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High Quality Content by WIKIPEDIA articles! Scale analysis is a powerful tool used in the mathematical sciences for the simplification of equations with many terms. First the approximate magnitude of individual terms in the equations is determined. Then some negligibly small terms may be ignored.In synoptic scale we can expect horizontal velocities about U = 101 m.s 1 and vertical about W = 10 2 m.s 1. Horizontal scale is L = 106 m and vertical scale is H = 104 m. Typical time scale is T = L/U = 105 s.