A Simple Scheme for Objective Analysis in Curved Flow

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  • 1 Program for Regional Observing and Forecasting Services, NOAA, Environmental Research Laboratories, Boulder, CO 80303, and National Center for Atmospheric Research, Boulder, CO 80307
  • | 2 Department of Meteorology, The Pennsylvania State University, University Park, PA 16802
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Abstract

An objective analysis scheme has been developed which combines use of different weighting functions, two of which are anisotropic (elliptical and banana-shaped). The “effective” distance between a grid point and an observation point used for the anisotropic functions may be applied in any objective analysis scheme which uses distance to calculate weights or correlations, but a successive-correlation scheme is used here as a vehicle for testing. This relatively simple and computationally inexpensive scheme produces wind and moisture analyses in which along-flow autocorrelation is accentuated, especially in regions of curved flow, and thus simulates conventional subjective analysis procedures. Sample analyses from a case study are presented which demonstrate the improvement which may result from using this scheme rather than one with the circular weighting function alone.

In tests with an analytically defined, curving jet stream, the multiple weighting function scheme with the “banana” function was superior to schemes using the circular function either alone or with an elliptical function for all of the error statistics considered, including a 30% reduction in rms vector error.

This objective analysis scheme also includes an alternative method for calculating corrections at individual grid points which is designed to eliminate discontinuities which may occur when more common correction methods are applied. Additional analytical tests and sample analyses confirm that the new correction method decreases noise in gradients (e.g., vorticity, divergence) of analyzed fields which result with the use of other correction methods in data-sparse regions or over the entire domain when the ratio between the grid space and the mean station separation is small (5–10%). The analytical tests also indicate that the new correction method performs slightly better than other methods for the analyzed variable itself (as well as the gradient) regardless of the scale.

Abstract

An objective analysis scheme has been developed which combines use of different weighting functions, two of which are anisotropic (elliptical and banana-shaped). The “effective” distance between a grid point and an observation point used for the anisotropic functions may be applied in any objective analysis scheme which uses distance to calculate weights or correlations, but a successive-correlation scheme is used here as a vehicle for testing. This relatively simple and computationally inexpensive scheme produces wind and moisture analyses in which along-flow autocorrelation is accentuated, especially in regions of curved flow, and thus simulates conventional subjective analysis procedures. Sample analyses from a case study are presented which demonstrate the improvement which may result from using this scheme rather than one with the circular weighting function alone.

In tests with an analytically defined, curving jet stream, the multiple weighting function scheme with the “banana” function was superior to schemes using the circular function either alone or with an elliptical function for all of the error statistics considered, including a 30% reduction in rms vector error.

This objective analysis scheme also includes an alternative method for calculating corrections at individual grid points which is designed to eliminate discontinuities which may occur when more common correction methods are applied. Additional analytical tests and sample analyses confirm that the new correction method decreases noise in gradients (e.g., vorticity, divergence) of analyzed fields which result with the use of other correction methods in data-sparse regions or over the entire domain when the ratio between the grid space and the mean station separation is small (5–10%). The analytical tests also indicate that the new correction method performs slightly better than other methods for the analyzed variable itself (as well as the gradient) regardless of the scale.

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