Abstract
The validity of a common radiometeorological application of Monin-Obukhov (M-O) similarity theory to potential refractivity (χ), which is a nonlinear combination of θ and q, is determined by whether the properly nondimensionalized χ gradient is a universal function of z/L. We develop expressions for the flux of χ (and its scaling parameter, χ*) in terms of temperature and moisture fluxes, and an M-O similarity expression for the vertical χ gradient. Results show that even if θ and q are accepted as exactly following M-O similarity expressions, when the surface layer is stable, χ does not obey such an expression. That is, when properly nondimensionalized, the vertical gradient of χ does not collapse to a single universal function of z/L. The assumption that χ behaves as a similarity variable is approximately correct for well-mixed surface layers under unstable and near-neutral conditions.
The gradient of χ is an important factor in determining microwave propagation conditions. We demonstrate the error induced in a simple algorithm when χ is assumed to obey M-O similarity theory. An alternative methodology, consistent with the application of similarity theory to θ and q, is then developed without requiring that χ itself satisfy similarity theory.
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Cook, J., Burk, S. Potential refractivity as a similarity variable. Boundary-Layer Meteorol 58, 151–159 (1992). https://doi.org/10.1007/BF00120756
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DOI: https://doi.org/10.1007/BF00120756