Objective Wind Field Analysis Using Line Integrals

Benedict F. Ceselski National Center for Atmospheric Research, Boulder, Colo. 90303

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Larry L. Sapp National Center for Atmospheric Research, Boulder, Colo. 90303

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Abstract

A two-dimensional wind field analysis technique based upon the objective analyses of vorticity and divergence obtained by the Bellamy method is defined. Point values of vorticity and divergence are approximated from line integrals around triangles (neighboring wind observations define vertices of the triangles). A one-scan anisotropic influence radius is incorporated to obtain grid-point estimates of vorticity and divergence. Streamfunction (ψ) and velocity potential (χ) are relaxed from vorticity and divergence fields and the total wind vector is defined by the derivatives of ψ and χ. In situations where temperature and wind are in quasi-balance, temperature fields may also be obtained by solving the balance equation.

By analyzing vorticity and divergence, this procedure has the advantage of explicitly defining perturbations in the wind field. Constraints upon the first derivatives of wind velocity are not required since the differentiated quantities are analyzed. The technique has maximum applicability in the tropics or under other weak geopotential gradient conditions where the relative error of observed temperature typically is large.

The technique is applied to a summertime weak-gradient situation over the United States and the results are compared to those obtained from a subjective analysis. A second case, for the extraordinary severe weather situation of 3 April 1974, is also examined. Results indicate the technique is capable of resolving subsynoptic-scale systems that likely play an important role in organizing convection.

Abstract

A two-dimensional wind field analysis technique based upon the objective analyses of vorticity and divergence obtained by the Bellamy method is defined. Point values of vorticity and divergence are approximated from line integrals around triangles (neighboring wind observations define vertices of the triangles). A one-scan anisotropic influence radius is incorporated to obtain grid-point estimates of vorticity and divergence. Streamfunction (ψ) and velocity potential (χ) are relaxed from vorticity and divergence fields and the total wind vector is defined by the derivatives of ψ and χ. In situations where temperature and wind are in quasi-balance, temperature fields may also be obtained by solving the balance equation.

By analyzing vorticity and divergence, this procedure has the advantage of explicitly defining perturbations in the wind field. Constraints upon the first derivatives of wind velocity are not required since the differentiated quantities are analyzed. The technique has maximum applicability in the tropics or under other weak geopotential gradient conditions where the relative error of observed temperature typically is large.

The technique is applied to a summertime weak-gradient situation over the United States and the results are compared to those obtained from a subjective analysis. A second case, for the extraordinary severe weather situation of 3 April 1974, is also examined. Results indicate the technique is capable of resolving subsynoptic-scale systems that likely play an important role in organizing convection.

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