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# Re: Probabilistic....

• To: seaoc(--nospam--at)seaoc.org
• Subject: Re: Probabilistic....
• From: "Bill Sherman" <SHERMANWC(--nospam--at)cdm.com>
• Date: Tue, 31 Dec 1996 19:29:25 +0500

```Thank you for clarifying the difference between probability of exceedance and
annual probability:

>This annual probability can be expressed in terms of exceedence probabilities
>for a given life using the following relationship.  This relationship assumes
>a poisson probability distribution.

>         p = 1 - e^(-LT)

>where:    p = probability of exceedence
>          L = annual probability of exceedence
>          T = time period

>Therefore for a 0.002 annual probability of exceedence, p for a 50 year
period
>is 0.095 or 9.5%.  For p = 0.1 or 10% and T=50 years, L = 0.00210721 or an
>equivalent average return period of 474.6 commonly rounded off to 475 years.

My oversimplified linear model wasn't too far off when "LT" was relatively
small (i.e., when the desired time period is significantly less than the
"return period").

It still isn't totally clear if there is a difference between "annual
probability of exceedance" and "annual probability of occurrence" (i.e. "L" in
the above equation)?  Thus, for a 100-year flood (100-year return period) with
a 0.01 annual probability of occurrence (exceedance?), the probability of
being exceeded in 50-years would be approximately 40% (LT=0.01x50=0.50)?  Is
this correct?

I am currently in a discussion with others on "how conservative is it to
design for a 100-year flood?"  While I don't see major differences in the
mathematical results using different terms to express the frequency of
occurrence, I do feel that expressing the risk in terms of exceedance
probability over a 50-year period makes it easier to understand risk versus
"return period".

```