111

Power Spectrum Analysis of Atmospheric Ozone Content over North India By J. CHATTOPADHYAY1)

Summary - Atmospheric total ozone contents over three stations in north India have been studied. A power spectrum analysis has been made of daily values recorded at these stations during the winter season. Three types of periodicities have been observed in the available records, namely, oscillations with a period of (a) 2.5-3.5 days, (b) 4.0-5.3 days and (c) 8.0-9.6 days. The first and third type of oscillations were also observed when the data were extended to cover an entire year, instead of the winter season alone. A possible mechanism for the occurrence of these periodicities is discussed.

1. Introduction R e c e n t studies o f a t m o s p h e r i c total ozone c o n t e n t over n o r t h I n d i a (SEN GUPTA [3] z)) have revealed a seasonal rise in the ozone a m o u n t d u r i n g winter. I n this season, well defined a n d often r a p i d fluctuations in ozone a m o u n t are frequently observed. Such fluctuations are n o t o b s e r v e d during s u m m e r o r in a n y other season in India. The p u r p o s e o f the present p a p e r is to m a k e a statistical analysis o f the available d a t a with a view to locate possible periodicities in winter ozone contents over n o r t h India.

2. M e t h o d o f Analysis A p o w e r s p e c t r u m analysis was m a d e o f the avilable d a t a (BLAcKMAN a n d TVKEY [1] a n d MITCHELL et al. [2]). W e first c o m p u t e d serial correlation coefficients o f the f o r m n--r

c(r)

-

1

xf xi+~

(2.1)

n--r i=1

where x i represents the d e v i a t i o n o f an i n d i v i d u a l o b s e r v a t i o n f r o m the overall mean, n is the size o f the sample a n d r represents the lag for which the serial correlation coefficient c(r) was c o m p u t e d . In o u r c o m p u t a t i o n s , the m a x i m u m lag (m) did n o t exceed ten to fifteen percent o f the sample size (n). 1) Department of Geophysics, Banaras Hindu University, Varanasi-5, India. 2) Numbers in brackets refer to References, pages 118/119.

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J. Chattopadhyay

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Subsequently, the serial correlation coefficients were normalised by division with c(0). Next, we obtained the raw spectral estimates by evaluating Fourier transforms of the normalised serial correlation coefficients [p(r)]. We have m-1

So = 2ram [1 + p(m)] + --m

p(r) r=l

m--1

~k

=

1 -/7l

+

2 ~ --

knr

p(r) cos - -

m

DI r=l

1

+ -- ( - 1)g p(m)

(2.2)

m

'Z m--1

~"=2mml [1 + (-- 1)mp(m)] + --m r

= 1 , 2 , 3 ....

(-- l)m p(r)

(m - 1).

The raw spectral estimates were then smoothed with the help of running weights. Our final spectral estimates were, So = . 5 4 S o + . 4 6 ~ S k = .23 ~k-1 + .54 gk + .23 Sk+l Sm= .54 ~,, + .46 ~,,_ t-

j ]

(2.3)

These spectral estimates correspond to the frequencies k

f

2 m At'

(2.4)

for k = 0 , 1, 2 ... m. By At we represent the time interval between successive observations. It is desirable to assess the results of power spectrum analysis by suitable tests of statistical significance. To each spectrum we first fitted a 'null continuum' (MITCHELL et aL [2]). This was carried out by evaluating the following equation for different values of k between k = 0 and k = m,

Sk = "I(1-- c2) + (l + c~ -- 2 q cos ? ) 1.

(2.5)

In this equation, g is the average of all (m+ 1) raw spectral estimates (Nk) in the computed spectrum. The resulting values of S k were then superposed on the spectrum to enable us to arrive at the 'null continuum'. After the 'null continuum' was superposed on the spectrum, we compared the value of each spectral estimate S k with the corresponding value of the 'null continuum'. The ratio of these two quantities may be reasonably assumed (TUKEY [4]) to have a distribution like that of Chi-square divided by the number of degrees of freedom. The number of degrees of freedom (v) of each spectral estimate depends on

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the sample size (n) and the maximum lag (m). We have, v = (2 n - m / 2 ) + m .

(2.6)

After evaluating v, we obtained the 95 per cent confidence limit from tables of the chi-square distribution. Together with the 'null continuum', this was superposed on each power spectrum. Once the above confidence limit of the continuum was added graphically, we could see at a glance if any of the spectral peaks exceeded the 95 per cent limit. Such peaks, which did exceed or equalled the above confidence limit, were considered to represent real oscillations in atmospheric total ozone content. 3. D a t a and results

of analysis

We have analysed the data from three north Indian stations namely, New Delhi (28~ 77~ Ahmedabad (23~ 72~ and Varanasi (25~ 83~ The location of these three stations is shown in figure 1. Daily values of 40~

70~E

BO~

90*E

40*N

30N

2

10

0

20*N

~

IO*N

N 70*E

80~

90*E

Figure l Location of ozone stations in north India atmospheric total ozone content were available from these stations for the three year period 1963-66. For New Delhi we had access to two years of additional data viz. from 1961 to 1963. The observations were made with the help of Dobson's Ozone Spectrophotometer at each station. The observations were made in direct sunlight using the customary A-D pair of wavelengths. Observations recorded at Varanasi (25~ 83~ were made by the author. For the other stations, data published by the Indian Meteorological Department were used for our analysis. Power spectra were evaluated for ozone observations from these three stations for the winter period (November to April). In all, we computed eleven spectra. The

8PAGEOPH83(1970/VI)

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J. Chattopadhyay

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winter records for the three stations were analysed year by year for the period 1963-66. For New Delhi, we analysed the additional data for the winter seasons of 1961-62 and 1962-63 also. The total length of the available record for each station varied from 150 to 180 days for the winter season. The maximum lag in our computations did not exceed 15 per cent of the total record. 0.16

o.14 I 0.12

I\ :I

1.1o '" 0.08

J \

~

J

re

~

0.06

u~ 0.04

..

0.02

%03*"

x-

HARMONIC (CYCLES PER 4,8 DAYS)

Figure 2 Power spectrum of total ozone at New Delhi, from November 1965-April 1966 0.16

I

0.14 0.12

4

t~

w 0.10

i !I

~o.oa

I A\\

rY 0.06 c/1 0.04

0,00

2

4

6

; 10 12 14 16 18 HARMONIC (CYCLES PER 48 DAYS)

20

22

Figure 3

Power spectrum of total ozone at Varanasi from November 1965-April 1966

24

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P o w e r S p e c t r u m Analysis of A t m o s p h e r i c O z o n e C o n t e n t

115

0.16 0.14

0.12

i~

~o.Io WO.O8

~

0.06

LA, '4

13.. tn

El

0,04 0.02

0o0

~

4

~

;

io

HARMONIC

i~ (CYCLES

1;

~

~;

2'0

12

24

PER 40 DAYS)

Figure 4 P o w e r s p e c t r u m o f total o z o n e at A h m e d a b a d f r o m N o v e m b e r 1965-April 1966

We observed that the records for each station were dominated by very strong seasonal trends. This problem was overcome by 'pre-whitening' the original data series before a spectrum analysis was made. Pre-whitening was carried out by evaluating the annual cycle present in the time series by FOURIER analysis and subtracting it from the data. In figures 2, 3 and 4 we have shown the power spectra for New Delhi, Varanasi Table I Periodicities in total ozone content

Station

N e w Delhi (28~ 77~

Ahmedabad (23~ 72~

Varanasi (25~ 83~

Year

Periodicity in days (Significant at 95 p e r cent confidence limit) (i)

(ii)

(iii)

1961-62 1962-63 1963-64 1964-65 1965-66

3.4 3.0 2.5 -

5.3 -

9.6 8.0

(i) 1963-64 (ii) 1964-65 (iii) 1965-66

3.5 2.8

4.8 4.0

(i) 1963-64 (ii) 1964-65 (iii) 1965-66

3.2

5.3 4.8

(i) (ii) (iii) (iv) (V)

9.6 -

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J. Chattopadhyay

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and Ahmedabad for the winter of 1965-66. As we have stated earlier, power spectra were obtained for these three stations for all the winter months of 1963-66. For New Delhi, we obtained power spectra for the winter seasons of 1961 and 1962 also. To save space, we are not reproducing the figures for each season and station separately, but the principal periodicities revealed by our analysis are summarised in table 1. It will be observed from table 1, that the analysis reveals three types of periodicities, namely, oscillations with periods of (i) 2.5-3.5 days, (ii) 4.0-5.3 days and (iii) 8.0-9.6 days. We could find no uniformity in the sequence with which these oscillations occur. It was also apparent that the same type of oscillations do not appear every year. It was felt worthwhile to determine whether the same periodicities are observed in the data for the year as a whole. For this purpose, we made a power spectrum analysis of ozone data from New Delhi for the year 1964. This is shown in figure 5.

oo4 I!.............

0"000

2

4

G B 10 12 14 1G 18 20 22 24 26 28 30 HARMONIC (CYCLES PER 60 DAYSI

Figure 5 Power spectrum of total ozone at New Dlhi for the annual data of 1964

The spectrum reveals that the periodicities corresponding to 2.5-3.5 days and 8.0-9.6 days, which are present in the winter data, are also reflected in the annual data. But, the medium periodicity of 4.0-5.3 days, which is a feature of several winter records is not found in the annual data. It is felt that this is not an entirely unexpected result, because winter is a season of migratory eastward moving low pressure systems across north India. These low pressure systems are known as 'western disturbances' in India. If, therefore, we treat the winter ozone records separately, the association between ozone and such transient systems will appear more prominently.

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4. Possible relationship between total ozone content and western disturbances I n table 2 we show the actual n u m b e r of western disturbances d u r i n g N o v e m b e r to April, for a period o f seventeen years from 1951 to 1967. The data were taken from M o n t h l y W e a t h e r Reviews prepared by the I n d i a n Meteorological D e p a r t m e n t . Table 2 Frequency of western disturbances Year

January

February

March

April

November

December

1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967

8 7 9 5 8 7 9 9 4 3 2 4 1 7 5 4 4

4 2 8 8 5 4 7 4 5 3 4 5 5 5 3 4 6

6 6 6 4 8 10 8 6 5 5 4 6 6 7 6 4 4

4 4 5 3 4 4 5 5 3 5 4 5 6 6 6 6 7

3 1 7 6 0 2 2 2 4 2 3 1 9 1 3 0 5

7 7 4 6 6 7 4 4 4 3 2 3 2 7 1 1 4

Total

96

82

101

82

51

72

Mean

5.6

4.8

6.0

4.8

3.0

4.2

It will be observed that there are five western disturbances per m o n t h on a n average. If, there is a systematic variation of ozone c o n t e n t with the passage of a western disturbance, then a 5-6 day periodicity in ozone c o n t e n t could be r e a s o n a b l y expected. I n section 3, we f o u n d that the power spectra did indeed reveal the existence of a cycle with 4.0-5.3 days periodicity. W e may, therefore, infer that this p a r t i c u l a r periodicity is closely linked with the passage of western disturbances across n o r t h India. W e observed m a r k e d fluctuations in total atmospheric ozone at almost all the n o r t h I n d i a n stations with the passage of western disturbances. Whenever, a western disturbance passed across n o r t h I n d i a from west to east, the ozone c o n t e n t was also observed to u n d e r g o rapid fluctuations in a similar m a n n e r . I n other words, as the western disturbance m o v e d f r o m the west to the east, the peak value of ozone also occurred first at a western station a n d then at a n eastern station. F o r example, it was observed that a peak value of ozone first occurred at Srinagar (34~ 74050 ' E). After a n interval of a day or two the same peak was observed at New Delhi (28~

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J. Chattopadhyay

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77~ which is 02o22 , to the east of Srinagar. Finally, after another interval of 1-2 days the peak was observed at Varanasi (25~ 83~ ' E), which is at a distance of 05~ ' to the east of New Delhi. The 2.5-3.5 day periodicity in daily total ozone data may be because of a fast moving wave around the globe. But the nature of this wave is still unknown. The 8.0-9.6 day periodicity may be closely linked to fluctuations of a planetary scale in the index cycle. Variations in the index cycle have been observed over north India. There is evidence to indicate that the index cycle has a periodicity varying from 10-14 days.

5. Conclusion We may summarise the main conclusions of this study as follows: (i) All the power spectra usually revealed one or two types of periodicities. These may be classified into three distinct groups of periodicities during the winter as follows. (a) Smaller periodicities in the range of 2.5-3.5 days (b) Medium periodicities in the range of 4.0-5.3 days (c) Larger periodicities in the range of 8.0-9.6 days. (ii) There is little uniformity in the sequence in which these periodicities appear. The same type of periodicities do not occur year after year. (iii) The periodicities corresponding to 2.5-3.5 days and 8.0-9.6 days which are present in the winter data are also reflected in the annual data. But the medium periodicity of 4.0-5.3 days which is observed in a number of winter records, is not found in the annual data. This result is very inspiring, because winter is the season of migratory eastward moving low pressure systems across north India. (iv) The 4.0-5.3 days periodicity is closely linked with the passage of western disturbances across north India. The 2.5-3.5 day periodicity may be associated with a fast moving wave around the globe. The 8.0-9.6 day periodicity may be related to fluctuations of a planetary scale in the index cycle.

Acknowledgements The author wishes to express his deep indebtedness to Prof. H. S. RATHOR of the Banaras Hindu University, and to Dr. P. K. DAS of the India Meteorological Department, for their valuable guidance and instruction throughout the period of the work. The author wishes to thank the C.S.I.R., New Delhi, for the award of a Fellowship under which this research was performed.

REFERENCES

[1] R. B. BLACKMAN and J. W. TUKEY, The measurement o f power spectrum (Dover Publications, New York 1958), 190 pp.

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[2] J. M. MITCHELL,JR., B. DZERDZEEVSKII, H. FLOHN, W. L. HOFMEYR, H. H. LAMB, K. N. RAO and C. C. WALLEN, Climatic change, W.M.O. Technical Note No. 79, Geneva (1966), 100 pp. [3] P. K. SENGUPTA, Characteristic pattern o f variations o f total ozone during recent winters at New Delhi, Beitr. Phys. Atmos. 37 (1964), 161-173. [4] J. W. TUKEY, The sampling theory o f power spectrum estimates. Symposium on applications of autocorrelation analysis to physical problems (U.S. Office of Naval Research Washington D.C. 1950), 47-67. (Received 9th February 1970)