Potential refractivity as a similarity variable |
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| Authors: | John Cook Stephen Burk |
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| Institution: | (1) Naval Oceanographie and Atmospheric Research Laboratory, Atmospheric Directorate, 93943-5006 Monterey, CA, USA |
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| Abstract: | The validity of a common radiometeorological application of Monin-Obukhov (M-O) similarity theory to potential refractivity ( ), which is a nonlinear combination of  and q, is determined by whether the properly nondimensionalized gradient is a universal function of z/L. We develop expressions for the flux of (and its scaling parameter, *) in terms of temperature and moisture fluxes, and an M-O similarity expression for the vertical gradient. Results show that even if and q are accepted as exactly following M-O similarity expressions, when the surface layer is stable, does not obey such an expression. That is, when properly nondimensionalized, the vertical gradient of does not collapse to a single universal function of z/L. The assumption that behaves as a similarity variable is approximately correct for well-mixed surface layers under unstable and near-neutral conditions.The gradient of is an important factor in determining microwave propagation conditions. We demonstrate the error induced in a simple algorithm when is assumed to obey M-O similarity theory. An alternative methodology, consistent with the application of similarity theory to and q, is then developed without requiring that itself satisfy similarity theory. |
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