20 Questions Statisticians Should Ask!

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20 Questions Statisticians Should Ask!

• Edward J. Wegman
• George Mason University
• ASA A Statistical Consensus on Global Warming
• October 27, 2007

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Looking Backwards Looking Forwards

• Paleoclimate reconstruction uses proxies to
  estimate temperature profiles in the past.
• Climate models use physical/statistical models
  usually based on PDEs to understand/predict/projec
  t temperature and other climate variables in the
  future.
• Both have a fundamental statistical/stochastic
  character.

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Paleoclimate Reconstruction
After Bradley (1999)
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Paleoclimate Reconstruction
After Bradley and Eddy (1991)
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Paleoclimate Reconstruction
Confounding Factors?
After Bradley and Eddy (1991)
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Paleoclimate Reconstruction

• climate field reconstruction (CFR)
• principal component based (almost)
• empirical orthogonal function analysis
• data matrix columns are time series of proxy data
• weighted to largest variance
• climate plus scale (CPS)
• simple averages of proxies

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Paleoclimate Reconstruction

• tree rings
• tree ring size and density variations
• best signal when trees are stressed
• latitude and altitude
• Precipitation and CO2 fertilization
• ice cores
• ice layer thickness
• oxygen and hydrogen isotope balance
• coral
• annual growth
• symbiosis with algae

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Paleoclimate Reconstruction
TREE RINGS
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Paleoclimate Reconstruction
Bristlecone Pines
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Paleoclimate Reconstruction
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Statistical Questions

• How were the 70 trees in NOAMER 1400 selected?
• How representative are these trees of the
  population of trees that grew from 1400-2000? In
  terms of geography, altitude, and type.
• If these trees seemed interesting to various
  individuals who took the core samples, should one
  believe those trees can/should be treated as a
  random sample? Are there biases in the
  selection of these trees?
• Presumably many trees could not be sampled
  because they had died or been harvested. What is
  the effect of this censoring on the data (and
  the analysis)?
• What is the correlation between temperature and
  tree ring growth?

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Hockey Sticks
Top Panel is original EOF (CFD) method applied to
North American Tree Proxy, PC1. Bottom Panel is
the result of the centered PCA.
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Paleoclimate Reconstruction
Ice Cores
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Paleoclimate Reconstruction
Lonnie Thompsons Ice Cores and Nobel Laureate Al
Gore
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Paleoclimate Reconstruction

• 5. Similar questions exist about ice cores
  and how representative such data might be. What
  are the effects of gas diffusion in the ice core
  layers?
• 6. In the ice core (Vostok) data that Al Gore
  illustrates in the Inconvenient Truth, the
  temperature time series leads, not lags, the CO2
  time series by 800 to 1000 years. What is the
  causal mechanism? It would seem that temperature
  increases cause CO2 release, not vice versa. The
  common answer is that there is an (unspecified)
  feedback mechanism.

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Paleoclimate Reconstruction
Corals
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Two Mode Proxy-Paper Network
Most Common Proxies
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Paleoclimate Reconstruction

1. Why are the same proxies used in so many papers?
   Most recently, Osborn and Briffa (2006), DArrigo
   et al. (2006), Juckes et al. (2007). Mann et al.
   (1998, 1999) was ground breaking in using
   hundreds of proxies. Most more recent papers
   focus on the top 15 or so in our two-mode
   network. Are they chosen because they show the
   hockey stick and those omitted dont?

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Statistical Questions

1. What calibration studies have been performed?
   Rescaling steps seem to suggest that the
   correlation must be near 100. Is that the case?
   How are the confounding variables removed?
2. The temperature proxy search is a regression
   problem. Why should one choose to use principal
   components (not appropriate for finding a
   nonstationary mean)?
3. What weights are used to combine different proxy
   types? Why?
4. If the data are not a random sample, then what
   confidence can be given to any modeling and to
   any error bars? Why pointwise confidence
   intervals in place of confidence bands? Is new
   theory needed?

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Statistical Questions

1. Most models are deterministic, estimating the
   expected temperature or other component. To what
   extent are these models chaotic systems? How
   thoroughly has this been investigated?
2. For coupled ocean-atmosphere-land models, how
   much more likely is this to induce chaotic
   behavior?
3. Models depend on initial conditions often derived
   from remote sensing sources. How well calibrated
   to ground truth are these?
4. CO2 modeling shows a rapid increase in the near
   term. What do the models show in the longer term?
   
5. Given the apparent high correlation between CO2
   and temperature in the model outputs, how direct
   is the link in the model itself?

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Statistical Questions

1. What data should be collected that would be most
   cost-effective in increasing our understanding of
   the climatic models and the underlying physics
   (and statistics)?
2. Are all data valuable? How does one avoid the
   desire to collect data at sites that appear
   interesting beforehand?

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Statistical Questions
Melbournes Historic Weather Station 1855 to
2007
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Statistical Questions

1. To what extent have the micro-climates changed
   the instrumented temperature record? How have
   this effect been compensated for, especially in
   the absence of accurate records of original
   micro-climate? What is the impact of changing and
   improving technology?
2. How is the instrumented temperature record
   associated with the increase or decrease in the
   number of weather stations?

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Statistical Questions
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Statistical Questions

• Bonus Question 21. Why to climate scientists show
  two side-by-side pictures and say look how well
  they compare? Subtract them and see how well they
  dont compare.

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Contact Information
Where to send climate police Edward J.
Wegman Department of Computational and Data
Sciences George Mason University Fairfax, VA
22030 Email ewegman_at_gmail.com