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Forootan, Ehsan, Kusche, Jürgen, Talpe, Matthieu, Shum, C. K., and Schmidt, Michael, 2018. Developing a Complex Independent Component Analysis (CICA) Technique to Extract Non-stationary Patterns from Geophysical Time Series. Surveys in Geophysics, 39(3):435–465, doi:10.1007/s10712-017-9451-1.
• from the NASA Astrophysics Data System • by the DOI System •
@ARTICLE{2018SGeo...39..435F,
author = {{Forootan}, Ehsan and {Kusche}, J{\"u}rgen and {Talpe}, Matthieu and {Shum}, C.~K. and {Schmidt}, Michael},
title = "{Developing a Complex Independent Component Analysis (CICA) Technique to Extract Non-stationary Patterns from Geophysical Time Series}",
journal = {Surveys in Geophysics},
keywords = {Independent component analysis (ICA), Complex ICA (CICA), Time series analysis, Signal separation, Non-stationary decomposition, Terrestrial water storage (TWS), Sea surface temperature (SST)},
year = 2018,
month = may,
volume = {39},
number = {3},
pages = {435-465},
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 real-valued 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 ICA algorithm based on
diagonalization of fourth-order cumulants is then applied to
decompose the new complex dataset in (a), and finally, (c) the
dominant independent complex modes are extracted and used to
represent the dominant space and time amplitudes and associated
phase propagation patterns. The performance of CICA is examined
by analyzing synthetic data constructed from multiple physically
meaningful modes in a simulation framework, with known truth.
Next, global terrestrial water storage (TWS) data from the
Gravity Recovery And Climate Experiment (GRACE) gravimetry
mission (2003{\textendash}2016), and satellite radiometric sea
surface temperature (SST) data (1982{\textendash}2016) over the
Atlantic and Pacific Oceans are used with the aim of
demonstrating signal separations of the North Atlantic
Oscillation (NAO) from the Atlantic Multi-decadal Oscillation
(AMO), and the El Ni{\~n}o Southern Oscillation (ENSO) from the
Pacific Decadal Oscillation (PDO). CICA results indicate that
ENSO-related patterns can be extracted from the Gravity Recovery
And Climate Experiment Terrestrial Water Storage (GRACE TWS)
with an accuracy of 0.5{\textendash}1 cm in terms of equivalent
water height (EWH). The magnitude of errors in extracting NAO or
AMO from SST data using the complex EOF (CEOF) approach reaches
up to \raisebox{-0.5ex}\textasciitilde50\% of the signal itself,
while it is reduced to \raisebox{-0.5ex}\textasciitilde16\% when
applying CICA. Larger errors with magnitudes of
\raisebox{-0.5ex}\textasciitilde100\% and
\raisebox{-0.5ex}\textasciitilde30\% of the signal itself are
found while separating ENSO from PDO using CEOF and CICA,
respectively. We thus conclude that the CICA is more effective
than CEOF in separating non-stationary patterns.}",
doi = {10.1007/s10712-017-9451-1},
adsurl = {https://ui.adsabs.harvard.edu/abs/2018SGeo...39..435F},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
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