems and HAURWITZ (1940) was the first to utilise spherical harmonics in meteorology. Since then many workers (see for example CRAIG, 1945: BLINOVA, 1943; NEAMTAN, 1946; ELIASEN, 1958) have used this method of analysis in their studies of atmospheric motion. Spherical harmonic and Fourier analyses have been made of the geopotential heights at the 50 and 30 mb levels, for each month of the years 1972 and 1975. Transports of moments and of sensible heat in the lower stratosphere, month by month have been studied by computing the vertical and horizontal tilts of the ridge line. Seasonal features of the stratospheric circulation in 1975 and in 1972 have been studied. Eddy transports of angular momentum and of sensible heat and the energy conversion terms, from i& to Kz and A, to Az have been computed for January and July of 1972 and 1975 for the 50 and 30 mb levels at 30”N and 60”N latitudes. The results have been discussed. 2. DATA ANDMETHODOF ANALYSIS The Institut fiir Meteorologic of the German Free University, Berlin, regularly publishes in Meteorologische Abhandlungen, the grid point values of monthly mean winds, temperatures and geopotential heights of the 50 and 30mb levels. These grid points are at intervals of 10” latitude and 10” longitude for the northern hemisphere. In the analysis, we have closely followed the method of ELIASEN and MACHENHAUER(1965,1969). Due to the poor state of the observations in the southern hemisphere, the study has been restricted to northern hemisphere. The height field is symmetric with respect to the equator, as a consequence of the balance equation (see for example ELIASEN and MACHENHAUER, 1965, p. 223). Along the latitude circle +, the height H is expressed by the relation H(A) = C a,(+)
c0S mh f b,(#) sin mh.
(1)
On a sphere the field is given by H(c#$A)=
c .f
(a,” cos mh
m=o
n=am
+ b,” sin ~~~P”m(~)
(2)
where Pnm(p) is the associated Legendre function of the first kind. m is the number of waves round the earth and n - m the number of zero points from north pole to south pole and p = sin 4. Due to
NAIR
restriction of the anaiysis to the northern hemisphere only and the assumption of symmetry about the the orthogonality condition for the equator, Legendre polynomials becomes, following ELIASEN and MACHENHAUER (1965)
For n # n’ and n f n’ even. Normalisation is
n-m
condition
is even.
The coefficients a,,“’ and b,” are given by 1 a, m=
I0
~~~~)p~m(~) +
(3
Here a,(4) and b,,,(#) are Fourier coefficients. The amplitude R,” and phase E,,~ are given by R” = &,m)2+ tane,“=;.
(b,“)‘,
(7)
b,“’ a,
u,,,(9) and b,(4) are determined by Fourier analysis of the grid point values at 10” latitude interval. P,“‘(p) have been computed for m = 1 to 16 and n - m = 0 to 16. Using these values of a,(+), b,(4) and P,“(p) values of ~l,~ and b,” are obtained by trapezoidal rule.
3. RESULTSOF SPDERICALHARMONICANALYSIS Figure 1 (a, b, c, d) shows the amplitudes of the different waves for typical months January and July 1972 for the 50 and 30 mb levels in an (m, n - m) diagram. Figure 1 suggests that the eddy energy in the lower stratosphere is primarily in wave numbers 1 to 4 for n - m = 0 to 4. Since substantial amount of energy is present in wave numbers m = 1, n = 1; m = 2, n = 2; and m = 1, n = 3 we have considered in this paper the amplitude and phases of these waves only. Greenwich meridian is reckoned as the longitude of phase zero. Figure 2 depicts the amplitudes of these waves month by month, for the years 1972 and 1975 at the 50 and 30mb levels. Important characteristics of the principal waves in the two years are discussed below.
Dynamics of the lower stratosphere
16
@=
r
(b)
(gpm) of waves for different values of m and n - m, in 1972; July (a) 50mb (b) 30 mb; January (c) 50 mb (d) 30 mb.
Fig. 1. Amplitude
@*
869
in the wave number domain
@=30mb
200
30mb
-
,972
50 mb
----
,375
@= 180
50mb
fl
----
,972
t975
to
60
70
r %M)
12
w CI
50
@
30 mb
-
@-
50 mb
----
(b)
IO
3
E _I
40
n 5
30
4
20
1972 ,975
;“O
10 0
JFMAMJJASOND MONTHS-----e
JFMAMJJASOND MONTHS
-
MONTHS-
Fig. 2. Annual march of amplitudes of waves (spherical harmonic analysis) (a) m = 1, n = 1; (b) m = 2. n = 2; (Cf m = 1. n = 3.
K. S. RAJARAO, S. T.
870 3 .l.
AWADE and M. V. HARINDRANAW NAIR
Amplitrcdes
m = 1, n = 1. The amplitude is a maximum in March at both the 50 mb and 30 mb levels in 1975. The annual march of amplitude in 1972 is similar to that in 1975 except for the maximum in March. There is marked decrease in amplitude from March to April in 1975 and a less steep decrease in 1972. In the monsoon months (June to September) amplitudes are lower than in the other months. There is an enhancement in amplitude at 30 mb. In general, the amplitude in the year 1975 is larger than in 1972 except in April and November. m = 2, n = 2. There is no predominant maximum for this wave. The magnitudes are one order lower than in the other two waves and the 1975 values are generally lower than the corresponding 1972 values at both 50 and 30 mb levels. m = 1,n = 3. The seasonal changes of this wave both for 1p72 and 1975 are similar to the m = 1, n = 1 wave. But the amplitude is about twice that of the m = 1, n = 1, wave in March and November. It is, however, somewhat small in monsoon months for this wave. 3.2. Phase
and tilts of the waues
Table 1 gives the positions of ridge line at the 50 and 30 mb levels and the tilt between these levels, for m= 1, n=l and m=l, n=3 for 1972 and 1975. We have considered only these waves as it is clear from Fig. 2(b) that wave m = 2, II = 2 is very weak. From the orientation of the ridge line at an isobaric level, we infer qualitatively the northsouth transfer of’ westerly momentum (STARR, 1948). If the orientation of ridge line is in NE-SW direction, in the horizontal plane, then the horizon-
tal tilt is eastward and transport of westerly momentum is northward. If the orientation is in NW-SE direction the horizontal tilt is westward and transfer of momentum is southward. If along a particular latitude belt, the orientation of the ridge line with increase in height (50 to 30 mb) is eastward, the vertical tilt is reckoned as eastward and transport of heat is southward. m = 1, n = 1. For 1975, the ridge position lies throughout the year between central North America and mid Pacific. The ridge positions at the 50 and 30 mb levels give an eastward tilt in May to September and a westward tilt in other months. For 1972 at both the levels, the ridge line lies in the west Pacific region, but it shifts to eastern Pacific area during monsoon months and during post monsoon period it again shifts back to western Pacific regions. During monsoon months the eastward tilt is more pronounced during 1972 than in 1975: in other months westward tilts are similar to 1975. But in the upper troposphere, the ridge line of this wave during monsoon months, lies over west Asia and vertical tilt is eastward (AWADE et al., 1975). m= 1, n= 3. During 1975 in the lower stratosphere the ridge lies over north American and adjoining Pacific regions and the vertical tilt is westward throughout the year. In 1972, the ridge lies over the Pacific Ocean area, nearer to America during non-monsoon months and nearer to Japan during monsoon months. During monsoon months (June to September), the vertical tilt is clearly eastward. In other months the tilt is westward. In the upper troposphere the ridge lies during monsoon months over central China and gives an eastward vertical tilt (AWADE et al., 1975).
Table 1. Monthly values of vertical tilt in degrees longitude of the ridge line (from spherical harmonic analysis) m=l
and n=l
1975
m=l 1972
and n=3
1975
1972
Month
50mb
30mb
Tilt
50mb
30mb
Tilt
50mb
30mb
Tilt
50mb
30mb
Tilt
January February March April
217 218 237 259 216 213 221 191 192 220 195 214
206 206 224 234 221 229 225 204 200 207 177 192
11W 12w 13W 25W -5E -16E -4E -13E -8E 13W 18W 22W
207 210 238 276 173 158 97 128 143 162 218 214
197 204 224 243 192 198 174 187 160 170 204 192
low
237 242 254 295 280 249 262 249 226 268 265 229
220 225 243 272 261 245
17w 17w 11w 23W 19w 4w 2w 15w 21w 25W 34w 19w
229
207 213 239 281 234 231 149 189 168 257 228 219
22w 7W 8W 9W 6W -6E -43E -86E -22E 29W 14w 22w
May June July August Septembex October November December
6W 14w 33w -19E -4OE -77E -59E -17E -8E 14w 22w
234 205 243 231 210
247 290 240 225 106 103 146 286 242 241
Dynamics of the lower stratosphere in the wave number 4. RESULTS
OF FOURIER
and phases
The difference between the amplitudes in the monsoon and non-monsoon months are larger at
gor(a)
@*
30mb
-
1972
@=
50rnb
----
1975
871
high latitudes than at low latitudes. In the months April to September the amplitude is very low, while in other months it is significantly high. Generally amplitudes at 60”N are higher in 1975 than in 1972 for m = 1 and m =3 except in April and November. Amplitudes of these waves during March are larger in 1975 than in 1972. In general, amplitudes during monsoon months are smaller in 1972 than in 1975 at all latitudes. The amplitude maximum at 60”N in February is more prominent for wave 2 than for wave 1 in 1972 and in 1975.
ANALYSIS
Fourier analysis has been performed of the grid point values along the latitudes circle 20”N, 30”N, 40”N and 60”N for each month of the years 1972 and 1975 for the 50 and 30 mb levels. The annual march of the amplitudes is represented in Fig. 3. 4.1. Amplitudes
domain
80 70
3a:3dN
n
60 B-30
mb
-
1972
@-SO
mb
----
,975
JFMAMJJASOND MONTHS
-
MONTHS
-
3b: 60 N
-
1972
----I975 400 360
600 (b)
ii
F
;: 1 + 1 !! 9
@s
30
mb
-
1972
0.
50
mb
----
1975
540
JFMAMJJASOND
JFMAMJJASOND MONTHS
Fig. 3a. Annual march of amplitudes 3b. Annual
march
of amplitudes
-
(Fourier Analysis). (a) m = 1, (b) m = 2, (c) m = 3 (30% Lat); (Fourier analysis) (a) m = 1, (b) m = 2, (c) m = 3 (60”N Lat).
K. S. F&IA RAO, S. T. AWADE and M. V. HARINDRANATHAN NAIR
872
Amplitudes of wave 3 are small compared to m = 1 and 2. Their maxima are more or less the same at both the 50 mb and 30 mb levels at 60”N latitude for 1975. The premonsoon maximum of wave 3 at the higher latitude occurs in February for 1972 and 1975. Other features are similar to m = 1. At high latitudes, the eddies become prominent in winter months in the lower stratosphere. This agrees with simlar results obtained for upper troposphere (WIIN-NIELSON et al. 1963). At the 50 and 30 mb levels amplitude fluctuations at 30”N and 60”N latitudes are similar. Enhancement of amplitude between 50 mb and 30 mb increases with latitude; amplitude maximum at 60”N latitude is an order of magnitude larger than at 30”N. At low latitudes amplitudes show larger fluctuations than at high latitudes. At both the 50 mb and 30 mb levels, the ridge position of wave 1 at 20”N is more eastward in 1975 than in 1972 in the April to August months. In the monsoon months the ridge line shifts eastward of the premonsoon position in 1975 while it is steady in 1972. At both the 50 mb and 30 mb levels the ridge position is generally less eastward at 40”N latitude in 1972 than in 1975 (shift from 0” to 360” is here taken as eastward). A more eastward position during monsoon months is indicated when there is good monsoon activity. The ridge positions in the monsoon months of wave number 2 in the lower
63)
PHASE
-
30 mb 1972 30mb
1975
30mb
1975
@-JULY
--x--x-
50mb
1972
-x-x-
50mb
1972
.......
SOmb
1975
... . .. .
5Omb
1975
----
@JULY
LINE)
The horizontal tilts at both the 50 and 30mb levels for waves 1 and 2 have been computed from 0” to 80”N latitudes for both the years 1972 and 1975 and have been depicted in Fig. 4 for typical months, January and July representing winter and
----
@--JANUARY
LONGITUDE
tilt
@JANUARY
M
IN
4.2. Horizontal
1972
-
(RIDGE
stratosphere is also found to be more eastward in 1975 than in 1972 at 40”N latitude. VAN LOON et al. (1973) studied the zonal harmonic of the height field in the stratospheric region for the years 1965 to 1969 which “span a large part of our ampof the possible range”. Comparison litude values at 30”N and 60”N latitudes in January and July with their average values as depicted in their Figs. 2,3,4 and 5 reveals that although there is some agreement between the two sets of amplitudes; disagreements are there. For example our amplitudes at 30”N are far smaller than theirs in 1972 and 1975 at both 50 mb and 30 mb levels, in January, for wave 2 and at 60”N for wave 1. However, a comparison with their amplitudes at 60”N (Fig. 10 of VAN LOON et al., 1973) shows that our amplitudes of waves 1 and 2 in 1975 agree with theirs but our 1972 amplitudes of wave 2 are more than double the highest values obtained by Van Loon and co-workers. This is perhaps due to the extraordinary nature of the general circulation prevailing in 1972 during which many geophysical phenomena showed abnormality.
rnb
PHASE
IN (RIDGE
Fig. 4. Horizontal tilt of the ridge line (a) m = 1, (b) m = 2.
LONGITUDE LINE)
Dynamics of the lower stratosphere
i
50 1::
mb
30mbII
I
1
3;LATITUOE.
‘:jf
I
I
I
I
I
1
1
JULY
II 6dLATITUDE.
JANUARY
300 LATITUDE.
_.\ I,
I
50mbIk
I II 200 240 260 PHASE
IN
320
o
LONGITUDES
873
in the wave number domain
I 40
1
I
(RIDGE
I,
120
60
JANUARY
160
LINES)
Fig. 5. Vertical tilt between 50 and 30 mb levels of the ridge line, 30”N and 60”N latitudes in January and July of 1972 and 1975. summer conditions respectively. The tilt has been defined earlier. January, m = 1. Tilt is eastward up to 20”N in 1972 and westward in 1975 at 50 mb and then it is eastward in both years up to 60”N; beyond 60”N it is westward in 1975 and eastward in 1972. At the 30 mb level the tilt is slightly eastward from 10”N to 60”N in both years but less eastward in 1972. January, m = 2. At 50 mb the wave shows westward tilt between the equator and 20”N, eastward tilt from 20”N to 60”N and beyond 60”N, the tilt is absent, in both the years. July, m = 1. At 50 mb the tilt is eastward up to 1O”N in both the years and thereafter it becomes less eastwards up to 40”N and westward up to 60”N in both the years. Beyond 60”N the tilt is eastward in 1972 but continues to be westward in 1975. At 30 mb from 10”N to 50”N the tilt is eastward in both the years and more westward in 1972 than in 1975 beyond 50”N latitude. July, m = 2. Beyond 20”N the tilt is more eastward in 1975 at both the levels while it is absent in the case of 1972. At 50 mb level the tilt is eastward at 30” lat and westward beyond 40”N in 1972 indicating northward transport of momentum at 30”N and southward transport beyond 30”N. In 1975 the tilt is absent up to 40”N and slightly westward beyond 40”N suggesting a southward transport of momentum. At 30 mb there is hardly any difference in the tilt
between the two years with the 50 mb level. 4.3.
beyond
20”N, in contrast
Vertical tilt
We have computed the vertical tilts between the 50 mb and 30 mb levels at 30”N representing the tropical regions and at 60”N representing the high latitudes, for January and July of 1972 and 1975. Figure 5 represents these tilts. m = 1. In both the years the tilt is generally westward with height at 30”N, in January. In July the tilt is eastward in 1972 and absent in 1975. The difference in tilt between 1972 and 1975 is very little in January at both 30”N and 60”N. But the difference is pronounced in July. m = 2. At 30”N latitude, the tilt is absent in both the years in January. The tilt is westward in July which is greater in 1972 than in 1975. At 60”N the tilt is westward both in January and July. In this respect waves m = 1 and m = 2 behave differently. The seasonal contrast between 1972 and 1975 is less at 60”N than at 30”N. 5. 5.1. Dynamical
DISCUSSION
considerations
In the foregoing sections the results of spherical harmonic analysis and of Fourier analysis of the geopotential heights have been indicated, for the principal waves. From the variations of amplitudes and phases with height and with latitude, the horizontal and vertical tilts have been inferred. These
K. S. R+UA RAO, S. T. AWADEand M. V.
874
tilts are indicative of the directions of transport of momentum and of sensible heat. We now discuss the important features brought out by the analysis. (1) It is seen that in general, amplitudes are larger at the 30 mb level than at the 50 mb level. We attribute this height variation to the density decrease with height. (2) Fourier analysis shows that the amplitude of waves 1 and 2 are in general larger in winter than in summer, and larger in high than in low latitudes. We speculate that these large amplitudes may be contributing towards the maintenance of the polar night jet (HOLTON, 1975, p. 114). (3) It is noticed that the vertical tilt at 30”N is more eastward in 1972 than in 1975, in the monsoon months, for m = 1. An eastward tilt indicates southward (eq~ato~ard) transport of sensible heat. This weakens the temperature gradient in 1972 and the reverse takes place in 1975. In our small sample of two years, there is a strong hint that a weakening of the temperature gradient in the lower stratosphere may be a sign of bad monsoon and its strengthening a sign of good monsoon. In the troposphere also it has been observed that a weak temperature gradient is an indication of bad monsoon, while a strong temperature gradient (more southward transport of sensible heat) is an indication of a good monsoon (AWADE, 1979). It should be remembered that the equator to pole temperature distribution in the troposphere is opposite to that in the stratosphere where the temperature decreases from pole to equator. (4) Wave 1 as well as 2 show contrasting features in 1972 and 19’75. These waves behave differently as regards amplitude fluctuations and also in the vertical and horizontal tilts in the monsoon months. The contrast is more clearly visible at 30”N latitude. Fluctuations in amplitude in the low latitudes revealed in the Fourier analysis, may be caused by
NAIR
~~D~A~AN
the wave disturbances in the equatorial region whose existence was established by YANA~ and MARUYAMA (1968) and by WALLACE and KOUSKY (1968). There is observational evidence that during the monsoon season, the rainfall fluctuates substantially at about 2O”N lat. with periods longer than 10 days and a major portion of rainfall asymmetry is presumably carried by wave numbers 1 and 2 (MURAKAMI, 1972). 5.2. Energetics in the lower stratosphere ,to monsoon actiuity
We have computed the mean zonal and meridional winds (0 and v) at 50 and 30mb levels for the typical months January and July representing winter and summer conditions, for the years 1972 and 1975. Using the basic monthly mean geopotential height data, we computed winds with the geostrophic approximation. a*, o* and T* have been worked out for latitudes 30”N and 60”N representing subtropical and high latitudes respectively. o*, v* and T* are the deviations from the latitudinal monthly averages of 0, v and T respectively. The eddy transport of angular momentum and of sensible heat have been worked out for the two stratospheric levels and given in Table 2. Transport of angular momentum is mainly poleward at 30”N in both the years during winter and summer (when it is very small), both at the 50 and 30 mb levels. However, it is somewhat larger at 30”N in summer during 1975 than during 1972. In winter there is very little difference between 1972 and 1975 at this latitude. At 60”N the transport is equatorward in 1975 but poleward in 1972 in winter as well as in summer. Transport of sensible heat, although small, is poleward at 3O”N during July of 1975 but equatorward in 1972 at both the levels, suggesting that intensification of meridional temperature gradient in summer months may be a characteristic of good monsoon. It may be recalled that the same result
Table 2. Transport of angular momentum and sensible heat by standing eddies 50 mb
30 mb
iJ* q* Year
30”N
60”N
January
1972 1975
4.01 3.17
22.26 -2.00
July
1972 1975
0.04 0.26
-0.43 0.01
Month
Units U* v* m2 s-*, P* ?*‘K m s-’
in relation
q* _T* 30”N 0.24 0.25
c* +7*
60”N
30”N
60”N
27.53 12.75
4.42 4.36
38.20 -0.36
-0.01 0.15
0.03 0.44
- 0.06 0.22
0.04 0.08
q* .p 30”N
60”N
0.96 0.84
35.44 19.49
0.04 0.15
- 0.03 -0.11
-
Dynamics of the lower stratosphere has been obtained earlier in this paper, from a study of the tilts in the vertical. Similar features have been noticed in the upper troposphere also (AWADE, 1979). Transports of momentum and sensible heat are larger in winter than in summer and they are larger in high than in low latitudes. From the values of angular momentum and of heat transports, we have calculated the terms of conversion from eddy kinetic energy (KE) to zonal kinetic energy (KZ) and also from zonal available potential energy (A,) to eddy available potential energy (AE) using the following equations (OORT, 1964) C(K,, I&)
-
-
[U*“*]
2
g
In summer at 30”N, there is conversion from KE to Kz at both the levels, but larger in 1975 than in 1972. There is therefore more transfer of kinetic energy from eddies to zonal flow (which is easterly) in 1975 than in 1972. This transfer helps in maintaining stronger easterlies in 1975 than in 1972. We therefore suggest that the strengthening of easterlies over the subtropical latitudes (or even northwards) is associated with good monsoon activity. The linkage between strong easterlies in the equatorial stratosphere and good monsoon activity has already been established (RAJA RAO and LAKHOLE, 1977). At 60”N, in summer the conversion is from KZ to KE at both the levels in 1975; in 1972 the quantities are extremely small. Therefore there is a transfer of kinetic energy from zonal flow (a weak easterly) to the eddies in 1975; there is very little transfer in 1972. In winter at 30”N there is a large conversion from KE to Kz and there is little difference between the two years in both the levels. At 60”N there is a large conversion from Kz to KE at 50 mb, it is 50% more in 1975 than in 1972, while at the 30 mb level the conversion is from KE to KZ in 1972 and the reverse in 1975, the magnitudes are about one fourth those of 1972. In summer at 30”N there is conversion from AE to A, in 1975 while it is A, to AE in 1972 at both the levels. But at 60”N there is conversion from AZ to A, at 30 mb level in both years; at 50 mb level it is from A, to A, in 1972 and extremely small conversion from A, to A, in 1975. In winter at 30”N the conversion is from A, to AZ, larger in 1975 than in 1972 at the 50 mb level, while the magnitude is small at the 30 mb level. At 60”N the conversion is from A, to A, at the 50 mb and 30 mb levels but an order of magnitude larger in 1972 than in 1975.
(9)
dm
I 1
C(A,,A,)--g
- t,
F(r,
amI”
- -
x [V*T*] a a4
dm
[ ] = zonal mean * = Deviation - = Aera
of the quantity from zonal mean
mean
” = Deviation
from area mean
- = Time average a = Radius
87.5
in the wave number domain
of earth
dm=acosQd4dhg. g These values are computed for 50 and 30 mb at 30”N and 60”N latitudes and are given in Table 3.
Table 3. Energy conversion terms C(K,, K,) and (AE, A,) 50 mb C(K,,
30 mb
K,)
C(A,,
Month
Year
30”N
60”N
January
1972
12.51
- 1.93
1975
15.24
-2.78
1972 1975
0.10 0.47
0.00 -0.17
0.77 - 0.36
July
Units: K,). C(K,,
C(A,,
A& = 10e2 (mWme2
K,) = 10e2 (mWme2
mb-‘)
A, )
30”N
60”N
30”N
- 2.82
316.88
- 19.29
32.40 - 1.02 0.10
rnb-‘) (positive
(positive
values
values represent
C(A,,
C(K,> Kz)
A,
1
60”N
30”N
60”N
16.20
42.47
- 3.54
427.60
17.40
-9.88
- 0.53
21.24
0.07 0.70
- 0.04 -0.17
0.23 -0.55
0.54 0.16
represent
conversion
conversion
from
KE to
from AA to AE).
K. S. RAJA RAO, S. T. AWADE and M. V. HARINDRANATHAN NAIR
816
It is therefore clear that the contrast between 1975 and 1972 is marked in subtropical latitudes in summer and in high latitudes in winter. It is hard to speculate whether any association exists between the physical processes pertaining to monsoon activities, in the stratospheric levels at the low and high latitudes. Further work being done by the present authors will hopefully enable them to express an opinion in this regard.
feature of good monsoon both in the upper troposphere and in the lower stratosphere; (4) large fluctuations in the amplitude in low latitudes are attributed to the equatorial disturbances; (5) there is a marked contrast between 1975 and 1972 in the subtropical latitudes in summer; in the high latitudes, this contrast is greatest in winter; (6) transport of kinetic energy from the eddies to the zonal flow in the subtropics in the summer months of 1975 suggests that the strengthening of the easterlies in association with monsoon activity extends from the equator up to 30”N lat. and beyond.
6. CONCJAJSlONS
From our drawn:
study
the
following
conclusions
are
(1) waves 1 and 2 show contrasting features in 1972 and in 1975; (2) large eastward tilt of the ridge line with height in monsoon months is a striking feature of 1972; (3) we speculate that the weakening of the equator to pole temperature gradient is a characteristic of bad monsoon and its strengthening a
Acknowledgements-The authors are grateful to the Director, Indian Institute of Tropical Meteorology, Poona, for the facilities provided to do this work. Two of us (K.S.R. and M.V.H.N.) are thankful to the Council of Scientific and Industrial Research, New Delhi for financial support for the project. The authors are thankful to Mr. S. M. BAWISKAR for his assistance in computational work.
REFERENCES
Met. Geophys.
AWADE S. T., ASNANI G. C. and KESAVAMURTHY R. N. BLINOVA E. M. CRAIG R. A. ELIASEN E. ELIASEN E. and MACHENHAUER B. ELIASEN E. and MACHENHAIJERB. HAURWITZ B. HOLTON J. R.
1975
Arch.
1943 1945 1958 1965 1969 1940 1975
MURAKAMI T. NEAMTAN S. M. OORT A. RAJA RAO K. S. and LAKHOLE N. J. SCHMIDT A.
1972 1946 1964 1977 1935
STARR V. P. VAN LOON H., JENNE R. L. and LABITZKE K. WALLACE J. M. and KOUSKY V. E. WIIN-NIELSON A., BROWN J. A. and DRAKE M. World Meteorological Organisation YANAI M. and MARWAMA T.
1948 1973 1968 1963 1973 1968
Dokl. Akad. Nauk. SSSR 39, 277 J. Met. 2, 173. Tellus 10, 206 Tellus, 17, 220 Tellus, 21, 149 .I. mar. Res. 3, 254. The Dynamic Meteorology of rhe Strarosphere and Mesosphere, American Met. Sot. Met. Monographs. J. atmos. Sci. 29, 1129. J. Met. 3, 53 Mon. Wea. Rev. 92, 483. Ind. J. Met. Geophys. 29, 403. Tafeln der normierten Kugelfunktionen, Sowie Formeln zur Entwicklung, Gotha, Engelhard-Reyer J. Met. 5, 39. J. geophys. Res. 78, 4463. J. atmos. Sci. 25, 900. Tellus, 15, 261 Bullerin J. met. Sot. Japan, 45, 196.
Reference
Bioklim.
Ser. A. 24, 189.
is also made to the following unpublished marerial:
AWADE S. T.
1979
Ph. D. Thesis, Poona
University
(India).
Dynamics
of the lower stratosphere in the wave number domain in relation to monsoon activity
K. S. RAJA RAO, S. T. AWADE and M. V. HARINDRANATHAN NAIR Indian Institute of Tropical Meteorology, Poona, India (Receiued 7 November 1979;
in reoised
form
8
April 1980)
Abstract-A
study has been made of the dynamics of the lower stratosphere in the wave number domain by spherical harmonic and Fourier analyses of the grid point values of the geopotential heights at the 50 and 30 mb levels for each month of the years 1972 and 1975. Only waves 1, 2 and 3 are dominant. Transports of momentum and of sensible heat in the lower stratosphere, month by month, have been studied by computing the vertical and horizontal tilts of the ridge line. The seasonal variations in the amplitude and in the tilt with height of the ridge line of these waves have been discussed. Weakening of the equator to pole temperature gradient in 1972 and its strengthening in 1975 are striking features. Eddy transports of angular momentum and of sensible heat and energy conversion terms from eddy to zonal kinetic energy and from eddy to zonal available potential energy have been computed for January and July of 1972 and 1975 for the levels 50 and 30 mb and at 30”N and 60”N latitudes and the results have been discussed. Transfer of kinetic energy from eddies to zonal flow in 1975 suggests that the strengthening of the easterlies extends to 30”N and beyond. 1. INTRODUCI’ION
The overall circulation in the stratosphere is maintained by the differential heating due to the net radiation field in which ozone, CO, and Hz0 play an important role. The stratosphere is a region of high static stability, while the troposphere is a region of relatively low static stability. The average equator to pole temperature gradient in the lower stratosphere is opposite to that in the troposphere. Topographical and thermal forcings in the troposphere introduce important non-linear interactions while in the stratosphere, the principal eddies comprise planetary scale waves which can mostly be treated to reasonable accuracy by linear wave dynamics. Many large scale features in the atmosphere become more evident in the stratosphere than in the troposphere, as a number of small perturbations disappear with increase in height. The seasonal nature of the stratosphere is well defined. It is felt that there are significant anomalies in the large scale global circulation pattern before and during the monsoon (June to September) which could be dynamically connected to the behaviour of the monsoon. In order to investigate some of these problems, the present authors have planned to study the lower stratospheric circulation in the wave number domain by the spherical harmonic analysis of the stratospheric parameters. The purpose of the study
is to examine the contrasting features between the stratospheric and tropospheric circulations and the anomaly of the monsoon in the overall stratospheric circulation on a global scale. In the present study we have chosen two years: 1972 and 1975. The year 1972 has been recognised as one of the worst drought years in India and elsewhere (see for example WMO bulletin 1973). Nineteen hundred and seventy-five was a year of good monsoon activity not only over India, but in other parts of Asia. In categorising a year as a “good” or “bad” monsoon year, the June to September rainfall over India is taken as the criterion. The rainfall deviation from normal, over the central parts of India
defines normal
a year as a normal (good) or as below (bad) monsoon year (RAJA RAO and
LAKHOLE, 1977). We have therefore considered 1972 as a typical year of bad monsoon and 1975 a good monsoon year. These two years span a large part of possible range of monsoon activity. As monsoon is a part of general circulation, the contrasting features of the circulations in these two years have been examined. Spherical harmonic analysis is a powerful tool in the study of the dynamics and climatology of the atmosphere, for a large amount of meteorological data can be analysed and the results expressed in a relatively few numbers which represent the global picture on the spherical earth. Spherical harmonics constitute the most natural set of orthogonal functions for the study of planetary scale meteorological 867
K. S. RAJA Fbo, S. T. AWADEand M. V. H~~A~~
868
systems. SCHMIDT (1935) was the pioneer in the application of spherical harmonics to geophysical problems and HAURWITZ (1940) was the first to utilise spherical harmonics in meteorology. Since then many workers (see for example CRAIG, 1945: BLINOVA, 1943; NEAMTAN, 1946; ELIASEN, 1958) have used this method of analysis in their studies of atmospheric motion. Spherical harmonic and Fourier analyses have been made of the geopotential heights at the 50 and 30 mb levels, for each month of the years 1972 and 1975. Transports of moments and of sensible heat in the lower stratosphere, month by month have been studied by computing the vertical and horizontal tilts of the ridge line. Seasonal features of the stratospheric circulation in 1975 and in 1972 have been studied. Eddy transports of angular momentum and of sensible heat and the energy conversion terms, from i& to Kz and A, to Az have been computed for January and July of 1972 and 1975 for the 50 and 30 mb levels at 30”N and 60”N latitudes. The results have been discussed. 2. DATA ANDMETHODOF ANALYSIS The Institut fiir Meteorologic of the German Free University, Berlin, regularly publishes in Meteorologische Abhandlungen, the grid point values of monthly mean winds, temperatures and geopotential heights of the 50 and 30mb levels. These grid points are at intervals of 10” latitude and 10” longitude for the northern hemisphere. In the analysis, we have closely followed the method of ELIASEN and MACHENHAUER(1965,1969). Due to the poor state of the observations in the southern hemisphere, the study has been restricted to northern hemisphere. The height field is symmetric with respect to the equator, as a consequence of the balance equation (see for example ELIASEN and MACHENHAUER, 1965, p. 223). Along the latitude circle +, the height H is expressed by the relation H(A) = C a,(+)
c0S mh f b,(#) sin mh.
(1)
On a sphere the field is given by H(c#$A)=
c .f
(a,” cos mh
m=o
n=am
+ b,” sin ~~~P”m(~)
(2)
where Pnm(p) is the associated Legendre function of the first kind. m is the number of waves round the earth and n - m the number of zero points from north pole to south pole and p = sin 4. Due to
NAIR
restriction of the anaiysis to the northern hemisphere only and the assumption of symmetry about the the orthogonality condition for the equator, Legendre polynomials becomes, following ELIASEN and MACHENHAUER (1965)
For n # n’ and n f n’ even. Normalisation is
n-m
condition
is even.
The coefficients a,,“’ and b,” are given by 1 a, m=
I0
~~~~)p~m(~) +
(3
Here a,(4) and b,,,(#) are Fourier coefficients. The amplitude R,” and phase E,,~ are given by R” = &,m)2+ tane,“=;.
(b,“)‘,
(7)
b,“’ a,
u,,,(9) and b,(4) are determined by Fourier analysis of the grid point values at 10” latitude interval. P,“‘(p) have been computed for m = 1 to 16 and n - m = 0 to 16. Using these values of a,(+), b,(4) and P,“(p) values of ~l,~ and b,” are obtained by trapezoidal rule.
3. RESULTSOF SPDERICALHARMONICANALYSIS Figure 1 (a, b, c, d) shows the amplitudes of the different waves for typical months January and July 1972 for the 50 and 30 mb levels in an (m, n - m) diagram. Figure 1 suggests that the eddy energy in the lower stratosphere is primarily in wave numbers 1 to 4 for n - m = 0 to 4. Since substantial amount of energy is present in wave numbers m = 1, n = 1; m = 2, n = 2; and m = 1, n = 3 we have considered in this paper the amplitude and phases of these waves only. Greenwich meridian is reckoned as the longitude of phase zero. Figure 2 depicts the amplitudes of these waves month by month, for the years 1972 and 1975 at the 50 and 30mb levels. Important characteristics of the principal waves in the two years are discussed below.
Dynamics of the lower stratosphere
16
@=
r
(b)
(gpm) of waves for different values of m and n - m, in 1972; July (a) 50mb (b) 30 mb; January (c) 50 mb (d) 30 mb.
Fig. 1. Amplitude
@*
869
in the wave number domain
@=30mb
200
30mb
-
,972
50 mb
----
,375
@= 180
50mb
fl
----
,972
t975
to
60
70
r %M)
12
w CI
50
@
30 mb
-
@-
50 mb
----
(b)
IO
3
E _I
40
n 5
30
4
20
1972 ,975
;“O
10 0
JFMAMJJASOND MONTHS-----e
JFMAMJJASOND MONTHS
-
MONTHS-
Fig. 2. Annual march of amplitudes of waves (spherical harmonic analysis) (a) m = 1, n = 1; (b) m = 2. n = 2; (Cf m = 1. n = 3.
K. S. RAJARAO, S. T.
870 3 .l.
AWADE and M. V. HARINDRANAW NAIR
Amplitrcdes
m = 1, n = 1. The amplitude is a maximum in March at both the 50 mb and 30 mb levels in 1975. The annual march of amplitude in 1972 is similar to that in 1975 except for the maximum in March. There is marked decrease in amplitude from March to April in 1975 and a less steep decrease in 1972. In the monsoon months (June to September) amplitudes are lower than in the other months. There is an enhancement in amplitude at 30 mb. In general, the amplitude in the year 1975 is larger than in 1972 except in April and November. m = 2, n = 2. There is no predominant maximum for this wave. The magnitudes are one order lower than in the other two waves and the 1975 values are generally lower than the corresponding 1972 values at both 50 and 30 mb levels. m = 1,n = 3. The seasonal changes of this wave both for 1p72 and 1975 are similar to the m = 1, n = 1 wave. But the amplitude is about twice that of the m = 1, n = 1, wave in March and November. It is, however, somewhat small in monsoon months for this wave. 3.2. Phase
and tilts of the waues
Table 1 gives the positions of ridge line at the 50 and 30 mb levels and the tilt between these levels, for m= 1, n=l and m=l, n=3 for 1972 and 1975. We have considered only these waves as it is clear from Fig. 2(b) that wave m = 2, II = 2 is very weak. From the orientation of the ridge line at an isobaric level, we infer qualitatively the northsouth transfer of’ westerly momentum (STARR, 1948). If the orientation of ridge line is in NE-SW direction, in the horizontal plane, then the horizon-
tal tilt is eastward and transport of westerly momentum is northward. If the orientation is in NW-SE direction the horizontal tilt is westward and transfer of momentum is southward. If along a particular latitude belt, the orientation of the ridge line with increase in height (50 to 30 mb) is eastward, the vertical tilt is reckoned as eastward and transport of heat is southward. m = 1, n = 1. For 1975, the ridge position lies throughout the year between central North America and mid Pacific. The ridge positions at the 50 and 30 mb levels give an eastward tilt in May to September and a westward tilt in other months. For 1972 at both the levels, the ridge line lies in the west Pacific region, but it shifts to eastern Pacific area during monsoon months and during post monsoon period it again shifts back to western Pacific regions. During monsoon months the eastward tilt is more pronounced during 1972 than in 1975: in other months westward tilts are similar to 1975. But in the upper troposphere, the ridge line of this wave during monsoon months, lies over west Asia and vertical tilt is eastward (AWADE et al., 1975). m= 1, n= 3. During 1975 in the lower stratosphere the ridge lies over north American and adjoining Pacific regions and the vertical tilt is westward throughout the year. In 1972, the ridge lies over the Pacific Ocean area, nearer to America during non-monsoon months and nearer to Japan during monsoon months. During monsoon months (June to September), the vertical tilt is clearly eastward. In other months the tilt is westward. In the upper troposphere the ridge lies during monsoon months over central China and gives an eastward vertical tilt (AWADE et al., 1975).
Table 1. Monthly values of vertical tilt in degrees longitude of the ridge line (from spherical harmonic analysis) m=l
and n=l
1975
m=l 1972
and n=3
1975
1972
Month
50mb
30mb
Tilt
50mb
30mb
Tilt
50mb
30mb
Tilt
50mb
30mb
Tilt
January February March April
217 218 237 259 216 213 221 191 192 220 195 214
206 206 224 234 221 229 225 204 200 207 177 192
11W 12w 13W 25W -5E -16E -4E -13E -8E 13W 18W 22W
207 210 238 276 173 158 97 128 143 162 218 214
197 204 224 243 192 198 174 187 160 170 204 192
low
237 242 254 295 280 249 262 249 226 268 265 229
220 225 243 272 261 245
17w 17w 11w 23W 19w 4w 2w 15w 21w 25W 34w 19w
229
207 213 239 281 234 231 149 189 168 257 228 219
22w 7W 8W 9W 6W -6E -43E -86E -22E 29W 14w 22w
May June July August Septembex October November December
6W 14w 33w -19E -4OE -77E -59E -17E -8E 14w 22w
234 205 243 231 210
247 290 240 225 106 103 146 286 242 241
Dynamics of the lower stratosphere in the wave number 4. RESULTS
OF FOURIER
and phases
The difference between the amplitudes in the monsoon and non-monsoon months are larger at
gor(a)
@*
30mb
-
1972
@=
50rnb
----
1975
871
high latitudes than at low latitudes. In the months April to September the amplitude is very low, while in other months it is significantly high. Generally amplitudes at 60”N are higher in 1975 than in 1972 for m = 1 and m =3 except in April and November. Amplitudes of these waves during March are larger in 1975 than in 1972. In general, amplitudes during monsoon months are smaller in 1972 than in 1975 at all latitudes. The amplitude maximum at 60”N in February is more prominent for wave 2 than for wave 1 in 1972 and in 1975.
ANALYSIS
Fourier analysis has been performed of the grid point values along the latitudes circle 20”N, 30”N, 40”N and 60”N for each month of the years 1972 and 1975 for the 50 and 30 mb levels. The annual march of the amplitudes is represented in Fig. 3. 4.1. Amplitudes
domain
80 70
3a:3dN
n
60 B-30
mb
-
1972
@-SO
mb
----
,975
JFMAMJJASOND MONTHS
-
MONTHS
-
3b: 60 N
-
1972
----I975 400 360
600 (b)
ii
F
;: 1 + 1 !! 9
@s
30
mb
-
1972
0.
50
mb
----
1975
540
JFMAMJJASOND
JFMAMJJASOND MONTHS
Fig. 3a. Annual march of amplitudes 3b. Annual
march
of amplitudes
-
(Fourier Analysis). (a) m = 1, (b) m = 2, (c) m = 3 (30% Lat); (Fourier analysis) (a) m = 1, (b) m = 2, (c) m = 3 (60”N Lat).
K. S. F&IA RAO, S. T. AWADE and M. V. HARINDRANATHAN NAIR
872
Amplitudes of wave 3 are small compared to m = 1 and 2. Their maxima are more or less the same at both the 50 mb and 30 mb levels at 60”N latitude for 1975. The premonsoon maximum of wave 3 at the higher latitude occurs in February for 1972 and 1975. Other features are similar to m = 1. At high latitudes, the eddies become prominent in winter months in the lower stratosphere. This agrees with simlar results obtained for upper troposphere (WIIN-NIELSON et al. 1963). At the 50 and 30 mb levels amplitude fluctuations at 30”N and 60”N latitudes are similar. Enhancement of amplitude between 50 mb and 30 mb increases with latitude; amplitude maximum at 60”N latitude is an order of magnitude larger than at 30”N. At low latitudes amplitudes show larger fluctuations than at high latitudes. At both the 50 mb and 30 mb levels, the ridge position of wave 1 at 20”N is more eastward in 1975 than in 1972 in the April to August months. In the monsoon months the ridge line shifts eastward of the premonsoon position in 1975 while it is steady in 1972. At both the 50 mb and 30 mb levels the ridge position is generally less eastward at 40”N latitude in 1972 than in 1975 (shift from 0” to 360” is here taken as eastward). A more eastward position during monsoon months is indicated when there is good monsoon activity. The ridge positions in the monsoon months of wave number 2 in the lower
63)
PHASE
-
30 mb 1972 30mb
1975
30mb
1975
@-JULY
--x--x-
50mb
1972
-x-x-
50mb
1972
.......
SOmb
1975
... . .. .
5Omb
1975
----
@JULY
LINE)
The horizontal tilts at both the 50 and 30mb levels for waves 1 and 2 have been computed from 0” to 80”N latitudes for both the years 1972 and 1975 and have been depicted in Fig. 4 for typical months, January and July representing winter and
----
@--JANUARY
LONGITUDE
tilt
@JANUARY
M
IN
4.2. Horizontal
1972
-
(RIDGE
stratosphere is also found to be more eastward in 1975 than in 1972 at 40”N latitude. VAN LOON et al. (1973) studied the zonal harmonic of the height field in the stratospheric region for the years 1965 to 1969 which “span a large part of our ampof the possible range”. Comparison litude values at 30”N and 60”N latitudes in January and July with their average values as depicted in their Figs. 2,3,4 and 5 reveals that although there is some agreement between the two sets of amplitudes; disagreements are there. For example our amplitudes at 30”N are far smaller than theirs in 1972 and 1975 at both 50 mb and 30 mb levels, in January, for wave 2 and at 60”N for wave 1. However, a comparison with their amplitudes at 60”N (Fig. 10 of VAN LOON et al., 1973) shows that our amplitudes of waves 1 and 2 in 1975 agree with theirs but our 1972 amplitudes of wave 2 are more than double the highest values obtained by Van Loon and co-workers. This is perhaps due to the extraordinary nature of the general circulation prevailing in 1972 during which many geophysical phenomena showed abnormality.
rnb
PHASE
IN (RIDGE
Fig. 4. Horizontal tilt of the ridge line (a) m = 1, (b) m = 2.
LONGITUDE LINE)
Dynamics of the lower stratosphere
i
50 1::
mb
30mbII
I
1
3;LATITUOE.
‘:jf
I
I
I
I
I
1
1
JULY
II 6dLATITUDE.
JANUARY
300 LATITUDE.
_.\ I,
I
50mbIk
I II 200 240 260 PHASE
IN
320
o
LONGITUDES
873
in the wave number domain
I 40
1
I
(RIDGE
I,
120
60
JANUARY
160
LINES)
Fig. 5. Vertical tilt between 50 and 30 mb levels of the ridge line, 30”N and 60”N latitudes in January and July of 1972 and 1975. summer conditions respectively. The tilt has been defined earlier. January, m = 1. Tilt is eastward up to 20”N in 1972 and westward in 1975 at 50 mb and then it is eastward in both years up to 60”N; beyond 60”N it is westward in 1975 and eastward in 1972. At the 30 mb level the tilt is slightly eastward from 10”N to 60”N in both years but less eastward in 1972. January, m = 2. At 50 mb the wave shows westward tilt between the equator and 20”N, eastward tilt from 20”N to 60”N and beyond 60”N, the tilt is absent, in both the years. July, m = 1. At 50 mb the tilt is eastward up to 1O”N in both the years and thereafter it becomes less eastwards up to 40”N and westward up to 60”N in both the years. Beyond 60”N the tilt is eastward in 1972 but continues to be westward in 1975. At 30 mb from 10”N to 50”N the tilt is eastward in both the years and more westward in 1972 than in 1975 beyond 50”N latitude. July, m = 2. Beyond 20”N the tilt is more eastward in 1975 at both the levels while it is absent in the case of 1972. At 50 mb level the tilt is eastward at 30” lat and westward beyond 40”N in 1972 indicating northward transport of momentum at 30”N and southward transport beyond 30”N. In 1975 the tilt is absent up to 40”N and slightly westward beyond 40”N suggesting a southward transport of momentum. At 30 mb there is hardly any difference in the tilt
between the two years with the 50 mb level. 4.3.
beyond
20”N, in contrast
Vertical tilt
We have computed the vertical tilts between the 50 mb and 30 mb levels at 30”N representing the tropical regions and at 60”N representing the high latitudes, for January and July of 1972 and 1975. Figure 5 represents these tilts. m = 1. In both the years the tilt is generally westward with height at 30”N, in January. In July the tilt is eastward in 1972 and absent in 1975. The difference in tilt between 1972 and 1975 is very little in January at both 30”N and 60”N. But the difference is pronounced in July. m = 2. At 30”N latitude, the tilt is absent in both the years in January. The tilt is westward in July which is greater in 1972 than in 1975. At 60”N the tilt is westward both in January and July. In this respect waves m = 1 and m = 2 behave differently. The seasonal contrast between 1972 and 1975 is less at 60”N than at 30”N. 5. 5.1. Dynamical
DISCUSSION
considerations
In the foregoing sections the results of spherical harmonic analysis and of Fourier analysis of the geopotential heights have been indicated, for the principal waves. From the variations of amplitudes and phases with height and with latitude, the horizontal and vertical tilts have been inferred. These
K. S. R+UA RAO, S. T. AWADEand M. V.
874
tilts are indicative of the directions of transport of momentum and of sensible heat. We now discuss the important features brought out by the analysis. (1) It is seen that in general, amplitudes are larger at the 30 mb level than at the 50 mb level. We attribute this height variation to the density decrease with height. (2) Fourier analysis shows that the amplitude of waves 1 and 2 are in general larger in winter than in summer, and larger in high than in low latitudes. We speculate that these large amplitudes may be contributing towards the maintenance of the polar night jet (HOLTON, 1975, p. 114). (3) It is noticed that the vertical tilt at 30”N is more eastward in 1972 than in 1975, in the monsoon months, for m = 1. An eastward tilt indicates southward (eq~ato~ard) transport of sensible heat. This weakens the temperature gradient in 1972 and the reverse takes place in 1975. In our small sample of two years, there is a strong hint that a weakening of the temperature gradient in the lower stratosphere may be a sign of bad monsoon and its strengthening a sign of good monsoon. In the troposphere also it has been observed that a weak temperature gradient is an indication of bad monsoon, while a strong temperature gradient (more southward transport of sensible heat) is an indication of a good monsoon (AWADE, 1979). It should be remembered that the equator to pole temperature distribution in the troposphere is opposite to that in the stratosphere where the temperature decreases from pole to equator. (4) Wave 1 as well as 2 show contrasting features in 1972 and 19’75. These waves behave differently as regards amplitude fluctuations and also in the vertical and horizontal tilts in the monsoon months. The contrast is more clearly visible at 30”N latitude. Fluctuations in amplitude in the low latitudes revealed in the Fourier analysis, may be caused by
NAIR
~~D~A~AN
the wave disturbances in the equatorial region whose existence was established by YANA~ and MARUYAMA (1968) and by WALLACE and KOUSKY (1968). There is observational evidence that during the monsoon season, the rainfall fluctuates substantially at about 2O”N lat. with periods longer than 10 days and a major portion of rainfall asymmetry is presumably carried by wave numbers 1 and 2 (MURAKAMI, 1972). 5.2. Energetics in the lower stratosphere ,to monsoon actiuity
We have computed the mean zonal and meridional winds (0 and v) at 50 and 30mb levels for the typical months January and July representing winter and summer conditions, for the years 1972 and 1975. Using the basic monthly mean geopotential height data, we computed winds with the geostrophic approximation. a*, o* and T* have been worked out for latitudes 30”N and 60”N representing subtropical and high latitudes respectively. o*, v* and T* are the deviations from the latitudinal monthly averages of 0, v and T respectively. The eddy transport of angular momentum and of sensible heat have been worked out for the two stratospheric levels and given in Table 2. Transport of angular momentum is mainly poleward at 30”N in both the years during winter and summer (when it is very small), both at the 50 and 30 mb levels. However, it is somewhat larger at 30”N in summer during 1975 than during 1972. In winter there is very little difference between 1972 and 1975 at this latitude. At 60”N the transport is equatorward in 1975 but poleward in 1972 in winter as well as in summer. Transport of sensible heat, although small, is poleward at 3O”N during July of 1975 but equatorward in 1972 at both the levels, suggesting that intensification of meridional temperature gradient in summer months may be a characteristic of good monsoon. It may be recalled that the same result
Table 2. Transport of angular momentum and sensible heat by standing eddies 50 mb
30 mb
iJ* q* Year
30”N
60”N
January
1972 1975
4.01 3.17
22.26 -2.00
July
1972 1975
0.04 0.26
-0.43 0.01
Month
Units U* v* m2 s-*, P* ?*‘K m s-’
in relation
q* _T* 30”N 0.24 0.25
c* +7*
60”N
30”N
60”N
27.53 12.75
4.42 4.36
38.20 -0.36
-0.01 0.15
0.03 0.44
- 0.06 0.22
0.04 0.08
q* .p 30”N
60”N
0.96 0.84
35.44 19.49
0.04 0.15
- 0.03 -0.11
-
Dynamics of the lower stratosphere has been obtained earlier in this paper, from a study of the tilts in the vertical. Similar features have been noticed in the upper troposphere also (AWADE, 1979). Transports of momentum and sensible heat are larger in winter than in summer and they are larger in high than in low latitudes. From the values of angular momentum and of heat transports, we have calculated the terms of conversion from eddy kinetic energy (KE) to zonal kinetic energy (KZ) and also from zonal available potential energy (A,) to eddy available potential energy (AE) using the following equations (OORT, 1964) C(K,, I&)
-
-
[U*“*]
2
g
In summer at 30”N, there is conversion from KE to Kz at both the levels, but larger in 1975 than in 1972. There is therefore more transfer of kinetic energy from eddies to zonal flow (which is easterly) in 1975 than in 1972. This transfer helps in maintaining stronger easterlies in 1975 than in 1972. We therefore suggest that the strengthening of easterlies over the subtropical latitudes (or even northwards) is associated with good monsoon activity. The linkage between strong easterlies in the equatorial stratosphere and good monsoon activity has already been established (RAJA RAO and LAKHOLE, 1977). At 60”N, in summer the conversion is from KZ to KE at both the levels in 1975; in 1972 the quantities are extremely small. Therefore there is a transfer of kinetic energy from zonal flow (a weak easterly) to the eddies in 1975; there is very little transfer in 1972. In winter at 30”N there is a large conversion from KE to Kz and there is little difference between the two years in both the levels. At 60”N there is a large conversion from Kz to KE at 50 mb, it is 50% more in 1975 than in 1972, while at the 30 mb level the conversion is from KE to KZ in 1972 and the reverse in 1975, the magnitudes are about one fourth those of 1972. In summer at 30”N there is conversion from AE to A, in 1975 while it is A, to AE in 1972 at both the levels. But at 60”N there is conversion from AZ to A, at 30 mb level in both years; at 50 mb level it is from A, to A, in 1972 and extremely small conversion from A, to A, in 1975. In winter at 30”N the conversion is from A, to AZ, larger in 1975 than in 1972 at the 50 mb level, while the magnitude is small at the 30 mb level. At 60”N the conversion is from A, to A, at the 50 mb and 30 mb levels but an order of magnitude larger in 1972 than in 1975.
(9)
dm
I 1
C(A,,A,)--g
- t,
F(r,
amI”
- -
x [V*T*] a a4
dm
[ ] = zonal mean * = Deviation - = Aera
of the quantity from zonal mean
mean
” = Deviation
from area mean
- = Time average a = Radius
87.5
in the wave number domain
of earth
dm=acosQd4dhg. g These values are computed for 50 and 30 mb at 30”N and 60”N latitudes and are given in Table 3.
Table 3. Energy conversion terms C(K,, K,) and (AE, A,) 50 mb C(K,,
30 mb
K,)
C(A,,
Month
Year
30”N
60”N
January
1972
12.51
- 1.93
1975
15.24
-2.78
1972 1975
0.10 0.47
0.00 -0.17
0.77 - 0.36
July
Units: K,). C(K,,
C(A,,
A& = 10e2 (mWme2
K,) = 10e2 (mWme2
mb-‘)
A, )
30”N
60”N
30”N
- 2.82
316.88
- 19.29
32.40 - 1.02 0.10
rnb-‘) (positive
(positive
values
values represent
C(A,,
C(K,> Kz)
A,
1
60”N
30”N
60”N
16.20
42.47
- 3.54
427.60
17.40
-9.88
- 0.53
21.24
0.07 0.70
- 0.04 -0.17
0.23 -0.55
0.54 0.16
represent
conversion
conversion
from
KE to
from AA to AE).
K. S. RAJA RAO, S. T. AWADE and M. V. HARINDRANATHAN NAIR
816
It is therefore clear that the contrast between 1975 and 1972 is marked in subtropical latitudes in summer and in high latitudes in winter. It is hard to speculate whether any association exists between the physical processes pertaining to monsoon activities, in the stratospheric levels at the low and high latitudes. Further work being done by the present authors will hopefully enable them to express an opinion in this regard.
feature of good monsoon both in the upper troposphere and in the lower stratosphere; (4) large fluctuations in the amplitude in low latitudes are attributed to the equatorial disturbances; (5) there is a marked contrast between 1975 and 1972 in the subtropical latitudes in summer; in the high latitudes, this contrast is greatest in winter; (6) transport of kinetic energy from the eddies to the zonal flow in the subtropics in the summer months of 1975 suggests that the strengthening of the easterlies in association with monsoon activity extends from the equator up to 30”N lat. and beyond.
6. CONCJAJSlONS
From our drawn:
study
the
following
conclusions
are
(1) waves 1 and 2 show contrasting features in 1972 and in 1975; (2) large eastward tilt of the ridge line with height in monsoon months is a striking feature of 1972; (3) we speculate that the weakening of the equator to pole temperature gradient is a characteristic of bad monsoon and its strengthening a
Acknowledgements-The authors are grateful to the Director, Indian Institute of Tropical Meteorology, Poona, for the facilities provided to do this work. Two of us (K.S.R. and M.V.H.N.) are thankful to the Council of Scientific and Industrial Research, New Delhi for financial support for the project. The authors are thankful to Mr. S. M. BAWISKAR for his assistance in computational work.
REFERENCES
Met. Geophys.
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1975
Arch.
1943 1945 1958 1965 1969 1940 1975
MURAKAMI T. NEAMTAN S. M. OORT A. RAJA RAO K. S. and LAKHOLE N. J. SCHMIDT A.
1972 1946 1964 1977 1935
STARR V. P. VAN LOON H., JENNE R. L. and LABITZKE K. WALLACE J. M. and KOUSKY V. E. WIIN-NIELSON A., BROWN J. A. and DRAKE M. World Meteorological Organisation YANAI M. and MARWAMA T.
1948 1973 1968 1963 1973 1968
Dokl. Akad. Nauk. SSSR 39, 277 J. Met. 2, 173. Tellus 10, 206 Tellus, 17, 220 Tellus, 21, 149 .I. mar. Res. 3, 254. The Dynamic Meteorology of rhe Strarosphere and Mesosphere, American Met. Sot. Met. Monographs. J. atmos. Sci. 29, 1129. J. Met. 3, 53 Mon. Wea. Rev. 92, 483. Ind. J. Met. Geophys. 29, 403. Tafeln der normierten Kugelfunktionen, Sowie Formeln zur Entwicklung, Gotha, Engelhard-Reyer J. Met. 5, 39. J. geophys. Res. 78, 4463. J. atmos. Sci. 25, 900. Tellus, 15, 261 Bullerin J. met. Sot. Japan, 45, 196.
Reference
Bioklim.
Ser. A. 24, 189.
is also made to the following unpublished marerial:
AWADE S. T.
1979
Ph. D. Thesis, Poona
University
(India).