Low-order models, initialization, and the slow manifold

A model of the shallow water equations is used as a testbed to compare several initialization strategies and to find points satisifying conditions of "slowness'. Several methods are explored to initialize the low order model: 1) Lorenz's method of successively zeroing tendencies; 2) minimization of the sum of the squares of the tendencies; 3) use of a balance condition. We find that the balance condition produces the smoothest solution on a consistent basis. In addition, Lorenz initialization, the Newton-Kantorovich Theorem, and the Nested Interval Property are used to compute points devoid of gravity waves. -from Authors