Editorial Type:
Article
Article Type:
Research Article

A Nonlinear Impedance Relation for the Surface Winds in Pressure Disturbances

Timothy A. Coleman Department of Atmospheric Science, University of Alabama in Huntsville, Huntsville, Alabama

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Kevin R. Knupp Department of Atmospheric Science, University of Alabama in Huntsville, Huntsville, Alabama

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Print Publication:
01 Oct 2010
DOI:
https://doi.org/10.1175/2010JAS3457.1
Page(s):
3409–3422
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Abstract

The “impedance relation” between the wind perturbation within an ageostrophic atmospheric disturbance and its pressure perturbation and intrinsic propagation speed has been in use for decades. The correlation between wind and pressure perturbation was established through this relation. However, a simple Lagrangian model of an air parcel traversing an idealized sinusoidal wave in the pressure field indicates that the impedance relation produces significant errors. Examination of the nonlinearized horizontal momentum equation with a sinusoidal disturbance in pressure reveals an additional nonlinear term in the impedance relation, not previously included.

In this paper, the impedance relation is rederived, with the solution being the original equation with the addition of the nonlinear term. The new equation is then evaluated against the Lagrangian model of an air parcel traversing an idealized gravity wave, as well as three observed cases. It is shown that the new impedance relation is indeed more accurate in predicting wind perturbations in disturbances based on pressure perturbations and intrinsic speed than the accepted equation. Implications for determination of the intrinsic phase speed of a disturbance when pressure and wind perturbations are known (another widely used application of the impedance relation) are also discussed.

Corresponding author address: Dr. Timothy A. Coleman, Department of Atmospheric Science, University of Alabama in Huntsville, NSSTC, 320 Sparkman Drive, Huntsville, AL 35805. Email: coleman@nsstc.uah.edu

Abstract

The “impedance relation” between the wind perturbation within an ageostrophic atmospheric disturbance and its pressure perturbation and intrinsic propagation speed has been in use for decades. The correlation between wind and pressure perturbation was established through this relation. However, a simple Lagrangian model of an air parcel traversing an idealized sinusoidal wave in the pressure field indicates that the impedance relation produces significant errors. Examination of the nonlinearized horizontal momentum equation with a sinusoidal disturbance in pressure reveals an additional nonlinear term in the impedance relation, not previously included.

In this paper, the impedance relation is rederived, with the solution being the original equation with the addition of the nonlinear term. The new equation is then evaluated against the Lagrangian model of an air parcel traversing an idealized gravity wave, as well as three observed cases. It is shown that the new impedance relation is indeed more accurate in predicting wind perturbations in disturbances based on pressure perturbations and intrinsic speed than the accepted equation. Implications for determination of the intrinsic phase speed of a disturbance when pressure and wind perturbations are known (another widely used application of the impedance relation) are also discussed.

Corresponding author address: Dr. Timothy A. Coleman, Department of Atmospheric Science, University of Alabama in Huntsville, NSSTC, 320 Sparkman Drive, Huntsville, AL 35805. Email: coleman@nsstc.uah.edu

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