A general formulation for nonlinear initialization of a numerical weather prediction model. Experiments with a shallow-water limited area model. (English) Zbl 0687.76012
Summary: A nonlinear initialization scheme which does not require an explicit computation of the eigenmodes (normal modes) of the linearized equations, is considered. Such a formulation is needed for limited-area models or for variable-mesh models for which the computation of the normal modes is too expensive. The formulation of such a scheme is given in abstract form in the case of the Machenhauer algorithm, which retains the slow mode components of the observed initial state and removes the spurious high- frequency mode components in a way coherent with the nonlinear equations. It is conjectured that such a formulation of initialization can be written in the physical space only in the case when the slow modes are stationary. Various tests of such an initialization scheme for a shallow- water limited-area model are presented.
MSC:
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 76M99 | Basic methods in fluid mechanics |
Keywords:
nonlinear normal model initialization; nonlinear initialization scheme; explicit computation of the eigenmodes; Machenhauer algorithm; shallow- water limited-area modelReferences:
| [1] | Machenhauer, B., On the dynamics of gravity oscillations in a shallow-water model, with application to normal mode initialization, Contrib. Atmos. Phys., 50, 253-271 (1977) · Zbl 0362.76040 |
| [2] | Daley, R., Normal Mode initialization, Rev. Geophys. Space Phys., 19, 450-468 (1981) |
| [3] | Hough, S. S., On the application of harmonic analysis to the dynamical theory of the tides, Phil. Trans. Roy. Soc. London Ser. A, 191, 139-185 (1898) · JFM 29.0651.02 |
| [4] | Brière, S., Nonlinear normal mode initialization of a limited area model, Mon. Weather Rev., 110, 1166-1186 (1982) |
| [5] | Craplet, A., Initialisation par modes normaux du modèle Péridot, Note de travail EERM No 139 (1985) |
| [6] | Imbard, M.; du Vachat, R. Juvanon; Joly, A.; Durand, Y.; Craplet, A.; Geleyn, J. F.; Audoin, J. M.; Marie, N.; Pairin, J. M., The Peridot fine-mesh numerical weather prediction system. Description, evaluation and experiments, J. Meteorol. Soc. Japan, 455-465 (1987), Special NWP Symposium Issue |
| [7] | Staniforth, A.; Mailhot, J., An operational model for regional weather forecasting, Comput. Math. Appl., 16, 1-22 (1988) · Zbl 0647.76020 |
| [8] | Courtier, Ph.; Geleyn, J. F., A global model with variable resolution. Application to the shallow-water equations, Quart. J. Roy. Meteorol. Soc., 14, 1321-1346 (1988) |
| [9] | Bourke, W.; McGregor, J. L., A nonlinear vertical mode initialization scheme for a limited area prediction model, Mon. Weather Rev., 111, 2285-2297 (1983) |
| [10] | Temperton, Cl., Application of a new principle for normal mode initialization, (Preprints Seventh Conf. on Numerical Weather Prediction. Preprints Seventh Conf. on Numerical Weather Prediction, Montréal. Preprints Seventh Conf. on Numerical Weather Prediction. Preprints Seventh Conf. on Numerical Weather Prediction, Montréal, Amer. Meteorol. Soc. (1985)), 105-107 |
| [11] | du Vachat, R. Juvanon, A general formulation of normal modes for limited-area models. Application to initialization, Mon. Weather. Rev., 114, 2478-2487 (1986) |
| [12] | B.A. Ballish, Initialization, theory and application on the NMC spectral model, Ph. D. Thesis, University of Maryland, 151 pp.; B.A. Ballish, Initialization, theory and application on the NMC spectral model, Ph. D. Thesis, University of Maryland, 151 pp. |
| [13] | du Vachat, R. Juvanon, Non-normal mode initialization. Formulation and application to the inclusion of the beta terms in the linearization, Mon. Weather Rev., 116, 2013-2024 (1988) |
| [14] | Baer, F.; Tribbia, J., On complete filtering of gravity modes through nonlinear initialization, Mon. Weather Rev., 105, 1536-1539 (1977) |
| [15] | Sadourny, R., The dynamics of finite difference models of the shallow-water equations, J. Atmos. Sci., 32, 680-689 (1975) |
| [16] | Kwizak, M.; Robert, A., A semi-implicit scheme for grid-point atmospheric models of the primitive equations, Mon. Weather Rev., 99, 32-36 (1971) |
| [17] | Davies, H. C., A lateral boundary formulation for multi-level prediction models, Quart. J. Roy. Metereol. Soc., 102, 405-418 (1976) |
| [18] | Errico, R., Normal modes of a semi-implicit model, Mon. Weather Rev., 112, 1818-1828 (1984) |
| [19] | Temperton, Cl., Implicit normal mode initialization, Mon. Weather Rev., 116, 1013-1031 (1988) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
