Several Earth system components are at a high risk of undergoing rapid, irreversible qualitative changes or “tipping” with increasing climate warming. It is therefore necessary to investigate the feasibility of arresting or even reversing the crossing of tipping thresholds. Here, we study feedback control of an idealized energy balance model (EBM) for Earth’s climate, which exhibits a “small icecap” instability responsible for a rapid transition to an ice-free climate under increasing greenhouse gas forcing. We develop an optimal control strategy for the EBM under different forcing scenarios to reverse sea-ice loss while minimizing costs. Control is achievable for this system, but the cost nearly quadruples once the system tips. While thermal inertia may delay tipping, leading to an overshoot of the critical forcing threshold, this leeway comes with a steep rise in requisite control once tipping occurs. Additionally, we find that the optimal control is localized in the polar region.

随着气候变暖的加剧，地球系统的几个组成部分极有可能发生快速、不可逆的质变或“倾倒”。因此，有必要研究阻止甚至逆转越过小费阈值的可行性。在这里，我们研究了地球气候理想化能量平衡模型 （EBM） 的反馈控制，该模型表现出“小冰盖”不稳定性，导致在温室气体强迫增加的情况下迅速过渡到无冰气候。我们开发了不同强迫情景下 EBM 的最优控制策略，以扭转海冰损失，同时最大限度地降低成本。该系统的控制是可以实现的，但一旦系统启动，成本几乎翻了两番。虽然热惯性可能会延迟倾翻，导致超过临界强迫阈值，但一旦发生倾翻，这种回旋余地会带来必要控制的急剧增加。此外，我们发现最优控制局限于极地区域。