The Top of the Atmosphere is used as the main reference for climate models. Energy in has to equal energy out and the atmosphere responds quickly, so the TOA imbalance would have to be small. For simplicity, the TOA is considered to be the Tropopause to Stratopause depending on the detail of the models. A problem I have is that internal imbalances can take paths outside of the simpler model boundaries. Sudden Stratospheric Warming Events, Deep Convection and the Brewer-Dobson circulation transfer energy internally while allowing more or less total heat loss. A SSW event can warm the polar Stratosphere by 50 degrees in just a matter of days collapsing the polar vortex and dramatically change the Jet Stream. On the order of 10^22 Joules can be released over weeks to possible two months during a major SSW event. That would be roughly 7 Wm-2 loss in a 30 day period or 0.6 Wm-2 for a annual basis. About the same as the estimated TOA imbalance.
To show how this can be missed in models, I put together a simple energy balance model.
The imbalance variable just changes the temperature distribution between hemisphere by changing the polar ocean surface temperature. 273.2K is the freezing point of fresh water which is used as the reference and the same value is used for the Moist Boundary Layer (MBL).
With a 5 degree imbalance, the northern polar region average temperature increases and the southern polar decreases. That changes the SST distribution, but not the average energy. The OLR and Window Energy change, but not the average and in the blue arrow above the TOA, there is an indication of the energy transfer that models would easily miss. The arrows look a lot like the Brewer-Dobson circulation because this should be the basic mechanism that produces the B-D circulation. Since the transfer is between two regions with roughly an areal weight of 0.1 or ten percent of the surface, the net internal impact should be on the order of 10% or about 1Wm-2. So based on this simple model and shift in the meridional imbalance of 5 degrees total would produce roughly the same imbalance that CO2 forcing is estimated to cause. That 5 degree imbalance would produce 2.5 C difference between the NH and SH SST and shift the Tropopause temperature profile, without having much initial impact on the TOA balance.
There is no consideration of TSI, CO2 concentration or Latent Heat only TOA and Ice/MBL sink temperatures and the BB efficiency of 0.926 estimated in the Stefan and Boltzmann equation. That is pretty interesting I think. The model though is still an Aqua world which is a lot simpler than a mixed surface situation. That likely causes the slight differences between the model and measured values, but given the margins of error, I am pretty happy with this crude approach.
The spreadsheet was done in OpenOffice and is not wanting to export properly.