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. I decided to show these forcings with GMST anomalies to see how well the quantifications of forcings agree with observations for warming. This means for this post 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.

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 18501-900 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 becaues 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 using the 4-year mean of CERES data for EEI from March 2022 to Feb 2026, which is 1.40 W/m², virtually unchanged from last year. Since I'm using the last 4 years for EEI, I'll use averages of the last 4 years for ΔT (HadCRUT5 anomaly above 1850-1950) and ΔF (from IGCC25). If I use only anthropogenic forcings I get:

ΔT = 1.39°C

ΔF = 2.84 W/m²

EEI = 1.40 W/m²

Since ΔF2xCO2 is 3.93 W/m² in AR6, we can calculate ECS and TCR as:

λ = ΔT/(ΔF - EEI)

λ = 1.39/(2.84-1.4) = 0.97°C/W/m²

ECS = λ*ΔF2xCO2

ECS = 0.97*3.93 = 3.8°C

λ = ΔT/ΔF = 1.39/2.98 = 0.49°C/W/m²

TCR = 0.49*3.93 = 1.9°C

This of course ignores any natural forcings contributing to global warming. If I sum both anthropogenic and natural forcings, I get a slightly higher value for ΔF and so a smaller number for ECS and TCR:

ΔF = 3.15 W/m²

λ = ΔT/(ΔF - EEI)

λ = 1.39/(3.15-1.4) = 0.80°C/W/m²

ECS = λ*ΔF2xCO2

ECS = 0.80*3.93 = 3.1°C

λ = ΔT/ΔF = 1.39/3.15 = 0.44°C/W/m²

TCR = 0.44*3.93 = 1.7°C

This second calculation 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 about 0.2 W/m² above 0, and this is what explains most of the difference in ΔF between the two calculations. I decided to do the calculation with anthropogenic and solar forcings alone (which average 0.1 W/m² for the last 4 years). This gives me:

ΔF = 2.95 W/m²

λ = ΔT/(ΔF - EEI)

λ = 1.39/(2.95-1.4) = 0.90°C/W/m²

ECS = λ*ΔF2xCO2

ECS = 0.90*3.93 = 3.5°C

λ = ΔT/ΔF = 1.39/3.15 = 0.47°C/W/m²

TCR = 0.47*3.93 = 1.9°C

The TCR value from this third calculation agrees precisely with the slope of the first regression graph above, so I'm taking this as the best estimate for TCR and ECS. These are just back-of-the-envelope calculations anyway, so I 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 ~1.9°C. Using 0.1 W/m^2 for solar forcings means that solar forcings contributes about 3% to global warming. In a few years, when the solar cycle is at a low point, this will be negated. Solar forcings add natural variability to the warming trend, but they are not responsible for a significant fraction of the warming above the 1850-1900 mean.