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Semi-Lagrangian Transport

The advection of moisture in CCM2 uses a semi-Lagrangian transport (SLT) method in conjunction with shape preserving interpolation [41]. The method updates the value of the moisture field at a grid point (the arrival point, A) by first establishing a trajectory through which the particle arriving at A has moved during the current timestep (). This trajectory is found iteratively using the interpolated velocity field at the mid-point, M, of the trajectory. From this mid-point the departure point, D, is calculated and the moisture field is interpolated at D using shape preserving interpolation. All the calculations involve physical space (grid point) data and are decomposed over the processors with the same mesh decomposition described above.

The modifications made for the parallel implementation involved a redefinition of the extended grid arrays already implemented for the SLT. Extended grids are necessary since cubic interpolation requires two additional points outside the region being interpolated. Extending the grids even further leads to regions of overlap among the processors, but it can be guaranteed that with enough extension the departure point and subsequent interpolation of the moisture field will use only the data on the extended grid, and thus local to the processor. The amount of the extension is controlled by separate parameters for the latitudinal and longitudinal directions.

The overlap regions on each processor must be updated each timestep. Communication is blocked in such a way to allow the possibility of overlap with more than one processor. This can occur, for example, when a large number of processors are used and each processor has only two latitudes. The setting of the extended grid at the poles also requires communication between processors. In particular, the pole point, which occupies an entire latitude line in the extended grid, is assigned a value based on the zonal average of nearby latitude lines. A sum across the pole processors is required for this to be calculated. Since the pole processors lie on the first row of the processor mesh, a separate procedure is used for these processors.



next up previous
Next: PARALLEL MODEL VALIDATION Up: PARALLEL ALGORITHMS Previous: Parallel Legendre Transform



John B. Drake
Wed May 15 09:51:22 EDT 1996