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Parameterizations of the Daytime Friction Velocity, Temperature Scale, and Upslope Flow over Gently Inclined Terrain in Calm Synoptic Conditions


doi: 10.1007/s00376-009-0577-z

  • A set of new parameterizations for the friction velocity and temperature scale over gently sloped terrain and in calm synoptic conditions are theoretically derived. The friction velocity is found to be proportional to the product of the square root of the total accumulated heating in the boundary layer and the sinusoidal function of the slope angle, while the temperature scale is proportional to the product of the boundary layer depth, the sinusoidal function of the slope angle and the potential temperature gradient in the free atmosphere. Using the new friction velocity parameterization, together with a parameterization of eddy diffusivity and an initial potential temperature profile around sunrise, an improved parameterization for the thermally induced upslope flow profile is derived by solving the Prandtl equations. The upslope flow profile is found to be simply proportional to the friction velocity.
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Manuscript History

Manuscript received: 10 May 2009
Manuscript revised: 10 May 2009
通讯作者: 陈斌, bchen63@163.com
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Parameterizations of the Daytime Friction Velocity, Temperature Scale, and Upslope Flow over Gently Inclined Terrain in Calm Synoptic Conditions

  • 1. Key Laboratory for Polar Science, Polar Research Institute of China, Shanghai 200136; State Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric Chemistry, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029;Key Laboratory for Polar Science, Polar Research Institute of China, Shanghai 200136; State Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric Chemistry, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029;Department of Geography, Michigan State University, East Lansing, MI 48824-111, USA;National Center for Atmospheric Research, Boulder, CO 80307, USA;Department of Meteorology, Naval Postgraduate School, Monterey, CA 93943, USA

Abstract: A set of new parameterizations for the friction velocity and temperature scale over gently sloped terrain and in calm synoptic conditions are theoretically derived. The friction velocity is found to be proportional to the product of the square root of the total accumulated heating in the boundary layer and the sinusoidal function of the slope angle, while the temperature scale is proportional to the product of the boundary layer depth, the sinusoidal function of the slope angle and the potential temperature gradient in the free atmosphere. Using the new friction velocity parameterization, together with a parameterization of eddy diffusivity and an initial potential temperature profile around sunrise, an improved parameterization for the thermally induced upslope flow profile is derived by solving the Prandtl equations. The upslope flow profile is found to be simply proportional to the friction velocity.

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