Reconstruction of the past total solar irradiance on short timescales

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109,, doi: /2003ja010222, 2004 Reconstruction of the past total solar irradiance on short timescales Kiran Jain and S. S. Hasan Indian Institute of Astrophysics, Koramangala, Bangalore, India Received 5 September 2003; revised 9 January 2004; accepted 16 January 2004; published 20 March [1] The aim of this investigation is to present a new analysis of short-term variations in total solar irradiance by developing regression models and to extend these to epochs when irradiance measurements were not available. In our models the sunspot area is used to quantify sunspot darkening while facular brightening is calculated using facular area, 10.7 cm radio flux and Mg II core-to-wing ratio. Models developed with various proxies are compared with a view to identify the role of key parameters in solar variability. We also study the relationship between different facular proxies and show that the facular area and 10.7 cm radio flux do not vary linearly with the Mg II core-to-wing ratio. We emphasize that the facular term in current empirical models (using facular area or radio flux proxies) on short time scale needs to have a nonlinear component in order to obtain a better correlation with observed irradiance. Our analysis demonstrates that the correlation for daily variations in solar irradiance improves by 10% using a quadratic term in the model based on radio flux as a facular proxy, which is a significant improvement on earlier models. On the other hand, the correlation remains unchanged in the model using Mg II core-to-wing ratio. Thus we point out that various proxies for facular brightenings contribute differently to solar irradiance. We estimate the solar irradiance variations at epochs before irradiance observation began, in particular to the start of the radio flux measurements, and find that there is no drastic increase in radiative output during the most active solar cycle 19 while for cycle 20 we observe a much lower irradiance during maximum. INDEX TERMS: 1650 Global Change: Solar variability; 7537 Solar Physics, Astrophysics, and Astronomy: Solar and stellar variability; 7536 Solar Physics, Astrophysics, and Astronomy: Solar activity cycle (2162); 7538 Solar Physics, Astrophysics, and Astronomy: Solar irradiance; KEYWORDS: solar, irradiance, variability, empirical model Citation: Jain, K., and S. S. Hasan (2004), Reconstruction of the past total solar irradiance on short timescales, J. Geophys. Res., 109,, doi: /2003ja Introduction [2] Space observations of the Sun over the past 2 decades have monitored UV spectral, X-ray, and total irradiance with sufficient precision to characterize 27-day rotations and the 11-year solar cycle. These observations clearly show that the brightness of the Sun varies in phase with the solar activity cycle over time scales from minutes to years and decades [Wilson and Hudson, 1988, 1991]. In the past, several efforts have been made to understand the physical mechanism responsible for such variations and to emphasize that the irradiance changes are associated with the evolution of solar magnetic fields [Lean et al., 1998, and references therein]. Magnetic fields weave through the outer third of the sun s interior and penetrate the solar surface extending outward through the solar atmosphere. Higher up in the solar atmosphere, the field lines fan out and either loop back to the surface to form large-scale emission structures or continue outward into the solar wind and Copyright 2004 by the American Geophysical Union /04/2003JA heliosphere. Magnetic fields nearer the Sun s equator rotate faster than those at higher latitudes. This differential rotation stretches and shears the field lines, organizing patterns of magnetism that repeat with 11-year cycles. The combination of the convective motion and differential rotation is thought to constitute a dynamo that drives solar activity and generates variability of solar phenomena including radiative output. [3] The main physical factors that contribute to the radiation changes are related to solar activity during the passage of active regions on the solar disk. It is well known that sunspots, which are relatively dark, lead to a reduction in irradiance, whereas the opposite effect occurs due to faculae. Therefore a competition of their relative strengths determines the solar irradiance variability. Near solar activity maximum, the facular emission exceeds the corresponding sunspot deficit, causing a net increase in total irradiance. In order to have a quantitative model for irradiance variation, it is essential to have a detailed understanding of the physical processes occurring in the solar atmosphere. Various studies based on empirical and theoretical models have been carried out to examine the mechanisms leading to such variations. 1of7

2 Foukal et al. [1983] constructed a time-dependent twodimensional model of heat flow block in a turbulent layer, in order to interpret the observed dips in irradiance. Possible theoretical factors responsible for irradiance variations have been reviewed recently by Spruit [2000]. Empirically, the measurements of solar features have been used to model total and spectral solar irradiance [Lean and Foukal, 1988; Lean, 1988; Foukal and Lean, 1990; Brandt et al., 1994; Fligge et al., 1998; Fröhlich and Lean, 1998; Fligge and Solanki, 2000; Lean, 2000a, 2000b; de Toma et al., 2001; Foukal, 2002; Krivova et al., 2003] and explain its variation up to the 11-year solar activity cycle which shows a difference between the maximum and minimum of nearly 0.1%, with the irradiance being higher during solar maximum. Moreover, the magnetic network plays an important role in modulating the solar cycle as pointed out by, e.g., Foukal and Lean [1988], and it may be the driver for even longer term changes back to the Maunder Minimum [e.g., Lean et al., 1995; Lean, 2001; Sofia and Li, 2001]. These studies provide an important clue to understanding climatic changes over several centuries. [4] In this paper we concentrate on short-term irradiance variations and develop suitable regression models to analyse them and also to extend them to periods when irradiance measurements were absent. Previous studies on short-term as well as long-term variations of solar irradiance using existing proxies for sunspot darkening and facular brightening are either confined to a linear combination of these terms [e.g., Lean and Foukal, 1988; Lean et al., 1995; Fröhlich and Lean, 1998; Foukal, 2002] or consider a single proxy to describe both [e.g., Solanki and Fligge, 1998, 1999; Lockwood and Stamper, 1999; Lean, 2001; Tobiska, 2002]. [5] The objective of this paper is to use existing proxies to make an improved prediction of solar irradiance variability at epochs for which measurements are absent, that is before November 1978, and more specifically back to the start of 10.7 cm radio flux measurements. Our reconstruction during these periods is based on Royal Greenwich Observatory (RGO) sunspot area and 10.7 cm radio flux data, similar to the work of Lean and Foukal [1988]. However, there are several important differences between their model and ours. The major difference is that they used total solar irradiance (TSI) data only for a short period of 4 years from 1981 to 1984, which covers the declining phase of the solar cycle 21, while in our work we use a much longer time series of about 25 years to obtain a significantly better reconstruction of irradiance variability. By comparing models developed with different proxies, we attempt to identify the role of key parameters in solar variability. [6] The plan of the paper is as follows: In section 2 we briefly outline the possible proxies which can be used to quantify the contributions from sunspots and faculae. In section 3 we parameterize the contributions from sunspots and faculae and use them to reconstruct the past solar irradiance. The implications of short-term and long-term variations in irradiance are discussed in section 4. Finally, we summarize the results of this investigation in section Solar Irradiance and Selection of Proxy Indices [7] The TSI has been monitored from space by various radiometers since A composite TSI time series has Figure 1. A composite time series of the total solar irradiance, where the daily variations are in grey. The thin and thick dark lines are for bin averages over 27 and 365 days, respectively. been constructed [Fröhlich and Lean, 1998] and we use version d25_07_0306, which is updated and contains version v5_007_0306 of VIRGO data up to 4 May The variation of TSI since 1978 is shown in Figure 1. This composite time series is an unbiased estimate of TSI variability during the last two solar cycles and provides consistent data to study solar irradiance variability. [8] To investigate the key parameter for temporal variations in TSI, one may consider different measures of solar activity. Sunspot darkening is generally quantified by the measured areas of sunspots while facular brightening can be alternatively calculated with facular area, Mg II core-to-wing ratio, 10.7 cm radio flux, SacPeak/NSO Ca II K emission index, McMath/NSO Ca II K plage index/areas, or He I Å equivalent width. The importance of the relative areas of sunspots and faculae in TSI modeling has been emphasized by several workers [e.g., Foukal, 1998; Chapman et al., 2001]. The sunspot area, generally, enters into irradiance reconstruction through the photometric sunspot index (PSI), which depends on the location and contrast of sunspots on the solar disk. It was further suggested by Brandt et al. [1994] that area-dependent bolometric contrast improves the correlation in irradiance modeling. However, to simplify our modeling efforts, we neglect these effects as a first approximation and emphasize that the total areas of these solar features can also reliably explain the irradiance variability on a timescale as short as 1 day. We use the photometric measurements from the San Fernando Observatory (SFO) for sunspot and facular areas as direct proxies for sunspot darkening and facular brightening [Chapman et al., 1997, 2001]. The facular area (A f ) is defined as the total area of all faculae on the nm Ca II line image while the sunspot area (A s ) is defined as the total area of all sunspots on the solar disk, computed from images in nm. Both areas are determined in millionths of the solar hemisphere. Since the daily values of these measurements are accessible only for a period from 1988 to 1998, these measurements are obviously not suitable for the reconstruction of long time series of TSI, specifically for the solar irradiance in the past. 2of7

3 Therefore one has to choose other suitable proxies which can be used to model past solar irradiance. [9] The longest and most complete record of sunspot area is that of the RGO. This data set, covering a period from 1874 to 1976, is almost free of gaps and provides an excellent database for calculating the sunspot contribution for more than a century. This database has been combined with USAF/NOAA spot areas, which after calibration provides a consistent data set to the present epoch and contains a long overlapping period of irradiance observations from space. To quantify the effect of sunspots on solar irradiance, we use a composite data set prepared by David Hathaway (referred to as the RGO/USAF/NOAA data set, available at daily_area.txt), which includes suitable corrections suggested by Hathaway. This data set contains daily values of the total projected area of all sunspots visible on the solar hemisphere since May [10] Possible proxies, which can be used to calculate facular brightening, have been discussed by several workers [Lean and Foukal, 1988; Foukal and Lean, 1990; Fligge and Solanki, 1998; Lean, 2000a]. However, it is difficult to decide which of these proxies to choose as the best representative of facular brightening. The daily observations for these indices either do not have long enough overlapping periods with space observations of TSI or do not extend sufficiently far back in time. For example, the plage area measurements obtained from the daily solar chromospheric spectroheliograms in Ca K from Mt. Wilson Observatory [Foukal, 1996] are available for a long time span, namely from 1915 to 1984, but owing to insufficient overlap with irradiance measurements the reconstruction of past irradiance is less reliable. The Mg II core-to-wing ratio has been successfully used in irradiance modeling [Fröhlich and Lean, 1998; de Toma et al., 2001; Fröhlich, 2002]. It is known to vary in response to bright faculae and is derived by taking the ratio of the H and K lines of the solar Mg II feature at 280 nm to the background or wings at approximately 278 nm and 282 nm [Viereck et al., 2001]. Since its daily measurement from space started only as recently as 1978, it can not be used effectively to extrapolate the contribution from facular brightening in the past. To circumvent the above difficulties, the long-term record of the 10.7 cm radio flux (F 10 ) can be utilized [Lean and Foukal, 1988] as its daily observations are available from the NGDC archive since The main source of radio flux are faculae and the enhanced network with some contributions from the undisturbed solar surface and sunspots. In the present study of short-term variations of total solar irradiance, we use the Mg II core-to-wing ratio and radio flux for the explicit calculation of facular brightening and compare the models obtained with these two proxies. 3. Empirical Models and Parameterization of Solar Irradiance 3.1. Comparison Between Models With One and Two Activity Indices [11] To study the influence of the magnetic field on the total solar irradiance, we develop multiple regression models using changes in the solar magnetic field structure and compare these models in order to identify the role of Figure 2. The reconstructed total solar irradiance for 14-day binned data set. The observed values are shown by grey lines. Epochs of sudden decrease in TSI are marked by R1 and R2. Models were constructed using two activity indices, i.e., SFO sunspot area with SFO facular area (dashed line) and SFO sunspot area with Mg II core-to-wing ratio (dark solid line). key parameter influencing solar variability. Since we are mainly interested in short-term irradiance variability, in particular, on a timescale of 1 solar rotation or less, the influence of various magnetic activities is studied on these timescales. As usual, a regression analysis, which includes both sunspots and faculae in a three-component linear model of the form: TSI ¼ C quiet þ C dark A dark þ C bright A bright ; is used. Here, we assume that the contribution from the quiet Sun, C quiet, is a constant over the period considered in this analysis. The other two terms refer to active regions which, of course, vary with time. The constants C dark and C bright are related to sunspot darkening and facular brightening, respectively, whereas A dark and A bright are measures of their area on the visible disk. The success of the threecomponent model is illustrated in Figure 2 and especially the sudden dips, R1 and R2, in observed TSI are well reproduced. These results are in agreement with the previous studies based on a three-component model using various activity indices [e.g., Lean, 2000a; Krivova et al., 2003, and references therein]. Table 1 shows R 2 for three different three-component models, where R is the multiple correlation coefficient. It is clear from the table that the model using Mg II ratio exhibits the best correlation on short timescales compared to the models with facular area and radio flux for all bin sizes Relationship of Facular Area and Radio Flux With Mg II Ratio [12] To understand the differences between these models, we examine the relationship between facular area and Mg II ratio in Figures 3a and 3b for 1-day and 27-day bin sizes, respectively. From the figures, it is evident that the facular area has a nonlinear relation with the Mg II ratio with high correlation coefficient, r (given in each ð1þ 3of7

4 Table 1. Variance, R 2 (Where R is the Coefficient of Multiple Correlation), Using Equation (1) for Various Regression Models for the Period a Bin Size Model A Model B Model C 1-day day day day a Model A is constructed with SFO sunspot and facular areas, model B is constructed with SFO sunspot area and Mg II core-to-wing ratio, and model C is constructed with SFO sunspot area and 10.7 cm radio flux. panel), which implies that the SFO facular area (deduced from the plage area) seems to overestimate the facular effect during periods of high activity. We use r for nonmultiple correlation coefficient in contrast to R, which is used for multiple correlation coefficient. The relationship between the radio flux and Mg II ratio is shown in Figures 3c and 3d which is similar to that obtained for the facular area. This explains the higher correlations obtained for model B of Table 1 than those for the other two models. Therefore Mg II ratio proves to be the best proxy for facular brightening in empirical models, which is well known. However, these data cannot be used for a reconstruction before the launch of NIMBUS-7 in Since a major aim of this paper is to extend irradiance reconstruction to those periods when observations were not available, the daily measurements of radio flux are used as a proxy for brightening. In view of nonlinear relationship Figure 4. Variation of R 2, where R is the coefficient of correlation, for modeled TSI with bin size based on RGO/ USAF/NOAA sunspot area for sunspot darkening and (1) Mg II core-to-wing ratio, (2) 10.7 cm radio flux for facular brightening. between the radio flux and the Mg II ratio, we include a quadratic term in equation (1) and write TSI ¼ C quiet þ C 1 A dark þ C 2 A bright þ C 3 A 2 bright : ð2þ Figure 3. Scatter diagrams for same day pairs of two facular brightening indices using (a) 1-day and (b) 27-day bin sizes for facular area (A f ) with Mg II core-to-wing ratio, (c) 1-day and (d) 27-day bin sizes for 10.7 cm radio flux (F 10 ) with Mg II core-to-wing ratio. The solid curves are the best fit quadratic regression lines and r denotes the correlation coefficient Comparison of Linear and Nonlinear Models With Mg II Ratio and Radio Flux [13] The RGO/USAF/NOAA sunspot area is used to quantify darkening as its daily measurement extends back to more than a century, as well as to determine the contribution from dimming in the past. Figure 4 depicts the correlation by R 2 obtained for the model with (1) the Mg II ratio and (2) the radio flux for facular area and it is evident that the inclusion of a quadratic term improves the correlation with radio flux but obviously not the ones with the MgII ratio, with an improvement for the former by 10% on a daily timescale. In earlier studies, Lean and Foukal [1988] and Foukal [1990] also used similar indices, i.e., sunspot area and radio flux, to reconstruct past irradiance. The major difference is that they used TSI data only for a short period of 4 years ( ) covering a declining phase of solar cycle 21 and thus could not find a need for a quadratic term because the linear approach fails mainly during maximum activity. If the full time series with three maxima is used, the correlation increases by almost 10% to 56% with the inclusion of the quadratic term Reconstruction of Past Irradiance [14] In Figure 5 we show a part of the reconstructed solar irradiance for 1-day and 27-day binned data sets for the period from 1989 to It is clear from the figure that 4of7

5 Figure 5. A part of the reconstructed total solar irradiance on short timescales based on (a) daily variations and (b) 27- day bin averaged values. The model is calibrated according to equation (2) against TSI covering the full period of the composite time series using RGO/USAF/NOAA sunspot area and the radio flux (dark line). The observed values are shown by the grey line. Table 2. Regression Fits Between Total Solar Irradiance, RGO/ USAF/NOAA Sunspot Area, and 10.7 cm Radio Flux for the Period From 1978 to the Middle of 2003 a Bin Size C quiet, C 1, Wm 2 Wm 2 /ppm C 2, C 3, Wm 2 /sfu b Wm 2 /sfu 2 R 2 1-day ± ± ± day ± ± ± day ± ± ± day ± ± ± a The coefficients C quiet, C 1, C 2 and C 3 are defined in equation (2) and R is the coefficient of multiple correlation. The 1s error in regression is also given below each coefficient. b 1 sfu (solar flux unit) = Wm 2 Hz 1. Figure 6. (a) The contributions from sunspot and facular terms to solar irradiance for 27-day binned data depicted by dotted lines below and above the horizontal line. The dark solid line represents the net contribution to the total solar irradiance. The solar cycle numbers are also given. (b) The calculated and observed total solar irradiance are shown by dark and grey lines, respectively. daily variations as well as those on the timescale of one solar rotations are well reproduced by the model. The calculated coefficients C quiet, C 1, C 2 and C 3 for 1-day, 7-day, 14-day, and 27-day timescales for the model with radio flux are given in Table 2 along with fitting statistics. The uncertainties in the coefficients for all bin sizes are quite different, e.g., the uncertainties in 27-day binned data are roughly 3 5 times larger than those for 1-day data. This is due to the fact that number of points fitted for 1-day data are much larger than for 27-day binned data. However, if we consider the uncertainties in 27-day binned data, all coefficients are within 1 2s error. Now, using these coefficients, we calculate the contributions from sunspot and facular terms for the last five solar cycles on a 27-day timescale. These contributions are plotted in Figure 6a, where the net contribution from both the terms is also shown by a dark solid line. Finally, the calculated solar irradiance is plotted in Figure 6b. It is evident from the figure that the Sun s radiative output follows the phase of the solar cycle and its peak value during each solar cycle varies depending upon the net contribution from dimming and brightening factors. 4. Discussion [15] Our reconstruction of the solar irradiance basically depends on the time series of 10.7 cm radio flux and the sunspot area, and therefore the uncertainties involved in the reconstruction reflects the uncertainties in the measurements of these quantities. On the basis of our model, we underestimate the irradiance during the maximum activity of solar cycle 21 while it is overestimated during cycle 23. It is noticed that the observed solar irradiance during cycle 21 was substantially higher than that for cycles 22 and 23. The maximum values of the monthly mean of the radio flux for these cycles were between 220 and 230 solar flux unit (sfu). On the other hand, the measured sunspot area during cycle 23 was less as compared with cycles 21 and 22. However, the facular brightening to sunspot darkening ratio during cycle 23 was not substantially low to provide smaller values of irradiance. As a result, the amplitudes of the 5of7

6 and Fligge [1998]. This cycle was the most active solar cycle in recent times but the combined influence of sunspots and faculae does not show any drastic increase in the solar radiation which means that the Sun was somewhat darker, rather than brighter as compared with other cycles. We further notice that TSI was substantially low during cycle 20 because the facular to sunspot contribution ratio was less than usual. This was already noted by Foukal [1990] and confirmed by using plage areas from Mt. Willson and Sacramento Peak observatories together with PSI [Foukal, 2002]. [17] In the reconstruction of past solar irradiance, the influence of large-scale magnetic fields or the contribution from the quiet Sun is an important factor to consider in order to explain the long-term irradiance variability [Lockwood and Stamper, 1999; Solanki et al., 2000]. Since we are interested in studying the short-term variations, mainly on the time of 1 solar rotation or less, we assumed that the contribution from the quiet Sun is constant over last few solar cycles. However, it was shown that the average strength of the large-scale magnetic field has been doubled in the past 100 years [Lockwood et al., 1999; Solanki et al., 2000]; as a result there would be an increase in the radiative output of the Sun [Lockwood and Stamper, 1999] over the last century. This effect will be considered in a future investigation. Figure 7. The reconstructed total solar irradiance (dark line) on short timescales based on 27-day bin averaged values using RGO/USAF/NOAA sunspot area and (a) He I Å equivalent width, (b) Mg II core-to-wing ratio. The observed values are shown by the grey line. calculated irradiance during maximum activity of cycles are comparable to each other. The uncertainties in the calculated amplitude can be directly estimated by comparing the uncertainty in the measurements of radio flux with other independent measures of the radiative output from faculae and the enhanced network. We consider Mg II ratio and He I Å equivalent width, which are widely used proxies for such measurements, and their relationship with the radio flux to judge the uncertainty in our calculations. We obtain a linear correlation coefficient r = 0.97 between the daily values of radio flux and Mg II over the period , when both are available. Similarly, the correlation coefficient between the He I Å equivalent width and radio flux is r = The solar irradiance reconstructed using these facular proxies with RGO/NOAA/USAF sunspot area is plotted in Figures 7a and 7b for the entire period of TSI observation. The coefficient of multiple correlation, R 2, for He I is 0.73 and for Mg II ratio is It is clearly evident from the figure that there is no significant change in the overall pattern of the irradiance cycle and amplitudes of the solar irradiance obtained with different facular proxies are comparable to each other, thus the choice of a facular proxy does not change the relative amplitudes of the cycles. We estimate an uncertainty of 0.015% in our reconstruction of a irradiance cycle using radio flux as a facular proxy. [16] On the basis of our model we find that there was no significant increase in the solar radiative output during activity cycle 19 in contrast to that estimated by Solanki 5. Summary [18] We have presented an improved reconstruction analysis of solar irradiance and its variation on different timescales. The composite time series of TSI from 1978 to the middle of 2003 is employed to examine the contributions of various solar activity indices. We also present models that extend the reconstruction of irradiance to those epochs when direct measurements of TSI were not available. The sunspot area is used to quantify sunspot darkening while facular brightening is represented by facular area, 10.7 cm radio flux, and Mg II core-to-wing ratio. A detailed study of the behaviour of the surrogates for facular area, the 10.7 cm radio flux and the MgII ratio, has shown that a quadratic term is needed in reconstructing TSI when using the radio flux as a proxy mainly because it overweighs high sunspot activity. Adding such a term improves the correlation by almost 10% to 56%. [19] The nonlinear model based on sunspot area and 10.7 cm radio flux as a surrogate for facular area explains about 80% of the 27-day binned TSI variance from 1978 to The result is used to predict the TSI modulation back to 1947, the start of the observation of 10.7 cm radio flux. The uncertainty of the amplitude of a given predicted cycle is estimated to be 0.015%. One of the most important result is that the TSI amplitude of cycle 19 is within the uncertainty comparable to the one of cycle 21, although it shows a maximum annual sunspot number of nearly 190 compared to 155 for cycle 21. This is in contrast to the findings of Solanki and Fligge [1998]. On the other hand, the low amplitude of cycle 20 is in agreement with Foukal [1990, 2002] and is as low as 0.03%. [20] Acknowledgments. We acknowledge receipt of the dataset (version d25_07_0306) from PMOD/WRC, Davos, Switzerland. This work utilizes unpublished data from the VIRGO Experiment on the cooperative ESA/NASA Mission SoHO. We are grateful to the referees for several useful comments and suggestions which helped us to improve the manu- 6of7

7 script. We gratefully acknowledge financial support from the Indo-French Centre for Advanced Research. [21] Shadia Rifai Habbal thanks Claus Froehlich and another referee for their assistance in evaluating this paper. References Brandt, P. N., M. Stix, and H. Weinhardt (1994), Modeling solar irradiance variations with an area dependent photometric sunspot index, Solar Phys., 152, Chapman, G. A., A. M. Cookson, and J. J. Dobias (1997), Solar variability and the relation of facular to sunspot areas ratio during solar cycle 22, Astrophys. J., 482, Chapman, G. A., A. M. Cookson, J. J. Dobias, and S. R. Walton (2001), An improved determination of the area ratio of faculae to sunspot, Astrophys. J., 555, de Toma, G., O. R. White, G. A. Chapman, S. R. Walton, D. G. Preminger, A. M. Cookson, and K. L. Harvey (2001), Differences in the Sun s radiative output in cycles 22 and 23, Astrophys. J. Lett., 549, Fligge, M., and S. K. Solanki (1998), Long-term behaviour of emission from solar faculae: Steps towards a robust index, Astron. Astrophys., 332, Fligge, M., and S. K. Solanki (2000), The solar spectral irradiances since 1700, Geophys. Res. Lett., 27, Fligge, M., S. K. Solanki, Y. C. Unruh, C. Fröhlich, and C. Wehrli (1998), A model of solar total and spectral irradiance variations, Astron. Astrophys., 335, Foukal, P. (1990), Solar luminosity variations over timescales of days to the past few solar cycles, Phil. Trans. R. Soc. London, A330, Foukal, P. (1996), The behavior of solar magnetic plages measured from Mt. Wilson observations between , Geophys. Res. Lett., 23, Foukal, P. (1998), What determines the relative areas of spots and faculae on Sun-like stars?, Astrophys. J., 500, Foukal, P. (2002), A comparison of variable solar total and ultraviolet irradiance outputs in the 20th century, Geophys. Res. Lett., 29(23), 2089, doi: /2002gl Foukal, P., and J. Lean (1988), Magnetic modulation of solar luminosity by photospheric activity, Astrophys. J., 328, Foukal, P., and J. Lean (1990), An empirical model of total solar irradiance variation between 1874 and 1988, Science, 247, Foukal, P., L. A. Fowler, and M. Livshits (1983), A thermal model of sunspot influence on solar luminosity, Astrophys. J., 267, Fröhlich, C. (2002), Total solar irradiance since 1978, Adv. Space Res., 29, Fröhlich, C., and J. Lean (1998), The Sun s total irradiance: Cycles, trends and related climatic change uncertainties since 1976, Geophys. Res. Lett., 25, Krivova, N. A., S. K. Solanki, M. Fligge, and Y. C. Unruh (2003), Reconstruction of solar irradiance variations in cycle 23: Is solar surface magnetism the cause?, Astron. Astrophys., 399, L1 L4. Lean, J. (1988), Modelling solar UV irradiance variability, Adv. Space Res., 8, Lean, J. (2000a), Short term, direct indices of solar variability, Space Sci. Rev., 94, Lean, J. (2000b), Evolution of the Sun s spectral irradiance since the Maunder minimum, Geophys. Res. Lett., 27, Lean, J. (2001), Solar irradiance and climate forcing in the near future, Geophys. Res. Lett., 28, Lean, J., and P. Foukal (1988), A model of solar luminosity modulation by magnetic activity between 1954 and 1984, Science, 240, Lean, J., J. Beer, and R. Bradley (1995), Reconstruction of solar irradiance since 1610: Implications for climate change, Geophys. Res. Lett., 22, Lean, J., J. Cook, W. Marquette, and A. Johannesson (1998), Magnetic sources of the solar irradiance cycle, Astrophys. J., 492, Lockwood, M., and R. Stamper (1999), Long-term drift of the coronal source magnetic flux and the total solar irradiance, Geophys. Res. Lett., 26, Lockwood, M., R. Stamper, and M. N. Wild (1999), A doubling of the Sun s coronal magnetic field during the past 100 years, Nature, 399, Sofia, S., and L. H. Li (2001), Solar variability and climate, J. Geophys. Res., 106, 12,969 12,974. Solanki, S. K., and M. Fligge (1998), Solar irradiance since 1874 revisited, Geophys. Res. Lett., 25, Solanki, S. K., and M. Fligge (1999), A reconstruction of solar irradiance since 1700, Geophys. Res. Lett., 26, Solanki, S. K., M. Schüssler, and M. Fligge (2000), Evolution of the Sun s large scale magnetic field since the Maunder minimum, Nature, 408, Spruit, H. (2000), Theory of solar irradiance variations, Space Sci. Rev., 94, Tobiska, W. K. (2002), Variability in the solar constant from irradiances shortward of lyman-alpha, Adv. Space. Res., 29, Viereck, R., L. Puga, D. McMullin, D. Judge, M. Weber, and W. K. Tobiska (2001), The Mg II index: A proxy for solar EUV, Geophys. Res. Lett., 28, Wilson, R. C., and H. S. Hudson (1988), Solar luminosity variations in solar cycle 21, Nature, 332, Wilson, R. C., and H. S. Hudson (1991), The sun s luminosity over a complete solar cycle, Nature, 351, S. S. Hasan and K. Jain, Indian Institute of Astrophysics, Koramangala, Bangalore , India. (kiran@iiap.res.in; hasan@iiap.res.in) 7of7