For the recent changes since the industrial revolution and the onset of anthropogenic climate change, daily reconstructions of solar irradiance — changes in the energy we receive from the Sun — require the use of the number of sunspots . Our best estimate of the change in solar irradiance over the last 400 years, based on these reconstructions, tell us that the Sun has increased in brightness only by about as much as the Sun changes over the 11-year solar cycle. The IPCC’s recent assessment, which looks at the change in the climate since 1750 suggests that the Sun probably contributed only 5% or less to changes in the global temperature increases .
In the first and second part of this Climate Snack trilogy, we introduced the observations and causes of solar irradiance variations. This third and final part discusses how we extend irradiance measurements into past centuries relevant for the Earth’s climate.
As in many areas of research, the key to extrapolate a certain quantity that cannot be measured directly is to use a model. In our case that quantity is solar irradiance. The first thing we need to do is make sure that our model works and is able to reproduce the measurements. As we have seen in parts one and two, current models of solar irradiance have reproduced successfully the observations available over the past 40 years [1,2].
The success of these models lies in the assumption that irradiance variations are driven by the magnetic fields on the solar surface. Maps of the distribution of the magnetic field (magnetograms) show that the field is not homogeneous over the Sun’s surface, but it forms clumps called active and ephemeral regions. Active regions are large bipolar concentrations composed of sunspots (dark patches) and faculae (bright structures) surrounding them. Ephemeral regions, in contrast, are very tiny bipoles seen as two bright points. Figure 1 depicts these two types of regions.
To model irradiance on a particular day we simply add up the irradiance coming from each magnetic feature — sunspots, faculae, and ephemeral regions. We need to know for each feature (1) its brightness, (2) the location and (3) the fraction of the solar surface it covers. Therefore, the variation of irradiance from one day to another is solely produced by changes in the distribution and total area covered by sunspots, faculae, and ephemeral regions.
In part two we only spoke about spots and faculae, and never mentioned ephemeral regions. This is because the irradiance model SATIRE-S [1,2] uses magnetograms to locate all the bright features, without needing to distinguish between active region faculae or ephemeral regions. Thus, every bright patch is classified as faculae in that model. However, when we do not have magnetograms we must make a distinction as they originate and evolve in different ways.
SATIRE-S is the most sophisticated model precisely because it uses daily magnetograms and images taken by telescopes that began observing 40 years ago [1,2]. But what happened before that? Well, we need a proxy (an indirect measurement) of the solar magnetic field that has been recorded for an even longer time. Of several options, the number of sunspots spans the longest time period, between 1610 and the present (see Fig. 2).
It is easy to estimate the amount of darkening from sunspots through linear correlations between the sunspot number and area since they are different ways of measuring the same feature. What is more challenging is to estimate the amount of brightening produced by faculae and ephemeral regions from the sunspot number.
Experience tells us that when the Sun is full of sunspots (cycle maximum) the Sun is brighter, so we can use a simple linear or quadratic relationship between the facular areas and the sunspot number . This is reasonable, since faculae are part of active regions, always appearing around sunspots.
The total number of ephemeral regions is trickier to estimate because they are not part of the active regions and thus are not directly related to sunspots. Over three decades, Karen Harvey investigated how the ephemeral regions are linked to sunspots . She found that ephemeral regions not only follow cycles like the sunspots, but that there are periods when the magnetic flux from two different cycles overlap: when a sunspot cycle is close to an end, ephemeral regions of that same cycle are still present on the solar surface when those of the next cycle start to emerge (Fig. 3).
Ephemeral regions appear on the solar surface even during the times of cycle minima. This means that the total magnetic flux on the solar surface never reaches zero; not even if the sunspot number is zero. Thus, the level of irradiance at each minimum depends on the amount of overlap between the cycles.
Models for the past
Several models have been developed to reconstruct irradiance, from 1600 to present day, based on the sunspot number. The two most widely used are the models of Krivova et al. (2010)  and Wang et al. (2005) , which were included in the recent IPCC report  (see Fig. 4). Both models connect the amount of faculae and ephemeral regions with the number of sunspots, and then combine the contribution of sunspots, faculae and ephemeral regions to produce the total solar irradiance.
One major difference between the models is how they combine this information. Wang et al. (2005) did multiple linear regressions between the area coverage of each magnetic feature and current measurements of irradiance, whereas Krivova et al. (2010) accounted for the brightness of each feature through physics-based models of the solar atmosphere. The latter can therefore provide a better physical understanding of the cause of the variation. Furthermore, Krivova et al.’s model is able to reconstruct irradiance on a daily basis over the past 400 years. Other models reconstruct irradiance even further back in time (9,000 years) using historical archives of the abundance of the isotope 10Be [see 9, 10, 11].
In terms of total forcing, it looks like the Sun has not been a major player in recent human-induced climate change. Evidence suggests that the Sun does impact the climate in more subtle ways. For example the UV part of the spectrum may influence the dynamics of the stratosphere . But more research is needed. All that, and more, in future snacks.