A Comparison of Explicit and Semi-Implicit Model Calculations of Geostrophic Adjustment

William G. Collins National Meteorological Center, National Weather Service, NOAA, Washington, DC 20233

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Abstract

The adjustment properties of numerical models are important both from the Point of view of the handling of noise and the ability to produce proper quasi-geostrophic states from physically derived imbalances between mass and motion fields. This paper considers the adjustment properties of simplified barotropic one-dimensional numerical models with explicit and semi-implicit time differencing.

The classical Rossby adjustment problem provides the framework for comparison with the numerical results. In addition, linear analysis of the models provides useful insight. Primary emphasis is on the time required for adequate adjustment and the accuracy of the adjusted state. The adjustment time increases with the scale of the initial disturbance, and does not differ significantly between the explicit and semi-implicit models. The grid increment is one of the dominant factors in determining the adjustment time. Both models accurately calculated the final adjusted state.

Abstract

The adjustment properties of numerical models are important both from the Point of view of the handling of noise and the ability to produce proper quasi-geostrophic states from physically derived imbalances between mass and motion fields. This paper considers the adjustment properties of simplified barotropic one-dimensional numerical models with explicit and semi-implicit time differencing.

The classical Rossby adjustment problem provides the framework for comparison with the numerical results. In addition, linear analysis of the models provides useful insight. Primary emphasis is on the time required for adequate adjustment and the accuracy of the adjusted state. The adjustment time increases with the scale of the initial disturbance, and does not differ significantly between the explicit and semi-implicit models. The grid increment is one of the dominant factors in determining the adjustment time. Both models accurately calculated the final adjusted state.

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