By Andy May
Frank Stefani, of the Helmholtz-Zentrum Dresden-Rossendorf, Institute of Fluid Dynamics, has published a very interesting new paper that compares the solar “aa” index and CO2 emissions to global SST (sea surface temperatures using the HadSST4.2 dataset) and finds a CO2 sensitivity (TCR or the “Transient Climate Response”) of 1.1 to 1.4K. This is at the low end of the IPCC TCR range of 1.2 to 2.4K (IPCC, 2021, p. 93), but quite close to the values calculated by Lewis and Curry and Nicola Scafetta (Lewis & Curry, 2018), (Scafetta, 2023), and (Lewis, 2023). Scafetta found a plausible range of TCR (versus HadSST4.2) of 1.0K to 1.2K and Lewis & Curry report a range of 0.9K to 1.7K for TCR versus HadCRUT4. The estimates are compared in Table 1.
Table 1. Estimates of TCR, or Transient Climate Response to a doubling of CO2. Sources: (Stefani, 2026), (Lewis & Curry, 2018), (Scafetta, 2023), and (IPCC, 2021, p. 93).
TCR Estimates | ||||
Author | Best Estimate | Range: Low end | Range: High end | Note |
Stefani | 1.26K | 1.1 | 1.4 | 2026 |
Lewis & Curry | 1.2K | 0.9 | 1.7 | 2018 |
Scafetta | 1.1K | 1 | 1.2 | 2023 |
IPCC AR6 | 1.8K | 1.2 | 2.4 | p. 93 |
All the estimates in table 1 are based on regression models of varying complexity and all attempt to account for the influence of solar variability. The Lewis and Curry estimate does not incorporate a solar activity proxy directly but does use the Atlantic Multidecadal Oscillation (AMO) as an indicator of natural climate variability, which is, in large part, solar variability. Stefani uses the aa index of geomagnetic activity, essentially how disturbed Earth’s magnetic field is by the sun. It is measured in nanoteslas (nT).
Nearly every observable form of solar variability is a magnetic phenomenon at its core, including sunspots, flares, and solar wind variability. Thus, the aa index is a good indicator of changes in the sun’s state and output. The aa index as a measure of solar-geomagnetic coupling has been measured consistently since 1868.
Table 1 shows that Stefani’s aa index + CO2 model compares well to Lewis and Curry’s AMO + CO2 model and Scafetta’s solar proxies + CO2 model. Scafetta uses three estimates of total solar irradiance (TSI) in his study, although he acknowledges that variations in TSI may be only ~20% of the sun’s total influence on Earth’s climate. None of these observation-based models support the high-end IPCC TCR estimate of 2.4K per doubling of CO2 or their best estimate of 1.8K, but all are near the lower end of the IPCC range. The Lewis (2023) correction to the Sherwood (2020) assessment of ECS and TCR relied upon in AR6 is not included in the table. However, after changing Sherwood’s subjective Bayesian assessment of multiple estimates of TCR to an objective Bayesian assessment, Lewis calculated a TCR of 1.37 to 1.4 depending upon the assumptions made. This is still close to the other observation-based objective estimates in Table 1.
Stefani found that the solar aa index can successfully predict HadSST4.2 up to 1990-2000 on its own. After 1990 to 2000 the role of CO2 in the regression increases significantly. In figure 1, Stefani’s robust aa index weight of 0.04 K/nT (that is the HadSST4.2 anomaly temperature in °C per the aa index in nanoteslas) plus CO2 with a sensitivity of 1.26K per doubling is shown as a thin dark gray line. It is compared to the HadSST4.2 anomaly (shown as black dots). His projected aa index plus CO2 at 1.26K per doubling function to 2100 is shown as a red line. The maximum departure in 2023 and 2024 looks startling, but we need to remember that this follows two strong El Niños (2018-19 & 2023-24) and the Hunga Tonga volcanic eruption. In particular the El Niño from June 2023 to May 2024 was one of the strongest El Niños on record. The HadSST4.2 global anomaly has been falling since September 2024. Thus, a portion of the difference between the aa index plus CO2 function and HadSST4.2 may just be ENSO, the Hunga Tonga eruption, and weather.
Stefani’s optimal model projection to 2100 assumes constant emissions of 30-50 Gt of CO2 per year (roughly current levels) plus a simple linear carbon sink model and predicts a global SST increase of 0.6°C (1.1°F) compared to the standard HadSST4.2 reference period of 1961-1990. Using pessimistic parameters (high CO2 emissions, a low sensitivity to the aa-index, and a high sensitivity to CO2) yields a 2100 temperature increase of ~1K over 1960-1990. This is still a benign result.
A word on Transient Climate Response
The transient climate response is the modeled warming due to increasing the atmospheric CO2 concentration by 1% each year until it doubles, which would take about 70 years. This is different from the commonly cited value of ECS, which is the equilibrium climate sensitivity, or the final warming due to a sudden doubling of CO2. ECS is an untestable number, since it would take over 1,000 years for the atmosphere to completely come to equilibrium after CO2 suddenly doubles. Given the implausible scenario, ECS can never be tested, except in a climate model. Thus, it is not a scientific quantity per Karl Popper (Popper, 1962). TCR on the other hand is very realistic and could be tested given enough time and effort.
Conclusions
The paper is a welcome addition to the growing group of observation-based estimates of climate sensitivity to CO2. It is appropriate that Stefani chose to create his model around HadSST4.2. SSTs are more stable than air temperatures on land and they respond mainly to changes in insolation, whether due to cloud cover changes or changes in the sun itself. The changes in SST due to the greenhouse effect are smaller for the reasons discussed in my previous post. I recommend the paper, it is interesting, significant, and a good read.
Works Cited
IPCC. (2021). Climate Change 2021: The Physical Science Basis. In V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, . . . B. Zhou (Ed.)., WG1. Retrieved from https://www.ipcc.ch/report/ar6/wg1/
Lewis, N. (2023, May). Objectively combining climate sensitivity evidence. Climate Dynamics, 60, 3139-3165. https://doi.org/10.1007/s00382-022-06468-x
Lewis, N., & Curry, J. (2018). The Impact of Recent Forcing and Ocean Heat Uptake Data on Estimates of Climate Sensitivity. Journal of Climate, 31, 6051-6071. DOI: https://doi.org/10.1175/JCLI-D-17-0667.1.
Popper, K. R. (1962). Conjectures and Refutations, The Growth of Scientific Knowledge. New York: Basic Books. Retrieved from http://ninthstreetcenter.org/Popper.pdf
Scafetta, N. (2023). Empirical assessment of the role of the Sun in climate change using balanced multi-proxy solar records. Geoscience Frontiers, 14(6). Retrieved from https://www.sciencedirect.com/science/article/pii/S1674987123001172
Sherwood, S. C., Webb, M. J., Annan, J. D., Armour, K. C., J., P. M., Hargreaves, C., . . . Knutti, R. (2020, July 22). An Assessment of Earth’s Climate Sensitivity Using Multiple Lines of Evidence. Reviews of Geophysics, 58. https://doi.org/https://doi.org/10.1029/2019RG000678
Stefani, F. (2026). Solar and Anthropogenic Climate Drivers: An Updated Regression Model and Refined Forecast. Atmosphere, 17(3). https://doi.org/10.3390/atmos17030252
Scafetta uses three estimates of total solar irradiance (TSI) in his study,
top of the atmosphere solar tsi has been measured by nasa satellites since the late nineteen seventies there’s no read for reason for any estimates … top of the atmosphere tsi changes caused none of the global warming since 1975
there are accurate satellite-based measures of global average Absorbed Solar Radiation (ASR), primarily provided by NASA’s CERES (Clouds and the Earth’s Radiant Energy System) mission.
there is no logical reason to use models or estimates
the effect on land temperatures is being ignored but that is far more important than ocean temperatures people live on land and food crops are grown on land not the ocean
the implication that the TCR of CO2 would be easier to estimate than the ECS of CO2 is false
there are at least 4 feedbacks that affect the warming of CO2 emissions and their net effect is unknown for the next 50 years or the next 1000 years
Richard,
As Loeb explains in his 2018 and 2022 papers (see bibliography here: https://andymaypetrophysicist.com/wp-content/uploads/2024/12/Bibliography-for-Climate-Models.pdf ), satellite measurements are not accurate enough to detect the Earth energy imbalance which is less than 1 W/m2.
The only way to estimate it is with ocean heat content changes and they aren’t really accurate enough either, they are just better than satellites.
ECS is an unreal, untestable, and non-scientific number made up with unvalidated models. It is hopeless to use it for any purpose. TCR is at least close to what is really happening and might be testable given enough time, say another 70-80 years.
I take your point that the net effect of other variations (feedbacks, ocean oscillations, and solar changes) are unknown now, but with careful observations over the next century we may get a handle on them. Main point, today we don’t know enough to compute TCR, and we will never know enough to compute ECS, it is too unreal.
What is new? I recommend to read Francois Gervais’ paper
“Anthropogenic CO2 warming challenged by 60-year cycle”
of 2016 (https://www.sciencedirect.com/science/article/abs/pii/S0012825216300277), not cited by Stefani.
The Abstract of Prof. Gervais’ paper reads:
“Time series of sea-level rise are fitted by a sinusoid of period ~ 60 years, confirming the cycle reported for the global mean temperature of the earth. This cycle appears in phase with the Atlantic Multidecadal Oscillation (AMO). The last maximum of the sinusoid coincides with the temperature plateau observed since the end of the 20th century. The onset of declining phase of AMO, the recent excess of the global sea ice area anomaly and the negative slope of global mean temperature measured by satellite from 2002 to 2015, all these indicators sign for the onset of the declining phase of the 60-year cycle. Once this cycle is subtracted from observations, the transient climate response is revised downwards consistent with latest observations, with latest evaluations based on atmospheric infrared absorption and with a general tendency of published climate sensitivity. The enhancement of the amplitude of the CO2 seasonal oscillations which is found up to 71% faster than the atmospheric CO2 increase, focus on earth greening and benefit for crops yields of the supplementary photosynthesis, further minimizing the consequences of the tiny anthropogenic contribution to warming.”
Figure 1 of Prof. Gervais’ paper not only illustrated results of both the Equilibrium Climate Sensitivity (ECS) and the Transient Climate Response (TCR) published by several authors since 2002, but also the trends in the results to lower numbers.
To me, it is highly awkward that the author Stefani did not cite Prof. Gervais’ paper.
Thanks. I didn’t know about Gervais’ paper either, but there are so many no one can read them all.