Parsimonious models emulating millennium-long Earth system model simulations

Parsimonious emulator models (PEMs) trained on Earth system models (ESMs) can be very useful when information  about global quantities like global mean surface temperature (GMST) and ocean heat content (OHC) are sought. Here, I use data over several millennia from ESM runs extracted from the LongRunMip repository to construct and test PEMs for GMST and net incoming radiation flux.

For the  GMST, I consider a linear impulse response in the form of a superposition of three decaying exponentials, comprising three weight coefficients and three characteristic decay times to be estimated by least square fitting to ESM runs with abrupt step function forcing. The model fit is good on all time scales, and the fitted model seems to perform even better for smoother forcing scenarios. This sugggests that the six model parameters represent essential features of each ESM.

Data for radiation flux, and its decomposition in longwave and reflected shortwave, are combined with GMST to produce Gregory plots. By fitting parabolic curves to these plots, I obtain a simple analytic expression for the evolution of the feedback parameter λt), the radiation fluxes, and the resulting increase in OHC.

From these PEMs we can easily compare the global performance of different ESMs under different forcing scenarios. For instance, a comparison of the GISS-E2-R and CESM104 models exhibit equilibrium climate sensitivities (ECSs) of 3.4  and 2.4 K, respectively. The main reason for the difference is very different albedo feedbacks in the two models. Resulting total feedback parameter  λ(t) drops from 2.1 to 1.0 Wm^-2 K^-1 in GISS-E2-R and from 1.4 to 0.6 Wm^-2 K^-1 in CESM104. The OHC grows at nearly the same rate in the two models during the first millenium, but GISS saturates earlier and at lower final OHC.