Finding Interesting ClimatePhenomena Using Source
Separation Techniques
Alexander Ilin
11.12.2006
Helsinki University of TechnologyLaboratory of Computer and Information Science
Introduction
• Exploratory analysis of large-scale climate spatio-temporal datasets
• Each instant measurement x(t) is one frame
time
Spatio-Temporal Datasets
Linear mixing models
• Modeling assumption:
xi(t) = ai1s1(t) + ai2s2(t) + ... aimsm(t)
x(t) = As(t) or X = 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)
Sources of climate variability
ai1s1(t)
aijsj(t)
aimsm(t)
++
xi(t)
=
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
WhiteningSource
estimationNonlinearfiltering
Update ofdemixing
Y = VX S = WY
Sf = filter(S)
W = orth( SfY
T )
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
Clarity-based analysis
Clarity-based analysis
Clarity-based analysis
Clarity-based analysis
Clarity-based analysis
Clarity-based analysis
Clarity-based analysis
Clarity-based analysis
Clarity-based analysis
El Niño as cleanest component
• El Niño as the component with the most prominent variability in the interannual timescale
temperature
pressure
rain
El Niño index
Derivative of El Niño index
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
Analysis of slow climate variations
Global warming component
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
Prominent variance components
Components with prominent decadal activations:
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
