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