Hybrid scheme for three-dimensional advective transport

A 3D hybrid (H) transport scheme has been developed that consists of the Prather (P) scheme for vertical transport and a semi-Lagrangian (SL) scheme for horizontal transport on a spherical surface. Two tests have also been developed to permit evaluation of the performance of any numerical transport scheme for flows similar to those found in the earth's atmosphere. In the first test, the 2D distributions of the wind field and the 3D distribution of the chemical species concentration are prescribed analytically and the consistent analytical expression for the species sources and sinks is determined from the constituent continuity equation. The analytical expressions for the winds and source and sink are then used by a numerical scheme to calculate the 3D distribution of the species concentration. Comparison of the numerical distribution with the analytical distribution then allows evaluation of the performance of the numerical scheme. This test has been used to compare the P, SL, and H schemes. The test shows that the SL scheme produces errors up to 6% in species concentration. The P scheme has high accuracy (about 1%) but requires substantial amounts of computer CPU time and memory. The accuracy of the H scheme is higher (better than 1.6%) than that of the SL scheme and is close to that of the P scheme. The H scheme is about nine times faster than the P scheme but does require about three times more memory than the SL scheme. In another test, the P, H, and SL schemes are tested for 2D zonally averaged transport of the conservative species "cloud" by analytically calculated wind velocities. Comparison of the results shows that the H scheme is superior to the SL scheme. It is concluded that the H scheme is a computationally efficient, accurate scheme for simulating the 3D global transport of both conservative and nonconservative species.