This paper investigates the concept of solar mirrors in a Earth orbit to provide large-scale terrestrial equatorial solar farms with additional solar power during the hours of darkness. A ower constellation of mirrors is considered in highly-eccentric orbits (semi-major axis=20270.4 km) in order to increase the time of visibility over the solar farms and, through this architecture, only two mirrors are needed to provide a complete night-coverage over three equatorial locations. Selecting the proper value for the orbit eccentricity, solar radiation pressure and Earth's oblateness perturbations act on the mirrors so that the apsidal motion of the orbit due to these perturbations is synchronized with the apparent motion of the Sun. Therefore, it can be guaranteed that the perigee always points towards the Sun and that the mirrors orbit mostly above the night side of the Earth. With respect to Geostationary orbit (GEO), the family of orbits considered in this paper allow a passive means to overcome issues related to orbital perturbations. Moreover, because of the large slant range from GEOs, a larger mirror is required to deliver the same energy that could be delivered from a lower orbit with a smaller mirror. As a result, a single anti-heliotropic ower constellation comprised of two mirrors of 50 km 2 would be able to deliver energy in the range of 4.60 − 5.20 GW h per day to 1000 km 2-solar farms on the equator. Finally, it is estimated that, deploying 90 of these constellations, the price of electricity could be reduced from 9.1 cents to 6 cents per kWh.

In order to investigate the effects of solar radiation management (SRM) technologies for climate engineering, an analytical model describing the main latitudinal dynamics of the Earth's climate with closed-loop control has been developed. The model is a time-dependent Energy Balance Model (EBM) with latitudinal resolution and allows for the evaluation of nonuniform climate engineering strategies. The resulting partial differential equation is solved using a Green's function approach. This model offers an efficient analytical approach to design strategies that counteract climate change on a latitudinal basis to overcome regional disparities in cooling. Multi-objective analyses are considered and time-dependent analytical expressions of control functions with latitudinal resolution can be obtained in several circumstances. Results broadly comparable with the literature are found, demonstrating the utility of the model in rapidly assessing new climate engineering controls laws and strategies. For example, the model is also used to quickly assess the trade-off between the number of degrees of freedom of SRM and the rms error in latitudinal temperature compensation. Moreover, using the EBM the dynamics of the ice line can be investigated and a Lyapunov stability analysis is employed to estimate the maximum reduction of solar insolation through climate engineering before the current climate falls into an ice-covered state. This provides an extreme operational boundary to future climate engineering ventures.

A low order three-box energy balance model for the climate system is employed with a multivariable control scheme for the evaluation of new robust and adaptive climate engineering strategies using solar radiation management. The climate engineering measures are deployed in 3 boxes thus representing northern, southern and central bands. It is shown that, through heat transport between the boxes, it is possible to effect a degree of latitudinal control through the reduction of insolation. The approach employed consists of a closed-loop system with an adaptive controller, where the required control intervention is estimated under the RCP 4.5 radiative scenario. Through the on-line estimation of the controller parameters, adaptive control can overcome key-issues related to uncertainties of the climate model, the external radiative forcing and the dynamics of the actuator used. In fact, the use of adaptive control offers a robust means of dealing with unforeseeable abrupt perturbations, as well as the parametrisation of the model considered, to counteract the RCP 4.5 scenario, while still providing bounds on stability and control performance. Moreover, applying multivariable control theory also allows the formal controllability and observability of the system to be investigated in order to identify all feasible control strategies.

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