Calculating ECS from The Indicators of Global Climate Change 2025

A prepublication version of the Indicators of Global Climate Change 2025 (IGCC25) has recently been released. This report provides an annual update to IPCC's AR6 WG1 report concerning human emissions and global warming. The data provided as excel spreadsheets related to this report was extensive, and this allows me to produce some graphs I haven't been able to do before. These data do a really good job of showing the relative impact of human and anthropogenic forcings since 1750. 

Using HadCRUT5 (1850-1900 Baseline)

First I decided to show these forcings with GMST anomalies from HadCRUT5 to see how well the quantifications of forcings agree with observations for warming. This means for this section I'm limiting myself to values from 1850 to present. The graph below shows an update to Gillett's analysis used in AR6 that made it possible to conclude that human activity is responsible for virtually all the warming above the 1850-1900 mean. For this graph, I set HadCRUT5 to the 1850-1900 mean, and Gillett's analysis tracks with temperature quite accurately. Given observed warming and known forcings, there's no room here for there to be a large natural forcing that hasn't been accounted for. If something else was responsible for a significant fraction of global warming, there would be a large gap between anthropogenic + natural forcings and GMST anomalies. The evidence we have does a good job of explaining observations. While some may point to the warm period in the 1940s as an example of a mismatch between forcings and GMST anomalies, this discrepancy is small and is within the uncertainties for HadCRUT5 and Gillett's analysis. In fact, if I plot HadCRUT5 with the sum of Anthropogenic + Natural forcings plotted as temperature (following Gillett) I get a slope of 1 with an r² of 0.91.
Likewise, the IGCC25 report quantifies individual forcings quantified in AR6, including natural forcings (solar and volcanic) as well as aerosols, contrails, land use change, black carbon on snow, and all GHGs including ozone and stratospheric H2O. I summed all the anthropogenic and natural forcings and plotted both. It's quite easy to see that natural forcings have been fairly constant except for when there were large volcanic eruptions, which cause large but short-lived negative forcings from volcanic aerosols. These dissipate in a couple years and the overall trend remains relatively constant. GMST is following anthropogenic forcings quite closely, and volcanic eruptions explain many of the dips in GMST anomalies in HadCRUT5. In the graph below, I set all the forcings to their 1850-1900 mean so that they would be directly comparable to HadCRUT5 set to the same baseline.
 
Below I also show just CO2 and solar forcings. Quite clearly and obviously, GMST is following CO2 forcings and not solar forcings, which are responsible only for some natural variability on the overall trend.
For the full natural and anthropogenic components in IGCC25, I decided to plot the regression for each separately. For anthropogenic forcings, GMST warms at a rate of 0.47°C/W/m² with an r² of 0.89, meaning that anthropogenic forcings are a very good predictor of GMST anomalies.

The same analysis using natural forcings show a slope of 0.22°C/W/m² with an r² of 0.04, meaning that natural forcings are a very poor predictor of GMST anomalies. There is a positive slope to the graph, though, possibly because large volcanic eruptions do have a strong negative forcing that does influence GMST short term. However, the r² is so low that we can't have any confidence this is real.
If I remove the volcanic component and show only solar forcings, the plot looks like a blob of dots and the r² drops to 0.03. This should be unsurprising because solar forcing only vary between -0.05 W/m² and 0.13 W/m² with no real trend to the data over time. It's just the variability in the 11-year solar cycle. Even though the slope is large, there can be no confidence that it's real. Solar forcings are a terrible predictor of GMST anomalies.

In my post from a year ago, I used IGCC24 to calculate TCR and ECS from that data. This year I'll repeat this with two calculations, one using 4-year means for 2022-2025 and 2013-2025. For 2022-2025, I used CERES data for EEI, which is 1.40 W/m², virtually unchanged from last year. I used ΔT from HadCRUT5 and ΔF taken from IGCC25. Averaging 2022-2025 for ΔF, I get anthropogenic forcings of ΔF = 2.84 W/m². Adding all natural forcings, I get ΔF = 3.15 W/m², but this artificially inflates ΔF, since I set all forcings to a 1850-1900 mean. There were some large volcanic eruptions during that time with large negative values, so when I set the mean to 0, it makes baseline conditions average ~0.2 W/m² above 0. So I decided to do the calculation with anthropogenic and solar forcings alone (which average 0.1 W/m² for the last 4 years). For 2013-2025, I used the The IGCC25 report for EEI at 1.12 W/m², along with ΔF from IGCC25 and ΔT from HadCRUT5.
The TCR sensitivity value from these calculations (0.47°C/W/m²) above agrees with the slope of the first regression graph above. The average is ECS 3.40°C. I strongly suspect that the 2022-2025 calculation was higher than 2013-2025 because of the warming spike beginning in 2023.

Using GloSAT + HadCRUT5 (1790-1839 Baseline)

I don't think there is a GMST dataset that reliably goes back to 1750 (the CIs for the Berkely graph seem too large for me). But the new GloSAT dataset has reasonable CIs back to 1790, so I decided to do the same basic calculations with GloSAT set to the 1790-1839 mean that I did with HadCRUT5 above, with one caveat. GloSAT ends in 2021 but was published with HadCRUT5 set to the same baseline. So I set both to 1790-1839 by the same offset so that HadCRUT5 can be set to a 1790-1839 baseline. The method I used is described in this post. The plots looks similar but with more variability before 1850 due to large volcanic eruptions. This shows Anthropogenic and Natural forcings separately. Clearly global warming follows anthropogenic forcings but volcanic forcings explains the larger dips in temperature.
Solar forcings again are negligible compared to anthropogenic forcings. They have very little influence on global warming.
If I use the same calculations with GlosSAT+HadCRUT5 set to a 1790-1839 baseline, I get similar, but slightly higher values. 
The TCR sensitivity values here also agrees with the slope of the first regression graph above (~0.52°C/W/m², r² = 0.67). Clearly there is pretty close agreement between these, whether I'm using GloSAT+HadCRUT5 set to 1790-1839 or HadCRUT5 set to 1850-1900. Here's a table summarizing all of the above results.

Of course, these are just back-of-the-envelope calculations, and I think my 1850-1900 calculations are probably better than 1790-1839. However, I do think it's fair to conclude from this report that the empirical data is consistent with an ECS that is ~3.5°C and a TCR that is ~2°C.

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