This document summarizes a final report on analyzing climate data from a network perspective. The report analyzes climate time series data from different locations as nodes in a network, connected by correlations between their temperature and precipitation values. Key findings include that the current set of climate indices may not be enough to represent the global climate given Earth's size and complexity, and that certain ocean and land regions show stronger connections in the network and could be candidates for additional climate indices.

1. KAIST Research Internship
Complex System and Statistical
Physics Lab.
Ridho M. Akbar
Final-Term Report

2. Prof. Hawoong Jeong
Byung Hwee Lee
Dr. Daniel Kim Hyungjoon Soh Hyewon Kim
Kihong Chung Jinhyuk Yun Sangyun Lee

3. “Spatial Analysis of
Climate Data from
Network Perspective”

4. Background
Monitoring
global
climate is a
challenging
work
We cannot
measure
everything in
everywhere
We cannot
measure
everything
in every
time
Accuracy
has always
been the
issue
It is
expensive
yet
important

5. Climate Indices
Climate time series records in certain places that
represent global climate state
Are those enough?
Places Climate Feature
Pacific Ocean • Surface Air Temperature
• Water Precipitation
• Sea Level Pressure
• Humidity
NAO (North Atlantic
Oscillation) - Atlantic
• Surface Air Temperature
• Sea Level Pressure
Greenland, Antarctic • Water precipitation
• Sea Level Pressure
• Sea Water SalinityTaken from NOAA Climate Indices,
http://www.esrl.noaa.gov/psd/data/climateindices/list/

6. Data Source (NCEP/NCAR
Reanalysis Project)
Temporal Coverage
 4-times daily, daily, and monthly
values for 1948/01/01 to
2015/09/30
Spatial Coverage
 2.5 deg x 2.5 deg latitude
longitude global grid (143 x 73)
 90N – 90S, 0E – 357.5E
 1.0 deg ~ 100km
Data Features
Air temperature
Water precipitation
Sea level pressure
Relative Humidity
Plot example of Surface Air Temperature Data (averaged from
1981 – 2010)

7. Data-Preprocessing
1. Normalizing the data (𝝁 = 𝟎, 𝝈 𝟐
= 𝟏)
𝒂 𝒎,𝒚
∗
=
𝒂 𝒎,𝒚 − 𝝁 𝒎
𝝈 𝒎
𝝁 𝒎 =
𝟏
𝒀
𝒚=𝟏𝟗𝟒𝟖
𝟐𝟎𝟏𝟒
𝒂 𝒎,𝒚 , 𝝈 𝒎
𝟐
=
𝟏
𝒀 − 𝟏
𝒚=𝟏𝟗𝟒𝟖
𝟐𝟎𝟏𝟒
𝒂 𝒎,𝒚 − 𝝁 𝒎
𝟐
- Karsten Steinhaeuser et.al (2011)-
Removing
autocorrelation
𝒎 = 𝐦𝐨𝐧𝐭𝒉
𝒚 = 𝐲𝐞𝐚𝐫
𝝁 = 𝐦𝐞𝐚𝐧
𝝈 = 𝐬𝐭𝐝. 𝐝𝐞𝐯𝐢𝐚𝐭𝐢𝐨𝐧

8. Pre-processing Result (south pole data example)
Raw data After Normalization

9. Constructing the network
Pearson Correlation
Coefficient
Month Temp
Jan-1948 X1
Feb-1948 X2
Mar-1948 X3
…. ….
…. ….
…. ….
…. ….
Dec-2014 X803
Month Temp
Jan-1948 Y1
Feb-1948 Y2
Mar-1948 Y3
…. ….
…. ….
…. ….
…. ….
Dec-2014 Y803
- Karsten Steinhaeuser et.al (2011)-
Weighted
Network

10. The Network
Number of nodes = 1032
Number of links = 1032*1031/2 = 531996
Distance between two nodes = 7.5 degree ~ 700 – 900 km

11. RESULT

12. Length-Weight Cross-Plot
Y-axis → Weight of the link = Pearson Correlation
Coefficient
X-axis → Length of the link = distance between two
points connected by the link (Haversin Formula)
hsin
𝑑
𝑟
= ℎ𝑠𝑖𝑛 ∆𝜙 + cos 𝜙1 cos(𝜙2) hsin(∆𝜆)
ℎ𝑠𝑖𝑛 𝜃 =
1 − cos 𝜃
2

13. Threshold
limit = 0.8
Threshold
limit = 0.6
Threshold
limit = 0.3
Threshold
limit = 0.5
“High threshold limit means high global effect and lower threshold limit means
lower global effect”
Giant Component Size
Measuring the number of nodes that connected to the giant cluster if we remove the
link with weight lower than a threshold value.
Threshold = 0.2
Coverage = 1.0
Threshold = 0.6
Coverage = 0.9
Threshold = 0.9
Coverage = 0.02
Example: Temperature Network

14. Climate Indices We Have Now is Not Enough
Earth circumference is about 40.075km
Earth Surface Area is about 510 𝐤𝐦 𝟐
Climate is very complex system

15. “High strength region means highly affects the climate system and lower strength region
means lower effect to climate system”
Node Strength Mapping
Simply compute total weight of links that connected to a node
0.1
0.2
0.7
0.3
0.4
Example
The strength of this yellow node is;
𝟎. 𝟏 + 𝟎. 𝟒 + 𝟎. 𝟑 + 𝟎. 𝟕 + 𝟎. 𝟐 = 𝟏. 𝟕

16. Places Climate Feature
Caribbean Sea • Surface Air Temperature
• Sea Level Pressure
• Precipitation Water
India Ocean • Surface Air Temperature
• Precipitation water
South Atlantic • Surface Air Temperature
• Sea Level Pressure
• Relative Humidity
North Atlantic • Relative Humidity
Central-South
Africa
• Precipitation Water
Places Climate Feature
West coast of
North America
• Surface Air Temperature
• Precipitation water
Brazil • Precipitation water
Southern Ocean • Precipitation water
• Sea Level Pressure
East Asia Sea • Precipitation water
• Sea Level Pressure
Indo-Australia • Sea Level Pressure
• Precipitation Water
POSSIBILITIES OF PLACES
FOR CLIMATE INDICES CADIDATES