On the Use of a Wider Class of Linear Systems for the Design of Constant-Coefficients Semi-Implicit Time-Schemes in NWP

The linearization of the meteorological equations around a specified reference state, usually applied in NWP to define the linear system of constant-coefficients semi-implicit schemes, is outlined as an unnecessarily restrictive approach that may be detrimental in terms of stability. It is shown theoretically that an increased robustness can sometimes be obtained by choosing the reference linear system in a wider set of possibilities. The potential benefits of this new approach are illustrated in two simple examples. The advantage in robustness is not obtained at the price of an increased error or complexity.