Guilloteau Clément, Mamalakis Antonios, Vulis Lawrence, Le Phong V V, Georgiou Tryphon T, Foufoula-Georgiou Efi
Department of Civil and Environmental Engineering, University of California Irvine, Irvine, California.
Faculty of Hydrology Meteorology and Oceanography, Vietnam National University, Hanoi, Vietnam.
J Clim. 2021 Jan 1;34(2):715-736. doi: 10.1175/jcli-d-20-0266.1. Epub 2020 Dec 23.
Spectral PCA (sPCA), in contrast to classical PCA, offers the advantage of identifying organized spatiotemporal patterns within specific frequency bands and extracting dynamical modes. However, the unavoidable trade-off between frequency resolution and robustness of the PCs leads to high sensitivity to noise and overfitting, which limits the interpretation of the sPCA results. We propose herein a simple nonparametric implementation of sPCA using the continuous analytic Morlet wavelet as a robust estimator of the cross-spectral matrices with good frequency resolution. To improve the interpretability of the results, especially when several modes of similar amplitude exist within the same frequency band, we propose a rotation of the complex-valued eigenvectors to optimize their spatial regularity (smoothness). The developed method, called rotated spectral PCA (rsPCA), is tested on synthetic data simulating propagating waves and shows impressive performance even with high levels of noise in the data. Applied to global historical geopotential height (GPH) and sea surface temperature (SST) daily time series, the method accurately captures patterns of atmospheric Rossby waves at high frequencies (3-60-day periods) in both GPH and SST and El Niño-Southern Oscillation (ENSO) at low frequencies (2-7-yr periodicity) in SST. At high frequencies the rsPCA successfully unmixes the identified waves, revealing spatially coherent patterns with robust propagation dynamics.
与经典主成分分析（PCA）相比，谱主成分分析（sPCA）具有能够识别特定频带内有组织的时空模式并提取动态模式的优势。然而，主成分在频率分辨率和稳健性之间不可避免的权衡导致对噪声高度敏感和过拟合，这限制了对sPCA结果的解释。我们在此提出一种简单的非参数sPCA实现方法，使用连续解析莫雷特小波作为具有良好频率分辨率的交叉谱矩阵的稳健估计器。为了提高结果的可解释性，特别是当同一频带内存在几种幅度相似的模式时，我们提出对复特征向量进行旋转以优化其空间正则性（平滑度）。所开发的方法称为旋转谱主成分分析（rsPCA），在模拟传播波的合成数据上进行了测试，即使数据中存在高水平噪声，也显示出令人印象深刻的性能。应用于全球历史位势高度（GPH）和海表温度（SST）的每日时间序列，该方法准确地捕捉到了GPH和SST中高频（3 - 60天周期）的大气罗斯贝波模式以及SST中低频（2 - 7年周期）的厄尔尼诺 - 南方涛动（ENSO）。在高频时，rsPCA成功地分解了识别出的波，揭示了具有稳健传播动态的空间连贯模式。
