Climate Change and Extreme Events: Lies, Damned Lies, and Statistics By David R. Legates University of Delaware And Delaware State Climatologist

“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

Lies, Damned Lies, Statistics …and Weather Observers!

DISCLAIMER The Delaware State Climatologist does represent either the Executive, Legislative, or Judicial branches of government and does not speak for the Governor or any other State agency or official. 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. “ of events associated with the subject of climate change has generated some confusion as to the role of the State Climatologist.” “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

Heavy Rainfalls Called Sign of Climate Change in New Report

Severe Weather Predicted as Norm

“Delaware…has 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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} ≈37% Days with Precipitation >2.0 Inches Porter Reservoir, Wilmington DE

Days with Precipitation >2.0 Inches Porter Reservoir, Wilmington DE

Days with Precipitation >2.0 Inches New Castle County AP, Wilmington DE

Days with Precipitation >2.0 Inches University Farm, Newark DE

Days with Precipitation >2.0 Inches Porter Reservoir, Wilmington DE

MMTS

Days with Precipitation >2.0 Inches Porter Reservoir, Wilmington DE

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Dr. Willie Soon Harvard University

Number of 3” Rainfalls per Year in Madison WI ASOS ERA

Number of 3” Rainfalls per Decade in Madison WI ASOS ERA

Number of 3” Rainfalls per Decade in Madison WI “Pre-ASOS”

Number of 3” Rainfalls per Decade in Madison WI “Pre-ASOS”

Number of 2” Rainfalls per Year in Stoughton WI

Number of 3” Rainfalls per Year in Stoughton WI

Number of 3” Rainfalls per Decade in Stoughton WI * *Actually, an 11-year ‘decade’

What is Wrong with the Statistics?

Number of 2” Rainfalls per Year in Stoughton WI FREQUENCY COUNTS!

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 > Median Error term is NOT iid ~ N(0,   )  OLS regression is inappropriate for these data!

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)

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