Climate modelling without irrelevant weather details: The Half-order Energy Balance Equation

Uncertainties in conventional numerical climate models –as measured by the spread between competing models - have for the first time in over four decades increased (IPCC, AR6, 2021). This approach is in crisis and the community is increasingly turning to Machine Learning i.e. to black boxes that “emulate” the standard (nearly) black box climate models. The root problem is that these models are based in the weather regime, i.e. they spend almost all their effort calculating irrelevant weather details. In this paper we summarize recent developments in a multidecadal effort to develop new models focused on the relevant details. We focus on the Half-order Energy Balance Equation (HEBE), that currently is the most promising candidate. It is based conservation laws (energy) and scale symmetries (scaling) and can already make low uncertainty hindcasts and projections to 2100.