A Theory for Bjerknes Compensation: The Role of Climate Feedback

Abstract

he response of the atmospheric energy (heat) transport (AHT) to a perturbation oceanic heat transport (OHT) is studied theoretically in a zonal mean energy balance model, with the focus on the effect of climate feedback, especially its spatial variation, on Bjerknes compensation (BJC). It is found that the BJC depends critically on climate feedback. For a stable climate, in which negative climate feedback is dominant, the AHT always compensates the OHT in the opposite direction. Furthermore, if local climate feedback is negative everywhere, the AHT will be weaker than the OHT (undercompensation) because of the damping on the surface oceanic heating through the top-of-atmosphere energy loss. One novel finding is that the compensation magnitude depends on the spatial scale of the forcing and is bounded between a minimum at the global scale and a maximum (of perfect compensation) at small scales. Most interestingly, the BJC is affected significantly by the spatial variation of the feedback, particularly a local positive climate feedback. As such, a regional positive feedback can lead to a compensating AHT greater than the perturbation OHT (overcompensation). This occurs because the positive feedback enhances the local temperature response, the anomalous temperature gradient, and, in turn, the AHT. Finally, the poleward latent heat transport leads to a temperature response with a polar amplification accompanied by a polar steepening of temperature gradient but does not change the BJC significantly. Potential applications of this BJC theory to more complex climate model studies are also discussed.