The associated Legendre projection provides a means for accelerating the dynamical core of a global weather or climate model. Therefore, the goal is to determine the fastest possible projection algorithm, of which this paper compares four: the standard method which computes the projection using a forward and backward associated Legendre transform; the direct method, which uses a single projection matrix when this approach results in fewer operations; the fast multipole method; and the weighted orthogonal complement method. Timing results indicate that all the projections behave like O(N³) algorithms up to at least N=200 spectral truncation. For this range of resolutions, the weighted orthogonal complement has the lowest operation count, best cache utilization and best overall timings.

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