How Much Can Solar Variability Affect Climate?

Expected Global Temperature Change from Solar Variability Alone, Assuming ECS = 3 C

In a previous post, I considered whether there is a "continuing debate" over whether current climate changes are being caused in part by solar variability. This is effectively part 2 of that post. The evidence we currently have is clear that solar variability has been negligible since 1850, and particularly after 1960. There no significant ongoing debate on this point, as best as I can tell. However, the question remains, how much can the Sun affect climate? After all, the Sun may well have affected climate between 1850 and today, even if the combined effects were negligible over the last 170 years. To answer this question, we can think of the Sun's affect on climate on at least three different time scales:

1. Decadal: Given that solar variability operates on roughly 11-year cycles, TSI increases and decreases on roughly decadal time scales. But what they add to warming as TSI increases they also take away as TSI decreases, and the net effect of these cycles is roughly 0 W/m^2.

2. Historical: Not every solar cycle is created equal. Some average higher solar output than others, and on historical time scales, we can witness upward and downward trends in TSI. On these time scales, the Sun can have some impact on climate. The question is, how much?

3. Geological: When the earth was formed about 4.57 billion years ago, the Sun was about 30% less bright than it is today, but as the Sun's nuclear reactions burn up hydrogen, they produce helium as a waste product, which is a heavier molecule. The denser hydrogen/helium mix means that the Sun's core is becoming denser, and this increases the pressure inside the Sun, making these nuclear reactions hotter and brighter. On geologic time scales, solar evolution has a profound impact on climate, which is important for paleoclimatology studies but not as relevant for how much human activity is affecting climate today.

The most significant time scale for evaluating to what extent solar activity could play a role in current warming is historical time scale - decades to hundreds of years. We saw in a previous post that the most current reconstructions of TSI since 1850 show that the Sun has had a negligible impact on climate over that time frame. Solar variability has not been large enough to account for a significant portion of warming since 1850. That post was a response to a recent paper that argued that there were "high variability" datasets for TSI that show more variability, and those datasets would produce a non-negligible warming influence on climate since 1850. We saw that the "low variability" reconstructions are more consistent with recent developments in the scientific literature, and reconstructions from Lean 2000[1] overestimate solar variability. Even using Lean 2000, plotted it in terms of radiative forcing, we see only about a 0.2 W/m^2 increase in radiative forcing from solar activity, and almost all of that is in the first half of the 20th century. Since 1960, TSI has been relatively stable to decreasing, while global temperatures have accelerated. Since CO2 forcings (2.2 W/m^2) are greater than 10x the radiative forcings from solar variability, the impact on temperature would be 0.2/2.4 = 8% of current warming.

And the reality is that we already know that Lean 2000 reconstructed too much variability. Lean based his TSI reconstruction for the Maunder Minimum on a  Baliunas and Jastrow paper, which evaluated the irradiance of cycling and non-cycling stars. The preliminary results of these comparisons did not hold up after more stars were evaluated. So the Sun is likely more stable than the Lean 2000 reconstruction shows. If we plot CO2 radiative forcings with two current reconstructions of solar forcings (Kopp and Lean 2018), they are negligible compared to CO2.

TSI Since 850 C.E.

The Lean 2018 paper improved its assessment of solar variability from Lean 2000 but also produced a historical reconstruction of TSI beginning in 850 C.E. The results show similar amounts of variability over nearly 1200 years. I put an 11-year running average on the the data above. The variability within this running average is less than 1.5 W/m^2 in TSI, or about 0.1%. So that means on time scales that we are concerned about, we should not see the Sun causing more than RF = 1.5*(1-0.306)/4 = 0.26 W/m^2 in radiative forcing. And if ECS = 3 C, then 0.26*3/3.71 =  0.21 C of variability in global temperatures.

This would also allow us to evaluate to what extent solar variability plays a role in the Medieval Warm Period and Little Ice Age. Above I shaded areas that are commonly attributed to these times. We can see a period of low TSI near the beginning of the MWP. Some historians place the LIA later than what I've shaded above, but there were at least two (or three) periods of high TSI values that averaged more than the MWP. So while TSI likely played a roll in these time periods, it can't be the only explanation for them.

Correlation of TSI with Temperature

Just as one more way to look at the data since 1850, I plotted GMST temperatures from HadCRUT5 from 1850 to 2021 on the y-axis and TSI on the x-axis. I then showed the r^2 value of the best fit line through this data. The r^2 for TSI was 0.075. In another post, I did the same thing with CO2 and found the r^2 for CO2 is 0.872. Any increase in radiative forcing will have a delayed impact on climate, and of course natural variability plays a role here as well. But what should be obvious here is that TSI is a terrible predictor of global temperatures, whereas CO2 is pretty good.

References:

[1] Lean, J. 2000.Evolution of the Sun's Spectral Irradiance Since the Maunder Minimum. Geophysical Research Letters, Vol. 27, No. 16, pp. 2425-2428, Aug. 15, 2000.
https://www1.ncdc.noaa.gov/pub/data/paleo/climate_forcing/solar_variability/lean2000_irradiance.txt

[2] Kopp. "Historical Total Solar Irradiance Reconstruction, Time Series." https://lasp.colorado.edu/lisird/data/historical_tsi/

[3] Rasmus Benestad, "How large were the past changes in the sun?"
https://www.realclimate.org/index.php/archives/author/rasmus/

[4] Lean, J. L. (2018). Estimating solar irradiance since 850 CE. Earth and Space Science, 5, 133– 149. https://doi.org/10.1002/2017EA000357
https://agupubs.onlinelibrary.wiley.com/doi/10.1002/2017EA000357