Can Bray and Eddy Cycles Explain Global Warming?

There's a schematic that is frequently promoted by John Shewchuk on X to claim thatt long-term solar cycles explain much more of temperature variability of the last 2000 years than changes in greenhouse gases like CO2. The implication is also frequently made that the current warming over the last century or so is due to these cycles and not to changes in GHG concentrations. One common version of this graph is here.

The Hallstatt-Bray cycle, which has a periodicity of ~2400 years, and the Eddy cycle, which has a periodicity of 976 years, are both related to sunspots, and so they indeed do have an impact on total solar irradiance (TSI), and therefore they can in principle have an effect on global temperatures on millennial timescales. But the significant question is, by how much?  Astute observers will note that Shewchuk didn't include any scale for the y-axis; the impact of these cycles could be negligible or large as far as this schematic is concerned. I do find ironic, though, that Shewchuk essentially "infilled" data from 1950 to 2200 - a procedure he elsewhere considers fraudulent data fabrication. However, in another graph by Javier Vinós, Vinos went ahead and fabricated a temperature scale for the combined effect of Bray and Eddy cycles.

Here Javier Vinós made up the scale for the combined effect so that he could match these cycles to temperature variability described in Moberg et al 2005. Is this legitimate? In another post, I explain in detail why the answer to this is "no." But is it possible to determine what the actual effect of these solar cycles may be? The answer to that, I believe, is "yes."

The Bray and Eddy cycles are two cycles two of many sources of solar variability along side the more well-known 11-year Schwabe cycle. Both of these cycles are related to sunspot activity, and the impact of sunspot activity on TSI has been both quantified and reconstructed. In another post, I shared the a reconstruction of TSI from Lean 2018[1] that goes back to 850 CE. This may not include the entirety of the last 2000 years or even to 500 CE as shown in Vinós' graph, but it's certainly long enough to understand typical solar variability on millennial time scales, and this reconstruction would be determined by the combined effect of Bray, Eddy and Schwabe solar cycles. The reconstruction from Lean 2018 is below, and the black line shows the 11-year running mean so you can see the solar variability apart from the Schwabe cycle.

The above graph shows that the 11-year mean varying by less than 1.5 W/m^2, or by about 0.1%. So even on millennial timescales, our Sun is a vary stable star. We can use this data to determine the impact of solar variability on temperature. First, calculate solar forcings from TSI by ΔRF = TSI*(1-albedo)/4 where albedo is set at ~0.3. Second, calculate the impact of ΔRF on temperature. If we assume that ECS = 3°C, that's equivalent to a sensitivity of 0.81°C/W/m^2. Now many contrarians believe the ECS is much less than 3°C, but if that's the case then sensitivity must also be less than 0.81°C/W/m^2. So by using the ECS = 3°C, I'm suggesting changes in TSI has a larger impact on GMST than contrarians would believe (if they are consistent). Here are the results.

If we examine the 11-year running mean (black line) on this graph, we can clearly see that solar variability is no more than 0.2°C on decadal time scales. So the maximum value for solar variability on millennial time scales is ± 0.1°C. Moreover, note that TSI in 1850-1900 is about the same as it is presently, suggesting that the total impact of solar variability since 1850 is indistinguishable from 0°C. If we look at GMST, CO2 forcing, and solar forcing data from 1850 to present, we can see that GMST tracks with CO2 forcing with a negligible impact from solar variability.

This seems to explain why Shewchuk didn't use any y-axis scale and why Javier Vinós just made one up. If they did they actually did their homework and presented the data honestly, it would falsify their claim that Bray and Eddy Cycles are relevant to global warming over the last century or so. The impact of all forms of solar variability on TSI is in the range of ± 0.1°C. Below I plot the impact of solar variability on GMST with the Pages 2K reconstruction. 

You can quite clearly see that sometime shortly after the beginning of the 20th century, GMST increases rapidly with no corresponding change in the ΔTSI-impact on global temperature. So we can confidently reject the notion that Bray and Eddy cycles are having any impact on global temperature over the last century or so. They do affect ΔTSI, but the total impact of  ΔTSI on global temperatures is in the range of  ± 0.1°C.

References:

[1] 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