Parsimonious Emulators for the Global Climate Response Across Millennia

Parsimonious emulators (PEs) trained on complex climate models (CCMs) are useful when global variables like global mean surface temperature and climate-system energy content are sought. CCM runs over millennia extracted from the LongRunMip repository are used to construct and test PEs for global mean temperature and net incoming radiation flux. For the temperature, the PE is a linear impulse response in the form of a superposition of k decaying exponentials, comprising k weight coefficients and k decay times to be estimated by least-square fitting to the temperature from CCM runs with abrupt step-function forcing. The model fit for k≥3 is good on all time scales, and the fitted model seems to perform even better for smoother forcing scenarios, suggesting that it reflects essential features of the CCM to which it is fitted. Data for radiation flux are combined with temperature data to produce low-order polynomial fits to Gregory plots and analytic expressions for the evolution of the effective feedback parameter, the radiation fluxes, the evolution of climate-system energy content, and an effective system heat capacity. The analysis reveals four stages of the ocean heat uptake, characterised by increasing effective heat capacity. From these Pes, one can compare the global performance of CCMs under different forcing scenarios, highlighting distinguishing features, such as evolution of albedo feedback and cloud radiative effect. Producing Gregory plots for all-sky and clear-sky outgoing long-wave and short-wave radiation, varying cloud albedo is identified as the main contributor to model spread of equilibrium climate sensitivity.