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In this paper, we investigate the well-posedness of a recently derived modelby A. Constantin and R.S. Johnson that describes nonlinear propagation of wavesin the troposphere, particularly the 'morning glory' cloud pattern. Moreprecisely, we establish the existence and uniqueness of global strong solutionsfor this model. To achieve this, we use the standard Galerkin approximationprocedure in combination with an anisotropic Sobolev inequality.

Global well posedness of leading order equations for nonlinear wave propagation in the troposphere