用于描述重力波的功率谱计算中的消除偏差技术:交错方法和误差分析

IF 2.9 3区 地球科学 Q2 ASTRONOMY & ASTROPHYSICS
Jackson Jandreau, Xinzhao Chu
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引用次数: 0

摘要

观测数据本身包含噪声,表现为测量参数的不确定性,并在方差、通量和光谱等二阶产品中产生正偏差或噪声底。历史方法可以估计并随后减去噪声下限,但在准确性方面却很困难。Gardner 和 Chu(2020,doi.org/10.1364/AO.400375)提出了一种交错数据处理方法,该方法从本质上消除了来自方差和通量的偏差,并提出该方法还能消除功率谱的噪底。我们通过理论研究、正向建模和激光雷达数据演示,对用于大气波谱分析的交错法进行了研究。我们的工作表明,从两个交错子样本计算交叉功率谱密度(CPSD)确实能显著降低频谱本底噪声。然而,只有共功率谱密度(CPSD 的实部)能完全消除本底噪声,而当样本数有限时,取 CPSD 的绝对值则会将降低的本底噪声加回频谱。通过对更多的观测数据进行平均,可以进一步降低噪底,这与传统的频谱计算完全不同,传统的频谱计算无法通过加入更多的样本来降低噪底。我们展示了交错法在频谱数据中的首次应用,在一个前向模型和南极洲麦克默多重力波垂直波长的激光雷达观测中使用 Co-PSD 成功消除了噪底。这种高精度是以牺牲光子计数分裂造成的精度为代价的,需要额外的观测来抵消这种影响。我们提供了准确度和精确度的定量评估以及应用建议。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Bias-Eliminating Techniques in the Computation of Power Spectra for Characterizing Gravity Waves: Interleaved Methods and Error Analyses

Bias-Eliminating Techniques in the Computation of Power Spectra for Characterizing Gravity Waves: Interleaved Methods and Error Analyses

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.

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来源期刊
Earth and Space Science
Earth and Space Science Earth and Planetary Sciences-General Earth and Planetary Sciences
CiteScore
5.50
自引率
3.20%
发文量
285
审稿时长
19 weeks
期刊介绍: Marking AGU’s second new open access journal in the last 12 months, Earth and Space Science is the only journal that reflects the expansive range of science represented by AGU’s 62,000 members, including all of the Earth, planetary, and space sciences, and related fields in environmental science, geoengineering, space engineering, and biogeochemistry.
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