Mathematical Excursions on the Data of Global Climate Destabilization

Andy LongNKU 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

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.

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."

Midwest:

Source: U.S. Global Climate Research Program

Summer: public health and quality oflife will be negatively affected by increasing heat waves, reducedair quality, and increasing insectand waterborne diseases. Increase in precipitation in winterand spring, more heavy downpours,greater evaporation in summer(more periods of both floods andwater deficits)Longer growing season: potentialfor increased crop yields, subject toIncreases in heat waves, floods,droughts, insects, and weeds presentincreasing challenges to managingcrops, livestock, and forests.Native species to face increasingthreats from rapidly changing climate

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 human-caused 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 human-caused climate change.

• We don’t need to know, in the end, whether the global climate change that is going on is human-caused or not: we just have to decide how to act. Then we ask:

• What are the consequences of our choice of action?

Global Climate Change

Action: Yes

Action:No

Human caused: Yes

We did the right thing.

Type II error

Human caused: No

Type I error: F Alarm…

We did the right 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 challengemy 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:

“Global atmospheric concentrations of CO2, CH4 and N2O have increased markedly as a result of human activities since 1750 and now far exceed pre-industrial 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]

Died 2005

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 DataDeniers 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. Personally: I recommend against buying beach-front property. Worst case scenarios are being exceeded.

2. Discover your confirmation bias, and work through it. 3. 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)

4. 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. Hannah, et. al. Conservation of Biodiversity in a Changing Climate. Conservation Biology, February 2002, 16(1), pp. 264-268.

2. IPCC (2007). Summary for Policymakers, Climate Change: Synthesis Report. Intergovernmental Panel on Climate Change (IPCC), Fourth Assessment Report

3. 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_literacy_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.

Motivation1. 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)– “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)

2. 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.