Information presented during the CLIM Undergraduate Workshop

1. What do climate statisticians do?
SAMSI
October 23, 2017
Michael F. Wehner
Lawrence Berkeley National Laboratory
mfwehner@lbl.gov

2. US DOE Policy 411.2A
SUBJECT: SCIENTIFIC INTEGRITY
When expressing opinions on policy matters to the public and media,
research personnel must make it clear when they are expressing their
personal views, rather than those of the Department, the U.S.
Government, or their respective institutions. Public representation of
Government or DOE positions or policies must be cleared through
their program management to include DOE headquarters.

3. Climate is what you expect
weather is what you get!
Ed Lorenz
or perhaps Robert Heinlein…

4. The Earth

5. The atmosphere is very thin.

6. The “greenhouse effect”
Credit: Koshland Science Museum

7. We have known about the greenhouse effect for more than 150 years.
It is steam engine science.
Tyndal measured the radiative absorbtive properties of many gases.
“The atmosphere admits of the entrance of the
solar heat, but checks its exit; and the result is a
tendency to accumulate heat at the surface of the
planet.”
-- John Tyndall, 1859
This is not rocket science
O2, N2 H2O, CO2,N2O CH4
Low ,Medium High

8. “Doubling of CO2 would raise surface
temperature by 5-6 °C, or 9-11 °F, above
pre-industrial temperatures.”
-- Svante Arrhenius,1896
Quantum mechanics
We now call the climate system’s response to doubling CO2
“The equilibrium climate sensitivity”.
1896: 5-6 oC (Arrhenius)
2013: 2-6 oC (Intergovernmental Panel on Climate Change)

9. Humans are changing the atmospheric composition
400ppm: CO2 in the atmosphere higher than in the last 600,000 years.
Charles Keeling: Mauna Loa
Ocean is becoming more acidic

10. No fooling:
Warming is “unequivocal”
Global mean surface air
temperature is rapidly increasing.
Is the human change to the
composition to the atmosphere
responsible?

11. Not all pollutants have the same “forcing” effect.
ABILITY TO
ABSORB
RADIATION
THE AMOUNT
EMITTED MATTERS
Black Carbon
(soot)
Carbon
Dioxide
Nitrous
Oxide
Methane
Credit: I. Ocko, EDF
Greenhouse gases
absorb sunlight energy
Some particles absorb
sunlight energy
Some particles reflect
sunlight energy
0
Sulfate Aerosols
(Acid Rain)

12. Detection and Attribution (D&A for short):
• Detection: Identify statistically significant trends in (usually) sparse
observational records.
– In situ data. Sometimes long temporal records, never enough spatial
coverage
– Satellite data: Complete spatial coverage, but limited in time. Records
start in 1979 or later.
• Attribution: Quantify the human contribution, if any, to observed climate
changes.
– Separate forced changes (signals) from natural variations (noise)
– Quantify the effects of different forcing agents.
– Natural: Solar variations, volcanoes
– Anthropogenic:
• Well mixed greenhouse gases (CO2,CH4, NO2, etc)
• Sulfate and other short lived aerosols
• Ozone
• Land use changes.
What do climate statisticians do?

13. • Observe a trend.
• Do an experiment.
• Run some climate models with and without human forcing agents
• Use simple linear regression statistical models to describe the observations
X=b*Y+x
• X=observations
• Y=climate model
• x=noise
• b=scaling factor
• Does the uncertainty range of b include zero?
• If yes, then we do not attribute the observed change to human activities.
• If no, then we do attribute the observed change to human activities!
Detection and attribution

14. “It is extremely likely that more than half of the global mean temperature
increase since 1951 was caused by human influence on climate (high
confidence). The likely contributions of natural forcing and internal variability
to global temperature change over that period are minor (high confidence).”
--Chapter 3, Key Finding #1
The most definitive attribution statement in a US NCA

15. “The likely range of the human contribution to the global mean temperature
increase over the period 1951–2010 is 1.1° to 1.4°F (0.6° to 0.8°C), and the
central estimate of the observed warming of 1.2°F (0.65°C) lies within this
range (high confidence). This translates to a likely human contribution of
93%–123% of the observed 1951–2010 change.”
The most definitive attribution statement in a US NCA

16. Extreme weather
• The tail of the distribution of all weather.
• But…
What else do climate statisticians do?

17. Categorizing an event as “extreme” is a somewhat arbitrary procedure.
• What is extreme at one space and time may be typical at another.
• Extremes are at the tails of the distribution. How is “tail” defined?
• Does extreme mean “rare” or simply high impact?
What else do climate statisticians do?
• Statisticians have given us an “asymptotic”
theory to describe the tails of distributions.
• The distribution of extremes.
• The distribution of the tail.
• Huh?
• Peaks over a high threshold.
• Block maxima.

18. • Extract the annual maximum temperature from the entire daily time series.
• This subset is a “block maxima” sample.
• Under the right conditions, the underlying distribution may be described by a
three parameter function known as the “Generalized Extreme Value” (GEV)
distribution.
• The conditions:
– Stationary.
– In the “asymptotic regime”
– i.i.d.
– Other things I don’t worry about.
Annual maximum daily temperatures
F(x) =
e
- 1-k(x-x )/a[ ]1/k
k ¹ 0
e-e-(x-x )/a
k = 0
ì
í
ïï
î
ï
ï
x = location
a = scale
k = shape

19. If shape parameter is negative*, the distribution is bounded.
If shape parameter is positive*, the distribution is unbounded.
Properties of the GEV
By R D Gill - Created by R D Gill, 4 January 2013, using R script, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=45005894
* Beware sign
conventions on the sign
of the shape parameter
GEV Probability density function (pdf)

20. GEV Return Value
If you can fit the GEV to the extreme
sample, you can then calculate useful
physically useful properties
The return value of a random variable, XT
is that value which is exceeded, on
average, once in a period of time, T





=

=
0))/11ln(ln(
0/)}/11ln({1[
kT
kkT
X
k
T
x
x
1 10 100
Return Time (years)
296
298
300
302
304
306
308
310
312
314
316
ReturnValue(kelvins)
1 10 100

21. Attributable change in temperature return values
fvCAM5.1

22. Projected change in 2K stabilized climate

23. Uncertainty quantification.
• There are many sources of uncertainty.
1. Different models have different sensitivities to external forcings.
– We have a rather broad range for an estimate of the true “climate sensitivity”.
2. We don’t know how much more CO2 society will permit to be emitted.
3. We don’t know the precise state of the climate system due to observational
constraints.
– The climate system is chaotic.
Another important thing that climate statisticians do:
Hawkins and Sutton BAMS

24. It is firmly established that global warming is real and that
humans are the cause.
• But there are many details that we can do better.
• Advances in high performance computing are improving simulations of extreme
storms, including hurricanes (movie).
• Statistical description of extreme precipitation usually leads to unbounded GEV
distributions. Why?
– Sample size limitations? Probably no.
– Mixing distributions across storm types? Probably yes. Violate i.i.d.
– Not in the asymptotic regime? Yes for block maxima in the deserts.
• Non-stationarity. Duh, its climate change!
– Covariate methods are a powerful way to incorporate known physical
behavior into the extreme value statistics. An active research area.
• Machine learning. Just scratching the surface.
– Berkeley Lab is using convolutional neural nets as a storm tracking tool.
Current topics

26. Thank you!
Questions?
mfwehner@lbl.gov