A Simple Model to Understand and Assess the Increase in the Earth's Energy Imbalance

2024 was the hottest year in the modern era, followed by 2023. At the same time, the Earth’s Energy Imbalance (EEI) appears to be rapidly increasing. In order to better understand the relation between these two phenomena, as well as their implications for the future, we develop a simple model based on the well-known result that the equilibrium temperature anomaly is approximately logarithmic in the concentration of CO2 in the atmosphere. By introducing an effective heat capacity for the earth, we extend the utility of the logarithmic dependence to non-equilibrium situations such as those at the present time when the earth’s radiation budget is out of balance. We also incorporate a temperature dependent albedo. All parameters can be determined from CERES_EBAF_Ed4.2.1 fluxes which cover the period 2001-20024. It is notable that the heat capacity is in good accord with that implied by recent work on the total heat stored in the earth’s climate system. The recent temperatures appear to be consistent with past fluctuations about the modeled trajectory for the global mean temperature. The energy imbalance may be more worrisome, though the fluctuations are quite large. Should the energy imbalance continue to trend higher, it will still be some years before the effects are fully manifested in the global mean temperature. One thing is quite clear: the drivers of the fluctuations need to be better understood.