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Cluster analysis of mean sea level pressure fields and multidecadal variability

David Fereday, Jeff Knight, Adam Scaife, Chris Folland, Andreas Philipp 13 March 2007

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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

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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

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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

k-meansSimulated annealing

Total Variance

Alternative clusters

Local minimum

Globalminimum

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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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Try to find local minima of total within cluster variance

For all but small numbers of clusters, many different alternatives

Local minima

Global minimum

Local minima

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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

Start with full set of dataForm clusters Go back to full data set Remove half of the data Form clusters Pair up clusters with originals Count the days that match up

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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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Negative summer NAO

July / August – summer NAO / AMO links

Positive 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