1. STATISTICS OF EXTREME EVENTS AMS Probability and Statistics Committee January 11, 2009 WELCOME! AMS SHORT COURSE

2. Outline Welcome Participants Introduction Introduction to the course topic Definitions Course structure overview

3. Participants Introduction Please state:  Your name  Affiliation  Work focus  Expectation from the course

4. Intro to the Course Topic Extreme events:  the furthest or highest degree of something; far beyond a norm in quantity or amount or degree; the greatest possible degree or extent or intensity; the most distant in any direction (http://wordnet.princeton.edu/perl/webwn?s=extreme )http://wordnet.princeton.edu/perl/webwn?s=extreme  In climatology, the highest and, in some cases, the lowest value of a climatic element observed during a given time interval or during a given month or season of that period (http://amsglossary.allenpress.com/glossary/ )climatologyclimatic elementseasonhttp://amsglossary.allenpress.com/glossary/ Statistics of extreme events:  The systematic analysis of random phenomena (http://amsglossary.allenpress.com/glossary/ )analysisrandomhttp://amsglossary.allenpress.com/glossary/

5. Intro to the Course Topic Some Examples of Extreme Events in Meteorology, Climatology and Hydrology:  ENSO events  Hurricanes  Tornadoes  Climate Variability Extremes versus Climate Change  Low River Flow  Flood  Drought

6. A Threshold Definition: ENSO El Niño has tremen- dous effects on global climate and weather due to the eastward migration of the warm pool. How do we define El Niño?

7. A Threshold Definition: ENSO El Niño: A phenomenon in the equatorial Pacific Ocean characterized by a positive sea surface temperature departure from normal (for the 1971-2000 base period) in the Niño 3.4 region greater than or equal in magnitude to 0.5C, averaged over three consecutive months. La Niña: A phenomenon in the equatorial Pacific Ocean characterized by a negative sea surface temperature departure from normal (for the 1971-2000 base period) in the Niño 3.4 region greater than or equal in magnitude to 0.5C, averaged over three consecutive months.

8. A Threshold Definition: ENSO Note: the standard deviation of this series is 0.83C and the threshold is ±0.50C 1982/1983, 1997/1998 are extreme El Nino events 1988/99 is an extreme La Nina. Others?

9. A Probabilistic Definition River flow recessions occur in May-Jul, and Oct –Jan

10. A Probabilistic Definition Low Flow statistics can include:  Recession daily averages  Minimal 30-day discharge  75% Probability of Exceedance (POE) Discharge Mean Median Mode Low flow

11. Probabilistic & Threshold Definitions Drought Monitoring Categories:  D0: Abnormally Dry  D1: Moderate  D2: Severe  D3: Extreme  D4: Exceptional Category Description Palmer SPI%tiles D0Abnormally Dry-1 to-1.9-.5 to -.721-30 D1Moderate Drought-2 to -2.9-.8 to-1.211-20 D2Severe Drought-3 to -3.9-1.3 to -1.56-10 D3Extreme Drought-4 to-4.9-1.6 to -1.93-5 D4Exceptional Drought<-5<-20-2 Objective Short and Long-term Drought Indicator Blends (Percentiles) CPC Soil Moisture Model (Percentiles) USGS Weekly Streamflow(Percentiles)

12. The Course Structure Overview VIEWING CLIMATE AND WEATHER EXTREME EVENTS IN A PROBABILISTIC CONTEXT Prashant Sardeshmukh EXTREME VALUE THEORY Richard Smith POISSON AND QUANTILE REGRESSION James Elsner PROBLEM APPLICATIONS, Exercise Session on Poisson and Quantile Regression, James Elsner PERFORMANCE EVALUATION MEASURES Caren Marzban PROBLEM APPLICATIONS, Exercise Session on Analyses of Extremes, Rick Katz