Optimization-Based Conservative Transport on the Cubed-Sphere Grid

Transport algorithms are highly important for dynamical modeling of the atmosphere, where it is critical that scalar tracer species are conserved and satisfy physical bounds. In this paper we present an optimization-based algorithm for the conservative transport of scalar quantities (i.e. mass) on the cubed sphere grid, which preserves monotonicity without the use of flux limiters. In this method the net mass updates to the cell are the optimization variables, the objective is to minimize the discrepancy between a high-order mass update (the “target”) and a mass update that satisfies physical bounds, whereas mass conservation is imposed by a single equality constraint. The resulting robust and efficient algorithm for conservative and monotone transport on the sphere further demonstrates the flexibility and scope of the recently developed optimization-based modeling approach [1, 2].