We know from direct observations that the Sun varies. We’ve been monitoring the energy received from the Sun at the top of the Earth’s atmosphere, known as the solar ‘irradiance’, for more than three decades. But, this is not enough time to understand the Sun’s contribution to climate change. Human-induced changes to the climate began with the industrial revolution, nearly two centuries ago. We need to extend the irradiance record back in time to better quantify its impact on our climate. To do that we need to know what causes the irradiance to change. When we can link the direct observations of irradiance to longer records of solar variation through this understanding, we can reconstruct the past behaviour of the Sun.
The Sun varies on a wide range of timescales from minutes to millions of years. On climate relevant timescales, variations of the Sun are due to the evolution of magnetic fields on the surface that form bright and dark features.
The darkest magnetic features are called `sunspots’. You can see one in the top image of Figure 1, which is a section from a full-disk image of Sun . Individual sunspots can range anywhere from 1,000 to 40,000 km in diameter. Energy reaches the surface of the Sun through convection, but when strong magnetic fields cover a wide area they shut down convection and the energy struggles to escape. The central region cools by over 1000 degrees Kelvin, from a typical temperature of ~5800 K, becoming dark relative to its surrounding, et voila, you have a sunspot.
The brightest magnetic features are typically a few hundred kilometres across and congregate in groups around sunspots: we call these faculae. They are bright because the magnetic fields evacuate the plasma in the region and we can see deeper into the Sun, where it is hotter and brighter.
The presence of sunspots on the surface decrease solar irradiance, while faculae increase solar irradiance. We can model the solar irradiance with the SATIRE-S model [2,3], which assumes that irradiance changes longer than a few hours can be reproduced by considering only changes in the surface magnetic fields. In Figure 2 , measured daily values of the Sun’s observed total irradiance are plotted in orange, with a five-month running mean shown in red and the SATIRE-S model is given by the blue lines. The model accounts for 92% of the observed variations in Figure 2, but better observations in recent years now yields over 98% agreement .
When the Sun has a low surface magnetic activity, e.g. in 1996, the daily irradiance barely deviates from the mean; we call this a ‘solar minimum’. As the activity ramps up to ‘solar maximum’, around 2001, the daily irradiance increases its variability. The pronounced dips in the daily values are due to sunspots that temporarily decrease the total energy reaching Earth. The overall increase to maximum shown by the mean is due to a global enhancement of the magnetic field, resulting in more faculae everywhere. In other words, more magnetic fields on the Sun means it is on average brighter, and more energy is arriving at Earth. The decline back to minimum around 2008 completes the ‘11-year solar cycle’.
If we take a look at timescales longer than the 11-year solar cycle, we will notice that there was a decrease in the level of irradiance from the minimum in 1996 to that in 2008; this underlying change is what we call the ‘secular’ change in the Sun and is the variation important for climate. Small though this one change may be, this might become large going back hundreds of years.
Since we can model the observed changes in solar irradiance to such high fidelity, we are confident that changes to the Sun on timescales of several decades are (almost entirely) due to changes in the surface magnetic fields. There’s a problem though: magnetograms (see Figure 1) only go back to 1974. We need a proxy to take us back further. The sunspot record is a good candidate as it goes back to 1610 (see Figure 3  back to 1700). We also know from the solar cycle that when there are more sunspots the Sun is, on average, brighter. The sunspots are not enough though as sunspots are just an indicator of the magnetic flux on the surface: it is the faculae that dictate how bright the Sun is on decadal and longer timescales. And, when the sunspot number is zero at the solar minima, there is still magnetic flux on the surface. That means that the amount of bright faculae, and the brightness of the Sun itself, can change even when there are no sunspots. We need a way to convert the sunspot record into a facular record; we need another model.
To build that model, we need to understand how magnetic flux can change and influence irradiance on secular timescales. We have an idea though: solar cycles are not discrete, the magnetic fields that produce faculae in the new cycle can start appearing before the previous cycle ends. Therefore, magnetic fields from one solar cycle overlap with the next. This is one reason why irradiance at solar minima may change over time and, therefore, why the energy from the Sun arriving at Earth may vary on climate relevant timescales.
The final step in reconstructing irradiance back to the 18th century is to connect sunspot number with the bright facular coverage. In the final snack of this series, we will investigate the various ways in which this is done and compare estimates of how much the Sun’s total output may have varied over the last two hundred and fifty years.
 HMI Homepage
 Fligge, M., Solanki, S.K., Unruh, Y.C., Modelling irradiance variations from the surface distribution of the solar magnetic field, A&A 353, 380, 2000
 Krivova, N. A., Solanki, S. K., Fligge, M., & Unruh, Y. C., Reconstruction of solar irradiance variations in cycle 23: Is solar surface magnetism the cause? A&A, 399, L1, 2003
 Ball, W.T., Unruh, Y.C., Krivova, N.A., Solanki, S., Wenzler, T., Mortlock, D.J., Jaffe, A.H., Reconstruction of total solar irradiance 1974–2009, A&A, 541, A27, 2012
 Yeo, K.L, Solanki, S.K., Krivova, N.A., Comparing Irradiance Reconstructions from HMI Magnetograms with SORCE observations
 SIDC website