**4. Concluding Remarks**

The use of fine aerosol particles, artificially injected into the stratosphere, is considered to be one of the most effective and feasible measures to counter global warming in the 21st century and beyond. Computer simulation using mathematical climate models of various degrees of sophistication and complexity is the most popular and reliable technique for exploring and estimating the effectiveness of stratospheric aerosol climate engineering and climate and weather manipulation. Numerical simulation of climate engineering requires the design of fairly realistic scenarios for aerosol injections. This paper introduced the optimal-control-based method for designing climate engineering scenarios. Considering Earth's climate as controlled dynamical system, we proposed to approach geoengineering from the standpoint of the optimal control theory, thereby formulating the goal of geoengineering projects in terms of extremal problem. The capability to apply this technique was illustrated using the two-layer energy balance model in which the global mean surface temperature anomaly and the deep ocean temperature perturbation were the state variables, and the emission rate of aerosol precursors was the control variable. Solutions to the unconstrained as well as state and control constrained problems were obtained on the basis of classical Pontryagin's maximum principle. The proposed method will provide additional useful insights for the development of optimal climate manipulation strategies to counter global warming in the 21st century.

**Funding:** This research received no external funding.

**Acknowledgments:** The author would like to thank two anonymous reviewers for their helpful comments.

**Conflicts of Interest:** The author declares no conflict of interest.
