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An improved implicit predictor-corrector scheme for boundary layer vertical diffusion
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DOI：10.1256/qj.05.37.png)
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Abstract
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Time integration of the parametrized boundary layer vertical diffusion in models of the atmosphere, used in numerical weather prediction (NWP) and climate modelling, can produce noise which appears as two-time-step oscillations in boundary layer tendencies. The origin of this noise was considered by Kalnay and Kanamitsu who analysed a number of schemes, two of which were based on a predictor-corrector approach. Here, a generalization of these two schemes is presented which results in unconditional stability for practical NWP vertical diffusion problems. The proposed generalization improves the stability of the original schemes. Asymptotic error analysis shows that this improvement is achieved without loss of accuracy, and that a small reduction in the leading error term is possible. Second-order accuracy is feasible but in this case unconditional stability can be achieved only for linear or mildly nonlinear problems. Numerical experiments and model simulations support the analysis presented in this paper. The limitations and strengths of the scheme are exposed and suggestions for a practical implementation are made. This scheme is ideally suited as a component of a more general predictor-corrector algorithm for the problem of physics-dynamics coupling. for example that of Cullen and Salmond.
Keywords:
numerical stability
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