A non-gaussian decomposition of Total Water Storage (TWS), using Independent Component Analysis (ICA)

Transcription

1 Titelmaster A non-gaussian decomposition of Total Water Storage (TWS, using Independent Component Analysis (ICA Ehsan Forootan and Jürgen Kusche Astronomical Physical & Mathematical Geodesy, Bonn University forootan@geod.uni-bonn.de Geodätische Woche 00,

2 Table of Titelmaster Contents Introduction & Motivation Method of EOF/PCA Rotation of PCA components towards a simplified structure Incorperate non-gaussianity inforamtion in the frame of ICA Results & Discussion

3 Introduction Titelmaster & Motivation GRACE s temporal information. Since 00, GRACE has provided a valuable information about mass redistribution within the Earth system.. TWS anomalies represent integrated mass over a vertical column which is caused by different phenomena. Task : to decompose the observed signals to its geophysically interpretable components. Time series of the Total Water Storage (TWS maps, derived from the process of ITG00 solutions TWS F ( t, s f, f, n m number of solutions number of grid points , f m

4 Method Titelmaster of EOF/PCA PCA is the most widely used method which works based on eigenvalue decomposition (Lorenz,956. PCA criterion constrain n Ma e m f e e i j T ( i i ij Diagonalization of the auto-covariance matri F ( t, s n m m k PCs k Uncorrelated ( t EOF k ( s Orthogonal 3 PCA de-correlates the dataset by decomposing it to the orthogonal components. Limitation: Derived components are data modes and are not always physically interpretable. Limitation: Physical processes are not necessarily orthogonal. (Orthogonality problem PCA solution is optimized when the observed signals are Gaussian. Limitation: hydrological parameters associated to physical process models contain a significant level of non-gaussianity. (Gaussianity problem

5 Method Titelmaster of REOF Rotated EOF: is a solution for the PCA s orthogonality constraint. REOF technique is simply based on rotating the PCA s components. either rotating EOFs or PCs orthogonal or oblique rotation Rotation criteria are various, namely: VARIMAX, QUARTIMAX, QUARTIMIN, Varima rotation, to derive simplified structure (Kaiser, 958 Choosing a subset of EOFs for rotation: Varima criterion Rotation of EOFs k p p f ( U Ma u j i p i ij u ij Varima simplifies the structure in the data, (Richman, 986. : U E k R

6 Method Titelmaster of ICA Non-Gaussian signals have non-zero high order statistical moments. Kurtosis: E ( / E ( Gaussian signals Sub Gaussian 0 Around 60% of the TWS signals are non-gaussian. This suggests to incorporate higher order moments within the decomposition procedure. Super Gaussian 5 Independence instead of uncorrelation: Independence implies uncorrelatedness but the reverse is not always true! For non-gaussian signals, maimally independent signals are also likely approimately uncorrelated. ICA algorithm: - perform the PCA to decorrelate, - to determine a suitable rotation to optimize an independence criterion

7 Method Titelmaster of ICA Selected criterion: fourth order cumulant: if : E ( C (,, 3, E ( E ( 3 E ( E ( E ( Similar to the JADE algorithm, (Cardoso, E ( E ( Rotation of EOFs : U E k R ICA criterion f ( U Ma k j C ( u j Rotating EOFs Spatial ICA Temporal ICA Temporal ICA The ICA derived decomposition are more physically interpretable

8 Simulation Titelmaster status

9 Simulation Titelmaster results

10 Results of decomposing TitelmasterITG

11 Results of decomposing TitelmasterITG

12 Results Titelmaster & Discussion The EOF/PCA breaks the data into modes of variability, these modes are in nature data modes, and are not necessarily interpretable. The PCA's conventional etension (e.g. Varima rotation did not improve the miing problem. The PCA method can be assumed as an initial step for the ICA method. This improves both the computational and interpretability of the decomposition procedure. Using the non-gaussianinty information in the frame of ICA shows a better performance with compare to the ordinary PCA and Varima to separate the GRACE's underlying signals even for such regions that ehibit different overlapping modes

13 Titelmaster Thank you for your attention References:. E. Lorenz, 956. Empirical Orthogonal Function and Statistical Weather Prediction, Tech. Rep. Science Report No. Statistical Forecasting Project, MIT, Cambridge U.S.A.. H. Kaiser, 958. The Varima criterion for analytic rotation in factor analysis, Psychometrika 3 (3, J.-F. Cardoso, 998. Blind signal separation: statistical principles, Proceedings of the IEEE DOI / (0, , ISSN