Limited-Area Forecasting Model Based on Semi-Lagrangian Semi-Implicit Scheme Leading to Solving the Separable Elliptic Equations

A significant number of atmospheric models use a semi-implicit algorithm in order to carry out the time integration. In the semi-implicit scheme, the size of the time step is no longer restricted by the phase speed of external gravity waves; it is limited mainly by the magnitude of the wind associat...

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Veröffentlicht in:Studia geophysica et geodaetica Jg. 48; H. 4; S. 811 - 828
Hauptverfasser: Baťka, M., Nam, T.T.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Prague Springer Nature B.V 01.10.2004
Schlagworte:
Advection
Algorithms
Approximation
Atmospheric models
Differential equations
Elliptic functions
Forecasting models
Gravity waves
Mathematical models
Modelling
Partial differential equations
Phase velocity
Time integration
ISSN:0039-3169, 1573-1626
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Zusammenfassung:A significant number of atmospheric models use a semi-implicit algorithm in order to carry out the time integration. In the semi-implicit scheme, the size of the time step is no longer restricted by the phase speed of external gravity waves; it is limited mainly by the magnitude of the wind associated with advection. Combining a semi-Lagrangian scheme with the semi-implicit technique introduces the possibility of integrating atmospheric models using relatively large time steps. In this paper, the semi-implicit algorithm in association with the semi-Lagrangian technique is presented. To solve the equations of semi-implicit schema we have used method of dimension reduction which reduces the three-dimensional problem to two-dimensional problems. The original contribution of this way is that semi-implicit approximation leads to the solution of two-dimensional separable partial differential equations. A detailed description is given and the model is tested by using the Lambert projection and the initial data provided by the ARPEGE model. The results are very satisfactory.
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ISSN:0039-3169
1573-1626
DOI:10.1023/B:SGEG.0000045485.54003.32