Implicit normal mode initialization for a global finite‐element semi‐Lagrangian shallow‐water model

It is shown that implicit normal mode initialization can be applied to a global finite‐element shallow‐water model where a semi‐Lagrangian treatment of the advection terms is used. The local time tendencies required by the initialization scheme are thus furnished by the semi‐Lagrangian model itself. Since the initialization scheme is formulated in physical space, it allows the non‐linear adjustment of the initial mass and wind fields at essentially the same accuracy as standard explicit normal mode initialization without having to rely on the explicit determination of the normal modes of the model. This property is especially useful in this study since we allow the spatial orientation of the model's grid to vary. For such a case, the usual separability in the longitudinal and latitudinal directions of the linearized dynamics is not possible if the variation of the Coriolis parameter is included in the analysis (as it should on the sphere). The use of a rotated coordinate system represents a new a...