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Detecting Waves Using an Array of Sensors

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  • 1 School of Mathematics and Statistics, University of Sheffield, Sheffield, United Kingdom
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Abstract

The method of frequency-wavenumber “beamsteering” is a familiar tool in seismic applications and radar work where it is commonly used to detect coherent, propagating disturbances in “noisy” data. However, its use in meteorological situations is not well documented. In this paper the beamsteering method is summarized and its application in a meteorological context is discussed. Three different algorithms are used to detect single waves in artificial data with varying signal-to-noise ratios. Two of these are different beamsteering algorithms:one is a low-resolution scheme where the frequency-wavenumber spectrum is estimated using a fixed wavenumber window and the other a high-resolution method where the wavenumber window is effectively optimized for each wavenumber. These are compared with a method based on the cross-correlation function, which is more routinely used in meteorological studies. The results from this analysis provide a quantifiable measure of the performance and reliability of the three methods when detecting single waves at a given frequency. The performance of the high-resolution beamsteering algorithm is then tested in a similar manner with two waves at the same frequency.

Corresponding author address: Dr. Julia M. Rees, School of Mathematics and Statistics, The University of Sheffield, Hounsfield Road, Sheffield S3 7RH United Kingdom.

Email: J.Rees@sheffield.ac.uk

Abstract

The method of frequency-wavenumber “beamsteering” is a familiar tool in seismic applications and radar work where it is commonly used to detect coherent, propagating disturbances in “noisy” data. However, its use in meteorological situations is not well documented. In this paper the beamsteering method is summarized and its application in a meteorological context is discussed. Three different algorithms are used to detect single waves in artificial data with varying signal-to-noise ratios. Two of these are different beamsteering algorithms:one is a low-resolution scheme where the frequency-wavenumber spectrum is estimated using a fixed wavenumber window and the other a high-resolution method where the wavenumber window is effectively optimized for each wavenumber. These are compared with a method based on the cross-correlation function, which is more routinely used in meteorological studies. The results from this analysis provide a quantifiable measure of the performance and reliability of the three methods when detecting single waves at a given frequency. The performance of the high-resolution beamsteering algorithm is then tested in a similar manner with two waves at the same frequency.

Corresponding author address: Dr. Julia M. Rees, School of Mathematics and Statistics, The University of Sheffield, Hounsfield Road, Sheffield S3 7RH United Kingdom.

Email: J.Rees@sheffield.ac.uk

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