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versión impresa ISSN 0187-6236

Atmósfera vol.19 no.4 Ciudad de México oct. 2006


A new reconstruction of total solar irradiance since 1832


Departamento de Física, Escuela Politécnica, Universidad de Extremadura,
Avda. de la Universidad s/n, 10071 Cáceres, España
Corresponding author e–mail:

Departamento de Física, Facultad de Ciencias, Universidad de Extremadura,
Avda. de Elvas s/n, 06071 Badajoz, España

Centro de Geofísica da Universidade de Lisboa, Portugal, Departamento de Engenharias,
Universidade Lusófona, Lisboa, Portugal

Departamento de Electrónica e Ingeniería Electromecánica, Escuela de Ingenieros Industriales,
Universidad de Extremadura, Badajoz, España

Departamento de Física, Facultad de Ciencias, Universidad de Extremadura,
Avda. Elvas s/s 06071 Badajoz, España


Received July 1, 2005; accepted April 21, 2006



Diferentes autores han propuesto que las variaciones de la irradiancia solar total y espectral son magnitudes que pueden influir en el clima. El objetivo de este artículo es reconstruir la irradiancia solar total desde 1832 hasta el presente. Las contribuciones de las regiones activas y del "sol quieto" se modelan separadamente usando el método de Solanki y Fligge (1999). El área de las manchas solares desde 1832 es utilizada para calcular la contribución de las regiones activas a los cambios en la irradiancia.



Variations of solar irradiance (total and spectral) are quantities purported to have an influence on climate. The aim of this paper is to reconstruct the total solar irradiance from 1832 to the present. The contributions of active regions and the quiet sun are modelled separately using the method developed by Solanki and Fligge (1999). The areas of sunspots observed since 1832 are used to compute the contribution of active regions to the irradiance changes.

Keywords: Total solar irradiance, solar forcing on climate, solar–terrestrial physics.


1.  Introduction

Some studies by both the astrophysical and the meteorological communities have shown the fingerprint of solar activity in our climate (Eddy, 1976; Friis–Christensen and Lassen, 1991; Kodera, 2002). However, the exact physical mechanisms responsible for this influence are as yet barely understood. One of the mechanisms proposed is the change in the total solar irradiance. However, accurate measurements of total solar irradiance (TSI), with sufficient precision to show its variability have become available only since 1978. A recent comprehensive review on solar irradiance variability is given in Solanki and Krivova (2004). Solar activity is now widely accepted to have played a major role over the last millennium and, in particular, during the significant warming (positive trend) observed in late 19th and early 20th centuries (IPCC, 2001). In fact, recent works have clearly detected the impact of solar variability in both stratospheric (Labitzke, 2005) and tropospheric circulation patterns (Kodera 2002; Baldwin and Dunkerton, 2005), in particular the shape and intensity of the major Northern Hemisphere atmospheric circulation mode, the North Atlantic Oscillation (Ogi et al., 2003; Gimeno et al., 2003; Bochnícek and Hejda, 2005). Unfortunately, the exact physical mechanisms responsible for this associationship are not yet well understood, despite some early attempts to describe such mechanisms (Shibata and Kodera, 2005). Readers looking for recent substantial summaries are refereed to the books by Benestad (2003) and by Pap and Fox (2004).

The reconstruction of solar activity is very important for climatologists and solar physicists because it allows extending into the past reliable time–series much required by both communities. There are a number of different methodologies to assess solar variability throughout the last four centuries. Some of these are based on observations of aurorae (Krivský, 1984; Silverman, 1992) or the shape of the solar corona during eclipses (Vaquero, 2003). However, the majority of these reconstruction techniques are based on sunspots characteristics. Vaquero et al. (2004) realized a contribution in this sense in order to reconstruct the monthly sunspot area since 1832. In recent years, several reconstructions of the total solar irradiance have been proposed (Foukal and Lean, 1990; Hoyt and Schatten, 1993; Zhang et al., 1994; Lean et al., 1995; Solanki and Fligge, 1998, 1999; Lockwood and Stamper, 1999; Fligge and Solanki, 2000; Lean, 2000; Foster, 2004). Here we intend to obtain a different reconstruction of solar activity based in sunspot areas since 1832, for this purpose we will use extensively the data provided by Vaquero et al. (2004).


2.  Method and data

The majority of the reconstruction of the Total Solar Irradiance (Srec) is based on the following model

Srec = S0 + ΔSact + ΔSqs                                                                                                                          (1)

where S0 is just a constant which is added in order to produce the correct absolute value of the observed irradiance. The term ΔSact is the contribution to the TSI of the solar active regions, while term ΔSqs corresponds to the contribution of the quiet–Sun. Thus, the contributions from the three different components of surface magnetism are included, namely: sunspots, faculae and the network. It is a well known fact that sunspots lead to a darkening of the Sun while faculae result in a brightening. The combined contributions of these two phenomena are reflected in the irradiance variations term (ΔSact), which is the main responsible for irradiance variations over time scales equal or smaller than the solar cycle. Finally, the network component provides the main contribution to irradiance variations on time scales longer than the solar cycle (ΔSqs).

Solanki and Fligge (1999) used the relationship between modern satellite measurements of solar irradiance and sunspot numbers in order to estimate the contribution of the solar active regions (ΔSact) to the TSI. We should stress that, due to the relatively short length, the contribution of the quiet–sun term (ΔSqs), during the period of availability of modern satellite data, is virtually zero. The sunspot area time–series reconstructed by Vaquero et al. (2004) is based on the Group Sunspot Number, hereafter RG (Hoyt and Schatten, 1998). Several studies have pointed to the advantage of using the RG instead of the Wolf Sunspot Number as it probably guarantees a better assessment of the real solar variability, particularly before 1880 (Usoskin and Kovaltsov, 2004). In fact, the RG can be easily adopted to obtain a different reconstruction of the ΔSact term. Using the approach presented by Solanki and Fligge (1999) to reconstruct the TSI, one could estimate ΔSact using the relationship between modern satellite measurements of solar irradiance (Fröhlich, 2000) and contemporaneous sunspots area values. Figure 1 shows precisely the relationship between these two quantities using annually averaged data. The constant S0 can be calculated as the TSI value when the sunspot area tends asymptotically to zero.

This relationship will be used for estimating the contribution to the TSI of the solar active regions, ΔSact from sunspot area measurements since 1832. We have fitted a quadratic function to obtain the relationship between modern satellite measurements of solar irradiances and sunspot area A values during the period 1979–2002. The best quadratic fit to the data is given by:

S= (1365.42 ± 0.05) + (6.8 ± 1.1) × 10–4 A + (–1.0 ± 0.4) × 10–7 A2                                                   (2)

therefore, the contribution of the solar active regions (AS^) to the TSI will be estimated based on the equation

ΔSact = (6.8 ± 1.1) × 10–4 A + (–1.0±0.4) ×10–7 A2                                                                          (3)

The estimated standard error of S and ΔSact is 0.1 W/m2. These values correspond to relative errors of about 0.007% and 10%, respectively. Thus, using the values of sunspot area A, since 1832 reconstructed by Vaquero et al. (2004), one can obtain the contribution of the solar active regions(ΔSact).

The following step in the reconstruction is to utilize estimations of the long–term quiet–Sun irradiance variations, ΔSqs. Two slightly different approaches have enabled Solanki and Fligge (1999) to obtain two different estimates of the term ΔSqs. These two time series, hereafter identified as A and B (Fig. 2), were kindly provided to us by Solanki and Fligge (1999). Series A is based on the amplitudes of the group sunspot number RG(Hoyt and Schatten, 1998), while series B is based on the length of the solar cycle (Lean et al., 1992; Baliunas and Soon, 1995).

Adding the contribution to the TSI of solar active regions and the contribution of the quiet–Sun, ΔSact and ΔSqs, we can obtain a reconstruction of the TSI since 1832.


3. Results and conclusions

Figure 3 shows our two different TSI time series reconstructed since 1832. As expected, the dominant term in both curves is due to the quiet–Sun contribution. The contribution of the active regions, although of smaller amplitude, causes clearly an 11 –years cycle in the series reconstructed. Moreover, both reconstructions show an increase of the TSI during the 20th Century, albeit more intense in model B.

Figure 4 shows the annual differences between the reconstructions of ΔSact derived by Solanki and Fligge (1999) and the one obtained in this work. We should stress that taking into account the procedure developed here, the difference between ΔSact values obtained with these two reconstruction techniques is independent from which model we consider. The maximum difference between the reconstructions can reach 0.5 W/m2, although the average value of these differences is only 0.02 W/m2 and the standard deviation is 0.12 W/m2. Moreover, Figure 4 shows a structural change between the two reconstructions after 1880. In fact, throughout most of the 19th century there is a clear periodicity that, after 1880, is mostly absent, particularly after the beginning of the 20th century. This change is explained by the different sunspot number used in the two reconstructions. Solanki and Fligge (1999) used the Wolf or Zurich Sunspot Number (RZ) and Group Sunspot Number (Rg). Two records of ΔSact were created using RG and RZ. The final ΔSact record is an average of the two. However, Vaquero et al. (2004) used in the reconstruction procedure the Group Sunspot Number (RG). The indexes RZ and RG are very similar from 1880 onwards, however before 1880, the amplitude of solar cycles using RG is lower than using RZ. Thus, there is a pattern –highly correlated with the solar cycle– before 1880, in the differences between the reconstructions of ΔSact derived by Solanki and Fligge (1999) and the one obtained in this work.

We can conclude that the use of the sunspot area as the unique element to compute the contribution of the solar active regions to the changes of irradiance agrees considerably well with the prior results obtained using the sunspot number (Solanki and Fligge, 1999).



The authors would like to thank Dr. Solanki and Dr. Fligge for providing the long–term quiet–Sun irradiance variations. We are also in debt with PMOD/WRC (Davos, Switzerland) for supplying the irradiance composite data.



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