Geography 3402: Natural Hazards
Exercise 1: The Probability of Extreme Events
Name:________________________
Introduction:
As discussed in class and the text, any measurable natural event can be analyzed in
several ways to assess the likelihood of its occurrence at certain magnitudes. Typically
the hazard analyst is interested in assessing the probability of an event of a given or
greater magnitude, which we do in this exercise.
The ingredients to such analysis are a reliable record of events over a sufficient period of
time to capture a good range of magnitudes. There is no magic period of record, but
generally longer records provide a more reliable measure of likelihood.
In this exercise you use a record of daily snowfalls in Boulder to assess the snow hazard,
focused specifically on the probability of certain snowstorm magnitudes, measured by
depth of snowfall in a calendar day. You will find on this web page a spreadsheet of daily
Boulder snowfalls for the period from winter 1948-49 through winter 2003-4, or 55 years
of observation. Data associated with missing values and less then 1” values for snowfall
have been deleted. The three spreadsheet worksheets (see tabs at bottom) give you the
original record, the record only for the snow-prone months (10-5), and the record
"ranked" by snowfalls. This last one is most useful to your analysis.
Instructions:
Analyze the snowstorm record to assess its statistical distribution, the recurrence
interval of specified snowstorm depths, and the probability of specified snowstorm
depths occurring in any given year. Print out this exercise, attach your histogram,
and answer the questions on this sheet.
1. Plot the Distribution (histogram): a plot of the number of occurrences within defined
equal ranges (or class limits) of magnitude (using 2 inch class limits: 0-2, 2-4, with the
highest class open-ended, e.g., 14+, and rounding snowfalls to whole numbers, should
best reveal the shape of the distribution). You can use spreadsheets, statistical analysis
packages, or as a last resort do this by hand on graph paper—be sure to label the x and y
axes, including the class limits. The shape and spread of the distribution reveals a first-cut
assessment of the natural system. Describe the distribution:
a) Peaked or spread-out (platykurtic or leptokurtic)?
Answer: _____________________________________
b) Are there one or more peaks (uni- or multi-modal), what is the mode? There
are plenty of good statistical websites, try:
http://www.stats.gla.ac.uk/steps/glossary/presenting_data.html
Answer: _____________________________________
c) Is it skewed – data is skewed toward lower or higher values (positive or
negative skew---in these cases the mean is larger or smaller than the mode).
Answer: _____________________________________
2. Calculate the recurrence interval or return period r (or Tr in the text) of an 11
inch or greater snowfall (this might close the schools!). Be sure to include the units of
your answer:
Formula Tr = years of observation / # of events
Answer: _____________________________________
3. Calculate the probability of an 11 inch or greater snowfall in a given year, as a
decimal and as a percentage.
Formula p = # events/years (Percent can also be calculated as: P% = 100/r)
Answer:__________________________________
4. Calculate the return period (with units noted) of a 16 inch or greater daily snowfall
(this should provide local kids a Snow Day, though CU rarely closes!)
Answer:__________________________________
5. Calculate the probability of a 16 inch or greater snowfall in a given year, as a
decimal and as a percentage.
Answer:__________________________________
6. Extra Credit:
(a) Estimate the magnitude of the 100 year event, this is most simply done by plotting
two R’s and applying simple linear extrapolation on 2-cyle log paper.
Answer:___________________________
(b) Normalize the distribution and re-plot it as deviations from the mean. Did this change
the shape?
Answer:_____________________________________________