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- Title
B-splines as a tool to solve constraints in a non-hydrostatic forecast model.
- Authors
Subías, Álvaro
- Abstract
The finite-element method has proved to be a useful tool to discretize the vertical coordinate in hydrostatic forecast models, allowing the definition of model variables at full levels so that no staggering is needed. In the non-hydrostatic case, a constraint in the vertical operators appears (called C1), which allows the set of semi-implicit linear equations to be reduced to a single equation in one variable as in the analytic case. Recently, vertical finite elements based on B-splines have been used with an iterative method to relax the C1 constraint. In this article, we aim to develop representations of vertical operators fully in terms of B-splines, in order to keep the C1 constraint. An invertibility relation between integral and derivative operators is also presented in order to have a bijective relationship between the vertical velocity and the vertical divergence. The final scope of this article is to provide a theoretical framework of development of finite-element vertical operators to be implemented in the ALADIN-HIRLAM numerical weather prediction system.
- Subjects
HYDROSTATICS; WEATHER forecasting; SPLINES; CONSTRAINTS (Physics); FINITE element method
- Publication
Quarterly Journal of the Royal Meteorological Society, 2017, Vol 143, Issue 706, p2272
- ISSN
0035-9009
- Publication type
Article
- DOI
10.1002/qj.3084