1. Bias‐Eliminating Techniques in the Computation of Power Spectra for Characterizing Gravity Waves: Interleaved Methods and Error Analyses.
- Author
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Jandreau, Jackson and Chu, Xinzhao
- Subjects
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GRAVITY waves , *OCEAN wave power , *ROSSBY waves , *ATMOSPHERIC boundary layer , *ATMOSPHERIC waves , *WAVENUMBER - Abstract
Observational data inherently contain noise which manifests as uncertainties in the measured parameters and creates positive biases or noise floors in second‐order products like variances, fluxes, and spectra. Historical methods estimate and subsequently subtract noise floors, but struggle with accuracy. Gardner and Chu (2020, doi.org/10.1364/AO.400375) proposed an interleaved data processing method, which inherently eliminates biases from variances and fluxes, and suggested that the method could also eliminate noise floors of power spectra. We investigate the interleaved method for spectral analysis of atmospheric waves through theoretical studies, forward modeling, and demonstration with lidar data. Our work shows that calculating the cross‐power spectral density (CPSD) from two interleaved subsamples does reduce the spectral noise floor significantly. However, only the Co‐PSD (the real part of CPSD) eliminates the noise floor completely, while taking the absolute magnitude of CPSD adds a reduced noise floor back to the spectrum when the sample number is finite. This reduced noise floor can be further minimized through averaging over more observations, completely different from traditional spectrum calculations whose noise floor cannot be reduced by incorporating more samples. We demonstrate the first application of the interleaved method to spectral data, successfully eliminating the noise floor using the Co‐PSD in a forward model and in lidar observations of the vertical wavenumber of gravity waves at McMurdo, Antarctica. This high accuracy is gained by sacrificing precision due to photon‐count splitting, requiring additional observations to counter this effect. We provide quantitative assessment of accuracy and precision as well as application recommendations. Plain Language Summary: Atmospheric waves serve a vital role in global energy and momentum transportation between the lower and upper atmosphere, driving major atmospheric circulations. These waves exist across many scales, from large planetary waves to medium‐ and small‐scale gravity waves (GW). GW are a key factor driving many atmospheric phenomena, but due to their relatively smaller scales, they are difficult to study. The spectra of GW are important to understanding wave dynamics and informing the development of atmospheric models, as these spectra contain critical information about how wave‐transported energy is distributed amongst different temporal and spatial frequencies. A major tool in improving our knowledge and modeling of GW is their direct observations. Although being powerful wave observation tools, lidar and radar data contain noise in their measurements which manifests as noise floors, obscuring derived wave power spectra. These floors cannot be removed by averaging more samples, as is done for other parameters, making it difficult to accurately interpret the spectra. Pre‐existing techniques can remove this floor, but they struggle with accuracy, especially in high‐noise conditions. This study introduces and demonstrates the use of an interleaved method of spectral processing, which eliminates the noise floors altogether, enabling high‐accuracy calculation of wave spectra. Key Points: We develop an interleaved data processing technique to compute cross‐power spectral density (CPSD) for deriving unbiased wave spectraAccuracy and precision analyses of coincident‐power spectral density (Co‐PSD) and CPSD magnitude show Co‐PSD eliminating noise floor entirelyThe spectral interleaved method is shown to eliminate noise floor, demonstrated using a forward model and Antarctic lidar observations [ABSTRACT FROM AUTHOR]
- Published
- 2024
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