TransEBM v. 1.0: Description, tuning, and validation of a transient model of the Earth’s energy balance in two dimensions

Abstract. Modeling the long-term transient evolution of climate remains a technical and scientific challenge. However, understanding and improved modeling of the long-term behavior of the climate system increases confidence in projected changes in the mid- to long-term future. Energy balance models (EBMs) provide simplified and computationally efficient descriptions of long timescales and allow large ensemble runs by parameterizing energy fluxes. This way, they can be used to pinpoint periods and phenomena of interest. Here, we present an extended version of the two-dimensional energy balance model by Zhuang et al. (2017a). Transient CO₂, solar insolation, orbital configuration, fixed ice coverage and land-sea distribution are implemented as effective radiative forcings at the land surface. We show that the model is most sensitive to changes in CO₂ and ice distribution, but the obliquity and land-sea mask have significant influence on modeled temperatures as well. We tune the new model to reproduce the 1960–89 C.E. global mean temperature, equator-to-pole, and seasonal temperature gradient of the ERA20CM reanalysis (Hersbach et al., 2015). The resulting latitudinal and seasonal temperature distributions agree well with reanalysis and the general circulation model (GCM) HadCM3 for a simulation of the past millennium. We find that the EBM lacks internal climatic variability. This is attributed mostly to its reduced descriptions of heat transport and the hydrological cycle. As the model facilitates long transient simulations, we envisage its use in exploratory studies of stochastic forcing and perturbed parameterizations, thus complementing studies with comprehensive GCMs.