Climate Change and Extreme Events: Lies, Damned Lies, and Statistics

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Climate Change and Extreme Events Lies, Damned
Lies, and Statistics

• By
• David R. Legates
• University of Delaware
• And
• Delaware State Climatologist

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Figures often beguile me, particularly when I
have the arranging of them myself in which case
the remark attributed to Disraeli would often
apply with justice and force There are three
kinds of lies lies, damned lies, and
statistics. Mark Twain Chapters from my
Autobiography North American Review, No. DCXVIII
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Lies, Damned Lies, Statisticsand Weather
Observers!
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DISCLAIMER

• The Delaware State Climatologist does NOT
  represent either the Executive, Legislative, or
  Judicial branches of government and does not
  speak for the Governor or any other State agency
  or official.
• Recent media coverage of events associated with
  the subject of climate change has generated some
  confusion as to the role of the State
  Climatologist.
• Governor Minner February 13, 2007

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Heavy Rainfalls Called Sign of Climate Change in
New Report
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Severe Weather Predicted as Norm
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• Delawarehas seen a 37 increase in storms
  dumping 2-inches or more of rainfall over a
  24-hour period.
• Environment America and USPIRG
• When it Rains, It Pours Global Warming and the
  Rising Frequency of Extreme Precipitation in the
  United States

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Days with Precipitation gt2.0 Inches Porter
Reservoir, Wilmington DE

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Days with Precipitation gt2.0 Inches Porter
Reservoir, Wilmington DE
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Days with Precipitation gt2.0 Inches New Castle
County AP, Wilmington DE
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Days with Precipitation gt2.0 Inches University
Farm, Newark DE
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Days with Precipitation gt2.0 Inches Porter
Reservoir, Wilmington DE
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http//www.surfacestations.org
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MMTS
http//www.surfacestations.org
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Days with Precipitation gt2.0 Inches Porter
Reservoir, Wilmington DE
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Dr. Willie SoonHarvardUniversity
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Number of 3 Rainfalls per Year in Madison WI
ASOS ERA
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Number of 3 Rainfalls per Decade in Madison WI
ASOS ERA
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Number of 3 Rainfalls per Decade in Madison WI
Pre-ASOS
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Number of 3 Rainfalls per Decade in Madison WI
Pre-ASOS
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Number of 2 Rainfalls per Year in Stoughton WI
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Number of 3 Rainfalls per Year in Stoughton WI
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Number of 3 Rainfalls per Decade in Stoughton WI

Actually, an 11-year decade
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• What is Wrong with the Statistics?

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Number of 2 Rainfalls per Year in Stoughton WI

FREQUENCY COUNTS!
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• Regarding the Dependent Variable
• It is composed of discrete events that are
  frequency counts and non-negative integers.
• Infrequently occurring events tend to cluster
  around 0 and/or 1 and exhibit low frequencies at
  higher values.
• It is highly positively skewed and truncated at 0
  Thus the Mean gt Median
• Error term is NOT iid N(0,s2)
• \ OLS regression is inappropriate for these data!

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• Two Alternatives to OLS Regression
• Poisson Regression
• Assumes a Poisson distribution, where values are
  non-negative integers, and is highly positively
  skewed.
• Assumes Equidispersion (i.e., mean is equal to
  the variance)
• Negative Binomial Regression
• Assumes a Poisson-like distribution values are
  non-negative integers and is positively skewed
• No assumption of Equidispersion appropriate for
  over-dispersed data (i.e., variance is greater
  than the mean)

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• Advantages of Poisson or Negative Binomial
  Regression
• Although OLS, Poisson and negative binomial
  regressions yield similar results, the
  non-normality of the errors leads to large
  standard errors and an arbitrary increase in the
  level of significance of the coefficients in OLS.
• Assumptions can be more easily met with Poisson
  or Negative Binomial regression than with OLS.
• OLS regression could lead to a Type I error
  (rejection of null hypothesis when true) and
  erroneously conclude that the variable is
  changing over time when, in fact, it is not.

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Climate Change and Extreme Events Lies, Damned
Lies, and Statistics

• By
• David R. Legates
• University of Delaware
• And
• Delaware State Climatologist