Data-driven parameterizations offer considerable potential for improving the fidelity of General Circulation Models. However, ensuring that these remain consistent with the governing equations while still producing stable simulations remains a challenge. In this paper, we propose a combined Variational-Multiscale (VMS) Artificial Neural Network (ANN) discretization which makes no a priori assumptions on the model form, and is only restricted in its accuracy by the precision of the ANN. Using a simplified problem, we demonstrate that good predictions of the required closure terms can be obtained with relatively compact ANN architectures. We then turn our attention to the stability of the VMS-ANN discretization in the context of a single implicit time step. It is demonstrated that the ANN parameterization introduces nonphysical solutions to the governing equations that can significantly affect or prevent convergence. We show that enriching the training data with nonphysical states from intra-time step iterations is an effective remedy. This indicates that the lack of representative ANN-induced errors in our original, exact training inputs underpin the observed instabilities. In turn, this suggests that data set enrichment might aid in resolving instabilities that develop over several time steps.

Temporary stratospheric aerosol injection (SAI) using sulphate compounds could help to mitigate some of the adverse and irreversible impacts of global warming. Among the risks and uncertainties of SAI, the development of a delivery system presents an appreciable technical challenge. Early studies indicate that specialised aircraft appear the most feasible (McClelan et al., Aurora Flight Sciences, 2010; Smith and Wagner, Environ Res Lett 13(12), 2018). Yet, their technical design characteristics, financial cost of deployment, and emissions have yet to be studied in detail. Therefore, these topics are examined in this two- part study. This first part outlines a set of injection scenarios and proposes a detailed, feasible aircraft design. Part 2 considers the resulting financial cost and equivalent CO₂ emissions spanned by the scenarios and aircraft. Our injection scenarios comprise the direct injection of H₂SO₄ vapour over a range of possible dispersion rates and an SO₂ injection scenario for comparison. To accommodate the extreme demands of delivering large payloads to high altitudes, a coupled optimisation procedure is used to design the system. This results in an unmanned aircraft configuration featuring a large, slender, strut-braced wing and four custom turbofan engines. The aircraft is designed to carry high-temperature H₂SO₄, which is evaporated prior to injection into a single outboard engine plume. Optimised flight profiles are produced for each injection scenario, all involving an initial climb to an outgoing dispersion leg at 20 km altitude, followed by a return dispersion leg at a higher altitude of 20.5 km. All the scenarios considered are found to be technologically and logistically attainable. However, the results demonstrate that achieving high engine plume dispersion rates is of principal importance for containing the scale of SAI delivery systems based on direct H₂SO₄ injection, and to keep these competitive with systems based on SO₂ injection.