Cluster analysis of mean sea level pressure fields and
multidecadal variability
David Fereday, Jeff Knight, Adam Scaife, Chris Folland, Andreas Philipp
13 March 2007
© Crown copyright 2007
Introduction
Use cluster analysis to examine circulation
variability
Are genuine clusters present in MSLP data?
Stability of different numbers of clusters
Multidecadal variability and links with SST
© Crown copyright 2007
Data
EMSLP dataset – daily mean MSLP fields
1850-2003
NAE region – 25°N-70°N, 70°W-50°E
5 degree x 5 degree resolution
© Crown copyright 2007
Methods
Divide data into two month seasons
Seasonally varying climatology removed
Apply cluster analysis to fields in each season
separately
Aim is to characterise daily variability – no low
pass filtering applied
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Cluster algorithm
Variant of k-means
Specify number of clusters beforehand
Each field belongs to one cluster
Random initial allocation
Minimise within cluster variance by exchanging
fields
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Simulated annealing
Aim to avoid local minima
Total Variance
Simulated
annealing
k-means
Local minimum
Alternative clusters
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Global
minimum
Are there clusters in MSLP fields?
Algorithm produces clusters whether any
present or not
If clusters are present, there must be a fixed
number of them
Number of clusters is specified beforehand –
how is this number decided?
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Local minima
Try to find local minima of total within cluster
variance
For all but small numbers of clusters, many
different alternatives
Local minima
Global minimum
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Pie slices not clusters
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Cluster stability
Best estimate of global minimum variance
Clusters stable to removal of data?
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Cluster stability method - schematic
Go back
Remove
Form
Pair
Count
up
clusters
the
clusters
to
half
days
fullof
data
that
the
with
set
match
originals
up
Start
with
full
set
of data
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Stability measure
Repeat analysis 100 times
Ratio of days that match to total days
Stability change with number of clusters
Optimum number?
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JF cluster stability
JF 1900-1949 (blue) 1950-1999 (red)
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Cluster conclusions
Many local minima - no strong clustering
Stability reduced as clusters increase
No optimum number of clusters
Choice of number of clusters is subjective
Clusters are nevertheless useful!
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Multidecadal variability
10 clusters per season
Circulation variability - frequency time series
Variability on many different timescales
Low pass filter (25 year half power)
SST links via regression analysis
HadISST from month before MSLP season
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Multidecadal variability in time series
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July / August – summer NAO / AMO links
Positive summer NAO
Negative summer NAO
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November / December – links to IPO?
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Conclusions
No genuine clusters, but clusters still useful
Clusters relate to EOF time series
Reproduce known relationships with SST
Many results – hint at new SST links
© Crown copyright 2007