Finding Interesting Climate Phenomena Using Source Separation Techniques

1. Helsinki University of Technology Laboratory of Computer and Information Science Finding Interesting ClimatePhenomena Using Source Separation Techniques Alexander Ilin 11.12.2006

2. Introduction • Exploratory analysis of large-scale climate spatio-temporal datasets • Each instant measurement x(t) is one frame time

3. Spatio-Temporal Datasets

4. Linear mixing models • Modeling assumption: xi(t) = ai1s1(t) + ai2s2(t) + ... aimsm(t) x(t) = As(t) orX = AS • Source separation: estimate sources sj(t) and mixing coefficients aij from observations xi(t) • Extra assumptions should be used: • localized effect in space or in time (factor analysis) • independence of sources (ICA) • some known/tested properties of interest (DSS)

5. ai1s1(t) aijsj(t) aimsm(t) + + Sources of climate variability xi(t) =

6. Denoising Source Separation • DSS unifies different separation approaches under one algorithmic framework • Components are found by linear transformation s(t) = Wx(t) or S = WX • Filtering retains only desired properties in S, these properties are therefore maximized Whitening Nonlinear filtering Update of demixing Source estimation Y = VX S = WY Sf=filter(S) W =orth( SfYT )

7. Study 1: Clarity-based analysis • The sources are expected to have prominent (clean) variability in a specific timescale • Clarity of a signal s is measured by c = var(sf )/ var(s), sf = filter(s) • Separation: use linear filtering which retains frequencies within the band of interest

8. Clarity-based analysis

9. Clarity-based analysis

10. Clarity-based analysis

11. Clarity-based analysis

12. Clarity-based analysis

13. Clarity-based analysis

14. Clarity-based analysis

15. Clarity-based analysis

16. Clarity-based analysis

17. El Niño as cleanest component • El Niño as the component with the most prominent variability in the interannual timescale temperature El Niño index pressure Derivative of El Niño index rain

18. Study 2: Spectral separation • Clarity-based analysis requires knowledge of the interesting variations • More general approach: extract sources with prominent but distinct spectral structures • Separation: Filtering changes the spectral contents of components, individual filters used • Filters are adapted to emphasize emerging spectral characteristics of the sources

19. Analysis of slow climate variations

20. Global warming component

21. Study 3: Variance phenomena • Structured variance analysis: sources with prominent activation structures in a specific timescale • Temperature anomalies in Helsinki: • The goal: to find components with prominent activation patterns in other timescales

22. Prominent variance components Components with prominent decadal activations:

23. Conclusions • Source separation approach allows for meaningful representation of complex climate variability • Fast algorithms are applicable because they scale well for high-dimensional data • Significant climate phenomena can be found by suitably designed separation techniques