146

The Sunspot Cycle and Solar and Lunar Daily

Variations in H

By D. R. K. RAo 1)

Summary - Results of sunspot cycle influence on solar and lunar ranges at a low latitude station, Alibag, outside the equatorial electrojet belt, show that the sunspot cycle association in solar ranges is three times that of the lunar ranges in the d- and j-seasons. This is in general agreement with the earlier results for non-polar latitude stations. The association with sunspot number of individual lunar amplitudes is greatest for lunar semidiurnal harmonic in the ]-season. During this season, the sunspot cycle influence on lunar variations is more than that on solar variations, thereby indicating that the lunar current is situated at a level more favourable for sunspot cycle influence than the level of the current associated with solar variations. With the increase in solar activity a shift appears in the times of maxima of semidiurnal lunar variation towards a later lunar hour in e- and j-seasons and in the year.

1. I n t r o d u c t i o n

'Does the solar cycle also influence the lunar daily magnetic variat ions? ' This

question has been debated since the discovery o f solar cycle and its influence on the

solar daily magnetic variation. Views of research workers are differing on this ques- tion. CHAt"MAN et al. [112), while examining the sunspot cycle influence on the solar

and lunar daily geomagnetic variations at a number of observatories during I G Y / C

and the preceding sunspot minimum, have listed the investigators who supported the association o f lunar variation with the solar cycle and those who argued against the

association. They have also examined longer series of data of some stations in the nor thern hemisphere, mostly in high latitudes, and arrived at the conclusion that the

sunspot cycle influence on the lunar variations is significant; but it is only about one

third, in magnitude, of the sunspot cycle influence on the solar variations. TRIVEDI

and RASTOGI [2] showed that the amplitude o f the lunar semidiurnal component in- creases with solar activity during two out of the three seasons at Kodaikanal , an

equatorial electrojet station in the lndian region. In this communicat ion, the results o f the sunspot cycle influence on solar and lunar

daily variations in the horizontal component , H, at Alibag (Geographic latitude:

1) Indian Institute of Geomagnetism, Colaba Observatory Compound, Colaba, Bombay-5, India.

8) Numbers in brackets refer to References, page 151.

The Sunspot Cycle and Solar and Lunar Daily Variations in H 147

18 ~ 38' N and Geomagnetic latitude: 9.5 ~ a low latitude station outside the equato- rial electrojet belt, are discussed using long series of data from 1925 to 1969.

2. Analyses and results~

Solar cycle variation in the solar and lunar variations has been investigated with the Zurich sunspot number, Rz, selected as the index of solar activity. In the division according to R~, they have been coded 1 to 3 corresponding to the mean R~, for con- secutive three-year periods, 0-50, 51-100 and > 100 respectively. Accordingly, these three-year periods in the entire length of data, 1925-1969, are coded as follows:

Set 1:1932-33-34 (8), 1942-43-44 (19), 1952-53-54 (17), 1963-64-65 (18);

Set2:192%28-29 (71), 1938-39-40 (89), 1950-51-52 (62), 1960-61-62 (68);

Set 3:1947-48-49 (141), 1957-58-59 (178).

The values in brackets are the average Rz for the three-year periods. Thus sets 1, 2 and 3 are representative of low, medium and high phases of solar activity respectively with average R z 15, 72 and 159.

For each of the three-year periods of the above ten groups, lunar and solar har- monics as well as the respective vector probable errors (P.E.'s) are determined upto four harmonics following the CHAPMAN and MmL~R [3] method. The computational details are the same as in an earlier paper (RAO [4]). Apart from this three-year period analysis (hereafter referred to as year), the data for each set were subdivided into three Lloyd's seasons and the harmonic components are derived for each of the seasons separately (d-season: November, December, January and February; e-season: March, April, September and October; j-season: May, June, July and August). In arriving at the solar and lunar harmonic components days for which all the 24 hourly values are available only are included. Out of the 160 lunar harmonic components determined for the three seasons and the year of the ten groups, only 74 amplitudes are significant when compared with the respective P.E. During the year and the d-season, 53 and during the e-season and j-season 21 out of 80 amplitudes are signi- ficant. MALIN [5] and CHAPMAN et al. [6] have shown that the inclusion of disturbed days increases the P.E. of the lunar daily harmonics without significantly changing their amplitudes. CHAPMAN et al. [1 ] obtained improved significant amplitudes when five International Disturbed days were omitted for each calendar month from the data. A small number of significant amplitudes observed during the e- and j-seasons may therefore be due to an increase of disturbance level in these seasons and con- sequent increase in the magnitudes of the P.E. As the purpose of the present investi- gation is to examine the association of the amplitudes and phases of each of the harmonic components with average Rz for the three-year periods, data of all the available days are, therefore, included for analysis. It is assumed that a larger number

148 D.R.K. Rao (Pageoph,

of amplitudes would be significant without much change in their magnitude if dis- turbed days were eliminated.

As a first step in examining the general variation of the amplitude over different phases of solar activity, average amplitudes of each of the harmonics are worked out for the three sets and are given in Table 1. It can be seen from Table 1 that there is a

Table 1 Average amplitudes in units of 0.01 ~ for three sets of solar activity

Amplitude Solar Activity

Low Medium High (Average R~ ~ 15) (Average Rz ~ 72) (Average Rz ~ 159)

Ampl. 1 74.2 112.8 79.4 Ampl. 2 61.8 78.4 76.6 Ampl. 3 35.5 35.5 31.1 Ampl. 4 12.9 18.2 18.0

general increase in amplitudes from low to high solar activity periods which is in conformity with the results from Greenwich and Abinger (LEATON et al. [7]). However, amplitudes for the medium solar activity periods are the largest.

Next, the solar cycle influence on the solar and lunar ranges is studied. The range of solar daily variation can be calculated from a 24-hr series of hourly values or the synthetic values obtained by harmonic components. Similar calculation for lunar range is more difficult to define, since the pattern of lunar variation does not repeat from day to day. Following GREEN and MALIN [8], the lunar range, R(L), is calcu- lated for each of the seasons and the year by

4-

R(L) = Z Z L., n = l

where R(L) represents the difference between the greatest and the least value that the amplitudes of lunar variations can attain over an indefinite period and L,, the nth harmonic of lunar amplitude. Similarly,

4

R(S)= 2 2 S,, n = l

where R(S) and S, are the solar range and the nth harmonic of solar amplitude re- spectively. Solar and lunar ranges are calculated separately for each of the ten three- year periods. Linear correlation coefficients (CCs) between the solar as well as the lunar ranges with R~, using ten pairs of values, are worked out for each of the seasons and the year. The quantities, slope divided by intercept for solar range, M, and for lunar range, m, are determined from the respective regression equations. Wolf 's

Vol. 98, 1972/VI) The Sunspot Cycle and Solar and Lunar Daily Variations in H 149

e-t ,~

~o

I

O'5 �9

7z

7z

I l l l l l

I I i l l

f l I

i I I I

I I

150 D.R.K. Rao (Pageoph,

ratios (CHAPMAN et aI. [1]) for solar range 10 4 M for lunar range 104 m which re- present the percentage change in the ranges associated with an increase in R~ from 0 to 100 are given in Table 2.

Finally, the solar cycle influence on the amplitudes and phases of the four har- monics are studied by computing CCs and the Wolf ratios, for both the solar and lunar variations in the three seasons and the year. The results of this analyses are given in Table 3.

3. Discussion

3.1 Solar cycle influence on solar and lunar ranges

Solar ranges, as expected, are significantly correlated with sunspot number whereas the association is not very significant in the case of lunar ranges. For lunar ranges, the correlations are higher in d- and j-seasons, although the magnitude is not significant at 5 percent level. However, for e-season the CC is insignificant and negative. In the d- and j-seasons, the Wolf ratio corresponding to solar range is about three times that of the lunar range, which suggests that although both solar and lunar ranges are generally intensified at sunspot maximum, the increase of solar range is three times that of the lunar range. CHAPMAN et al. [1] have shown that the sunspot cycle variation of solar range, measured by the Wolf ratio, is about three times that of lunar range in the annual means and state that this appears true with moderate spread, in all elements at all non-polar latitudes and for different sunspot cycles. GREEN and MALIN [8] in their analysis of long series of geomagnetic data from Watheroo to determine the variations of the solar and lunisolar components with the annual sunspot number, apart from the association of other parameters, have also shown that the solar variation with sunspot number is about three times that of lunar variation. The difference in the association of solar and lunar ranges with the sunspot number noticed here may be attributed to the difference in the levels of the main parts of solar and lunar current system in the ionosphere as the air tide generating potential for both lunar and solar tides do not vary in the course of a sunspot cycle to produce the observed change (CHAPMAN et al. [1]).

3.2 Solar cycle influence on the amplitudes and phases of solar and lunar harmonic components

Amplitudes of solar components are significantly correlated and show a definite positive association with the sunspot number in all seasons and the year. On the other hand, none of the CCs of the amplitudes of lunar harmonics with sunspot numbers are significant at 5 percent level except the second harmonic (Ampl. 2) in the j-season, the CC being plus 0.735. However, the main semidiurnal harmonic in the lunar daily variations (Ampl. 2), is positively correlated; the magnitudes of CCs are higher

Vol. 98, 1972/VI) The Sunspot Cycle and Solar and Lunar Daily Variations in H 151

than the CCs for other harmonic amplitudes in the year as well as for the d- and j-

seasons. In e-season, however, the CC is small and negative. The relationship between solar and lunar association with sunspot number is considered by comparing the Wolf ratio of the significant diurnal component of the solar variations (Ampl. 1) with that of the semidiurnal component of the lunar variations (Ampl. 2). The quantity X, which is equal to Wolf ratio of solar Ampl. 1 divided by similar ratio of lunar Ampl. 2, is 4.1 for the year, 2.6 for the d-season and 0.8 for the j-season. These results for the year and the d-season in general agree with similar results for solar and lunar

ranges. But in the j-season the solar cycle influence on the lunar variations is more than that on the solar variations. I f it is accepted that the currents responsible for the solar and lunar variations are situated at different levels in the ionosphere, then the above result suggests that the lunar current is situated at a level more favourable for sunspot cycle influence in j-season than the level of the current associated with solar variations.

CCs of the phase angle of the first harmonic (phase 1) and sunspot number is negative and significant in all the seasons and the year. This further confirms the results of YACOB and RAO [9] of a systematic retardation (occurring later in the day) of the time of maximum of the first harmonic of Sq(H) with increasing solar activity. LEATON et al. [7] have indicated that there is little evidence of any systematic variation of phase of the lunar terms with sunspot number. But the CCs corresponding to phase 2 in the lunar semidiurnal component are negative and higher in magnitude, although insignificant at 5 percent level, for the year and the e- and j-seasons. During these

periods, therefore, it appears that the time of maximum of semidiurnal lunar com- ponent shifts towards the later lunar hours with the increase in the solar activity. TRIVEDI and RASTOGI [2] have shown an increase in the lunar semidiurnal amplitude in H at Kodaikanal during the d- and e- seasons, and decrease in the j-season, with solar activity. They have obtained a constant phase angle for the lunar semidiurnal component for all the seasons. Amplitude and phase angle variations obtained here are not consistent with those of TRIVEDI and RASTOGI [2]. Perhaps use of still longer series of data with more divisions into different phases of solar activity may yield a more definite evidence of the solar cycle influence on lunar variations.

Acknowledgement

The author wishes to thank Mr. B. N. BHARGAVA, Director, Indian Institute of Geomagnetism, for suggesting the problem and for his guidance.

REFERENCES

[1] S. CHAPMAN, J. C. GUPTA and S. R. C. MALIN, Proc. Roy. Soc. Lond. A. 324 (1971), 1. [2] N. B. TRIVEDI and R. G. RASTOOI, Indian J. Met. Geophys. 20 (1969), 235. [3] S. CHAPMAN and J. C. P. MILLER, Monthly Not. of R.A.S., Geophysical Supplement 4 (1940), 649. [4] D. R. K. RAG, Pageoph (1971), in press. [5] S. R. C. MALIN, Geophys. J. R. astr. Soc. 13 (1967), 397.

152 D.R.K.Rao

[6] S. CHAPMAN, J. C. GUPTA and S. R. C. MALIN, Beitr. Geophys. 79 (1970), 5. [7] 1]. R. LEATON, S. R. MALIN and H. F. FINCH, Royal Observatory Bulletins, No. 63 (1962). [8] P. GREEN and S. R. C. MALIN, J. Atmosph. Terr. Phys. 33 (1971), 305. [9] A. YACOB and D. RADHA KRmHNA RAO, J. Atmosph. Terr. Phys. 28 (1966), 351.

(Received January 3rd 1972)