Roger Marvin Cooke, Willy Aspinall

Improved high-resolution paleo records of atmospheric carbon dioxide (CO2) concentrations and reconstructions of Earth’s surface temperature are available. We analyze one authoritative Pleistocene data set to explore how the climate sensitivity parameter S varies under different system states, using linear regression of mean annual surface temperature changes against CO2 forcing changes. On the whole data set, S = 2.04K/Wm^(-2) and CO2 forcing explains 64% of the variance in temperature. Partitioning the data by path (glaciation / de-glaciation); during de-glaciation episodes, S = 2.34K/Wm^(-2), explaining 75% of the temperature variance; during glaciations, S = 1.59K/Wm^(-2) explaining 48% of the temperature variance. Further partitioning into epochs before and after the Marine Isotope Stage 11 424 kaBP (thousand years before present); for de-glaciation paths after 424 kaBP, S = 2.63 K/Wm^(-2) explaining 83% of the variance. Partitioning into levels of CO2 concentration has much less explanatory power; 20% for concentrations above 210 ppmv and 2% for concentrations below 210 ppmv. These partitions conflate glaciation and de-glaciation episodes and pre/post 424 kaBP epochs. Possible process-related explanations for the path-related differences are conjectured. The common assumption that changes in temperature are proportional to changes in CO2 forcing constrains the regression intercept to pass through the origin and inflates the regression error to the extent that the regression model becomes a worse predictor of temperature changes than simply predicting the population mean for all values of CO2 forcing. The consequences of this assumption are substantive in the context of estimating future temperature trajectories and should be carefully weighed.