Climate Change:
What Do the Data Suggest?
Deborah Hughes Hallett
Department of Mathematics, University of Arizona
Harvard Kennedy School
Minneapolis Metrodome on December 12, 2010,
after a 17 inch snowfall (luckily at 5 am)
In 2009
http://sports.yahoo.com/nfl/blog/shutdown_corner/post/Amazing-before-and-after-pictures-of-theMetrodo?urn=nfl-295249 and
http://www.eurweb.com/wp-content/uploads/2010/12/metrodome_roof_collapse2010-medwide.jpg
At least 350,000 people stranded in Europe
London Dec 21, 2010
http://www.thedailybeast.com/blogs-and-stories/2010-12-21/heathrowairport-shutdown-whats-the-real-cause/
http://www.spiegel.de/fotostrecke/fotostrecke-62886-12.html
Europe’s airports, December 2010
Helsinki, Finland
“The last time [the airport]
was forced to close because
of the weather was in 2003.
That closure lasted for half
an hour.” Dec 20, BBC
London, UK, Dec 17
Frankfurt, Germany, Dec 21
http://www.spiegel.de/fotostrecke/fotostrecke-62886-12.html
http://www.bbc.co.uk/news/world-europe-12042213
http://www.boston.com/news/local/massachusetts/gallery/2010_2011_snowstorms
http://boston.cbslocal.com/2011/02/01/bostons-top-ten-snow-storms-of-all-time/
Jan 21, 2011
Boston, Winter 2011
Jan 27, 2011
Snow Measurements at Logan
Airport:
1. February 17-18, 2003 27.5”
2. February 6-7, 1978 27.1”
3. February 24-27, 1969 26.3”
4. March 31-April 1, 1997 25.4”
5. January 22-23, 2005 22.5”
6. January 20-21, 1978 21.4”
7. March 3-5, 1960 19.8”
8. February 16-17, 1958 19.4”
9. February 8-10, 1994 18.7”
10. January 7-8, 1996 18.2”
10. December 20-22, 1975 18.2”
10. December 26-27, 2010 18.2”
“Bundle Up, It’s Global Warming”
Judah Cohen, December 25, 2010, NY Times
http://www.nytimes.com/2010/12/26/opinion/26cohen.html?_r=1
“All of this cold was met with perfect comic
timing by the release of a World Meteorological
Organization report showing that 2010 will
probably be among the three warmest years on
record, and 2001 through 2010 the warmest
decade on record.”
On Dec 29, 2010: Climate Change Dispatch writes:
“George Ifft, the American consul at Bergen, Norway,
reported in 1922 the disappearance of icebergs….”
http://climatechangedispatch.com/home/8388-snow-blind
What Has Happened to Date:
• Temperatures rose 1-2 F during 1906-2005
• Sea level rise:
• In UK, increases of 2-4 inches since 1920
• In India, about 0.12 inches a year until 2000,
since then, about 0.2 inches annually
• Carbon dioxide, CO2, in atmosphere increased
from 316 ppm in 1959 to 386 ppm in 2008.
(CO2 is believed by many to warm the planet.)
From Tom Pfaff and http://www.epa.gov/climatechange/science/stateofknowledge.html and http://www.esrl.noaa.gov/gmd/ccgg/trends/index.html#mlo and
http://www.cbsnews.com/stories/2010/03/24/world/main6329339.shtml and http://www.decc.gov.uk/en/content/cms/statistics/climate_change/data/data.aspx
Average Global Temperature
Average Global Temperature in degrees
Celsius
Average Global Temperature over Time
15.00
14.80
14.60
14.40
14.20
14.00
13.80
13.60
13.40
13.20
1880
1900
1920
1940
1960
1980
Year
http://data.giss.nasa.gov/gistemp/tabledata/GLB.Ts.txt
2000
2020
Hockey Stick Graph
introduced in 1998 by Michael Mann
Intergovernmental Panel on Climate Change
A nearly yearlong
effort by Attorney
General Kenneth T.
Cuccinelli II of Virginia
to force the University
of Virginia to turn over
the documents of a
prominent
climatologist is
headed to the state’s
Supreme Court.
John Collins Rudolf,
New York Times March 12, 2011
http://green.blogs.nytimes.com/2
011/03/12/hearing-is-set-inclimate-fraud-case/
Sea Level Rise in UK
Aberdeen in northeast and Newlyn in southwest
150
100
50
0
Newlyn: Change in sea level
(1916-2008)
-50
-100
-150
1862 1880 1898 1916 1934 1952 1970 1988 2006
100 mm is about 4 inches
http://www.decc.gov.uk/en/content/cms/statistics/climate_change/data/data.aspx
Change in sea level since 1920 /
mm
Change in sea level since 1920 / mm
Aberdeen: Change in sea level
(1862-2008)
250
200
150
100
50
0
-50
-100
1916
1946
1976
2006
Alaska
“Future sea-level
rise is an
important issue
related to the
continuing buildup
of atmospheric
greenhouse gas
concentrations.”
Alley, Richard B., Peter U.
Clark, Philippe Huybrechts,
and Ian Joughin (2005). "IceSheet and Sea-Level
Changes". Science 310
Pictures from
www.globalwarmingart.com
Pictures from www.globalwarmingart.com
The Arctic
Sept 12, 2009
“two merchant
ships completed
an historic
shortcut over the
once ice-bound
top of the world.”
http://drake.marin.k12.ca.us/academics/rock/bears_files/polarice-caps-melting.jpg
http://www.dailymail.co.uk/news/worldnews/article-1213025/Meltingice-cap-opens-Northeast-Passage-British-ships.html#ixzz1BS647LMq
http://euobserver.com/9/26723
Carbon Dioxide Levels
Average Carbon Dioxide, Mauna Loa, Hawaii
400
CO2, parts per million (ppm)
390
380
370
360
350
340
330
320
310
300
1940
1950
1960
http://cdiac.ornl.gov/new/keel_page.html
1970
1980
Year
1990
2000
2010
2020
Modeling Carbon Dioxide Levels
Average Carbon Dioxide, Mauna Loa, Hawaii
400.00
380.00
370.00
360.00
350.00
y = 1.3x - 2282
R² = 0.97
340.00
330.00
320.00
310.00
300.00
1940
1950
1960
1970
1980
Year
http://cdiac.ornl.gov/new/keel_page.html
1990
2000
CO2, parts per million (ppm)
CO2, parts per million (ppm)
390.00
2010
2020
400.00
390.00
380.00
370.00
360.00
350.00
340.00
330.00
320.00
310.00
300.00
1940 1950
Average Carbon Dioxide,
Mauna Loa, Hawaii
y = 0.1684e0.0038x
R² = 0.98
1960
1970
1980
Year
1990
2000
2010
2020
http://www.theozonehole.com/cfc.htm
Montreal Treaty and CFCs:
Signed September 16, 1987; went into force January 1,
1989
CFCs in thousands of tons
Chlorofluorocarbon (CFC) usage since Montreal Protocol
1400
1200
1000
800
600
400
200
0
0
2
4
6
8
10
Years since 1988
12
14
16
18
http://www.theozonehole.com/cfc.htm
Montreal Treaty and CFCs:
Signed September 16, 1987; went into force January 1,
1989
CFCs in thousands of tons
Chlorofluorocarbon (CFC) usage since Montreal Protocol
1400
1200
1000
800
y = 1156.6e-0.187x
600
R² = 0.9613
400
200
0
0
2
4
6
8
10
Years since 1988
12
14
16
18
What are the Projected Growth Patterns?
• The carbon dioxide level increased by 1.3 ppm per year:
Linear (if continued)
• The carbon dioxide level increased at a continuous rate
of 0.4% per year (an annual increase of 0.4%):
Exponential (if continued)
• The CFC usage decreased at a continuous rate of 18.7%
per year (an annual decrease of 18.3%):
Exponential (if continued)
Teaching Opportunities:
Rates of Change and Projections
•
•
•
•
•
•
•
Slope
Linear and exponential growth
Change and percent change
Rate of change and percent rate of change
The number e
Continuous and annual rate of change
Extrapolation and interpolation
Question: Are the changes significant?
Richard Lindzen, Meteorologist, MIT
doesn’t believe warming will be substantial
http://www.sourcewatch.org/index.php?title=Richard_S._Lindzen
http://www.heartland.org/events/NewYork09/
"I think it's [concern about global
warming] mainly just like little
kids locking themselves in dark
closets to see how much they can
scare each other and themselves."
http://www.sourcewatch.org/index.php?title=Richard_S._Lindzen
NOVEMBER 30, 2009
“The Climate Science Isn't Settled: Confident
predictions of catastrophe are unwarranted
http://online.wsj.com/article/SB10001424052748703939404574567423917025400.html
.”
What is Predicted for the Future?
• Temperatures will rise about 3˚C (so 5-6˚F)
over the next century, perhaps accelerating
• Polar ice caps and Greenland’s ice sheet
will melt further
• Sea levels will rise about 1 meter over the
next century, leading to flooding
• Carbon dioxide in atmosphere will
increase, perhaps accelerating
From Intergovernmental Panel on Climate Change (IPCC) and
http://www.esrl.noaa.gov/gmd/ccgg/trends/ and http://data.giss.nasa.gov/gistemp/tabledata/GLB.Ts.txt
Why Are Ice Caps and Glaciers Melting?
• Average global temperature is rising
– Past decade was warmest on record
• Why is the temperature rising?
– Due to increase in greenhouse gasses in
atmosphere, especially carbon dioxide (CO2)
• What causes the increase in CO2?
– This is where the controversy lies:
• Man-made or natural?
• Systematic trend or random fluctuations?
• How much change will there be in the future?
What is the Evidence that CO2
Causes Temperature to Increase?
• Two types of evidence:
– Data shows an association
– A scientific mechanism
• Historical data shows temperature and CO2 tend
to fluctuate together—but the relationship might
not be causal
• There is a scientific mechanism explaining how an
increase in CO2 causes temperature increases
• But some still doubt that the changes are large
enough to be a problem
What is the Effect of Increasing Carbon
Dioxide in the Atmosphere?
Carbon Dioxide and Temperature
14.80
380.00
Carbon Dioxide, ppm
14.60
370.00
360.00
14.40
350.00
14.20
340.00
330.00
14.00
320.00
CO2
310.00
Temp
13.80
300.00
Average temperature, Celsius
390.00
13.60
0
10
20
30
40
50
60
70
Years since 1950
Data http://data.giss.nasa.gov/gistemp/tabledata/GLB.Ts.txt and http://cdiac.ornl.gov/new/keel_page.html
Carbon Dioxide and Temperature
Carbon Dioxide, ppm
450.00
14.80
400.00
14.60
350.00
300.00
14.40
250.00
14.20
200.00
150.00
14.00
CO2
100.00
13.80
50.00
0.00
13.60
0
10
20
30
40
50
60
70
Average temperature, Celsius
Other Ways of Looking at the Same Data
Years since 1950
CO2, ppm
Carbon Dioxide and Temperature
Data
http://data.giss.nasa.gov/gistemp/tabledata/GLB.Ts.txt
and http://cdiac.ornl.gov/new/keel_page.html
390.00
380.00
370.00
360.00
350.00
340.00
330.00
320.00
310.00
300.00
13.60
R² = 0.7962
13.80
14.00
14.20
14.40
14.60
Average temperature, Celsius
14.80
Evidence of Association
Graph of carbon dioxide (CO2) (green), temperature (blue), and dust concentration (red)
measured from the Vostok, Antarctica, ice core …(Petit et al. 1999). The close
correspondence between carbon dioxide changes and temperature changes is a
characteristic feature of the recent ice ages …… the greenhouse gas feedbacks indicated
here are believed to be responsible for most of the ice age climate change …… (Weaver et
al. 1998). Higher dust levels are characteristic of cold, dry periods.
Teaching Opportunities: Carbon Dioxide and
Average Temperature
• Graphs
– Axes and scales
• Correlation
– Range of values
– Interpretation
– Relation to causation
• Establishing causation
– Scientific mechanism
Is the Temperature Rise Significant?
Practical versus Statistical Significance
Global Temperature since 1880
Average temperature in ⁰C
15.00
14.80
14.60
14.40
14.20
14.00
13.80
13.60
y = 0.0063x + 1.7824
13.40
13.20
1860
1880
1900
1920
1940
Year
1960
1980
2000
2020
http://www.brophygen.com/
Sea levels will rise
about 1 meter over
the next century
http://www.epa.gov/climatechange/effects/co
astal/slrmaps_ne_mass.html
At Risk of Flooding
from Sea Level Rise
Maps all from Sea Level Explorer,
www.globalwarmingart.com
Nepal
Cabinet Meeting:
Everest Base Camp
Dec 4, 2009
Maldives
Cabinet Meeting:
President Nasheed
Oct 17, 2009
http://www.npr.org/templates/story/story.php?storyId=121079253
http://news.xinhuanet.com/english/200912/04/content_12588821.htm
http://www.telegraph.co.uk/news/newstopics/howaboutthat/6356036/
Maldives-government-holds-underwater-cabinet-meeting.html
Island sinks below
waves
Wed 24 March 2010
“For nearly 30 years, India and
Bangladesh have argued over
control of a tiny rock island in the
Bay of Bengal. Now rising sea
levels have resolved the dispute
for them: the island's gone.”
http://www.guardian.co.uk/worl
d/cif-green/2010/mar/24/indiabangladesh-sea-levels
http://www.independent.co.uk/n
ews/world/asia/rising-seasclaim-island-at-centre-of30year-dispute-1927002.html
http://www.cbsnews.com/stories
/2010/03/24/world/main632933
9.shtml
Is the Temperature Rise Significant?
Coefficients
Standard
Error
P-value
Lower
95%
Upper
95%
t Stat
Intercept
1.7824
0.75215
2.37
0.019
0.2943
3.2706
Year
0.0063
0.00039
16.28 4.53E-33
0.0055
0.0071
Global Temperature since 1880
Average temperature in ⁰C
15.00
14.80
14.60
14.40
14.20
14.00
13.80
13.60
y = 0.0063x + 1.7824
13.40
13.20
1850
1900
1950
Year
2000
2050
Practical
versus
Statistical
Significance
http://www.nenanaakiceclassic.com/
Nenana Ice Classic, Alaska
Putting up tripod; March 6, 2011
April 23, 2010
Is the Ice Breaking Significantly Earlier?
Standard
Coefficients
Error
t Stat
P-value
Lower 95% Upper 95%
Intercept
160.85
41.84
3.844
0.00022
77.74
243.95
Year
-0.0741
0.0213
-3.479
0.00077
-0.116
-0.032
Nanana Ice Classic, AK
35
Days since April 20
30
y = -0.0741x + 160.85
R² = 0.1163
25
20
15
10
5
0
1900
1920
1940
1960
Year
1980
2000
2020
Teaching Opportunities: Temperature and
Nenana Ice Classic
• Linear Regression
• Interpolation and extrapolation
• Interpretation of Slope
• Confidence Intervals
• P-value
• Practical versus Statistical significance
“Warming increases the risk of civil war in Africa”
M. Burke at al, Proceedings of the National Academy of Sciences, Dec 8, 2009
Panel regression of civil war incidence suggests that increases in
temperature are more strongly related to an increase in civil wars than
are changes in precipitation. (Previous studies suggested precipitation
was important because if its role in agriculture.) The next slide shows
the predicted change in civil wars till 2030.
Analysis in “Warming increases the risk of civil war in Africa”
predicts a roughly 54% increase in civil war conflicts by 2030
Civil War: Somali Piracy
17 January 2011
“Maritime piracy costs the global
economy between $7 billion and $12
billion a year”
http://af.reuters.com/article/topNews/idAFJOE70G09720110117
From NATO
March 17. 2011
At 0612 UTC / 17 MAR / a merchant
vessel was reported under attack by
1 skiff from nearby suspected pirate
mothership SINAR KUDUS.
http://www.shipping.nato.int/CounterPir/copy_of_copy_of_SOMALIAPIR
Why Somalia?
For 20 years, there’s
been no government
http://news.bbc.co.uk/2/hi/africa/8010061.stm
http://news.blogs.cnn.com/2011/01/18/report-2010-was-worst-year-yet-forpiracy-on-high-seas/
Teaching Opportunities:
Climate Data and Civil Wars
• Descriptive statistics
– Percentage vs. percentage point
– Median, interquartile range
– Box plots, error bars
• Regression tables
– Linear functions of several variables
• Significance levels
• Parameter estimates
– Standard errors
• Bootstrap simulations
How Good Is the Data We Are Using?
• How can we check?
• What biases might it have?
– Who collected it?
– Why was it collected?
– Compare with other data sets
Temperature
Global mean land-ocean temperature index, 1880 to present.
The dotted black line is the annual mean and the solid red line
is the five-year mean. Green bars show uncertainty estimates.
http://data.giss.na
sa.gov/gistemp/gr
aphs/Fig.A2.lrg.gif
US Greenhouse Gas Emissions Compared Internationally
http://cait.wri.org/figures.php?page=/USToIntlGHGMap-Regions
Dr. Pieter Tans, NOAA/ESRL (www.esrl.noaa.gov/gmd/ccgg/trends/)
Atmospheric Carbon Dioxide
Carbon dioxide data from Mauna Loa started by David Keeling in March
of 1958. The red line is the monthly mean values. The black line
represents the same, after correction for the average seasonal cycle.
Charles David
Keeling,
Scripps Institution of
Oceanography, San
Diego
At Mauna Loa, Hawaii,
data on carbon dioxide
has been collected
since the 1950s with
Dave Keeling’s
“legendary exactitude”
http://www.nytimes.com/2010/12/22/science/earth/22carbon.html
http://green.blogs.nytimes.com/2010/12/21/does-the-keeling-curvestill-need-a-keeling/
http:// e-education.psu.edu
Keeling
Oxygen
Curve
Ralph Keeling has
produced a record of
atmospheric levels of
oxygen. … that is helping
scientists understand what
to expect from climate in
the future.
http://scrippsco2.ucsd.edu/home/index.php
In his colleagues’ view, he
has established a record of
painstaking measurement
that nearly matches his
father’s legendary exactitude.
http://green.blogs.nytimes.com/2010/12/21/does-thekeeling-curve-still-need-a-keeling/#more-85421
Teaching Opportunities: Carbon Dioxide Levels
• Curve fitting and prediction:
– Linear, exponential, periodic
– Long-term behavior of functions
– Averages and smoothing
• Calculus:
– Optimization
– Least squares
Issues for Discussion
• How should we balance context and
quantitative methods?
• How do we teach students to transfer a
quantitative technique from one context to
another?
• What is the best way to get students up to
speed if they know little about the context?
• How can we include students with different
political perspectives?