Understanding Bjerknes Compensation in Atmosphere and Ocean Heat Transports Using a Coupled Box Model

A coupled box model is used to study the compensation between atmosphere and ocean heat transports. An analytical solution to the Bjerknes compensation (BJC) rate, defined as the ratio of anomalous atmosphere heat transport (AHT) to anomalous ocean heat transport (OHT), is obtained. The BJC rate is determined by local feedback between surface temperature and net heat flux at the top of atmosphere (TOA), and the AHT efficiency. In a stable climate that ensures global energy conservation, the changes between AHT and OHT tend to be always out of phase, and the BJC is always valid. This can be demonstrated when the climate is perturbed by freshwater flux. The BJC in this case exhibits three different behaviours: the anomalous AHT can undercompensate, overcompensate or perfectly compensate the anomalous OHT, depending on the local feedback. Stronger negative local feedback will result in a lower BJC rate. Stronger positive local feedback will result in a larger overcompensation. If zero climate feedback occurs in the system, the AHT will compensate the OHT perfectly. However, the BJC will fail if the climate system is perturbed by heat flux. In this case, the changes in AHT and OHT will be in phase, and their ratio will be closely related to the mean AHT and OHT. In a more realistic situation when the climate is perturbed by both heat and freshwater fluxes, whether the BJC will occur or not depends largely on the interplay among meridional temperature and salinity gradients, and the thermohaline circulation strength. This work explicitly shows that the energy conservation is the intrinsic mechanism of BJC, and establishes a specific link between radiative feedback and the degree of compensation. It also implies a close relationship between the energy balance at the TOA and the ocean thermohaline dynamics.