Abstract
Equilibrium climate sensitivity (ECS) refers to the total global warming caused by an instantaneous doubling of atmospheric CO2 from the pre-industrial level in a climate system. ECS is commonly used to measure how sensitive a climate system is to CO2 forcing; but it is difficult to estimate for the real world and for fully coupled climate models because of the long response time in such a system. Earlier studies used a slab ocean coupled to an atmospheric general circulation model to estimate ECS, but such a setup is not the same as the fully coupled system. More recent studies used a linear fit between changes in global-mean surface air temperature (ΔT) and top-of-atmosphere net radiation (ΔN) to estimate ECS from relatively short simulations. Here we analyze 1000 years of simulation with abrupt quadrupling (4 × CO2) and another 500-year simulation with doubling (2 × CO2) of pre-industrial CO2 using the CESM1 model, and three other multi-millennium (~5000 year) abrupt 4 × CO2 simulations to show that the linear-fit method considerably underestimates ECS due to the flattening of the −dN/dT slope, as noticed previously. We develop and evaluate three other methods, and propose a new method that makes use of the realized warming near the end of the simulations and applies the −dN/dT slope calculated from a best fit of the ΔT and ΔN data series to a simple two-layer model to estimate the unrealized warming. Using synthetic data and the long model simulations, we show that the new method consistently outperforms the linear-fit method with small biases in the estimated ECS using 4 × CO2 simulations with at least 180 years of simulation. The new method was applied to 4 × CO2 experiments from 20 CMIP5 and 19 CMIP6 models, and the resulting ECS estimates are about 10% higher on average and up to 25% higher for models with medium–high ECS (> 3 K) than those reported in the IPCC AR5. Our new estimates suggest an ECS range of about 1.78–5.45 K with a mean of 3.61 K among the CMIP5 models and about 1.85–6.25 K with a mean of 3.60 K for the CMIP6 models. Furthermore, stable ECS estimates require at least 240 (180) years of simulation for using 2 × CO2 (4 × CO2) experiments, and using shorter simulations may underestimate the ECS substantially. Our results also suggest that it is the forced −dN/dT slope after year 40, not the internally-generated −dN/dT slope, that is crucial for an accurate estimate of the ECS, and this forced slope may be fairly stable.
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