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A Wind Transform for Acoustic Adjustment in Compressible Models

Brian H. FiedlerDepartment of Meteorology, University of Oklahoma, Norman, Oklahoma

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Abstract

A three-dimensional, anelastic wind field on a staggered grid, with a specified normal wind component on the lateral boundaries, can be reversibly transformed into two scalar fields. In a conformal, terrain-following coordinate system these two quantities are closely related to the divergence of the horizontal wind and the vertical vorticity. The finite-difference implementation of the transform is emphasized. The exactness of the transform, and its consistency with the boundary conditions, are easily demonstrated when the transform is viewed as a problem of linear algebra in a discrete model.

The transform is shown to be useful in initializing a model wind field. A demonstration is provided with the removal of a spurious storm from the background wind field that is to be used in a forecast–analysis cycle. The divergence of the horizontal wind in the vicinity of the storm is removed. In the reconstructed wind field, the storm updraft is gone, and the adjusted horizontal velocity allows for the anelastic continuity equation to be satisfied. With integral constraints on the distribution of divergence satisfied, all boundary conditions on normal velocity are satisfied. The transform essentially provides an acoustic adjustment, preventing large-amplitude sound waves at initialization.

Corresponding author address: Dr. Brian Fiedler, School of Meteorology, University of Oklahoma, 100 E. Boyd St., Rm. 1310, Norman, OK 73019. Email: bfiedler@ou.edu

Abstract

A three-dimensional, anelastic wind field on a staggered grid, with a specified normal wind component on the lateral boundaries, can be reversibly transformed into two scalar fields. In a conformal, terrain-following coordinate system these two quantities are closely related to the divergence of the horizontal wind and the vertical vorticity. The finite-difference implementation of the transform is emphasized. The exactness of the transform, and its consistency with the boundary conditions, are easily demonstrated when the transform is viewed as a problem of linear algebra in a discrete model.

The transform is shown to be useful in initializing a model wind field. A demonstration is provided with the removal of a spurious storm from the background wind field that is to be used in a forecast–analysis cycle. The divergence of the horizontal wind in the vicinity of the storm is removed. In the reconstructed wind field, the storm updraft is gone, and the adjusted horizontal velocity allows for the anelastic continuity equation to be satisfied. With integral constraints on the distribution of divergence satisfied, all boundary conditions on normal velocity are satisfied. The transform essentially provides an acoustic adjustment, preventing large-amplitude sound waves at initialization.

Corresponding author address: Dr. Brian Fiedler, School of Meteorology, University of Oklahoma, 100 E. Boyd St., Rm. 1310, Norman, OK 73019. Email: bfiedler@ou.edu

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