A spectral limited-area model formulation with time dependent boundary conditions applied to the shallow-water equations

Journal Article · Wed Sep 01 04:00:00 EDT 1993 · Monthly Weather Review; (United States)

DOI:https://doi.org/10.1175/1520-0493(1993)121<2618:ASLAMF>2.0.CO;2· OSTI ID:5644797

Haugen, J E ^[1]; Machenhauer, B ^[2]

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1. Norwegian Meteorological Institute, Oslo (Norway)
2. Max-Planck-Institute fuer Meteorologie, Hamburg (Germany)

This paper presents a method where double Fourier series are used in a limited-area model (LAM). The method uses fast Fourier transforms (FFT) in both horizontal directions and takes into account time-dependent boundary conditions. The basic idea is to extend the time-dependent boundary fields into a zone outside the integration area in such a way that periodic fields are obtained. These fields in the extension zone and the forecasted fields inside the integration area are connected by use of a narrow relaxation zone along the boundaries of the limited area. The extension technique is applied to the shallow-water equations. A simple explicit (leapfrog) integration is shown to give results that are almost identical to the hemispherical forecast used as boundary fields. A nonlinear normal-mode initialization scheme developed in the framework of the spectral formulation is shown to work satisfactorily. The initialization scheme is furthermore used in a normal-mode time extrapolation scheme. Combined with the leapfrog scheme this method is stable for time steps similar to those used in the semi-implicit scheme and has the advantage that it is able to reduce the noise introduced in the forecast from unbalanced boundary fields. Experiments are made where the semi-Lagrangian treatment of advection is combined with either a semi-implicit or a normal-mode adjustment scheme. An efficient semi-Lagrangian scheme without any interpolations is introduced and shown to be unconditionally stable and nondamping for advection by a constant wind field. This scheme is tested and compared with the usual semi-Lagrangian schemes where interpolations are involved. The overall efficiency and accuracy of the proposed spectral formulation applied to the shallow-water model encouraged the development of a baroclinic spectral LAM, now in progress. 14 refs., 15 figs., 1 tab.

• OSTI ID: 5644797
• Journal Information: Monthly Weather Review; (United States), Journal Name: Monthly Weather Review; (United States) Vol. 121:9; ISSN MWREAB; ISSN 0027-0644
• Country of Publication: United States
• Language: English

Related Subjects

54 ENVIRONMENTAL SCIENCES
540110*
ADVECTION
ATMOSPHERIC CIRCULATION
BOUNDARY CONDITIONS
COMPUTERIZED SIMULATION
EARTH ATMOSPHERE
FORECASTING
FOURIER ANALYSIS
FUNCTIONS
GLOBAL ASPECTS
LAGRANGIAN FUNCTION
MASS TRANSFER
SIMULATION
TIME DEPENDENCE
WIND