Bjerknes compensation assumes a constant total poleward energy transport (and an inverse relation between oceanic and atmospheric heat transport fluxes (Bjerknes, 1964)). Contrary to this assumption, there is empirical evidence of a simultaneous increase in poleward oceanic and atmospheric heat transport during the most recent warming period since the mid-1970s (aka the Great Pacific Climate Shift). This paper argues that TSI directly modulates ocean–atmospheric meridional heat transport.
Solar irradiance modulation of Equator-to-Pole (Arctic) temperature gradients: Empirical evidence for climate variation on multi-decadal timescales, Willie Soon and David R. Legates. PDF
This paper raises more questions than it addresses. How sensitive is the estimate of global temperature to a change in the equator to pole temperature gradient? Can a change in the gradient produce an apparent ‘amplification’?
Another thought that has occurred to me is that climate models overestimate global warming but they underestimate Arctic melting. Could both failures be due to underestimating the response of meridional heat transfer from the equator to the poles?