Complex Empirical Orthogonal Function analysis of wide-area system dynamics

Esquivel, P.; Messina, A.R.

doi:10.1109/pes.2008.4596270

Cited by 8 publications

(7 citation statements)

References 7 publications

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“…A clear explanation of this technique can be found in Esquivel and Messina (2008), so we give only a brief summary. Consider a scalar field u ( x j , t k ), where x j are the different positions ( j =1, …, M ) and t k are the different times the signal is sampled ( k =1, …, N ).…”

Section: Complex Empirical Orthogonal Functionmentioning

confidence: 99%

Decomposition of Geomagnetic Secular Acceleration Into Traveling Waves Using Complex Empirical Orthogonal Functions

Chi-Durán

Avery

Knezek

et al. 2020

Geophysical Research Letters

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Satellite observations reveal short pulses in the second time derivative of the geomagnetic field. We seek to interpret these signals using complex empirical orthogonal functions (CEOFs). This methodology decomposes the signal into traveling waves, permitting estimates for the period, angular wave number, and phase velocity. We recover CEOFs from the CHAOS‐6 model, focusing on three geographic regions with strong secular acceleration. Two regions are confined to the equator, while the third is located under Alaska. We find evidence for both eastward and westward traveling waves with periods between 7 and 20 years. There is also evidence for weaker standing waves with complex spatial patterns. Two of the three regions have waves that are compatible with predictions for waves in a stratified fluid. Our results yield estimates for the structure of fluid stratification at the top of the core.

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Section: Complex Empirical Orthogonal Functionmentioning

confidence: 99%

Decomposition of Geomagnetic Secular Acceleration Into Traveling Waves Using Complex Empirical Orthogonal Functions

Chi-Durán

Avery

Knezek

et al. 2020

Geophysical Research Letters

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“…Specifically, we used the Hilbert empirical orthogonal functions analysis, introduced by Rasmusson et al (1981), based on the relation of the data samples with their (shifted) Hilbert transforms. The main advantage for our study is that it reveals (in addition to the variance characteristics) the change of the geophysical processes (von Storch and Zwiers 2002) and so provides quantitative understanding of the underlying oscillating mechanisms (Esquivel and Messina 2008). To deal with data gaps, the methods by von Storch and Zwiers (2002) were applied.…”

Section: Complex Empirical Orthogonal Function Analysismentioning

confidence: 99%

How Oceanic Oscillation Drives Soil Moisture Variations over Mainland Australia: An Analysis of 32 Years of Satellite Observations*

et al. 2013

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Australia is frequently subject to droughts and floods. Its hydrology is strongly connected to oceanic and atmospheric oscillations (climate modes) such as the El Niño-Southern Oscillation (ENSO), Indian Ocean dipole (IOD), and southern annular mode (SAM). A global 32-yr dataset of remotely sensed surface soil moisture (SSM) was used to examine hydrological variations in mainland Australia for the period 1978-2010. Complex empirical orthogonal function (CEOF) analysis was applied to extract independent signals and to investigate their relationships to climate modes. The annual cycle signal represented 46.3% of the total variance and a low but highly significant connection with SAM was found. Two multiannual signals with a lesser share in total variance (6.3% and 4.2%) were identified. The first one had an unstable period of 2-5 yr and reflected an east-west pattern that can be associated with ENSO and SAM but not with IOD. The second one, a 1-to 5-yr oscillation, formed a dipole pattern between the west and north and can be linked to ENSO and IOD. As expected, relationships with ENSO were found throughout the year and are especially strong during southern spring and summer in the east and north. Somewhat unexpectedly, SAM impacts strongest in the north and east during summer and is proposed as the key driver of the annual SSM signal. The IOD explains SSM variations in the north, east, and southeast during spring and also in the west during winter.

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“…A common alternative that allows treating space and time separately is known as complex PCA [34]. The complex PCA returns a more accurate decomposition and interpretable eigenvectors for geophysical data analysis than the plain PCA version since it allows expressing the spatial and temporal components in terms of magnitude and phase [33].…”

Section: B Complex Pcamentioning

confidence: 99%

“…• Space and time decoupling. The method operates in the complex (kernel) domain to account for space and time features [8], [10], [33], [34]. The spatial and temporal modes are treated via the Hilbert transform [35], thus leading to spatial and temporally explicit eigendecompositions easy to analyze.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear PCA for Spatio-Temporal Analysis of Earth Observation Data

Bueso

Piles

Camps‐Valls

2020

IEEE Trans. Geosci. Remote Sensing

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Remote sensing observations, products and simulations are fundamental sources of information to monitor our planet and its climate variability. Uncovering the main modes of spatial and temporal variability in Earth data is essential to analyze and understand the underlying physical dynamics and processes driving the Earth System. Dimensionality reduction methods can work with spatiotemporal datasets and decompose the information efficiently. Principal Component Analysis (PCA), also known as Empirical Orthogonal Functions (EOF) in geophysics, has been traditionally used to analyze climatic data. However, when nonlinear feature relations are present, PCA/EOF fails. In this work, we propose a nonlinear PCA method to deal with spatio-temporal Earth System data. The proposed method, called Rotated Complex Kernel PCA (ROCK-PCA for short), works in reproducing kernel Hilbert spaces to account for nonlinear processes, operates in the complex kernel domain to account for both space and time features, and adds an extra rotation for improved flexibility. The result is an explicitly resolved spatio-temporal decomposition of the Earth data cube. The method is unsupervised and computationally very efficient. We illustrate its ability to uncover spatio-temporal patterns using synthetic experiments and real data. Results of the decomposition of three essential climate variables are shown: satellite-based global Gross Primary Productivity (GPP) and Soil Moisture (SM), and reanalysis Sea Surface Temperature (SST) data. The ROCK-PCA method allows identifying their annual and seasonal oscillations, as well as their non-seasonal trends and spatial variability patterns. The main modes of variability of GPP and SM match expected distributions of land-cover and eco-hydrological zones, respectively; the inter-annual component of SM is shown to be highly correlated with El Niño Southern Oscillation (ENSO) phenomenon; and the SST annual oscillation is perfectly uncoupled in magnitude and phase from the global warming trend and ENSO anomalies, as well as from their mutual interactions. We provide a working source code of the presented method for the interested reader in https://github.com/DiegoBueso/ROCK-PCA.

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Complex Empirical Orthogonal Function analysis of wide-area system dynamics

Cited by 8 publications

References 7 publications

Decomposition of Geomagnetic Secular Acceleration Into Traveling Waves Using Complex Empirical Orthogonal Functions

Decomposition of Geomagnetic Secular Acceleration Into Traveling Waves Using Complex Empirical Orthogonal Functions

How Oceanic Oscillation Drives Soil Moisture Variations over Mainland Australia: An Analysis of 32 Years of Satellite Observations*

Nonlinear PCA for Spatio-Temporal Analysis of Earth Observation Data

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