A global numerical weather prediction model with variable resolution

A conformal transformation suggested by F. Schmidt is followed to implement a global spectral model with variable resolution. A conformal mapping is defined from a physical sphere (like the earth) to a transformed (computational) sphere. The model equations are discretized on the computational sphere, and the conventional spectral technique is applied to march forward in time. Two types of transformations are investigated in the present study, namely the rotation and the stretching transformation. Application of the stretching transformation leads to finer resolution in the meridional direction; however, due to the spherical geometry, the resolution becomes finer in the latitudinal direction also, and furthermore. the rotation can be used to relocate the model poles. The idea is now to rotate the north pole and refine the resolution around the new north pole by applying the stretching transformation. A multilevel global spectral model is formulated from the current Florida State University global spectral model to implement the total (rotation followed by stretching) transformation. The control run in this study is a conventional T-170 resolution global spectral model. The transformed T-83 resolution global spectral model is used to study Hurricane Andrew. The performance of the transformed model is clearly seen to be improved in describing the structure, intensity, and motion of the hurricane over the conventional T-85 resolution spectral model. The computational cost for the transformed model is approximately one-half the cost for the conventional T-170 model. The conformal transformation technique can be thus used as a viable alternative to the limited-area models.