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Estimating Moisture Profiles Using a Modified Power Law

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  • 1 Cooperative Institute for Meteorological Satellite Studies, University of Wisconsin—Madison, Madison, Wisconsin
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Abstract

Using first principles, it is shown that the vertical variation of the mixing ratio can be approximated by a power law if the relative humidity is also expressed in terms of a power law. Nevertheless, variability in the relative humidity is a major source of error in estimating moisture profiles. This error arises because of a lack of knowledge about a parcel’s source region and its recent transport history. To understand the physics of relative humidity better, its temperature and pressure dependences are examined. Using this knowledge, a small correction or modification to the moisture power law is formulated by assuming that the relative humidity is known at some location far above the base of the profile. Although not always obtainable, relative humidity is available during numerical weather prediction’s data assimilation. The method works well at estimating profiles associated with large-scale moisture patterns and in cases where inversions and isolated dry or moist layers are not pervasive. Additionally, from the knowledge of the temperature and pressure dependency of the relative humidity, it is easy to construct a simple analytic method in terms of relative humidity to identify adiabatic changes induced by turbulent mixing schemes used in numerical weather forecast models. This technique is especially useful in parameterizing shallow nonprecipitating clouds when the depth of the boundary layer is known, or when using nonlocal turbulent mixing parameterizations.

Corresponding author address: William H. Raymond, Cooperative Institute for Meteorological Satellite Studies, University of Wisconsin—Madison, Madison, WI 53706.

wraymond@mail.ssec.wisc.edu

Abstract

Using first principles, it is shown that the vertical variation of the mixing ratio can be approximated by a power law if the relative humidity is also expressed in terms of a power law. Nevertheless, variability in the relative humidity is a major source of error in estimating moisture profiles. This error arises because of a lack of knowledge about a parcel’s source region and its recent transport history. To understand the physics of relative humidity better, its temperature and pressure dependences are examined. Using this knowledge, a small correction or modification to the moisture power law is formulated by assuming that the relative humidity is known at some location far above the base of the profile. Although not always obtainable, relative humidity is available during numerical weather prediction’s data assimilation. The method works well at estimating profiles associated with large-scale moisture patterns and in cases where inversions and isolated dry or moist layers are not pervasive. Additionally, from the knowledge of the temperature and pressure dependency of the relative humidity, it is easy to construct a simple analytic method in terms of relative humidity to identify adiabatic changes induced by turbulent mixing schemes used in numerical weather forecast models. This technique is especially useful in parameterizing shallow nonprecipitating clouds when the depth of the boundary layer is known, or when using nonlocal turbulent mixing parameterizations.

Corresponding author address: William H. Raymond, Cooperative Institute for Meteorological Satellite Studies, University of Wisconsin—Madison, Madison, WI 53706.

wraymond@mail.ssec.wisc.edu

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