The Development of Efficient Time Integration Schemes Using Model Normal Modes

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Abstract
The development of nonlinear normal mode initialization for shallow water models by Machenhauer (1977) and Baer (1977) and its subsequent successful extension to baroclinic models has provided the impetus for further exploitation of model normal modes. The present work is a straightforward application of model normal mode expansions to the problem of taking long timesteps in primitive equation models. A methodology is developed which treats the “fast” gravity modes of the model in a special manner while treating the ensemble of “slow” gravity modes and Rossby modes by explicit leapfrog techniques. The schemes developed were tested experimentally using the GCM of Bourke et al. (1977) and found to be numerically stable, efficient and accurate.

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