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S. J. Bijlsma

Abstract

Application of the nonlinear normal mode initialization method requires the construction of the normal modes of the linearized model equations.

In the case of a limited area model the Coriolis parameter in this linear system is usually assumed to be constant, so that the Rossby modes are stationary. Since inclusion of the beta terms might be important in practical applications of nonlinear normal mode initialization, we investigate this effect by including specific beta terms so that the Rossby modes are nonstationary. Results of the methods with stationary and nonstationary Rossby modes are compared.

They show that the two methods are virtually identical in their effect upon the initial fields and upon their development during the first hours of the forecast.

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S. J. Bijlsma

Abstract

A nonlinear normal mode initialization method with all of the beta terms included in the linearized model equations is formulated for a limited-area model. It is the extension of an earlier method examining the sensitivity of nonlinear normal mode initialization to the inclusion of nonstationary Rossby modes. It is shown that the eigenmodes of the two methods for sufficiently large equivalent depths do coincide approximately. Results of the two methods are compared. They show the equivalence between the f-plane approach and the inclusion of all or some of the beta terms for midlatitude initialization.

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S. J. Bijlsma
and
R. J. Hoogendoorn

Abstract

In this paper the convergence of an iterative method for solving the nonlinear balance equation is analyzed. It is shown that this iterative method, originally proposed by Miyakoda and Shuman, is convergent if a sufficiently accurate initial approximation is used and if the successive iterates satisfy the ellipticity condition. Otherwise the method may be divergent. Experimental results are presented.

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S. J. Bijlsma
and
L. M. Hafkenscheid

Abstract

A nonlinear normal mode initialization method is applied to a baroclinic limited arm forecast model. This method is very effective in reducing the amplitude of the rapid oscillations during the first hours of the forecast. The results are compared with those using a bounded derivative initialization. The latter method gives equally satisfactory results, requiring less computation than the normal mode method.

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S. J. Bijlsma
,
L. M. Hafkenscheid
, and
Peter Lynch

Abstract

A wind field given over a limited domain can be partitioned into nondivergent and irrotational components in an infinity of ways. A particular solution, selected by requiring the velocity potential to vanish on the boundary, has minimum divergent kinetic energy and is numerically easy to obtain.

The reconstruction of the wind field from the vorticity and divergence together with the boundary velocity is more difficult, since the potential equations are coupled by the boundary conditions. A numerical procedure is devised, which solves the two potential equations simultaneously, modifying both interior and boundary values in a converging iterative technique. The method is capable of reconstructing the wind field to any accuracy desired.

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