Occurrence probability of solar-geomagnetic-weather relations

JournalofA tmasphericand TerrestrialPhysics,Vol. 45, No. 8/9, pp. 569-572, 1983.

0021-9169183 $3.00 "t-0.l~0 ~) 1983 Pergamon Press Ltd.

printed in Great Britain.

Occurrence probability of solar-geomagnetic-weather relations B. R. ARORA Indian Institute of Geomagnetism, Colaba, Bombay, India

(Receired in final form 25 February 1983) Abstract-- Relationshipsof the vorticity area index (VAI)and the geomagneticactivity(Ap)to solar magnetic sector boundary passage (SBP) are examined in terms of the probability of occurrence of these associations with individual SBP. The results reveal that the probability of occurrence of the characteristic variation in the VAI in relation to the SBP is comparable to the well-establishedassociation between Ap and SBP. This similarity in the occurrence probability of VAI-SBP association to that of Ap-SBP association with a value close to 60~ may be considered to be adequate to dispel the doubt that sector related effects on the VAI have arisen from statistical samplingfluctuations.Iris further shown that even though the occurrenceprobability of these associations are nearly equal, the sector related effectson VAI are completelyindependent of the nature of transient changes in the geomagnetic activity accompanying the SBP.

I. I N T R O D U C T I O N

WILCOXet al. (1974, 1976) first described an association between the passage of solar magnetic sector boundaries and the vorticity area index (VAI). Typically, the VAI descends from a maximum about 2 days prior to the sector boundary passage (SBP) to a sharp minimum on the day following the SBP and then rises rapidly to a maximum about 3 or 4 days after the SBP. This VAI-SBP association is shown to be of high statistical significance (HINTS and HALEVY, 1977). Results of further analysis by WILLIAMSand GERETY (1978) and ARORA and PADGAONKAR(1980) for the epochs of 1974-1977 and 1947-1957 respectively failed to reveal the characteristic response. SHAPIRO(1979) is of the opinion that the association has most likely arisen from statistical sampling fluctuations. While correlation between the VAI and the SBPin astatistical sense is fairly well examined, no indication is yet available about the frequency of occurrence of the average feature with individual crossings of sector boundaries. In this communication the empirical occurrence probability of this basic result is evaluated following the numerical procedure outlined by AMBROZ (1979), and is compared with that of the well established association between the SBP and geomagnetic activity. 2. METIlOI)

The method employed, after Ar,II3ROZ(1979), is in fact a refined form of the conventional superposed epoch method wherein, apart from deriving the average features of the variation associated with key days, certain criteria to determine the persistence characteristic together with the occurrence probability of the

statistical results are incorporated. The computational procedure, in brief, is as follows. The column averages and variances in the matrix formed from the values of the VAI are first obtained. The number of rows (Af) is the number of SBPs considered and the number of columns in each row (N), is determined by number of days on either side of the key day and data interval between two successive values of VAI. Variation in column averages typify the nature of the statistical dependence of the VAI on the SBP. The statistical reliability of the result is tested employing parametric test on the difference corresponding to extreme values. Persistence in the data sample is obtained by computing the linear correlation coefficient, R~, of the individual row (i) sample with the statistical average result and forming the histogram of percentage frequencies of individual groups classified according to R~. Since R~s are determined in the interval -- 1 to + I, the M values of Ri can be divided into 10 subgroups with AR = 0.2. Nature of the frequency distribution curve permits one to evaluate the quality of the relationship between the two phenomena. For each of the small sub-groups, classified according to the value of Ri, response variations are evaluated. The difference of extreme values in each group is tested through the parametric test. The critical value of Ri (R,) is determined by the lower range of that R i group from where the group responses tend to be significant. Finally the empirical probability (EP), i.e. frequency of occurrence of statistical result, is given by the ratio of the number of rows (M) for which Ri/> Re, to the total number of rows analysed (m). The relationship gets established only if EP considerably exceeds 0.5.

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Though the nature of statistical association as revealed by column averages is independent of N, the frequency distribution curve as well as EP may differ depending upon N. By the repeated application of the method with various values of N, the optimum time interval in the neighbourhood of the zero day in which the run ofcolumn averages lead to the largest empirical occurrence probability is achieved. 3. A N A I . Y S I S A N D R E S U L T S

3.1. Application of the method to evaluate V A I - S B P associat ion The VAI data corresponding to 500 mb in the form of 00 and 12 UT values are taken from OLSO,~et al. (1977, 1979). The time series of 12-hourly VAI values was passed through a single band-pass digital filter which retains all the variations with wavelengths in the interval 2.5-13 days. A total of 190 sector boundaries occurring within the winter months, NovemberMarch, during 1963-1978, were selected. If more than three successive values of the VAI were missing within the interval of -t-6 days of any SBP, those SBPs were excluded from the analysis. As a first step, superposed epoch analysis is conducted on the VAI for 6 days before and after the day zero, defined as a day of SBP. As the VAI data employed are at an interval of 12 h, columns (N) are equal to 25. The behavior of the VAI resulting from averages over 190 SBPs (M) is illustrated in Fig. la. The resulting pattern is consistent wiih those reported earlier. A measure (D) of the depth of -6

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minimum is defined as the average VAI determined by the mean of the two maxima on either side of the key day minus the VAI minimum following the key day. In Fig. la, D is 3.10x 105 km 2 and as shown by the parametric test, the amplitude is significant at 570 level. Figure lb is a histogram of the percentage relative frequency of the types of responses grouped according to the values orris. The frequency distribution curve is wide and contains both positive and negative values, suggesting that the data can be divided into two sets, one ofwhich is highly persistent with the average result and the second, which is not. tlowever, the occurrence frequency with the positive R~ exceeds that with the negative R;, indicating that majority of rows reveal fair persistency among themselves and also with the statistical result obtained through superposed epoch analysis. To obtain the statistical significance of the degree of persistency of row samples with average values, superposed epoch analysis was performed on the row samples grouped according to Rl values, i.e. 10 groups. The groups in which certain amount of anticorrelation is involved, i.e. negative R~ groups, cannot be considered the realization of the statistical result. Application of parametric tests to the averaged variation corresponding to the positive R~ groups reveals that the magnitude of the effect in VAI, represented by the parameter D, is conspicuously significant right from the lowest positive R~ group, i.e. R~ = 0.0-0.2. The value of EP works out to be 60.870. To evaluate the significance of varying the row length on the resulting persistence, we have re-computed the linear correlation ofeach row with the statistical result

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Fig. I.The average response of(a) VAI and (c) Ap to the I M F sector boundary passage during winter months of 1963-1978.The percentage frequency distribution of the different types of responses classifiedaccording to the correlation coefficientbetween each row and average result for (b) VAI and (d) Ap. Solid line corresponds to the case when row length is over _ 6 days. Broken curve represents the result with reduced row lengths (see text).

Probability of solar-geomagnetic-weather relations restricting the row length to 15 columns, i.e. from - 3 to +4 days. ttistograms of the revised percentage frequency distribution is shown in Fig. 1b (broken line). Though the spread of frequency distribution curve appears to be narrower, there is no increase in the resulting EP (61.5~o) when the lengths of the row is taken to be 15 as against 25 columns initially used. 3.2. Sector structure and geomagnetic activity association (Ap-SBP association) One of the large-scale solar effects organised around the sector boundary passage is the geomagnetic activity (WILCOX, 1968; SHAPIRO, 1974). An estimate of the empirical probability of the occurrence of SBP influence on geomagnetic activity, in addition to providing the quantitative measure of the association, would also be helpful in assessing the physical reality of the VAI-SBP relationship. The daily geomagnetic planetary index, Ap, is taken as representative of the global geomagnetic activity. The form of the statistical association and percentage frequency over different values of R~ resulting from the application of the procedure detailed in Section 2, by restricting the row size to + 6 days of the SBP, are included in Fig. 1. The behaviour of Ap variation in the vicinity of the SBP is consistent with that reported by WILCOX (1968) and SItAI'IRO (1974). The most conspicuous feature of this association is that Ap rises from a minimum approx. 2 days prior to the SBP to a maximum approx. 2-3 days following the SBP. The distribution of the relative frequency of the correlation coefficient has a broad maximum approaching R~ = 0.6-0.8, suggesting a good deal of persistency in the data set. But the presence of rows with negative correlation is also indicative that the data set also contains few rows which are inhomogeneous in relation to the average characteristics. The overall empirical probability of occurrence is only 58~o. However, when the length of the row is taken to vary from - 4 to + 4 days in relation to the SBP (9 columns), i.e. the region where the signature of association is very strong, the fresh value of EP improves to 69.8~. With the aid of linear correlation coefficient (Ri), obtained in respect of Ap-SBP association, the list of 190 sector boundaries were divided into three groups, the R~ range is taken as - 1.0 to - 0 . 4 , - 0 . 4 to 0.4 and 0.4 to 1.0. Figure 2 (left panel) illustrates the average Ap variation in these three groups. The superposed epoch analysis on the VAI data performed separately for the above three categories of SBP yields the results presented in the right panel of Fig. 2. In contrast to Ap, VAI responses are identical in the three categories, suggesting that the VAI response to the SBP is independent of geomagnetic activity. This is consistent

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Fig. 2. The average response of the VAI (right panel) for three categories of sector boundary passages classifiedaccording to whether the average Ap response (left panel) shows (a) positive (b) absence of and (c) negative characterization of statistical result (Fig. Ic).

with the observation of WILCOX(1979) that an increase in geomagnetic activity following a boundary transit is not a necessary condition for a minimum in the VAI following the sector boundary transit. 4. DISCUSSION AND CONCLUSION While the probability of the occurrence of the characteristic variation in VAI and Ap with reference to SBP is more or less equal, the two effects are completely independent ofeach other. Although the EP ofAp-SB P and VAI-SBP associations is nearly equal, it is surprising to note that while the Ap--SBP association is claimed to be well-established, the reality of the VAISBP association is still in doubt. Obviously, the reluctance to accept the validity of the sun-weather relationship stems from the absence of a clear physical mechanism to link the small solar energy variation with the weather modification. Both VAI and Ap are influenced by many physical factors. In superposed epoch analysis, physical effects having random phases would be averaged out. In the individual runs of variation in VAI near each of SBP, the random effects would, however, be present and the

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result would be determined by the relative strength of the physical effects related with SBP and from other sources. When in phase with sector related effects, the other sources would augment the magnitude of the effect, but at other times they would tend to obscure the sector-related effects. The fact that the probability of occurrence for VAI is at least 6070, it can be taken to indicate that the sector-related effect on VAI is a major factor. Yet another argument in favour of the physical reality of this association is that statistically the

association is nearly as consistent as the well-known A p - S B P association. Consequently, variable solar activity may be a factor affecting the meteorological phenomena but much more needs to be known about the physical coupling mechanisms and their modification by other factors before the sun-weather relations can be unequivocally established. Acknowledgement-The author wishes to express thanks to

G. K. Rangarajan for many informal discussions.

REFERENCES ARORAB. R. and PADGAONKARA. D.

1979 1980

Bull. astr. lnsts Csl. 30, 114. Low Lat. Aeronomical Processes, COSPAR Symp. Ser.,

HINESC. O. and HALEVYI. OLSON R. G., ROBERTSW. O. and GERETYE.

1977 1977

J. atmos. Sci. 34, 382.

OLSONR. G., ROBERTSW. O. and GERETYE.

1979

SHAPIRO R. SHAPIRO R.

1974 1979 1968 1979 1976 1974

Phys. Meteoro: SCOSTEP Working II, WDC-A(STP) Boulder, p. 84. Phys. Meteoro: SCOSTEP Working III, WDC-A (STP) Boulder, p. 87. J. geophys. Res. 79, 298. J. atmos. Sci. 36, 1105. Space Sci. Rev. 8, 258. Nature, Lond. 278, 840. J. atmos. ScL 33, 1113. J. atmos. ScL 31, 581.

1978

Nature, Lond. 275, 200.

AMBROZ P.

Vol. 8, p. 241.

WILCOXJ. M. WILCOX J. M.

WILCOXJ. M., SCtlERRERP. H. and SVALGAARDL. WILCOXJ. M., SCHERRERP. H., SVALGAARDL., ROBEaTSW. O., Or.soN R. H. and JEromER. L. WILLIAMSR. G. and GERETYE. J.

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