1. © Crown copyright 2007 Cluster analysis of mean sea level pressure fields and multidecadal variability David Fereday, Jeff Knight, Adam Scaife, Chris Folland, Andreas Philipp 13 March 2007

2. © 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

3. © 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

4. © 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

5. © Crown copyright 2007 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

6. © Crown copyright 2007 Simulated annealing  Aim to avoid local minima k-means Simulated annealing Total Variance Alternative clusters Local minimum Global minimum

7. © Crown copyright 2007 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?

8. © Crown copyright 2007  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

9. © Crown copyright 2007 Pie slices not clusters

10. © Crown copyright 2007 Cluster centroids don’t match

11. © Crown copyright 2007 Cluster stability  Best estimate of global minimum variance  Clusters stable to removal of data?

12. © Crown copyright 2007 Cluster stability method - schematic Start with full set of data Form clustersGo back to full data setRemove half of the dataForm clustersPair up clusters with originals Count the days that match up

13. © Crown copyright 2007 Stability measure  Repeat analysis 100 times  Ratio of days that match to total days  Stability change with number of clusters  Optimum number?

14. © Crown copyright 2007 JF cluster stability  JF 1900-1949 (blue) 1950-1999 (red)

15. © Crown copyright 2007 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!

16. © Crown copyright 2007 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

17. © Crown copyright 2007 Multidecadal variability in time series

18. © Crown copyright 2007 Negative summer NAO July / August – summer NAO / AMO links Positive summer NAO

19. © Crown copyright 2007 Clusters match JA EOF1 series (black)

20. © Crown copyright 2007 AMO index / cluster frequencies

21. © Crown copyright 2007 November / December – links to IPO?

22. © Crown copyright 2007 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