Improved methods for estimating equilibrium climate sensitivity from transient warming simulations

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.