Abstract
In this paper, we apply the optimal control theory to obtain the analytic solutions of the two-component globally averaged energy balance model in order to estimate the influence of solar radiation management (SRM) operations on the global mean surface temperature in the 21st century. It is assumed that SRM is executed via injection of sulfur aerosols into the stratosphere to limit the global temperature increase in the year 2100 by 1.5 °C and keeping global temperature over the specified period (2020–2100) within 2 °C as required by the Paris climate agreement. The radiative forcing produced by the rise in the atmospheric concentrations of greenhouse gases is defined by the Representative Concentration Pathways and the 1pctCO2 (1% per year CO2 increase) scenario. The goal of SRM is formulated in terms of extremal problem, which entails finding a control function (the albedo of aerosol layer) that minimizes the amount of aerosols injected into the upper atmosphere to satisfy the Paris climate target. For each climate change scenario, the optimal albedo of the aerosol layer and the corresponding global mean surface temperature changes were obtained. In addition, the aerosol emission rates required to create an aerosol cloud with optimal optical properties were calculated.
Highlights
Climate change is among the most significant threats to human civilization in the 21st century and beyond [1]
CU and CD are the effective heat capacities of the upper and lower models, respectively; λ is a climate radiative feedback parameter; γ is a coupling strength parameter that describes the rate of heat loss by the upper layer; ∆RCO2 is the radiative forcing caused by global increase in the atmospheric CO2 concentration; ∆R A is the negative radiative forcing generated by the artificial aerosols at the top of the atmosphere; and α0 is Earth’s planetary albedo
Maximum global mean surface temperature anomaly T calculated without state constraint
Summary
Climate change is among the most significant threats to human civilization in the 21st century and beyond [1]. The Paris Climate Accord proposed to hold average temperature increase “to well below 2 ◦ C above pre-industrial levels” and to pursue efforts to keep warming “below 1.5 ◦ C above pre-industrial levels” [2]. To reach these goals, eight countries have already presented long-term low-emission strategies, which aims to reduce greenhouse gas emissions; several countries are currently in the process of preparing such strategies [3]. There is high confidence that planetary warming will continue throughout the 21st century even if we immediately stopped emitting greenhouse gases into the atmosphere (e.g., References [5,6,7,8,9]). Some resent studies (e.g., References [10,11,12,13]) suggest that geoengineering technologies can serve as a supplementary measure to stabilize climate as “in the absence of external cooling influence” [14], it is hard to achieve the Paris Agreement climate goals
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