The Earth climate system has an intrinsic mechanism to maintain its energy conservation by impelling opposite changes in meridional ocean and atmosphere heat transports. This mechanism is briefed as the Bjerknes compensation (BJC). We set up a global coupled two-hemisphere box model in this study, and obtain an analytical solution to the BJC of this system. In the two-hemisphere model, the thermohaline circulation is interhemispheric and parameterized by the density difference between two polar boxes. The symmetric poleward atmosphere heat and moisture transports are considered and parameterized by the temperature gradient between tropical and polar boxes. Different from the BJC in the one-hemisphere box model that depends only on the local climate feedback, the BJC here is determined by both local climate feedback and temperature change. The asymmetric thermohaline circulation leads to a better BJC in the Northern Hemisphere than in the Southern Hemisphere. Furthermore, an analytical solution to the probability of a valid BJC (i.e., negative BJC) is derived, which is determined only by the local climate feedback. The probability of a valid BJC is very high under reasonable climate feedback. Based on observational data, the climate feedback can be estimated and the BJC in real world can be calculated using the analytical formulae. It is found that at the decadal and longer timescales the BJC for both hemispheres are robust in reality.

地球气候系统具有通过推动经向海洋和大气热量传输的相反变化来维持其能量守恒的内在机制。这种机制被简述为 Bjerknes 补偿 (BJC)。我们在本研究中建立了一个全局耦合的两半球盒模型，并获得了该系统 BJC 的解析解。在两半球模型中，温盐环流是半球间的，并由两个极框之间的密度差参数化。对称的极地大气热量和水分传输由热带和极地箱之间的温度梯度考虑和参数化。与单半球盒模型中的 BJC 仅依赖于局地气候反馈不同，这里的 BJC 是由局地气候反馈和温度变化共同决定的。非对称温盐环流导致北半球比南半球更好的 BJC。此外，还导出了有效 BJC（即负 BJC）概率的解析解，这仅由当地气候反馈决定。在合理的气候反馈下，有效 BJC 的概率非常高。基于观测数据，可以估计气候反馈，并使用解析公式计算现实世界中的 BJC。发现在十年和更长的时间尺度上，两个半球的 BJC 在现实中都是稳健的。这仅由当地气候反馈决定。在合理的气候反馈下，有效 BJC 的概率非常高。基于观测数据，可以估计气候反馈，并使用解析公式计算现实世界中的 BJC。发现在十年和更长的时间尺度上，两个半球的 BJC 在现实中都是稳健的。这仅由当地气候反馈决定。在合理的气候反馈下，有效 BJC 的概率非常高。基于观测数据，可以估计气候反馈，并使用解析公式计算现实世界中的 BJC。发现在十年和更长的时间尺度上，两个半球的 BJC 在现实中都是稳健的。