Re: a simple(?) probability question...



On Jan 25, 2:57 am, "Joe" <jconcor...@xxxxxxxxxxx> wrote:
On Jan 21, 4:16 pm, James Waldby <j-wal...@xxxxxxxx> wrote:





Joe wrote:
[...] By definition, a 100 Years Storm is a storm that will occur at
least once in 100 years. That means certainty within 100 years, i.e.
probability equals 1 in the elapsed time of 100 years....

That doesn't agree with common terminology as stated, for example,
inhttp://bcn.boulder.co.us/basin/watershed/flood.htmlandhttp://en.wikip.... From the former:
The terms "10 year", "50 year", "100 year" and "500 year" floods
are used to describe the estimated probability of a flood event
happening in any given year. [...] A 10 year flood has
a 10 percent probability of occurring in any given year, a 50
year event a 2% probabaility, a 100 year event a 1% probability,
and a 500 year event a .2% probability. While unlikely, it is
possible to have two 100 or even 500 year floods within years or
months of each other.

Given the likelihood of 1% for a 100-year event to occur in a
given year, one could figure 1 - (1-0.01)^50 or ~ .395 likelihood
for it to occur at least once in any given 50-year period, or
1 - (1-0.01)^100 or ~ .634 likelihood for any 100-year period.

A Poisson process (http://en.wikipedia.org/wiki/Poisson_process)
with lambda = 0.01 per year has probability ~ .632 of 1 or more
events occurring in any 100-year period, which is about the same
as for the Bernoulli process mentioned in the preceding paragraph,
just as one would expect for a small probability and many years.

-jiwWhile that calculation provides a numerical result of 0.634, I think
the notion that a
100 year storm has only a 63% chance of happening in 100 years would
seem silly
to engineers. It would also be rather inconsistent with decisions by
rational people
to spend tremendous amounts of money on facilities to deal with planned
100 year
storm situations.

I think the real weather data would show the calculation as giving a
conclusion that
is faulty. The threshold rainfall levels for the 100 year storm are set
by examining available
data, based on real events. The value of the rainfall intensity is
selected because
such storms have actually occured, not that they "might" occur.

Some interesting data is available from the National Climatic Data
Center to support the
concept that when a given rainfall intensity is stated for the 100 year
storm it certainly
will occur. After looking at the actual data for a 50 year interval I
am quite convinced of this.

I think you will find that a "hundred-year storm" is a storm that is
expected to occur *on average* once every hundred years. In any given
hundred year interval it may occur once, it may occur more than once,
or it may not occur at all. Indeed, it is impossible to construct a
plausible model that assigns a probability of one (certainty) to a
"hundred-year storm" occurring either exactly once or at least once
every hundred years. (If you can construct one then I would be
interested to see it!)

.

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