An Explanation of the Wind Speed Underestimation Obtained from a Least Squares Type Single-Doppler Radar Velocity Retrieval Method

Yu-Chieng Liou Department of Atmospheric Sciences, National Central University, Chung-Li, Taiwan

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Abstract

The errors produced by a least squares type single-Doppler velocity retrieval scheme based on variational analysis are studied. With proper simplifications of the retrieval formulation, it can be found that the strength of the retrieved radial wind is comparable to the true one. By contrast, the retrieved azimuthal component is, in most cases, underestimated. For a given radar site, this underestimation is directly related to the discrete nature of the radar observations. It occurs when the time period between two radar scans, Δt, is greater than Δx/u, where Δx is the radar's spatial resolution and u is the speed of the observed weather phenomenon. This condition unfortunately is often true for today's Doppler radar operational modes. As a result, an underestimation of the retrieved wind speed becomes inevitable. Retrieval work performed on an optimized moving frame of reference can reduce the aforementioned error in the retrieved azimuthal component of wind. The experiment also demonstrates that the search for this moving reference frame can be achieved as long as Δt is less than λ/2u, where λ is the wavelength of the weather phenomenon. This condition is somewhat relaxed, and it can be fulfilled without much difficulty by the current operational Doppler radars. The results predicted by the theoretical analyses are confirmed by a real case study.

Corresponding author address: Dr. Yu-Chieng Liou, Department of Atmospheric Sciences, National Central University, Chung-Li, 320, Taiwan, Republic of China. tyliou@atm.ncu.edu.tw

Abstract

The errors produced by a least squares type single-Doppler velocity retrieval scheme based on variational analysis are studied. With proper simplifications of the retrieval formulation, it can be found that the strength of the retrieved radial wind is comparable to the true one. By contrast, the retrieved azimuthal component is, in most cases, underestimated. For a given radar site, this underestimation is directly related to the discrete nature of the radar observations. It occurs when the time period between two radar scans, Δt, is greater than Δx/u, where Δx is the radar's spatial resolution and u is the speed of the observed weather phenomenon. This condition unfortunately is often true for today's Doppler radar operational modes. As a result, an underestimation of the retrieved wind speed becomes inevitable. Retrieval work performed on an optimized moving frame of reference can reduce the aforementioned error in the retrieved azimuthal component of wind. The experiment also demonstrates that the search for this moving reference frame can be achieved as long as Δt is less than λ/2u, where λ is the wavelength of the weather phenomenon. This condition is somewhat relaxed, and it can be fulfilled without much difficulty by the current operational Doppler radars. The results predicted by the theoretical analyses are confirmed by a real case study.

Corresponding author address: Dr. Yu-Chieng Liou, Department of Atmospheric Sciences, National Central University, Chung-Li, 320, Taiwan, Republic of China. tyliou@atm.ncu.edu.tw

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