Approximations and Sensitivity Experiments with a Baroclinic Semi-Lagrangian Spectral Model

This study examines the extensions that have been made to a basic semi-Lagrangian semi-implicit multilevel spectral primitive equation model in preparing it for use as an operational data assimilation and medium-range forecast model. The authors present an optimized formulation using accurate approximations to alternate trigonometric calculations for finding the upstream positions and performing the transformations for treating a vector form of the equation of motion in spherical geometry. The impact of the order of accuracy of the interpolators used in the semi-Lagrangian algorithms is also examined. It is shown that the recommended approximations have no significant meteorological consequences, but in a typical model step they reduce the time spent in the semi-Lagrangian calculations from about 50% to about 30%. Through a series of sensitivity tests, the authors establish the viability of the semi-Lagrangian semi-implicit method for spectral models with a more comprehensive physical parameterization package, and on a wider range of meteorological situations than in the previous study. First of all it is confirmed that even in these global runs with full physical parameterizations the sensitivity to the conversion from an Eulerian to a semi-Lagrangian formulation is acceptably small. In time truncation error tests with a T79 horizontal resolution it is found that, on average and with full physics, 30 min is about the upper limit for the time step based on acceptable time truncation errors. Since the Courant-Friedrichs-Lewy limit for the corresponding Eulerian model is about 10 min and the overhead of the semi-Lagrangian calculations is less than 30% per time step, there is a significant gain in efficiency by using the optimized semi-Lagrangian formulation. Results are also presented showing the improvement in the accuracy of the, 5-day forecasts obtained by raising the model top and by increasing the horizontal resolution.