Developing a Complex Independent Component Analysis (CICA) Technique to Extract Non-stationary Patterns from Geophysical Time Series

Abstract

In recent decades, decomposition techniques have enabled increasingly more applications for dimension reduction, as well as extraction of additional information from geophysical time series. Traditionally, the principal component analysis (PCA)/empirical orthogonal function (EOF) method and more recently the independent component analysis (ICA) have been applied to extract, statistical orthogonal (uncorrelated), and independent modes that represent the maximum variance of time series, respectively. PCA and ICA can be classified as stationary signal decomposition techniques since they are based on decomposing the autocovariance matrix and diagonalizing higher (than two) order statistical tensors from centered time series, respectively. However, the stationarity assumption in these techniques is not justified for many geophysical and climate variables even after removing cyclic components, e.g., the commonly removed dominant seasonal cycles. In this paper, we present a novel decomposition method, the complex independent component analysis (CICA), which can be applied to extract non-stationary (changing in space and time) patterns from geophysical time series. Here, CICA is derived as an extension of realvalued ICA, where (a) we first define a new complex dataset that contains the observed time series in its real part, and their Hilbert transformed series as its imaginary part, (b) an

An Iterative ICA-Based Reconstruction Method to Produce Consistent Time-Variable Total Water Storage Fields Using GRACE and Swarm Satellite Data

“…The advantages of applying ICA (instead of PCA) for reconstruction include: (1) ICA can better separate signal from noise, especially when the distribution of data sets are not Gaussian (this is the case for TWSC time series as shown by [13,45,46]); (2) Theoretically, independent components can better extract the physically separated phenomena such as trend, seasonality (see, e.g., [43]) and variations of TWSCs due to large-scale teleconnection indices (see e.g., [44,67]); therefore, relying on the ICA modes offers more representative basis to combine various types of data; (3) One usually needs a smaller number of ICA modes (than the number of PCA modes) to reconstruct a certain portion of variance in the original data [68], which makes the computation of reconstruction more stable. The first m ICA components can be used to re-estimate the data matrix X as:…”

“…In order to estimate uncertainties of the reconstruction from Approach 1 and Approach 2, we followed the Bootstrap approach used similar to that in [44]. First, n realizations of the data matrix X i , i : 1; ...; n were generated by considering the original data matrix X and adding errors from GRACE and Swarm TWSC fields.…”

“…In the light of our results in the previous section, we believe that the reconstruction results from Approach 2 have better quality, i.e., contain less noise and the mass anomalies are well localized. Therefore, these fields are used to assess the global mass redistribution of 2003-2018 in terms of trends, seasonal and sub-seasonal cycles, as well as those related to teleconnection evens, see similar studies, e.g., [14,44,50,56,78]. To illustrate the benefit of the iterations in Approach 2 to reduce the noise in TWSC fields, a comparison between the results of the first iteration with those of 250th iteration in terms of basin-averaged TWSC is shown in Figure A1.…”

“…The proposed approach of this study entirely relies on gravity field outputs, which can be derived from different satellite missions. For both formulations, one can apply statistical decomposition techniques such as principal component analysis (PCA, [42]) and independent component analysis (ICA, [13,43]) or their extensions (Complex PCA and Complex ICA, as in [44]). Here, we prefer ICA over PCA, since it performs better to separate TWSC signal from noise (see, e.g., [45,46]).…”

Understanding linkages between global climate indices and terrestrial water storage changes over Africa using GRACE products

“…Other studies that have employed GRACE to study climate-related impacts include Chen et al, (2010), Becker et al, (2010), Thomas et al, (2014), Zhang et al, (2015), Cao et al, (2015) and Kushe et al, (2016). Given ENSO's dominant impact on global TWS changes, statistical decomposition techniques are developed and applied in Eicker et al (2016) and Forootan et al (2018) to separate variations in TWS that are related to ENSO from the rest, which are called 'non-ENSO' modes. Such separation seems to be significant to understand TWS trends without the impact of extreme events such as those associated with ENSO.…”