Correlation of Solar Indices with Solar euv Fluxes

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  • CORRELATION OF SOLAR INDICES WITH SOLAR EUV FLUXES

    R. P. KANEInstituto Nacional de Pesquisas Espacias, INPE, Caixa Postal 515, 12201-970, So Jos dos

    Campos, SP, Brazil (e-mail: kane@laser.inpe.br)

    (Received 4 September 2001; accepted 30 November 2001)

    Abstract. The paper presents a more extensive comparison of Extreme Ultraviolet (EUV) irradi-ances during AE-E (19771980), Pioneer Venus (19791992) and SEM/SOHO (1996 onwards)with other solar indices than has been discussed previously. For long-term changes (solar cycle), allindices had similar trends and inter-correlations were high, so that any one could serve as a proxy forthe other. For intermediate time-scales (monthly means), only L, F10 (2800 MHz) and Mg II hadreasonably high correlations with EUV. The 2695 MHz radio emission also had a high correlation.For daily values, data for many indices are intermittant and these cannot serve as proxies. Again, onlyL, F10 (and 2695 MHz), Mg II stand out as possible proxies for EUV, particularly during intervalsof strong 27-day sequences.

    1. Introduction

    The Sun emits a wide variety of radiations, originating in different parts (photo-sphere, chromosphere, chromospherecorona transition region, corona) of the so-lar atmosphere. Solar ultraviolet (UV) irradiance (11504200 ) originates mostlyin the solar photosphere and chromosphere. When absorbed in the Earths at-mosphere, it plays a dominant role in the temperature distribution, photochemistry,and overall momentum balance in the stratosphere, mesosphere, and lower ther-mosphere. The solar EUV flux, particularly below 130 nm (1300 ) originatesin the chromosphere, the chromospherecorona transition region, and the solarcorona (Donnelly, Hinteregger, and Heath, 1986). It is the primary cause of ionproduction in the ionosphere and contributes to the heating of the thermosphere.However, except for some brief periods, there have been very few solar EUV mea-surements on a daily basis. A discussion of the early satellite measurements is givenin Lean (1987) and Schmidtke (1992). Some data of daily values for several monthscontinuously were obtained by the AE-E satellite from 19741980, OSO 4 in thelate 1960s, AEROS A in the early 1970s, Prognoz 10 in 1985, and the San Marcosatellite in 1988 (Tobiska and Barth, 1990). The period from 1980 onwards wastermed by Donnelly (1987) as the EUV hole, as full spectrum measurements werenot expected to occur till the late 1990s (Tobiska, 1996). However, during January1979 to December 1991, the Pioneer Venus Orbiter (PVO) carried a Langmuirprobe to measure the temperature and concentration of electrons in the ionosphereof Venus, and when the probe was outside the Venus ionosphere and was in the

    Solar Physics 207: 1740, 2002. 2002 Kluwer Academic Publishers. Printed in the Netherlands.

  • 18 R. P. KANE

    solar wind, it measured integrated EUV flux in the range 1001500 , with 55%contribution from L, 30% from the 3001100 continuum, and the rest fromstrong ionization lines such as He II, He I, C III, etc. (e.g., Hoegy et al., 1993). Inrecent times (1996 onwards), there are SEM/SOHO measurements of EUV in the1500 region (Judge et al., 1998).

    Since EUV data are very important for studying terrestrial effects but are notavailable all the time, several studies in the past have studied the correlation be-tween EUV fluxes and other solar indices with a view to see whether any indexcould serve as a proxy for EUV (Donnelly, Hinteregger, and Heath, 1986; Ataand Ozgu, 1998, 2001; Ivanov, Obridko, and Ananyev, 1998; Mahajan et al., 1998;Parker, Ulrich, and Pap, 1998; Ramesh, 1998; and several others). L 1216 ,Mg II 2800 , He 10830 , F10 (2800 MHz, 10.7 cm), solar flare index, magneticfield and others are suggested as possible proxies. In the present communication,the relationship of EUV with many indices is reexamined during the AE-E data in-terval(19741980), the Pioneer Venus interval (19791992) and the SEM/SOHO inter-val (1996 onwards), for long-term (solar cycle), intermediate-term (months), andshort-term (27-day) time scales. Data were obtained mostly from the NOAA web-site http://www.ngdc.noaa.gov/stp/, but some were obtained from private sources.

    2. AE-E EUV Measurements

    The AE-E data are in 15 wavelength groups of flux ratios F/Fref, where F isthe measured flux for a particular day and wavelength group, while Fref refersto the reference period 1328 July 1976 (Hinteregger, Fukui, and Gilson, 1981).The wavelength groups are: 168190 , 190206 , 206255 , 255300 ,304 , 510580 , 584 , 590660 , 1026 , 325 , 284 , 200204 , 178183 , 169173 , 1216 . The L data (1216 ) were from a fixed wavelengthmonochromator, and the rest were from four other wavelength-scanning monochro-mators with completely independent and physically different diffraction gratings(Hinteregger, Bedo, and Manson, 1973). It was noticed that the daily values ofthese 15 groups were very highly inter-correlated (correlations exceeding +0.95).Hence, 13 of these were combined to give values for 3 broad ranges, namely,168204 , 206335 , and 510660 , while L (1216 ) and L (1026 )were considered separately.

    2.1. LONG-TERM VARIATION

    Figure 1 shows a plot of the 12-month moving averages of the various indicesexpressed as percentage deviations from their respective means, for the interval19771981 (ascending part and peak of solar cycle 21). The plots are arrangedroughly in the order of solar altitudes. Thus, plots for sunspots are at the bottom,

  • CORRELATION OF SOLAR INDICES WITH SOLAR EUV FLUXES 19

    Figure 1. Plots of the 12-month moving averages (percentage deviations from the mean) of thevarious solar indices during the AE-E data interval 19771981, with sunspots at the bottom and245 MHz solar radio emission at the top. The EUV data (168204 , 206335 , and 510660 )are in the middle. Peaks are marked with full dots, and the transition from negative deviations topositive deviations is marked with triangles. KPNO is Kitt Peak National Observatory. Group SF ismonthly counts of grouped solar flares, grouped meaning that observations of the same events bydifferent sites are lumped together and counted as one. X-ray data are from GOES.

    low frequency solar radio emissions (245 MHz) at the top (upper corona), andAE-E data in the middle (lower and middle corona). As these are deviations fromthe mean, the transitions from negative to positive values (indicated by triangles)occurred near about the end of 1978, for all indices except the low-frequency radioemissions, for which higher altitudes seem to show later transitions. A correlationmatrix showing the intercorrelation of all these parameters was obtained but is notshown here due to its abnormally large dimension (2424). The noteworthy pointswere:

    (1) The three EUV ranges 168204 , 206335 , and 510660 and L1026 were highly inter-correlated (exceeding +0.95). As these originate in awide altitude range (transition region, and lower to upper corona), the conclusionwould be that the long-term trend is very similar for such a wide altitude range.

    (2) The EUV was highly correlated (exceeding +0.95) with sunspots, Ca plageintensity index as well as area index, sunspot group area, Group SF (monthly

  • 20 R. P. KANE

    counts of grouped solar flares, source Solar Geophysical Data, grouped meaningthat observations of the same events by different sites are lumped together andcounted as one), He 10830 , F10 (2800 MHz flux), and solar radio emissions at2695, 4995, 8800 MHz. Thus, surface phenomena as well as some middle coronalindices had similar long-term variations. For L, Woods et al. (2000) have givenan improved model for 19471999, using UARS (Upper Atmosphere ResearchSatellite) as reference and adjusting AE-E measurements to agree with the UARSvalues. Here, the values of this modeled L series are also used, termed L com-posite, plotted just below the AE-E L. The correlation for L composite was veryhigh, +0.99.

    (3) EUV correlations were slightly lower with L AE-E (+0.92), Kitt peakMagnetic field KPNO (+0.91), Coronal green-line index (+0.91), soft X-raysGOES 18 (+0.82), and radio emissions 245, 410, 606, 1415 MHz ( +0.90),indicating slightly complicating factors. EUV correlation with 15400 MHz radioemission was very poor, almost zero. Neupert (1992) had indicated similar lowcorrelations of OSO-3 EUV with radio frequencies in the GHz region.

    Overall, many indices (including sunspots) can serve as adequate proxies, mainlybecause all these have a similar long-term trend. Of course, this comparison is onlyqualitative, indicating good parallelism. It could be valid even if some indices sufferfrom instrumental drifts, provided the drift rate is constant. With a high correlation,the quantitative relationship could be established by regression analysis, but theaccuracy of the data would then be very important. This is discussed later.

    2.2. VARIATION OVER INTERMEDIATE TIME SCALE

    Figure 2 shows a plot of monthly values (percentage deviation from mean). Toavoid the overwhelming influence of the long-term up trend, only values fromSeptember 1978 up to April 1981 (32 monthly values at the peak of solar cycle 21)are considered. Whereas four maxima are indicated by many indices, the trendsare not similar (monthly data for 245 MHz are unreliable). The full (24 24)correlation matrix is not shown here, but the correlations of the monthly values ofthe three EUV bands with other indices are shown in Table I(a). The correlationmatrix indicated the following:

    (1) The three EUV ranges 168204 , 206335 , and 510660 and L1026 were well inter-correlated ( +0.90).

    (2) The next best correlations were: L composite (+0.79), 2695 MHz (+0.75),He 10830 (+0.72), 1415 MHz (+0.70), 8800 MHz (+0.69), F10 (+0.68).

    (3) Others in descending order were: Ca Pl index and 4995 MHz (+0.64),sunspots (+0.63), L AE-E (+0.62), 410 MHz (+0.53).

    (4) Others were below +0.50, some very poor (X-rays GOES +0.04).Thus, the matching of the monthly values gives poorer correlations as compared

    to the long-term trend and there is not much to choose between He 10830 (+0.72),F10 (+0.68), sunspots (+0.63), though Donnelly, Hinteregger, Heath (1986) have

  • CORRELATION OF SOLAR INDICES WITH SOLAR EUV FLUXES 21

    Figure 2. Plots of the monthly means (percentage deviations from the mean) of the various solarindices during 19781981, with sunspots at the bottom and 245 MHz solar radio emission at the top.The EUV data (168204 , 206335 , and 510660 ) are in the middle. Peaks are marked withfull dots.

    considered differences like these as meaningful. (The standard error of a correlationcoefficient r is approximately (1r2)/n1/2, where n is the number of pairs. For32 pairs, correlations of say, 0.60 and 0.90 will have standard errors, respectively,of 0.11 and 0.03). For proxy purposes, none of these can be considered asfully satisfactory, as a correlation +0.70 implies only 50% common (explained)variance. Incidentally, the 2695 MHz radio emission shows a correlation +0.75,higher than the F10 (2800 MHz) correlation +0.68, though similar values for sim-ilar frequencies would be expected. (The difference is not statistically significant,

  • 22 R. P. KANE

    Figure 3. Plots of the daily values (percentage deviations from the mean) of the various solar indicesduring the 112-day interval 26 October 197915 February 1980, with sunspots at the bottom and245 MHz solar radio emission at the top. The EUV data (168204 , 206335 , and 510660 )are in the middle. Peaks are marked with full dots. Missing values are manipulated as shown by thedashed lines.

    though). Also, the three EUV ranges, roughly centered at 180 , 270 , and 580 ,should have originated respectively from middle corona, lower corona, and uppertransition region and should have decreasing correlations with F10 or 2695 MHzand increasing correlations with He 10830 and L 1216 . The observed cor-relations are F10 (0.68, 0.80, 0.53); 2695 MHz (0.75, 0.79, 0.60); He 10830 (0.72, 0.83, 0.60); L AE-E, 1216 (0.62, 0.52, 0.79). Thus, no clear increasingor decreasing pattern of correlations is seen, and the association of these indiceswith specific solar altitudes seems to be ambiguous.

  • CORRELATION OF SOLAR INDICES WITH SOLAR EUV FLUXES 23

    2.3. SHORT-TERM VARIATIONS

    The major difficulty of comparing day-to-day changes is intermittent data for manyindices (including EUV). Almost every second or third value and often data forseveral days are generally missing. Donnelly, Hinteregger, and Heath (1986) stud-ied the interval November 1979 to February 1980 when AE-E data were morecomplete than in previous intervals. Figure 3 shows the plots of percentage de-viations from mean. Four major peaks roughly 27 days apart are seen in manyindices. Missing data were manipulated as shown by the dashed lines. Donnelly,Hinteregger, and Heath (1986) noticed many differences in the various plots. Inparticular, the ratios of the first peak near 9 November 1979 to the second peaknear 13 December 1979 were reported to be 0.95, 1.04, 1.11, 1.22, 1.36, and 1.54for L, L, 304 , 284 , 335 , and F10. Similar ratios are seen in Figure 3.Donnelly, Hinteregger, and Heath (1986) concluded that the short-term variationsof the EUV wavelengths could not be estimated by using linear regression relationswith other indices like sunspots, F10, plage index, X-rays, etc. Correlations of thedaily values of the three EUV ranges are shown in Table I(b). A correlation matrixfor the various indices shown in Figure 3 indicated the following:

    (1) The two EUV ranges 168204 , 206335 , Mg II Composite and L1026 were well inter-correlated (+0.86 or more), but the EUV range 510660 ,L AE-E, L composite, and sunspots had a slightly lower correlation ( +0.82).(With 110 data pairs, a correlation of say 0.80 will have a standard error of 0.03.)

    (2) The next best correlations were: 2695 MHz (+0.80), F10 (+0.79).(3) Others in descending order were: 4995 MHz (+0.67), 8800 MHz (+0.62).(4) Others were below +0.60. X-rays GOES had +0.56. Many data, notably

    calcium plage intensities and areas, Kitt Peak magnetic field and He 10830 , hadbig gaps and are obviously inadequate as proxies.

    Overall, considering short-term and long-term time scales, L, L, Mg II, F10,2695 MHz, and even sunspots were equally satisfactory as proxies if correlations ofthe order of +0.7 (common variance 50%) were acceptable. Only for long-termtrends, proxies were better than 50% common variance. Workers using regres-sion equations of this order should allow for 3050% uncertainties in the EUVestimates.

    3. Pioneer-Venus EUV Measurements

    During January 1979 to December 1991, the Pioneer Venus Orbiter (PVO) carrieda Langmuir probe. When the probe was outside the Venus ionosphere and was inthe solar wind, it measured integrated EUV flux (called EIpe) in a broad range1001500 , with 55% contribution from L (1216 ), 30% from 3001100 continuum, and rest from strong ionizing lines such as He II, He I, C III, etc. (e.g.,Mahajan et al., 1998).

  • 24 R. P. KANE

    Figure 4. Plots of the 12-month moving averages (percentage deviations from the mean) of thevarious solar indices during Pioneer Venus interval 19791992, with sunspots at the bottom and245 MHz solar radio emission at the top. The Pioneer Venus EUV data (EIpe, 1001500 ) are inthe middle. Peaks are marked with full dots. MW is Mt. Wilson.

    3.1. LONG-TERM VARIATION

    Figure 4 shows the plots of 12-month moving averages of the various indices, withsunspots at the bottom and Pioneer Venus EUV in the middle (EIpe, thick line). Allthe plots seem to run parallel, with broad maxima in 19791981 (peak of cycle 21)and 19891991 (peak of cycle 22), except that in the end part, EUV seems tocontinue to rise during 19901992 (marked with a big rectangle), while many otherindices show saturation. Kitt Peak magnetic field KPNO (marked with a smallrectangle) also continued to rise, but Mt. Wilson magnetic field MW did not showthe rise. Separate correlatons were calculated for (a) 19791983, (b) 19841988,and (c) 19881992. The correlation matrices indicated the following:

  • CORRELATION OF SOLAR INDICES WITH SOLAR EUV FLUXES 25

    Interval (a) 19791983:(1) Many indices showed correlations with EUV exceeding +0.93.(2) The next best were: 606 MHz (+0.92), X-rays GOES (+0.87), 410 MHz and

    8800 MHz (+0.86), 1415 MHz (+0.85), Ca PL intensity index (+0.80), 245 MHz(+0.69).

    (3) Poor correlations were: coronal green line index (+0.21), 15 400 MHz(0.02).

    Interval (b) 19841988:(4) Most of the indices showed correlations with EUV exceeding +0.93.(5) Some were low: 606 MHz (+0.59), 8800 MHz (+0.37), 15 400 MHz (+0.32).Interval (c) 19881992:(6) The high correlations with EUV were: magnetic fields at Kitt Peak and Mt.

    Wilson (+0.93, +0.83), radio emissions 606 MHz (+0.94), 4995 MHz (+0.92),410 MHz (+0.79), 2695 MHz (+0.77).

    (7) Others were: Mg II composite (+0.61), He 10830 (+0.58), 15 400 MHz(+0.49), L composite (+0.40).

    (8) Some others were very poor, even negative.Thus, the EUV increase during 19901992 is shown by Kitt Peak magnetic

    field and some radio emissions only. In the rest of the period (19791989), allindices show similar long-term trends and any of these (including sunspots) couldbe a good proxy for EUV.

    3.2. VARIATIONS OVER INTERMEDIATE TIME SCALE

    For comparison of monthly values, the values near the peaks and troughs of thesolar cycle were chosen so that the main up trends or downtrends would be avoided.The intervals considered were (a) 19791982 (peak of cycle 21), (b) 19841987(end of cycle 21 and beginning of cycle 22), (c) 19891992 (peak of cycle 22), andthe plots are shown in Figure 5. Correlations of the monthly values of EUV withother indices are shown in Table I(a), in three columns corresponding to the threetime intervals. The correlation matrices indicated the following:

    Interval (a) 19791982:(1) The largest correlation was with Mg II composite (+0.77), followed by L

    composite (+0.72), magnetic field Mt. Wilson (+0.69), F10 (2800 MHz) and2695 MHz (+0.62), 8800 MHz (+0.60), magnetic field Kitt Peak KPNO (+0.59).

    (2) Sunspots had +0.53, 4995 MHz +0.48, Group SF +0.40. Others werelower, some even negative.

    (3) Figure 5(a) shows the plots of the percentage monthly means for a fewselected indices. About seven peaks for some indices (shown by full dots) roughlytally between themselves and indicate a spacing of 7 months, but the EUVpattern is different (fewer peaks). The thick line on the EUV plot is a 3-monthmoving average.

  • 26 R. P. KANE

    Figure 5. Plots of the monthly means (percentage deviations from the mean) of the various solarindices during (a) 19791983, (b) 19841988, (c) 19891992, for Pioneer Venus EUV (thick line),F10, L composite, Group SF, Kitt Peak magnetic field KPNO, and sunspots.

    Interval (b) 19841987:(1) Almost all the indices showed correlations in the range +0.63 to +0.75.(2) The only low correlations were: total solar irradiance (+0.28), 8800 MHz

    (+0.42), 15 400 MHz (+0.33).(3) Figure 5(b) shows the plots. The EUV plot of 3-month moving averages

    (thick line) shows a few 7-month cycles. Cycles of 5 and 7 months in solar indices(sunspots, F10, and others) have been reported earlier (Hoegy and Wolff, 1989,and references in their Table I).

    Interval (c) 19891992:(1) EUV correlations with all indices were very poor (even negative), except

    with the magnetic field (Kitt Peak, +0.51; Mt. Wilson, +0.54), 606 MHz (+0.44),L composite (+0.40).

  • CORRELATION OF SOLAR INDICES WITH SOLAR EUV FLUXES 27

    Figure 6. Plots of the daily values (percentage deviations from the mean) of the various solar indicesduring the 112-day interval 18 June10 October 1982, with sunspots at the bottom and 245 MHzsolar radio emission at the top. The Pioneer Venus EUV data (1001500 ) are in the middle (thickline). Peaks are marked with full dots. Missing values are manipulated as shown by the dashed lines.

    (2) The EUV plot in Figure 5(c) shows the abnormal increase in 19911992,in contrast with a steady level in other indices, except in Kitt Peak magnetic fieldKPNO, which also shows an increase (above the dashed line). The low correlationsare because of the odd feature (increase) in EUV during 19911992.

    3.3. SHORT-TERM VARIATIONS

    Figure 6 shows a plot of the daily values (percentage deviation from mean) forthe 112-day interval 18 June8 October 1982 when strong 27-day oscillationsoccurred (peaks indicated by full dots). These peaks are prominent in many indicesand, for EUV and some other indices (L, Mg II, etc.), all the four peaks are of the

  • 28 R. P. KANE

    same magnitude. However, for some other indices (e.g., sunspots, F10), the firstpeak near 16 July is larger than the next peak near 9 August. Correlations of thedaily values of EUV with other indices are shown in Table I(b) (just one column).A correlation matrix indicated the following:

    (1) The best correlation was with L composite (+0.95), followed by Mg IIcomposite (+0.94), He 10830 (+0.89), Mt. Wilson magnetic field (+0.87), KittPeak magnetic field and 1415 MHz (+0.82), 606 MHz (+0.81), F10 (+0.80).

    (2) Next followed: sunspots and Ca PL intensity index (+0.76), 2695 MHz(+0.71), 4995 MHz and coronal green-line index (+0.66), 8800 MHz and sunspotarea (+0.60).

    (3) Others were: X-rays GOES (+0.44), 410 MHz (+0.41), 15 400 MHz (+0.38),Group SF (+0.31), 245 MHz (+0.30). Total solar irradiance was (0.04).

    Thus, L and Mg II composites seem to be very good proxies. He 10830 wasreasonably good, but F10 was not very good.

    As mentioned earlier, an intriguing aspect of the Pioneer Venus EUV measure-ments is the abnormal rise during 19911992 (marked by a rectangle on the EUVplot in Figure 4), when several other solar indices showed a plateau (exceptions:Kitt Peak Magnetic Field and 2695 MHz radio emission). A possible check couldbe through the effects on terrestrial ionosphere. EUV is known to be correlated tothe electron density N at the F2 peak, while N is proportional to (foF2)2. Forthe Pioneer Venus EUV data, Hoegy and Mahajan (1992) presented the results ofa comparison with (foF2)2 at Boulder and Wallops, but their study was confinedto 19791990 only. Our Figure 9 shows a plot of Pioneer Venus EUV at the top,followed by (foF2)2 at Wallops Island, Boulder and Slough. In each case, the val-ues are expressed as ratios with the 1986 solar minimum as base 1.0. Since foF2is strongly dependent on seasons, a 12-month moving average was calculated, toeliminate or at least minimize considerably, the seasonal effect. For uniformity, thesame procedure was adopted for EUV, though no seasonal effects are involved. Ascan be seen, during 19791981, the levels were constant (flat plateau). Thereafter(from the first vertical line in the end part of 1981), there was a monotonic decreaseup to 1986 , followed by a monotonic increase up to roughly the latter half of 1989(the second vertical line). Thereafter, the (foF2)2 plots show an almost flat plateauup to the end of 1991, matching in level with their respective 19791981 plateau.In contrast, the EUV value reached the same level as the 19791981 plateau inthe end of 1989, but continued to rise thereafter till the end of 1991. This risewas not accompanied by the ionospheric (foF2)2. This leaves some doubt aboutthe correctness of the EUV data during 19911992. On the other hand, similarincreases in the 12-month moving averages of Kitt Peak magnetic field (dots) and2695 MHz radio emission (crosses) during 19911992 indicates that this could bea very, very unusual interval when EUV and some other indices had a 1020%increase but the ionospheric effects were nil. Nothing like this has been reportedearlier.

  • CORRELATION OF SOLAR INDICES WITH SOLAR EUV FLUXES 29

    Figure 7. Plots of (a) the 12-month moving averages (percentage deviations from the mean) of thevarious solar indices during SEM-SOHO interval 1996 onwards and (b) monthly values for July1999July 2001. Sunspots are at the bottom and 245 MHz solar radio emission at the top. The SOHOEUV data (260340 and 1500 ) are in the middle (thick lines). Peaks are marked with full dots.KAND SF is solar flare index from Kandilli Observatory, Istanbul, Turkey. MPSI is magnetic plagestrength index.

    4. SOHO EUV Measurements

    During 19921996, there were no EUV measurements. From 1996 January on-wards, i.e., from the beginning of solar cycle 23, EUV measurements are avail-able from the Solar EUV Monitor (SEM) aboard the SOLar and HeliosphericObservatory (SOHO) satellite, for two ranges, 260340 and 1500 .

  • 30 R. P. KANE

    4.1. LONG-TERM VARIATIONS

    Figure 7(a) shows a plot of the 12-month moving averages, for sunspots at thebottom, for the two EUV ranges in the middle, and radio emissions in the upperpart. As can be seen, almost all indices had an almost monotonic increase witha maximum in the middle of 2000, with the exception of GOES X-rays (18 )which peaked in the beginning of 1999. (For some indices, data were not yet avail-able for 1999 onwards.) Data for protons with energies exceeding 1 Mev show arise still continuing in 2000. A correlation matrix indicated the following:

    (1) EUV correlations were very high (exceeding +0.95) with almost all indices,including sunspots and KAND SF (Kandilli Observatory, Istanbul, Turkey, solarflare index, Ata and Ozgu, 1998, 2001).

    (2) Slightly lower correlations were: sunspot area (+0.91), X-rays GOES(+0.85), 15 400 MHz (+0.90), protons (+0.62).

    4.2. VARIATIONS OVER INTERMEDIATE TIME SCALE

    In previous cycles, the sunspot number had a broad plateau near sunspot maxi-mum, for almost two years. Presently, cycle 23 attained a maximum in 2000 andthe sunspot number has declined since then, but it may (or may not) oscillate atthe present level for the next several months. To avoid the predominant effectof the long-term trend, monthly data for July 1999 onwards only are plotted inFigure 7(b). As can be seen, some prominent maxima are seen in almost all indices,but details differ. Correlations of the monthly values of EUV (two columns) withother indices are shown in Table I(a). A correlation matrix indicated the following:

    (1) Correlations with EUV (both 260340 and 1500 ) were very high(+0.95 or more) for: sunspots, magnetic fields (Kitt Peak and Mt. Wilson both),He 10830 , L composite 1216 , Si III 1206 , F10, 606, 1415, 2695 MHz.

    (2) Slightly lesser correlations were: 4995 MHz (+0.94), 410 and 8800 MHz(+0.93), group solar flares, Mg II composite, total solar irradiance (+0.92),245 MHz (+0.91).

    (3) Others were: sunspot area (+0.88); KAND SF (+0.84); 15 400 MHz(+0.80); X-rays GOES (+0.73); protons >1 Mev (+0.52).

    Thus, many conventional indices had high correlations, but X-rays had a differ-ent behaviour.

    4.3. SHORT-TERM VARIATIONS

    To examine short-term variations, the 112-day interval 11 October 1997 to 31 Jan-uary 1998 was chosen, as this had strong 27-day oscillations throughout the solaratmosphere (Kane, 2002). Figure 8 shows the plots of daily values expressed aspercentage deviations from the mean of this interval. Major maxima are indicatedwith full dots and these are common to some indices, but details differ considerably.A correlation matrix indicated the following:

  • CORRELATION OF SOLAR INDICES WITH SOLAR EUV FLUXES 31

    Figure 8. Plots of the daily values (percentage deviations from the mean) of the various solar indicesduring the 112-day interval 11 October 199731 January 1998, with sunspots at the bottom and245 MHz solar radio emission at the top. The SOHO EUV data (260340 and 1500 ) are inthe middle (thick lines). Peaks are marked with full dots. Missing values are manipulated as shownby the dashed lines.

    (1) There were no correlations of the order of +0.90 or more. The maximumcorrelation was +0.82, for Si III 1206 and 1415 MHz, followed by L com-posite 1216 (+0.80), 2695 MHz (+0.79), magnetic field Mt. Wilson (+0.75),4995 MHz (+0.74).

    (2) Other correlations were lower: Mg II composite (+0.69), 606 MHz (+0.63),F10 (+0.62), 8800 MHz (+0.61).

    (3) Some others were still lower as: magnetic field Kitt Peak (+0.59), He10830 (+0.58), 410 MHz (+0.55), X-rays (+0.48), sunspot area (+0.42), sun-spots (+0.41), protons (+0.40), KAND SF (+0.35), total solar irradiance (+0.34),15 400 MHz (+0.24), 245 MHz (+0.14).

  • 32 R. P. KANE

    Figure 9. Plots of the 12-month moving averages of the Pioneer Venus EUV (top plot) andionospheric (foF2)2 at Wallops Island, Boulder and Slough during 19791992, all expressed asratios with respect to their base levels of 1986 as 1.0. For 19901992, the right-hand upper cornershows Kitt Peak magnetic field KPNO (dots) and 2695 MHz radio emission (crosses).

    Particularly intriguing is the low value for F10 (2800 MHz, +0.62 0.06),while the 2695 MHz has a higher value (+0.79 0.04), and the low value forHe 10830 (+0.58 0.06) as compared to the higher value for Mg II (+0.69 0.05). Thus, some of these conventional indices have relationships with EUV indifferent degrees in the three sets of EUV considered here. Since the maximum cor-relation is only +0.85, a regression equation would explain 70% of the variance,leaving 30% uncertainty in EUV estimates based upon the proxy. Particularlydistressing is the fact that in every month, many daily values are missing and suchindices can hardly serve as proxies in any meaningful way. There is also the pos-sibilty of errors in absolute levels as discussed in the next section. For long-termchanges, all indices show high correlations. For monthly values and daily valuesequences, the correlations are listed in Tables I(a) and I(b).

    In Table I(a), the correlations of the monthly values of SOHO/SEM EUV withother indices (260340 , column 8) are much higher than the correlations ofHinteregger EUV 206335 with other indices (column 3). Both are for intervalsnear the peak of a solar cycle. The larger correlations probably indicate the bet-ter accuracy of the SOHO/SEM data. A similar conclusion seems to follow fromFigures 2 and 8, where the maxima are marked with dots. The dots in Figure 8(SOHO/SEM EUV) are better lined with other indices as compared to the dots inFigure 2 (Hinteregger EUV).

  • CORRELATION OF SOLAR INDICES WITH SOLAR EUV FLUXES 33

    TAB

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    oft

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    Vw

    ithdi

    ffere

    nts

    ola

    rin

    dice

    sfo

    r(a)

    month

    lyval

    ues

    and

    (b)da

    ilyval

    ue

    sequ

    ence

    s.K

    PNO

    ,K

    ittPe

    akN

    atio

    nal

    Obs

    ervat

    ory

    ;M

    W,

    Mt.

    Wils

    on;K

    AN

    D,K

    andi

    lliO

    bser

    vato

    ry,

    Ista

    nbul,

    Turk

    ey.

    X-r

    ayda

    taar

    efro

    mG

    OES

    .

    (a) Mon

    thly

    %H

    inte

    regg

    er19

    79

    1981

    Pionee

    r10

    015

    00

    SOH

    O19

    99

    2000

    168

    204

    20

    633

    5

    510

    660

    19

    79

    1982

    1984

    19

    8719

    89

    1992

    260

    340

    1

    500

    L

    0.90

    0.91

    0.95

    L0.

    620.

    520.

    79Su

    nsp

    ots

    0.63

    0.64

    0.56

    0.53

    0.68

    00.

    950.

    95Ca

    Pin

    dex

    0.64

    0.62

    0.62

    0.17

    0.73

    0.16

    CaP

    area

    0.22

    0.32

    0.35

    SPar

    ea0.

    440.

    390.

    320.

    280.

    670

    0.88

    0.88

    Mag

    F-K

    PNO

    0.40

    0.60

    0.22

    0.59

    0.74

    0.51

    0.96

    0.96

    Mag

    F-M

    W0.

    690.

    700.

    540.

    970.

    98G

    roup

    SF0.

    370.

    530.

    350.

    400.

    650.

    920.

    93K

    AN

    D.S

    F0.

    840.

    84M

    gII

    0.77

    0.73

    0.35

    0.92

    0.92

    Tot.

    sol.

    irr.

    0.31

    0.28

    0.03

    0.92

    0.91

    HeI

    -10

    830

    0.72

    0.83

    0.60

    0.30

    0.70

    0.26

    0.98

    0.98

    Lco

    m0.

    790.

    890.

    690.

    720.

    750.

    40.

    970.

    98Si

    III

    0.95

    0.95

    F10

    0.68

    0.80

    0.53

    0.62

    0.72

    00.

    970.

    97Co

    r.gr

    een

    0.29

    0.39

    0.12

    0.00

    0.67

    024

    5M

    Hz

    0.72

    0.65

    0.55

    0.25

    0.63

    00.

    910.

    90

  • 34 R. P. KANE

    TAB

    LEI

    Contin

    ued

    .

    (a) Mon

    thly

    %H

    inte

    regg

    er19

    79

    1981

    Pionee

    r10

    015

    00

    SOH

    O19

    99

    2000

    168

    204

    20

    633

    5

    510

    660

    19

    79

    1982

    1984

    19

    8719

    89

    1992

    260

    340

    1

    500

    41

    0M

    Hz

    0.53

    0.52

    0.51

    0.00

    0.67

    0.06

    0.93

    0.93

    606

    MH

    z0.

    440.

    580.

    170.

    370.

    650.

    440.

    960.

    9614

    15M

    Hz

    0.70

    0.72

    0.47

    0.19

    0.72

    00.

    970.

    9726

    95M

    HZ

    0.75

    0.79

    0.60

    0.62

    0.71

    0.21

    0.96

    0.95

    4995

    MH

    z0.

    640.

    690.

    580.

    480.

    640.

    260.

    940.

    9388

    00M

    Hz

    0.69

    0.65

    0.66

    0.60

    0.42

    00.

    930.

    9315

    400

    MH

    z0

    00

    0.05

    0.33

    0.20

    0.80

    0.79

    X-ra

    ys0.

    040.

    220

    0.10

    0.66

    00.

    730.

    73Pr

    oto

    ns

    0.52

    0.49

  • CORRELATION OF SOLAR INDICES WITH SOLAR EUV FLUXES 35

    TAB

    LEI

    Contin

    ued

    .

    (b) Daily

    %26

    Oct

    .19

    79

    15Fe

    b.19

    8018

    June

    .8

    Oct

    .19

    8211

    Oct

    .19

    971

    9Fe

    b.19

    98H

    inte

    regg

    erA

    E-E

    Pionee

    rSO

    HO

    168

    204

    20

    633

    5

    510

    660

    10

    015

    00

    260

    340

    1

    500

    L

    0.86

    0.91

    0.89

    L0.

    830.

    830.

    81Su

    nsp

    ots

    0.82

    0.82

    0.71

    0.76

    0.41

    0.42

    CaP

    inde

    x0.

    76Ca

    Par

    eaSP

    area

    0.60

    0.42

    0.45

    Mag

    F-K

    PNO

    0.82

    0.59

    0.59

    Mag

    F-M

    W0.

    870.

    750.

    76G

    roup

    SF0.

    310.

    430.

    450.

    31K

    AN

    D.S

    F0.

    350.

    42M

    gII

    0.91

    0.88

    0.81

    0.94

    0.69

    0.69

    Tot.

    sol.

    irr.

    00.

    340.

    31H

    eI-10

    830

    0.89

    0.58

    0.56

    Lco

    m0.

    820.

    880.

    710.

    950.

    800.

    80Si

    III

    0.82

    0.83

    F10

    0.79

    0.90

    0.77

    0.80

    0.62

    0.67

    Cor.

    gree

    n0.

    420.

    290.

    300.

    660.

    470.

    4924

    5M

    Hz

    0.30

    0.14

    0.17

    410

    MH

    z0.

    340.

    460.

    370.

    410.

    550.

    5860

    6M

    Hz

    0.81

    0.63

    0.65

    1415

    MH

    z0.

    820.

    820.

    8526

    95M

    Hz

    0.80

    0.90

    0.79

    0.71

    0.79

    0.83

    4995

    MH

    z0.

    670.

    810.

    710.

    660.

    740.

    7988

    00M

    Hz

    0.62

    0.76

    0.65

    0.60

    0.61

    0.66

    1540

    0M

    Hz

    0.36

    0.51

    0.41

    0.38

    0.24

    0.27

    X-ra

    ys0.

    560.

    640.

    630.

    440.

    480.

    55Pr

    oto

    ns

    0.40

    0.37

  • 36 R. P. KANE

    5. Data Inaccuracies: Irradiance Models

    Following the first solar UV rocket flight in 1946, many EUV rocket observationsprovided absolute flux estimates (review by Tobiska, 1993, and references therein).The first extensive observations of EUV and UV were from AE-E (19771980).Soon after these data for 15 wavelengths were published by Hinteregger, Fukui, andGilson (1981), Bossy and Nicolet (1981), Bossy (1983), and Oster (1983) claimedthat AE-E data suffered from shifts in instrument sensivities, particularly L.

    As inputs in the terrestrial atmosphere, one needs Irradiance models. Theseinvolve (i) Reference spectra, i.e., the flux versus wavelength, and (ii) formulaefor their variations with solar cycle. Prior to AE-E, reference XUV-EUV spec-tra were based on rocket observations. Donnelly and Pope (1973) gave a refer-ence spectrum for moderate solar activity (F10 = 150) for a wavelength binsize 310 . Using the AE-E data, Hinteregger, Fukui, and Gilson (1981) provideda reference spectrum (SC#21REFW) for low solar activity (cycle 21 solar mini-mum, F10 = 68), with a bin size of 12 . Following this model, Nusinov (1984)developed a model with an emperically determined active-region background com-ponent Fb, which incorporated modeled physical features and was combined withF10 to produce full-disk irradiances. Tobiska (1988) developed a two-index modelwhere, instead of using just one index F10 for all solar atmospheric layers, L wasused to estimate chromospheric irradiances and 18 X-rays to estimate coro-nal irradiances. Tobiska and Barth (1990) replaced 18 X-rays with F10 andutilised additional rocket measurements, to lower uncertainties. This model wastermed SERF2 and covered the interval October 1981April 1989. Both SERF1and SERF2 were compared by Lean (1990) over time scales of the 27-day solarrotation and the 11-year solar cycle, and were found to have significant differenceswith the datasets upon which the models were based.

    Schmidtke (1992) provided a moderate solar activity (F10 = 150) compositeof rocket and satellite observations with a wavelength bin size of 10 . Mean-while, Tobiska (1991) developed a revised solar EUV flux model (termed EUV91),using L (1216 ) and He 10830 as independent model parameters for thechromospheric irradiances, and F10 and its 81-day running means as indepen-dent model parameters for the coronal and transition region irradiances. Richards,Fennelly, and Torr (1994a, b) evolved a model (termed EUVAC) based on themeasured F74113 solar EUV reference spectrum and the solar cycle variation ofthe flux measured by the AE-E satellite and reproduced the EUV flux in 37 wave-length bins. Tobiska and Eparvier (1998) upgraded the SERF2 (Tobiska and Barth,1990) and EUV91 (Tobiska, 1991) models, incorporating revised soft X-ray fluxesfrom SOLRAD 11 and using L recaliberated to the UARS satellite SOLSTICEL. For UV (spectral range 12002000 ), three models have been developed.Cook, Brueckner, and Vanhoosier (1980) developed a two-component model usingparameterization of the daily sunspot number to provide plage region and quietregion emission. Lean et al. (1982) and Lean and Skumanich (1983) used a three-

  • CORRELATION OF SOLAR INDICES WITH SOLAR EUV FLUXES 37

    component model incorporating flux contributions from the quiet Sun, moderatelybright active network, and bright plage areas. Worden (1996) developed a simi-lar three-component model and Worden, White, and Woods (1998) and Worden,Woods, and Neupert (1999) sought to determine how solar surface structures con-tribute to Ca II K and He II 304 irradiance variability. Fontenla et al. (1999) usedsolar images to identify seven components of the solar atmosphere (cell intereior,network, plage, etc.) and calculated an emission source function using seven staticmodels of the solar atmosphere for a limited time period.

    6. SOLAR2000 Empirical Solar Irradiance Model

    All the empirical solar EUV models referred to above derived from the AE-Edata. However, some accurate EUV measurements from sounding rockets duringsolar cycle 22 (19921994) indicated that the irradiances based on the AE-E datacould be underestimates by as much as a factor of 2 at some wavelengths (Woods,Rottman, and Solomon, 2000). Hence, a big, collaborative project was plannedand started in 1998 and has resulted in SOLAR2000 (Tobiska et al., 2000), whichis a new image- and full-disk proxy emperical solar irradiance model, with 10 resolution in the spectral range 1010 000 000 for historical modeling and fore-casting. For use of research workers who would like to have a quantitative measureof solar input in the terrestrial atmosphere, a new solar proxy has been generated asan output product of the SOLAR2000 model. It is the time-dependent, integratedsolar EUV flux at the top of the Earths atmosphere reported in 10.7 cm (F10)radio flux units. Alternatively, one may use the long-term (1947 through 1999)composite L series produced by Woods et al. (2000), using the measurementsfrom the Atmospheric Explorer E (AE-E), the Solar Mesospheric Explorer (SME),and the Upper Atmosphere Research Satellite (UARS) along with predictions fromproxy models, and considering UARS values as the reference, with AE-E and SEMvalues adjusted to agree with UARS values. The L composite is an integral partof SOLAR2000.

    Discussing the accuracy of SOLAR2000 and/or its utility is not very meaning-ful, for the following reasons. The model relies heavily on the SOHO EUV data(Ken Tobiska, private communication) which is the most accurate EUV measure-ment so far. When a comparison between the model and the SOHO EUV was madefor the 260340 range, the values were found to be matching within 5%, but thisis as expected. For the 19791989 interval, the L composite (an integral partof SOLAR2000) matched very well with Pioneer Venus EUV (as already seen inFigure 4), indicating that Pioneer Venus EUV was mainly L and had very littleof low wavelength EUV. For 19901992, the L composite does not match withPioneer Venus EUV and the latter data are suspect. For earlier years, SOLAR2000do not match well with the AE-E data, but then, the accuracy of the AE-E data(particularly long-term) is now known to be poor. Thus, there is nothing which

  • 38 R. P. KANE

    one can compare meaningfully at present. Estimates from rocket measurements ofEUV have already been taken into account in evolving SOLAR2000. In future,if any EUV measurements become available, these will be used for refining themodel as an on-going process, as mentioned in Tobiska et al. (2000). The solarirradiance formats (irradiance versus wavelength) initiated by Donnelly and Pope(1973) and Hinteregger, Fukui, and Gilson (1981) are now updated and refined asshown in Figure 1 of Tobiska et al. (2000) and its time variation in the past hasbeen determined by using the proxies, (1) XUV 10100 , 18 X-rays, F10,Coronal hole images, (2) EUV 1001200 , F10, L, (3) FUV 12002000 ,L, He 10830 , Mg II, Ca K 1 , Ca II K images, photospheric PSI, (4) UV 20004000 , same as for (3), (5) VIS-IR 400010 000 000 , photospheric PSI. Inthe XUV-EUV range, SOLAR2000 version 1.03a uses short- and long-term vari-ations of L to represent chromospheric emissions and F10 to represent coronalemissions. In the future, more proxies may be added.

    7. Conclusions

    The EUV measurements of three different data sets, namely AE-E 19771980(Hinteregger, Fukui, and Gilson, 1981), Pioneer Venus Orbiter 19791992 (e.g.,Mahajan et al., 1998), and SEM/SOHO 1996 onwards (Judge et al., 1998) werecorrelated with various other solar indices for long-term (solar cycle), intermediate-term (monthly values for 24 years), and short-term (27-day sequences) time scales.The following was noted:

    (1) For long-term changes, all indices showed similar behaviour, with correla-tions exceeding +0.90. Thus, any index could serve as a proxy for any other index,including EUV.

    (2) For monthly values, only F10 (2800 MHz, 10.7 cm flux), L composite,and Mg II composite had consistent and reasonably high correlations with EUV.The 2695 MHz radio emission also had good correlation with EUV.

    (3) For daily values, many indices had intermittant data, and values were oftenmissing for several days. Obviously, these could not have the pretense of serving asa proxy for anything, much less for EUV. With many values missing, their monthlymeans and the associated correlations would be unreliable. On this score, F10,L and Mg II had the advantage of continuous data and fairly high correlationswith EUV and could serve as proxies. (Sunspot data are available continuously, butcorrelations are generally inferior to those of F10, L and Mg II.) He 10830 dataare often used but are intermittant (observations lost because of cloudiness, etc.).For radio emissions, daily data are available from four observatories, SagamoreHill, Massachusetts; Palehua, Hawaii; San Vito, Italy; Learmonth, Australia. Evenif data for some days may be missing at one observatory, these are generally avail-able at one or more of the other observatories, so that an average is available fairlycontinuously. This does not seem to have been used anywhere.

  • CORRELATION OF SOLAR INDICES WITH SOLAR EUV FLUXES 39

    Acknowledgements

    Thanks are due to Helen Coffey and Edward Erwin for help in getting data fromthe NOAA websites, and to Dick Donnelly, Thomas Woods, Kent Tobiska, KarenHarvey, K. K. Mahajan, N. K. Sethi, Atila Ozgu, and Donald McMullin for pro-viding some data privately and for useful discussions and suggestions. This workwas partially supported by FNDCT, Brazil, under contract FINEP-537/CT.

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