Mathematical Excursions on the Data
of Global Climate Destabilization
Andy Long
NKU Department of Mathematics and Statistics
Outline of this talk:
1. Motivation: Why does it matter?
2. What’s the science?
3. What’s the non-science?
4. Keeling CO2 Data
5. A peek at an Ice Core (Temp and CO2)
6. Conclusions
Motivation
Climatologists are gloomy:
“Warming of the climate system is unequivocal, as is now evident from
observations of increases in global average air and ocean temperatures,
widespread melting of snow and ice and rising global average sea level.”
[IPCC Fourth Assessment Report: Climate Change 2007]. The
Copenhagen Climate Science Congress, attended by over 2,000
scientists, concluded: "the worst-case IPCC scenario trajectories (or even
worse) are being realized."
Motivation
Climatologists are gloomy:
“Warming of the climate system is unequivocal, as is now evident from
observations of increases in global average air and ocean temperatures,
widespread melting of snow and ice and rising global average sea level.”
[IPCC Fourth Assessment Report: Climate Change 2007]. The
Copenhagen Climate Science Congress, attended by over 2,000
scientists, concluded: "the worst-case IPCC scenario trajectories (or even
worse) are being realized."
About as gloomy as the biologists:
“Dozens of studies are documenting changes in phenology,
species ranges, and ecology due to climate change. Butterflies in
North America have shifted northward in range, trees are blooming
earlier in eastern Europe, and tropical bird species are shifting their
range upslope.” [Hannah, et. al. Conservation of Biodiversity in a
Changing Climate.] Projections: 1 million species lost by 2050.
Midwest:
Summer: public health and quality of
life will be negatively affected by
increasing heat waves, reduced
air quality, and increasing insect
and waterborne diseases.
Increase in precipitation in winter
and spring, more heavy downpours,
greater evaporation in summer
(more periods of both floods and
water deficits)
Longer growing season: potential
for increased crop yields, subject to
Increases in heat waves, floods,
droughts, insects, and weeds present
increasing challenges to managing
crops, livestock, and forests.
Native species to face increasing
threats from rapidly changing climate
Source: U.S. Global Climate Research Program
What is (good) science?
1. Science is not about proof, it’s about theories:
Scientists propose theories (which are hypotheses
on steroids, that have generally passed many
tests).
A theory is only a scientific theory if it is falsifiable.
Theories must make testable predictions: if a theory
makes a prediction that is not borne out, then the
theory is false (broken). If we can’t perform any
such tests, then the theory has no power: it’s just
an act of faith. Faith is good, it’s just not science.
What is good science? (cont.)
2. Science is without bias (well, it’s supposed to be, at any
rate!):
– There’s obvious bias (agenda trumps facts); when the
coal company weighs in on GCD, why am I skeptical?
– There’s more subtle bias:
• A drug researcher owns stock in company
• Al Gore reputedly has a stake in carbon trading companies
(just “putting his money where his mouth is?” – what if others
are putting their money there because of his mouth, and he’s
reaping the financial rewards? Might he trump up the
science….)
– Then there’s Confirmation Bias
What is good science? (cont.)
2. Science is without bias:
– obvious bias (agenda trumps facts)
– subtle bias: promoting something in your self-interest
– Confirmation Bias — the notion that we overlook what
we don't agree with, and accentuate what we want to
hear: we start with belief and then look for evidence.
“The only way to have real success in science… is to
describe the evidence very carefully without regard to
the way you feel it should be. If you have a theory,
you must try to explain what’s good about it and
what’s bad about it equally. In science you learn a
kind of standard integrity and honesty.”
Richard Feynman, Nobel Laureate
What is non-science?
• Denialism:
what happens “when an entire segment of
society, often struggling with the trauma of
change, turns away from reality in favor of a
more comfortable lie.” [Michael Specter, Firing
Bullets of Data at Cozy Anti-Science]
• We don't know our science well enough to
insult it properly.
• Non-scientists demand proof.
What is non-science?
• Denialism
• We Americans don't know our science, and neither do our
“leaders”
– Sen. Jim DeMint (R-S.C.):“it’s going to keep snowing in D.C.
until Al Gore cries ‘uncle.’”
– Sen. Mitch McConnell (R-KY) quipped, “Where’s Al Gore now?”
– Sean Hannity: “It’s the most severe winter storm in years, which
would seem to contradict Al Gore’s hysterical global warming
theories.”
– Former House Speaker Newt Gingrich: “Historic snowstorm in
Washington — third this year — where is Al Gore to explain it
snows this heavily as a sign global warming is imminent.”
– 28% science literate – Science News, 3/13/2010
• Non-scientists demand proof.
What is non-science?
• Denialism
• We don't know our science.
• Non-scientists demand proof, as though science is
mathematics:
– Deniers don’t understand that there's no scientific
consensus on anything. Complete consensus is
the death of a theory.
– There's no consensus on gravity — scientists are
looking for evidence that disproves the inverse square
law of gravity (i.e. they’re trying to falsify it!)
– The absence of complete consensus on humancaused global warming does not pardon us from the
need to act – even if we choose not to act.
What leads us so far astray?
Scientific Opinion versus Public Opinion on Climate Change: Pew Center.
Scientists were selected from the American Assoc. for the Advancement of Science
Blowing Smoke with GCD?
January 4, 1954:
A Frank Statement to
Cigarette Smokers
March 10, 2010:
Lawmakers from Coal States
Seek to Delay Emission Limits
(New York Times)
The real question: Do we act?
• Null, H0: no humancaused climate change.
• We don’t need to know, in
the end, whether the
global climate change
that is going on is humancaused or not: we just
have to decide how to
act. Then we ask:
• What are the
consequences of our
choice of action?
Global Action:
Climate Yes
Change
Action:
No
Human We did Type II
caused: the right error
Yes
thing.
Human Type I We did
caused: error: F the right
No
Alarm… thing.
Type I Error Consequences
Type II Error Consequences
By James Hansen, widely respected and
widely hated climate scientist
What’s my plan? Act.
I’m going to challenge
my confirmation bias:
• Study the data
myself, and
• uncover the claims
of climate deniers,
and address them:
either confirm them,
or debunk them, but
deal with them.
Charles Keeling:
Died 2005
“Global atmospheric concentrations of CO2, CH4 and N2O have increased
markedly as a result of human activities since 1750 and now far exceed preindustrial values determined from ice cores spanning many thousands of
years (Figure 2.3). The atmospheric concentrations of CO2 and CH4 in 2005
exceed by far the natural range over the last 650,000 years. Global
increases in CO2 concentrations are due primarily to fossil fuel use, with
land-use change providing another significant but smaller contribution.”
[IPCC Fourth Assessment Report: Climate Change 2007]
Modeling Keeling’s Data
• Periodic component
(Earth’s forests breathing!)
• Trend: appears super-linear
• Attempt a (non-linear) model
of the form
(The non-linearity is in the computation of the period, T.)
Estimate: period = 365.070 (.088) – what to do?
Modeling Keeling’s Data (2)
Replace with a model using linear regression:
Data, Model, and Residuals
Vostok Ice Core Data
Deniers say: Doesn’t CO2 lag Temperature?
Correlation is not Causation:
Was Al Gore asserting in “An Inconvenient Truth” that because CO2 and
Temperature are correlated, and because CO2 is rising, then
Temperature will rise?
Does CO2 lag Temperature?
At long time scales, yes….
Temporal Decomposition of
Variance: Temp and CO2
We’ve found Milankovitch Cycles:
The Big Weather Picture!
Conclusions:
1.
2.
3.
4.
Personally: I recommend against buying beach-front
property. Worst case scenarios are being exceeded.
Discover your confirmation bias, and work through it.
Our model predicts that CO2 levels will reach
dangerous levels by 2034: levels implicated in the
melting of all terrestrial ice, which would raise world
sea levels by many, many meters…. (not just ½)
Temperature and CO2 do show a long-standing
correlation; causation is not well understood. CO2
does appear to lag Temperature on very long time
scales (which aren’t appropriate for human-caused
global climate destabilization). CO2 appears much
more regular than Temperature in the variograms.
Resources
1.
2.
3.
Hannah, et. al. Conservation of Biodiversity in a Changing
Climate. Conservation Biology, February 2002, 16(1), pp. 264268.
IPCC (2007). Summary for Policymakers, Climate Change:
Synthesis Report. Intergovernmental Panel on Climate Change
(IPCC), Fourth Assessment Report
Science literacy: U.S. college courses really count. Science
News, 3/13/2010 (accessed via the web at
http://www.sciencenews.org/view/generic/id/56517/title/Science_lit
eracy_U.S._college_courses_really_count)
Why “Global Climate Destabilization”?
“Global Warming” is too limited. While global warming
is happening, it’s only one piece. The climate, more
generally, is the issue:
“Biodiversity will also be confronted with changing
rainfall patterns, declining water balances, increased
extreme climate events, and changes in oscillations
such as El Nino.”
[Hannah, et. al, Conservation of Biodiversity in a
Changing Climate]
Welcome!
While it is possible to make a strictly scientific study of the elements of global climate
change, the monstrous economic impacts have meant that the issue has become a
political and social football. There are really just two major salient questions:
–
–
Is the Earth warming?
Is the warming human-related?
The next questions only come into play provided the two important questions are
answered in the affirmative:
–
–
What can humans do about global climate change?
What shall humans do about global climate change?
In fact, it's the difference between the two, represented by our actions, that is under our
control. Doing nothing is a choice, too. Here’s an exercise in logic:
–
–
–
If the Earth's temperature is not changing, then we don't need to worry about climate change;
If the warming is not human-related, then humans should just buckle in for the ride (of figure
out how to either live with it, or how to affect the weather — e.g. seeding clouds);
If the warming is human-caused, then we should explore the best ways to deal with it.
Motivation
1.
Personal Background
–
–
A background based on “Stewardship of the Earth”.
News Flash (both of these at the National Joint Math Meetings: Copper and the Ogallala aquifer
are going away… soon!
I’m a conspiracy Theorist at heart. I don’t trust those in power to do the right thing:
–
•
Something old: "A Frank Statements to Cigarette Smokers" (January 4, 1954)
–
–
•
•
•
2.
“RECENT REPORTS on experiments with mice have given wide publicity to a theory
that cigarette smoking is in some way linked with lung cancer in human beings.”
Distinguished authorities point out:
»
That medical research of recent years indicates many possible causes of lung cancer.
»
That there is no agreement among the authorities regarding what the cause is.
»
That there is no proof that cigarette smoking is one of the causes.
»
That statistics purporting to link cigarette smoking with the disease could apply with equal force to any one of many
other aspects of modern life. Indeed the validity of the statistics themselves is questioned by numerous scientists.
Lawmakers from Coal States Seek to Delay Emission Limits (3/5/2010)
A Face-Off on the Safety of a Drug for Diabetes (2/22/2010)
Hidden Ingredient: The Sweetener (2/24/2010)
40 years of bad news is my non-parametric statistical test that we’re in trouble. But
maybe I’m just gloomy.
- Example of a non-parametric test: the other day, on NPR, I heard a report that “methane…” (my ears
perk up) “is seaping out from under the arctic ocean’s…” (I knew that!) “…faster than researchers
had anticipated….” (it’s in the wrong direction again!)
What is non-science?
Denialism: what happens “when an entire segment of society, often struggling with the
trauma of change, turns away from reality in favor of a more comfortable lie.” [Michael
Specter, Firing Bullets of Data at Cozy Anti-Science]
We Americans don't know our science (28% science literate – Science News,
3/13/2010), and neither do our “leaders”:
– Sen. Jim DeMint (R-S.C.):“it’s going to keep snowing in D.C. until Al Gore cries
‘uncle.’”
– Sen. Mitch McConnell quipped, “Where’s Al Gore now?”
– Sean Hannity: “It’s the most severe winter storm in years, which would seem to
contradict Al Gore’s hysterical global warming theories.”
– Former House Speaker Newt Gingrich: “Historic snowstorm in Washington —
third this year — where is Al Gore to explain it snows this heavily as a sign global
warming is imminent.”
Non-scientists demand proof, as though science is mathematics:
– Deniers don’t understand that there's no consensus on anything.
– There's no consensus on gravity — scientists are looking for evidence that
disproves the inverse square law of gravity (i.e. they’re trying to falsify it!)
– The absence of complete consensus on human-caused global warming does not
pardon us from the need to act.