Two-dimensional Morlet wavelet transform and its application to wave recognition methodology of automatically extracting two-dimensional wave packets from lidar observations in Antarctica
Two-dimensional Morlet wavelet transform and its application to wave recognition methodology of automatically extracting two-dimensional wave packets from lidar observations in Antarctica
复制标题
二维Morlet小波变换及其在南极激光雷达观测自动提取二维波包的波识别方法中的应用
DOI：
10.1016/j.jastp.2016.10.016
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发表时间：
2017
影响因子：
1.9
通讯作者：
X. Chu
中科院分区：
文献类型：
--
作者：
Cao Chen;X. Chu
大气和海洋中的波本质上是间歇性的，其振幅、频率或波长随时间和空间的变化而变化。大多数波表现出波包的性质，以斜角传播，并且通常在二维（2-D）数据集中被观察到。这些特征使得小波变换，尤其是二维小波方法，比传统的加窗傅立叶分析更有吸引力，因为前者允许自适应时频窗宽（即，在高频时自动缩小窗口大小，在低频时自动扩大），而后者使用固定的包络函数。本文建立了改进的1-D和2-D Morlet小波变换的数学形式，保证了小波变换在频率/波数域的幂等于其在时间/空间域的平均幂。因此，改进的小波变换消除了传统小波方法和许多现有代码对高频/小尺度波的偏置。基于改进的二维Morlet小波变换，提出了一种自动识别和提取二维准单色波包的波识别方法，并推导出二维准单色波包的波周期、波长、相速度和时间/空间跨度等波属性。通过分析2014年6月28日至30日在南极洲麦克默多拍摄的激光雷达数据，逐步演示了这种方法。新开发的波识别方法随后被应用于2014年5月和7月的两次激光雷达观测，以分析最近在南极洲发现的持续重力波。分解后的惯性-重力波特征与Chen et al. （2016a）的结论一致，即3-10 h波持续存在且占主导地位，且具有多天的寿命。它们的垂直波长为20-30公里，垂直相位速度为0.5-2米/秒，在中间层和低层热层（MLT）的水平波长可达数千公里。冬季不同月份提取波性质的变化反映了南极MLT区域重力波活动的逐月变化。
Waves in the atmosphere and ocean are inherently intermittent, with amplitudes, frequencies, or wavelengths varying in time and space. Most waves exhibit wave packet-like properties, propagate at oblique angles, and are often observed in two-dimensional (2-D) datasets. These features make the wavelet transforms, especially the 2-D wavelet approach, more appealing than the traditional windowed Fourier analysis, because the former allows adaptive time-frequency window width (i.e., automatically narrowing window size at high frequencies and widening at low frequencies), while the latter uses a fixed envelope function. This study establishes the mathematical formalism of modified 1-D and 2-D Morlet wavelet transforms, ensuring that the power of the wavelet transform in the frequency/wavenumber domain is equivalent to the mean power of its counterpart in the time/space domain. Consequently, the modified wavelet transforms eliminate the bias against high-frequency/small-scale waves in the conventional wavelet methods and many existing codes.Based on the modified 2-D Morlet wavelet transform, we put forward a wave recognition methodology that automatically identifies and extracts 2-D quasi-monochromatic wave packets and then derives their wave properties including wave periods, wavelengths, phase speeds, and time/space spans. A step-by-step demonstration of this methodology is given on analyzing the lidar data taken during 28–30 June 2014 at McMurdo, Antarctica. The newly developed wave recognition methodology is then applied to two more lidar observations in May and July 2014, to analyze the recently discovered persistent gravity waves in Antarctica. The decomposed inertia-gravity wave characteristics are consistent with the conclusion in Chen et al. (2016a) that the 3–10 h waves are persistent and dominant, and exhibit lifetimes of multiple days. They have vertical wavelengths of 20–30 km, vertical phase speeds of 0.5–2 m/s, and horizontal wavelengths up to several thousands kilometers in the mesosphere and lower thermosphere (MLT). The variations in the extracted wave properties from different months in winter indicate a month-to-month variability in the gravity wave activities in the Antarctic MLT region.