Flood Statistics 1

[cab454]

How would one calculate, for example, how many times a 2-year storm should occur in a 100-year period from a statistical viewpoint?

That is not to say what is the likelihood a 2-year event would occur in a 100-year period; that calculation is relatively straight forward and widely published.

The goal of this exercise is to compare historical rain data in which I know how many 2-year events we had over a given time period to how many 2-year events we should have had in that same time period with the idea being to get an idea of the "accuracy" of our 2-year precipitation depth based on historical data.

The specific recurrence interval and time period are less important. I am more just looking for how to set up the calculation.

 

[swazimatt]

don't know the answer but interested to know what your ultimate findings are

 

[phamENG]

Exceedance Probability

1-(1-p)[sup]n[/sup]

p=Annual exceedance probability (1/return period)
n=number of years

1=1-(1-(1/2))[sup]n[/sup]
n=10

So you have a "100%" chance of that storm happening in 10 years. So one would expect a 2 year storm to happen 10 times in a 100 year period.

 

[CarlB]

If you had yearly data for highest storm/runoff for a period of 100 years, that should be sufficient data to determine the various return period storms. You'd use some assumed distribution, such as Pearson III.

Since a 2-yr storm is exceeded on the average once every 2 years, over a long period about 1/2 the annual peaks should exceed the 2-yr flow.
So I'd say expect 50 storms of 2-yr or greater over 100 years.

I don't know a formula to determine the probability of N x-year storms over y years. I'd expect like phamENG says, it's close to 100% there will be 10 or more 2-yr storms in a 100-yr period.
I'd guess it's close to 50% probable there will be 50 or more.

**EDIT**
OK I think I found equation.
From bulletin 17B, at

https://water.usgs.gov/osw/bulletin17b/dl_flow.pdf

If I followed equation correctly, probabilities are:
30 or more: 1.00
40 or more: 0.98
50 or more: 0.54
55 or more: 0.18
60 or more: 0.02

Make what you will from this, but seems likely you should have 40-55 2-yr storms occurring over a 100-yr period.

 

[cab454]

CarlB-

Very helpful. You obviously are more brushed up on your statistics than I am. To calculate the values you posted, are you using equation 10-1? I am having a little trouble recreating your results. If I read them correctly, you are saying there is:

100% Risk/Chance (R) of 30 or more events occurring
98% Risk/Chance (R) of 40 or more events occurring
So on and so forth?

 

[CarlB]

Yes I was using equation 10-1. It was a little hard to wrap my mind around. The equation is the chance of that number of events occurring, but you want the number exceeding that, so need to subtract it from 1.

So for example, to determine the chance of 2 or more events, you need to do the calc for I=0 and I=1, add them together, subtract that from 1.
Lends itself to an equation in Excel, row for each year.

And yes, you interpreted my results correctly.

 

[cab454]

I found this Calculator . It confirms your results. Thanks for the help, CarlB.