Solar and anthropogenic climate drivers: an updated regression model and refined forecast

TL;DR

This work refines the attribution of past and future climate change between solar-driven and anthropogenic forcings by analyzing SST correlations with the geomagnetic aa-index and $\log_2(\mathrm{CO_2})$ in a moving-average regression framework. It shows that early SST variability is aa-dominated while CO$_2$ becomes increasingly influential toward the end of the 20th century; by fixing the long-term aa contribution and performing a CO$_2$-only regression, the CO$_2$ sensitivity is narrowed to $w_{\mathrm{CO_2}}\approx 1.1$–$1.4\,\mathrm{K}$ per doubling, down from a prior range of $0.6$–$1.6\,\mathrm{K}$. Forecasts to 2100 combine three CO$_2$ emission scenarios with a synchronised solar-dynamo aa-index projection, yielding a likely warming of about $0.6\,\mathrm{K}$ under moderate emissions, with a total uncertainty of roughly $\pm 0.3$–$0.4\,\mathrm{K}$ and only a small chance of surpassing 1.0–1.5\,\mathrm{K}$ in the pessimistic case. The study highlights persistent uncertainties in solar variability and emission trajectories, while suggesting that, within the two-predictor framework, future data are essential to confirm whether recent rapid warming is CO$_2$-driven or partly solar-activity related.

Abstract

In a recent paper attempts were made to quantify the respective solar and anthropogenic influences on the terrestrial climate, and to cautiously predict the global mean temperature over the next 130 years. In a double regression analysis, both the binary logarithm of carbon dioxide concentration and the geomagnetic aa-index were used as predictors of the sea surface temperature (SST) since the mid-19th century. The regression results turned out to be sensitive to end effects, leading to a broad range of the climate sensitivity between 0.6 K and 1.6 K per doubling of CO$_2$ when varying the final year. The aim of this paper is to narrow down this range. To this end, the correlations between the two predictors and the dependent variable (SST) are analysed in detail. It is demonstrated that the SST can be predicted until around 2000 almost perfectly using only the aa-index, whereas for later periods the role of CO$_2$ increases significantly. Hence, the weight of the aa-index is fixed to its robust outcome (around 0.04 K/nT) from the regressions up to 1990. The SST data, reduced by the aa-contribution thus specified, are then used in a single regression with CO$_2$ as the only remaining predictor. This results in a significant reduction in the range of CO$_2$ sensitivity, narrowing it to 1.1-1.4 K. Given the exceptionally high temperatures in recent years, these values are considered a kind of upper limit that could still be subject to downward corrections when future data are incorporated. Based on this estimate, the temperature forecast until 2100 is refined by using more precise predictions of the aa-index and the paths of atmospheric CO$_2$ content which are based on constant emission scenarios combined with a linear sink model. With the exception of the most ``pessimistic'' variant, the temperature is predicted to remain below the extraordinarily high value measured in 2024.

Figures (7)

• Figure S1: Data on the HadSST sea surface temperature anomaly $\Delta T$ (a), the aa-index (b), and $\log_2$ of the ratio of the CO$_2$ concentration to the reference value of 280 ppm (c). Centred moving averages with windows of 11 years (full lines) and 23 years (dashed lines) complement the annual data between 1850 and 2024. The sources of the data are described in the text.
• Figure S2: Regression results in dependence on the chosen end year for a moving average window (${\rm MAW}$) of 11 years. (a) $R^2$ for the double regression and the two single regressions with either the aa index or the binary logarithm of CO$_2$ as the independent variable. (b) The same as (a), but for the adjusted version ${\overline{R}}^2$. (c) Resulting $w_{\rm aa}$ for the double regression and the single regression with aa as the only independent variable. (d) Resulting $w_{\rm CO_2}$ for the double regression and the single regression with CO$_2$ as the only independent variable.
• Figure S3: The same as Figure 2, but with an MAW of 23 years. Note that in (b) the adjusted version ${\overline{R}}^2$ formally acquires, for early years, negative values that are not shown.
• Figure S4: Regression results in dependence on the chosen end year for a moving average window (${\rm MAW}$) of 11 years. (a) $R^2$ for the double regression (as in Figure 2a) and the three single regressions on the binary logarithm of CO$_2$ as the independent variable, when subtracting beforehand from $\Delta T$ the aa-contribution weighted with three different values of $w_{\rm aa}$ (0.03 K/nT, 0.04 K/nT, and 0.05 K/nT). (b) Resulting $w_{\rm CO_2}$ for the double regression and the three single regressions.
• Figure S5: Same as Figure 4, but for an MAW of 23 years.