1. Some aspects of climate dynamics from a complex network perspective Potsdam Institute for Climate Impact Research & Institut of Physics, Humboldt-Universität zu Berlin & King‘s College, University of Aberdeen juergen.kurths@pik-potsdam.de Jürgen Kurths http://www.pik-potsdam.de/members/kurths/

2. Johannes Martinus Burgers Lecture 2015 1895 born – 120 years 1955 joined UMD – 60 years 2015 Burgers Lect.- 12 th

3. Main Collaborators: - PIK Potsdam N. Boers, J. Donges, N. Marwan, N. Molkenthin, J. Runge, Main Collaborators: - PIK Potsdam N. Boers, J. Donges, N. Marwan, N. Molkenthin, J. Runge, V. Petoukhov, V. Stolbova V. Petoukhov, V. Stolbova - UC Sta Barbara B. Bookhagen - Uni North Carol.N. Malik, P. Mucha - INPE (Brazil)J. Marengo -UWA (Austral.)M. Small -Uni Utrecht H. Dijkstra - Acad Sc (Czech) M. Palus, J. Hlinka

4. Contents Introduction Climate networks Event synchronization Extreme floods in Central Andes Monsoon dynamics in India Conclusions

5. Complex Networks Origin in Social Networks

6. Complex Network Approach to Climate

7. Network Reconstruction from a continuous dynamic system (structure vs. functionality) New (inverse) problems arise! Is there a backbone underlying the climate system?

8. Basic Idea: Use of rich instrumentarium of complex network (graph) theory for system Earth and sustainability Hope: Deepened understanding of system Earth (with other techniques NOT possible)

9. Climate Networks Observation sites Earth system Time series Climate network Network analysis

10. Infer long-range connections – Teleconnections

11. Complex network approach to climate system

13. Artifacts and Interpretation of (Climate) Network Approach

14. Reconstructing causality from data 14 ? Artefacts due to - Common drivers - Indirect links Achievements 1.Causal algorithm to efficiently detect linear and nonlinear links (Phys. Rev. Lett. 2012) 2.Quantifying causal strength with Momentary Information Transfer (Phys. Rev. E 2012) 3.Reconstructing Walker Circulation from data (J. Climate 2014, )

15. Reconstructing causality from data Classic techniquesAdvanced method Correlation/regressionconditional independencies

16. Identifying causal gateways and mediators in complex spatio-temporal systems Step 1: Dimension reduction via VARIMAX (principal components, rotation, significance) Step 2: Causal reconstruction: identify causalities based on conditional dependencies (different time lags) Step 3: Causal interaction quantification: identify strongest paths Step 4: Hypothesis testing of causal mechanisms Nature Commun, 6, 8502 (2015)

18. Atmospheric data Reanalysis data – NCEP/NCAR (Boulder) surface pressure 1948 – 2012 Spatial resolution: 2.5º → 10,512 grid points Weekly data: each node time series of 3,339 points

19. 60 strongest VARIMAX components refer to main climatic patterns ENSO: “0” – western uplift, “1” – eastern downdraft limbs Monsoon: “33” Arabian Sea high-surface-pressure sector, “26” tropical Atlantic West African Monsoon system

20. Identification of causal pathways Effects of sea level pressure anomalies in ENSO region to pressure variability in the Arabic Sea via the Indonesian Archipelago

21. Analysis of Simulation (Model) Data Case Study: Atlantic Meridional Overturning Circulation (MOC) With Henk Dijkstra & group GRL 40, 4386 (2013)

22. How stable is the conveyor belt? Changing parameter: anomalous fresh water flux (from North Atlantic)

23. 2D meridional depth model of the Atlantic MOC (Den Toom, Dijkstra, Wubs, 2011) 32x16 (x,z) spatial grid Network reconstruction

27. Extreme Events Strong Rainfall during Monsoon Challenge: Predictability

28. New Technique: Event Synchronization

29. 29 METHOD Network Nodes: geographical locations Links: synchronization of extreme rainfall events between nodes 1. Network approach Network measures degree betweenness Average link lengths Step 2. Event synchronization – use time lags to compare individual events between two grid points Step 1. Apply a threashold to time series of each grid point to obtain event series Step 3. Construct the network by creating links between points with the highest synchronization values 2. Event synchronization Rainfall amount (mm/day) Time (days) Quiroga et.al. 2002 Malik et.al. 2011 Boers et.al. 2013

30. Extreme Rainfall Events of the South American Monsoon System TRMM 3B42 V7 daily satellite data Measured: Jan 1, 1998 – March 31, 2012 Spatial resolution: 0.25 x 0.25 Spatial coverage: Method: event synchronization Extreme event: > 99 % percentile Dec-Feb (DJF) – summer monsoon months

31. Non-symmetric Adjacency Matrix (in – out) > 0 – sink: extreme events here preceded by those at another location < 0 – source: extreme events follow at another location

32. SESA – Southeast South America ECA – Eastern Central Andes

36. > 60 % (90 % during El Nino conditions) of extreme rainfall events in Eastern Central Andes (ECA) are preceded by those in Southeastern South America (SESA) Low pressure anomaly from Rossby- wave activity propagates northwards (cold front) and low-level wind channel from Amazon Nature Commun. (2014), GRL (2014), J. Clim. (2014), Clim. Dyn. (2015)

37. Model comparison via networks TRMM data, ECHAM6 (Global circulation model), ECMWF (Re-Analysis), ETA (regional climate model) → Strong differences found ECHAM6 closest to data

38. Complex climate networks promising approach Network divergence: a general tool to analyze extreme event propagation in complex systems Explains intraseasonal variability of moisture flux from the Amazon to the subtropics: Rossby Waves Prediction of floods in the Central Andes Approach in its infancy – many open problems Summary

39. Our papers on climate networks Europhys. Lett. 87, 48007 (2009) Phys. Rev. E 81, 015101R (2010) Climate Dynamics 39, 971 (2012) PNAS 108, 20422 (2011) Phys. Rev. Lett. 106, 258701 (2012) Europhys. Lett. 97, 40009 (2012) Climate Past 8, 1765 (2012) Geophys. Res. Lett. 40, 2714 (2013) Climate Dynamics 41, 3 (2013) J. Climate 27, 720 (2014) Nature Scientific Reports 4, 4119 (2014) Climate Dynamics (2014) Geophys. Res. Lett. 41, 7397 (2014) Nature Commun. 5, 5199 (2014) Climate Dynamics 44,1567 (2015) J. Climate 28, 1031 (2015) Climate Past 11, 709 (2015) Climate Dynamics (online 2015) Nature Commun. 6, 8502 (2015)

40. Codes available Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn software package, CHAOS 25, 113101 (2015) https://github.com/pik-copan/pyunicorn Causal network identification: Python software script by J. Runge http://tocsy.pik-potsdam.de/tigramite.php