1. Fuzzy Cluster Analysis Investigating Wavebreaking in the Tropics Philippe P. Papin Team Torn Meeting – April 15, 2015 Department of Atmospheric and Environmental Sciences, University at Albany, State University of New York

2. Motivation: PV Streamer Anticyclonic Wavebreaking (AWB) in the tropics can direct high upper-level potential vorticity (PV) air deep into the tropics 0000 UTC 25 Sep 2011 These “PV streamers” can impact tropical cyclones Ophelia (2011) Uncertainty related to position and size of PV streamer can impact TC predictability. 0000 UTC 25 September 2011 200-hPa PV (shaded, PVU), theta (blue contours, K), and winds (barbs, kt) IR Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/ir.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/ir.php PV Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/pv200.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/pv200.php AWB

3. Motivation: PV Streamer 0000 UTC 25 September 2011 IR Brightness Temperature (shaded, o C), TC tracks (colored lines by intensity) Anticyclonic Wavebreaking (AWB) in the tropics can direct high upper-level potential vorticity (PV) air deep into the tropics 0000 UTC 25 Sep 2011 These “PV streamers” can impact tropical cyclones Ophelia (2011) Uncertainty related to position and size of PV streamer can impact TC predictability. AWB IR Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/ir.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/ir.php PV Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/pv200.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/pv200.php

4. Motivation: PV Streamer 1200 UTC 27 September 2011 IR Brightness Temperature (shaded, o C), TC tracks (colored lines by intensity) Anticyclonic Wavebreaking (AWB) in the tropics can direct high upper-level potential vorticity (PV) air deep into the tropics 0000 UTC 25 Sep 2011 These “PV streamers” can impact tropical cyclones Ophelia (2011) Uncertainty related to position and size of PV streamer can impact TC predictability. IR Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/ir.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/ir.php PV Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/pv200.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/pv200.php

5. Motivation: PV Streamer 0000 UTC 27 September 2011 200-hPa PV (shaded, PVU), theta (blue contours, K), and winds (barbs, kt) Anticyclonic Wavebreaking (AWB) in the tropics can direct high upper-level potential vorticity (PV) air deep into the tropics 0000 UTC 25 Sep 2011 These PV streamers can impact tropical cyclones Ophelia (2011) Uncertainty related to position and size of PV streamer can impact TC predictability. IR Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/ir.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/ir.php PV Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/pv200.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/pv200.php

6. Assessing PV streamer uncertainly Fuzzy Clustering Technique used to organize data into groups based on dataset similarities Mathematically described Bezdek (1981) Applied more recently using ensemble data in Harr et al. (2008) Uses EOFs to objectively assess varience and categorize solutions

7. Fuzzy Cluster Domain 0000 UTC 27 September 2011 200-hPa PV (shaded, PVU), theta (blue contours, K), and winds (barbs, kt) Domain: 15-35 o N / 75 o -60 o W Wanted to capture PV streamer region 144 h forecast Couldn’t use PV at 200-hPa (not enough vertical levels in TIGGE) Use 500km area average 200- hPa vorticity instead Still testing best method DT/theta? Dataset: 0.5 o ECMWF EPS Initialized 0000 UTC 21 Sep 2011 Clustering applied on 144 h forecast (0000 UTC 27 Sep 2011)

8. Fuzzy Cluster Domain 0000 UTC 27 September 2011 200-hPa area average vorticity (shaded, > 1x10 -5 s -1 ), winds (barbs, kt) Domain: 15-35 o N / 75 o -60 o W Wanted to capture PV streamer region 144 h forecast Couldn’t use PV at 200-hPa (not enough vertical levels in TIGGE) Use 500km area average 200- hPa vorticity instead Still testing best method DT/theta? Dataset: 0.5 o ECMWF EPS Initialized 0000 UTC 21 Sep 2011 Clustering applied on 144 h forecast (0000 UTC 27 Sep 2011)

9. EOFs 0000 UTC 27 September 2011 Mean 200-hPa Vorticity (shaded, > 1x10 -5 s -1 ), Variance of 200-hPa Vorticity (black contours [dotted negative], every 0.5x10 -5 s -1 ) EOF 1 Explains 41.3 % of total variance Related to E-W position difference in ensemble distribution EOF 2 Explains 19.6 % of total variance Related to magnitude + SW/NE position difference in ensemble distribution First two EOFs used to create Principle Components (PCs) that will be used for Fuzzy Clustering

10. EOFs EOF 1 Explains 41.3 % of total variance Related to E-W position difference in ensemble distribution 0000 UTC 27 September 2011 Mean 200-hPa Vorticity (shaded, > 1x10 -5 s -1 ), Variance of 200-hPa Vorticity (black contours [dotted negative], every 0.5x10 -5 s -1 ) EOF 2 Explains 19.6 % of total variance Related to magnitude + SW/NE position difference in ensemble distribution First two EOFs used to create Principle Components (PCs) that will be used for Fuzzy Clustering

11. Scatter Plot of Ensemble Solutions 3 Distinct Clusters Cluster 1 Closest match to verification Associated with less progressive upper-level cyclone in eastern US Results in further west PV-streamer in subtropical Atlantic Cluster 1 0000 UTC 27 September 2011 200-hPa area average vorticity (contour, 1x10 -5 s -1 ) East-West position differences

12. Scatter Plot of Ensemble Solutions 3 Distinct Clusters Cluster 2 Most progressive upper-level cyclone in EUS Atlantic PV streamer east of cluster 1 and smaller/weaker Cluster 2 0000 UTC 27 September 2011 200-hPa area average vorticity (contour, 1x10 -5 s -1 ) East-West position differences

13. Scatter Plot of Ensemble Solutions 3 Distinct Clusters Cluster 3 Slightly more progressive upper-level cyclone but still cutoff from mid-latitude flow Atlantic PV streamer east of cluster 1 Cluster 3 0000 UTC 27 September 2011 200-hPa area average vorticity (contour, 1x10 -5 s -1 ) East-West position differences

14. Differences between Cluster 1 and Cluster 2

15. 200 hPa Geopotential Height (contours, labeled), height difference (shaded, m) and Wind (barbs, kt) EPS analysis valid 0000 UTC 21 September 2011 R1 T1 Cluster 1 (Good) – Cluster 2 (Bad) Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/200diff.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/200diff.php

16. 200 hPa Geopotential Height (contours, labeled), height difference (shaded, m) and Wind (barbs, kt) 24 h EPS forecast valid 0000 UTC 22 September 2011 R1 T1 Cluster 1 (Good) – Cluster 2 (Bad) Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/200diff.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/200diff.php

17. 200 hPa Geopotential Height (contours, labeled), height difference (shaded, m) and Wind (barbs, kt) 48 h EPS forecast valid 0000 UTC 23 September 2011 R1 T1 R2 T2 AWB1 Cluster 1 (Good) – Cluster 2 (Bad) Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/200diff.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/200diff.php

18. 200 hPa Geopotential Height (contours, labeled), height difference (shaded, m) and Wind (barbs, kt) 72 h EPS forecast valid 0000 UTC 24 September 2011 T1 R2 AWB2 T2 Cluster 1 (Good) – Cluster 2 (Bad) Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/200diff.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/200diff.php

19. Cluster 1 (Good) – Cluster 2 (Bad) 200 hPa Geopotential Height (contours, labeled), height difference (shaded, m) and Wind (barbs, kt) 96 h EPS forecast valid 0000 UTC 25 September 2011 R2 T2 Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/200diff.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/200diff.php

20. 200 hPa Geopotential Height (contours, labeled), height difference (shaded, m) and Wind (barbs, kt) 120 h EPS forecast valid 0000 UTC 26 September 2011 Cluster 1 (Good) – Cluster 2 (Bad) Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/200diff.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/200diff.php

21. 200 hPa Geopotential Height (contours, labeled), height difference (shaded, m) and Wind (barbs, kt) 144 h EPS forecast valid 0000 UTC 27 September 2011 Cluster 1 (Good) – Cluster 2 (Bad) Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/200diff.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/200diff.php

22. EPS analysis valid 0000 UTC 21 September 2011 Cluster 1 (Good) – Cluster 2 (Bad) L1 R1 850-hPa Geopotential Height (color contours), Theta-E difference (shaded, K) and Wind (barbs, kt) Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/850diff.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/850diff.php

23. 24 h EPS forecast valid 0000 UTC 22 September 2011 Cluster 1 (Good) – Cluster 2 (Bad) L1 R1 850-hPa Geopotential Height (color contours), Theta-E difference (shaded, K) and Wind (barbs, kt) Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/850diff.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/850diff.php

24. 48 h EPS forecast valid 0000 UTC 23 September 2011 Cluster 1 (Good) – Cluster 2 (Bad) L1 R1 850-hPa Geopotential Height (color contours), Theta-E difference (shaded, K) and Wind (barbs, kt) Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/850diff.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/850diff.php

25. 72 h EPS forecast valid 0000 UTC 24 September 2011 Cluster 1 (Good) – Cluster 2 (Bad) L1 R1 850-hPa Geopotential Height (color contours), Theta-E difference (shaded, K) and Wind (barbs, kt) Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/850diff.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/850diff.php

26. 96 h EPS forecast valid 0000 UTC 25 September 2011 Cluster 1 (Good) – Cluster 2 (Bad) R1 850-hPa Geopotential Height (color contours), Theta-E difference (shaded, K) and Wind (barbs, kt) Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/850diff.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/850diff.php

27. 850-hPa Geopotential Height (color contours), Theta-E difference (shaded, K) and Wind (barbs, kt) 120 h EPS forecast valid 0000 UTC 26 September 2011 Cluster 1 (Good) – Cluster 2 (Bad) Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/850diff.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/850diff.php

28. 144 h EPS forecast valid 0000 UTC 27 September 2011 Cluster 1 (Good) – Cluster 2 (Bad) 850-hPa Geopotential Height (color contours), Theta-E difference (shaded, K) and Wind (barbs, kt) Loop: http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/850diff.php http://www.atmos.albany.edu/student/ppapin/lb13_img/conferences/netw_2015/850diff.php

29. Final Thoughts AWB on subtropical waveguide induced by AWB on polar waveguide Cutoff upper-Level cyclone less progressive in Eastern US More ridge growth off EUS coastline Subsequent AWB on subtropical waveguide is displaced west PV streamer also advected further westward in more westward AWB More anticyclonic flow over location where TC Ophelia dissipated Favorable Environment for redevelopment? Still needs to be shown and proven, but it appears to be a step in the right direction.