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A simple form of the Prandtl model addressing pure katabatic flows is solved. The new analytic solution is valid for almost any assigned eddy diffusivity K(z) and constant Prandtl number. This model assumes a onedimensional steady state for momentum and heat balance. Its approximate solution, obtained using the WKB method, appears as a generalization and improvement of the classic analytic solution for the constant-K case. It is compared favorably against a numerical solution. A comparison with observations from PASTEX, Austria 1994, shows that the new solution is much closer to the data than the constant-K solution. The dynamics revealed with this new solution is discussed (relatively sharper near-surface profiles, their gradients, and the low-level jet), and a suggestion toward improving boundary layer parameterizations is offered.