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Solar cycle variation offiF

R. P. KANE INPE-C.P. 5 15-SIo Jose dos Campos-SP 12201-Brasil

(Recriced in,fincrl,firm 19 August 1991: ucwpted I October 1991)

Abstract-For solar cycle 19 (1954-1964), the 12 monthly mean values of noon-timefoF2 at Ahmedabad (23’N, 73’E) show a large hysteresis effect when plotted against sunspot number or against geomagnetic Ap. However, a multiple regression analysis for the dependence of,fuF2 on solar 2800 MHz tlux and geomagnetic Ap, simul/uneousl~, shows a better matching. Thus, long-term predictions need to take into account not just sunspot number but some solar index and geomagnetic index as two key parameters, simultaneously.

1. INTRODUCTION San Marco satellite. HEATH and SCHLESINGER(1986) showed that the core-to-wing ratio of the Mg II h and ionospheric electron density is mainly due to the ion- k absorption lines near 280 nm, obtained from Solar ization of neutral atmosphere by solar radiation, Backscatter Ultraviolet (SBUV) observations from mainly in the ultraviolet and X-ray region. Since the the NIMBUS-7 satellite, provides a measure of solar solar radiation has an 1 I-yr cycle, similar changes are UV variability. These measurements are available expected in ,foF2. Traditionally sunspot number is since 1979. However, there is another solar index considered a primary index of solar activity. However, namely the Ottawa 10.7 cm solar radio flux F(10) a comparison of ,ftiF2 and sunspot numbers shows available regularly since 1947. The F( 10) index is some discrepancies. For low and medium sunspot roughly similar to the sunspot number. so much so numbers, the relationship is reasonably linear. At that almost linear relationships have been formulated large sunspot numbers&F2 seems to show saturation by MEDD and COVINGTON(1958) and JOACHIM(1966). effects. Also,,foF2 behaviour during the rising part of However, on a finer scale, F( 10) differs from the the solar cycle is different from the behaviour during sunspot number. For example, during solar cycle 21 the falling part, resulting into a sort of hysteresis effect (197551986), the sunspots reached a maximum value (OSTROW and POKEMPNEK. 1952 ; G~PALA RAO and of - I60 in 1979 and then fell to - 140 by the end of SAMBASIVA RAO, 1969). APPLETON and PIGGOTT 198 1. In this interval, F( 10) was almost constant at (1955) pointed out that, for the same sunspot number, - 190. Also, during solar minima (1975-1976 and the degree of magnetic storminess may cause different 198551986), the sunspot number dropped to -20 but effects on,fbF2. F(lO) remained near - 80. On the other hand, F(10) The sunspot number is convenient for use because has some similarities with the variations of some EUV of its long series of reliable observations. However, and UV components of solar radiation (DONNELLYet what is relevant for ,foF2 changes is the variation al., 1986; DONNELLY, 1987). For long-term variations, of extreme ultraviolet radiation. All solar radiations F( 10) seems to have a behaviour intermediate between show the II-yr sunspot cycle; but the magnitudes sunspot numbers and EUV. For example, LAKSHMIet are different in different wavelengths. Also, all rise a/. (1988) showed that the saturation effect of,jbF2 simultaneously from the sunspot minimum but some for large sunspot numbers disappeared when EUV reach their maximum values earlier than the others flux in the range 17-l 9 nm was used instead of sunspot (LEAN, 1987; DONNELLY, 1988). Hence, a part of the number. Recently, KANE (1992) re-examined that saturation and hysteresis effects could be due to the analysis and showed that use of F(lO) showed satu- fact that sunspot numbers were used instead of the ration effects in between those using sunspot number relevant EUV radiation. However, measurements of and EUV. In the present communication, we re-exam- EUV have been rather meagre. especially in the past. ine the analysis of GOPALA RAO and SAMBASIVARAO HINTERECGER (1980) reported an intercomparison of (1969) to check whether the hysteresis effects are EUV data from several monochrometers on the AE-E reduced by using F( IO) instead of sunspot number and satellite for 1976-1980. However, these data stopped also examine quantitatively the effect of geomagnetic after 1980 and may be available in future only from the activity. 1201 1202 R. P. KANE

2. DATA peaks, one in 1957-1958 and another (larger) one in 1960. GOPALARAO and SAMBASIVARAO (1969) analysed the monthly median values of noon foF2 from 1954 3. HYSTERESIS to 1964 for 42 stations. Plots vs sunspot numbers showed hysteresis effects which were large at middle Figure 2a shows a plot of foF2 (Ahmedabad) vs latitudes and small at equatorial and high latitudes. sunspot number RZ and is the same as that in Fig. 1 From these, we chose the plots for Ahmedabad of GOPALA RAO and SAMBASIVARAO (1969). Full (23.O”N, 72.6-E) which showed a substantial hys- lines refer to 19541960 (rise of sunspot cycle). The teresis effect. hysteresis effects, as also the saturation effects, are Figure 1 shows a plot of the 12-month moving visible. Figure 2b shows a plot of the same foF2 averages (3 months apart) of the sunspot number R,, (Ahmedabad) vs F(10) (2800 MHz) solar flux. The F(lO), foF2 (Ahmedabad) and geomagnetic Ap for hysteresis effect is still quite large and the saturation solar cycle 19 (19541964). The sunspot number RZ effect can also be seen. It seems, therefore, that using and the 2800 MHz solar radio flux F(lO) are not the solar radio flux F( 10) instead of sunspot numbers exactly alike. The F( 10) decay lasted longer. ThefbF2 does not resolve these two problems. Since the geo- peak is rather flat (saturation effect?) and lasted for magnetic Ap index attains large values during the almost 4 yr (19561960). The Ap variation had two declining sunspot cycle also, a plot offoF vs Ap could

54 5s 56 57 58 59 60 61 62 63 64 I I I I I I I I I I I I 200 - SUNSPOT RZ Rz X-X-X 2800 MHz, F ( IO) 160 AAA foF2 (AHMD)

O-O-Q Ap

- 425 -

60

I I I I I I D D D D D D D D 0 D 0 D 54 55 56 57 56 59 60 61 62 63 64

YEAR Fig. 1. Twelve-month moving averages (3 months apart) of sunspot number R,, 2800 MHz solar flux F(lO), foF2 at Ahmedabad (23”N, 73”E) and geomagnetic Ap, for solar cycle 19 (19541964). Solar cycle variation of fiF2 1203

where y = foF2, x = Ap and z = F(lO) solar flux. (a) Using standard formulae (BEVINGTON, 1969). the 16 direct correlation coefficients were :

__-- rvy = 0.9184; ?yl = 0.9626; Y, = 0.8387. 14 .’ (2) / ,’ The partial correlation coefficients were : : 12 : r.,l,L = 0.7532; r_ = 0.8923. (3)

IO RZ Both of these are almost equally large, indicating that ~~ fnF2 was dependent on both these variables namely Ap and solar flux. The final regression equation is :

y = 6.23+(0.2042)Ap+(0.0210)F(10). (4) When the values of Ap and F(lO) are substituted in the right-hand side of equation (4), one gets the set of values y’, that is, the expected values of y. Figure 3a shows the observed (triangles) and expected (crosses) values of foF2 (Ahmedabad) for 1954-1964. The matching is reasonably good, indicating that solar flux 2600 MHz, F (IO) and geomagnetic Ap together can account for thefoF2 variation better, as compared to solar flux alone or 0 100 150 200 250 Ap alone. Figure 3b shows a plot of the observed vs

(cl expected values. The values are near the 45” slope line. The correlation coefficient is + 0.9793. However, when points referring to the rising part of the sunspot cycle (full lines) are compared with those for the declining part (dashed lines), a small hysteresis effect is still seen, indicating that even solar flux and AP together do not explain,foF:! variations completely.

5. CONCLUSIONS AND DISCUSSlON Fig. 2. Twelve-month moving averages of noon-time~~2 at Ionospheric parameters are known to be dependent Ahm~abad vs (a) sunspot R, (b) 2800 MHz solar flux F(10) on solar indices, for which the moving averaged sun- and (c) geomagnetic Ap, during 1954-1964. Full lines refer to the rising part (19% 1960)of the sunspot cycle and dashed spot numbers are usually used. In this communi- lines represent the declining part (1960-1964). cation, we showed that dependence on solar indices (sunspots or 2800 MHz flux) was only partial and that a considerble dependence on geomagnetic activity was indicated. For ionospheric long-term predictions, the key parameter used is sunspot numbers (e.g. see be instructive. Figure 2c shows such a plot. As can be REDDY et al., 1979). To allow for saturation effects, a seen, the relationship is roughly linear but the scatter second degree relationship like: is large. Also, a reversed hysteresis effect is seen. As such, Ap alone cannot be considered as well-correlated JtiF2 = A+BR+CR2 (5) with,foF2. was tried fR = Sunspot number). However, for the same sunspot number, the behaviour of fuF2 could 4. MULTIPLE REGRESSION ANALYSB be quite different, depending upon the geomagnetic activity. As such, predictions based on sunspots (or Since foF2 seems to be related to solar activity as any other solar index) alone may not be always well as geomagnetic activity, a simultaneous depen- adequate. dence on these two variables can be explored by a We suggest that a dependence on geomagnetic Multiple Regression Analysis of the form : activity also, simultaneously with the solar index, y = a,+a,x+a,z (1) should be incorporated on a routine basis. A major 1204 R. P. KANE

54 55 56 57 56 59 60 6, 62 63 64 I I I 1 I I I I I I I

foFil ( AHMDf &AA OBSERVED x-x-x EXPECTED

(a)

I 1 I I I I I I I I I 54 55 56 57 58 59 60 61 62 63 64

15 COEFF. (+ 0.9793)

9

9 10 lf 12 13 14

foF2 (EXPECTED)

Fig. 3. (a) ~bse~ed~o~~ at Ahmedabad (triangles) vs their values expected (crosses) from a regression equation with 2800 MHz flux and geomagnetic Ap as the two simultaneous dependent variables ; (b) Plot of the observed vs expected values offoF2. The full lines represent the rising part (19541960) and the dashed lines represent the declining part (1960-1964) of the sunspot cycle.

difficulty would be predicting the key parameters. At of the maximum sunspot level to be obtained in the present, sunspot numbers are predicted in various next cycle seems to give fairly satisfactory results ways. However, none of these are completely reliable. (OHL, 1976; KANE, 1978, 1989). If geomagnetic Methods based on periodicities obtained from earlier activity is introduced as an additional parameter, data often give erroneous predictions (KANE and TRI- additional predictions for that parameter would be

VEDI, 1985). A method based on the level of geo- needed. This will not be an easy task (see KANE, 1988). magnetic activity in a solar minimum as a precursor In general, Ap has a double-peak structure during an Solar cycle variation off0nF2 1205

1I-yr solar cycle. But the peaks have varying ampli- greatly upon the local time of the relevant SSC (Storm tude ratios and their positions uis-his the sunspot Sudden Commencement) and the main storm. Thus, peak (lag or lead) vary considerably from cycle to for the same geomagnetic storm period, predictions cycle and the peak Ap amplitudes are not related to for locations at different longitudes and latitudes the sunspot amplitudes. As such, an average pattern could be substantially different (MENDILLO, 197 1, for Ap is not very meaningful. Nevertheless, the use 1973; KANE 1973, 1975). The likely occurrence of a of some pattern of Ap as an additional key parameter geomagnetic storm could be roughly guessed from is likely to give better predictions than using solar precursors like solar flares. But the actual evolution of index alone as a key parameter. For. short-term pre- a storm is almost impossible to predict and predictions dictions (weeks, months), the sunspots alone would can go haywire. These limitations should be kept in be still more unsatisfactory. In particular, the (geo- mind while using predictions. magnetic) storm-time effects would be of great Acknowle~~rment-This work was partially supported by importance. The storm-time changes of,/&F2 depend FNDCT. Brasil under contract FINEP 537/CT.

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