We present a review of the activities carried out by various members of the “Extremes and Networks” working sub-group. In particular, we discuss our initial findings on different connectivity metrics on networks and their applicability on data on extremes, and case studies on networks of precipitation extremes for southern USA and for India. A considerable part of this work is ongoing, and some challenges and features of this research will be discussed.

1. “Networks and Extremes”
sub-group of Extremes working group,
SAMSI
program on
Program on Mathematical and Statistical Methods for Climate
and the Earth System (CLIM)
Members:
Whitney Huang, Adway Mitra, Chen Chen,
Zhonglei Wang, Imme Ebert-Uphoff, Dan Cooley,
Ansu Chatterjee, …

2. The 8th International Workshop
on Climate Informatics
Topics included: any research combining climate
science with approaches from statistics, machine learning and
data mining, including position papers and work in progress.
Submissions due (abstracts / short papers): June 30, 2018.
Workshop: Sept 20-21, 2018 @ NCAR MESA Lab (Boulder, CO).
For more information: www.climateinformatics.org
Organizing committee includes:
Chairs: Dan Cooley & Eniko Szekely
PC chairs: Chen Chen & Jakob Runge
Local chair: Dorit Hammerling
Steering committee: Doug Nychka, C. Monteleoni, I. Ebert-Uphoff

3. Our goals about 9 months back
• This is more of a exploratory, “learn as you go”
working group.
• Get folks who know extremes (networks)
educated on networks (extremes).
• Review existing literature on climate
networks, find open problems.
• Find measures of relating ``vertices’’ that may
be pertinent for understanding climate
extremes, causality.

4. Networks and Graphs
• V: set of nodes
• E: set of edges; an edge connects two nodes
• Each node represents an entity of some kind
• Edges represent interactions between them
• Examples: computer networks, social networks,
biological networks, road/transport networks

5. Networks
• Social Network
• Gene Networks
• Transport networks
SOCIAL
NETWO
RK
PROTEI
N
NETWO
RK
TRANSP
ORT
NETWO
RK

6. Climate Networks
• Climate networks to visualize and analyse
spatio-temporal climatic data
• To identify regions whose climate conditions
are strongly related
• To identify teleconnections
• To identify causal relationships between
climatic events
• To identify relationships among different
climatic variables

7. Climate Networks: a bit of history
• Define edge weight W(i,j) = Pearson correlation
coefficient between the time-series on a variable of
interest at two locations
• Seminal paper by Tsonis and Roebber (2004):
Identify all pairs of points with correln > 0.5.
 “Correlation Network”Tsonis, A. A., & Roebber, P. J.
(2004). “The architecture of the climate network.” Physica A:
Statistical Mechanics and its Applications, 333, 497-504.
• Several other measures of affinity proposed. Most
are not useful/relevant for extremes.

8. Climate Network Edges: Event
Synchronization
• Define “events” for each time-series.
• E.g. annual rainfall at a location exceeding a
threshold.
• Event a in time-series Vi, event b in time-
series Vj are synchronized if |a-b|<
threshold.
• How often are events of two time-series
synchronized?
• Very relevant for extreme event analysis!

9. Climate Network Edges: Chi
Measure
• Here, X1 and X2 are ``extremes’’ at two
locations.
• We connect all pairs of non-negligible tail
dependence
• Spatial block bootstrap is used for uncertainty
quantification

10. Our main activities:
• Event synchronization network for extreme
rainfall during the Indian summer monsoons.
• Chi network for Gulf coast hurricane related
rainfall extremes.
• Life cycle of extreme events revealed by
networks.
• Resampling methods for extremes and tails.

11. Example: Indian monsoon
precipitation networks
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12. Example: Gulf coast precipitation
networks

13. Life cycle graphical model + state transition probability
13
Duration: PEN-EN
EN-LN transition: PEN-LN
Local persistence: PCPEN-CPEN
westward propagation: PEPEN-CPEN
eastward propagation: PCPEN-EPEN
Diversity in zonal propagation:
I-e/w ~Peastward – Pwestward
For both EN and LN
EN-LN asymmetry in
amplitude: I-amplitude ampEN / ampLN
duration: I-duration PEN-EN / PLN-LN
transition: I-transition PEN-LN – PLN-EN
For given time interval τ
t t+τt-τ
t t+τt-τ

14. Our targets:
• Publish at least four (4) papers out of these: a
review/overview paper, two/three case
studies, maybe one on resampling in
networks.
• The review and two case studies quite well
progressed. (Need suggestions on journals, we
have discussed a few ourselves.)
• Continue this working group.

15. Additional details….
• More details (from Whitney, Adway, Chen)
tomorrow in the “Climate Extremes”
workshop.
Thank you!