Externalizing the lateral boundary conditions from the dynamic core in semi-implicit semi-Lagrangian models

Abstract

Research is still undertaken to develop so-called transparent lateral boundary conditions (LBC) for limited-area numerical weather prediction models. In the widely used semi-implicit semi-Lagrangian schemes, this naturally leads to LBC formulations that are intrinsically intertwined with the numerics of the dynamic core. This may have profound consequences for the implementation and the maintenance of future model codes. For instance, scientific development on the dynamics may be hindered by constraints coming from today’s choices in the LBC formulation and vice versa. Building further on the work of Aidan McDonald, this paper proposes an approach where (1) the LBCs can be imposed by an extrinsic numerical scheme that is fundamentally different from the one used for the dynamic core in the interior domain and (2) substituting one such LBC scheme for another is possible in a manner that leaves the Helmholtz solver unmodified. It is argued that this concept may provide the necessary frame for formulating transparent boundary conditions in spectral limited-area models. Since this idea touches all aspects of the LBC problem, its feasibility can only be established by a rigorous systematic approach. As a first step, this paper provides promising experimental support in a one-dimensional shallow-water model.