Temperatures from energy balance models: the effective heat capacity matters

Energy balance models (EBMs) are highly simplified models of the climate system, providing admissible conceptual tools for understanding climate changes. The global temperature is calculated by the radiation budget through the incoming energy from the Sun and the outgoing energy from the Earth. The argument that the temperature can be calculated by this simple radiation budget is revisited. The underlying assumption for a realistic temperature distribution is explored: one has to assume a moderate diurnal cycle due to the large heat capacity and the fast rotation of the Earth. Interestingly, the global mean in the revised EBM is very close to the originally proposed value. The main point is that the effective heat capacity and its temporal variation over the daily and seasonal cycle needs to be taken into account when estimating surface temperature from the energy budget. Furthermore, the time-dependent EBM predicts a flat meridional temperature gradient for large heat capacities, reducing the seasonal cycle and the outgoing radiation and increasing global temperature. Motivated by this finding, a sensitivity experiment with a complex model is performed where the vertical diffusion in the ocean has been increased. The resulting temperature gradient, reduced seasonal cycle, and global warming is also found in climate reconstructions, providing a possible mechanism for past climate changes prior to 3 million years ago.