Relationship of the Variances of Temperature and Velocity to Atmospheric Static Stability—Application to Radar and Acoustic Sounding

Earl E. Gossard Cooperative Institute for Research in the Environmental Sciences, University of Colorado/NOAA, Boulder, CO 80309

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A. Shelby Frisch NOAA/ERL/Wave Propagation Laboratory, Boulder, CO 80303

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Abstract

The relationship between the variances of temperature and vertical velocity fluctuations is examined experimentally and theoretically. Comparison of the variance data and the mean gradient data recorded on the 300 m tower at the Boulder Atmospheric Observatory leads to the conclusion that the remotely sensed ratio of the temperature and velocity variances offers hope of measuring gradients of temperature and radar refractive index from ground-based acoustic or radar clear-air sounders. Relationships in which temperature gradient depends only on the ratio of the variances of temperature and vertical velocity are found both from the flux equation and from the energy budget/temperature variance equations. From the two independent relations, a theoretical expression for Prandtl number versus Richardson number is found for a limited range of Richardson numbers. Finally, the character and magnitude of the influence of the stress and conductivity terms are estimated from the linearized problem, and solutions are found in terms of eddy viscosity and conductivity.

Abstract

The relationship between the variances of temperature and vertical velocity fluctuations is examined experimentally and theoretically. Comparison of the variance data and the mean gradient data recorded on the 300 m tower at the Boulder Atmospheric Observatory leads to the conclusion that the remotely sensed ratio of the temperature and velocity variances offers hope of measuring gradients of temperature and radar refractive index from ground-based acoustic or radar clear-air sounders. Relationships in which temperature gradient depends only on the ratio of the variances of temperature and vertical velocity are found both from the flux equation and from the energy budget/temperature variance equations. From the two independent relations, a theoretical expression for Prandtl number versus Richardson number is found for a limited range of Richardson numbers. Finally, the character and magnitude of the influence of the stress and conductivity terms are estimated from the linearized problem, and solutions are found in terms of eddy viscosity and conductivity.

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