Use the directions on this sheet to help you calculate the probability that a flood of a given magnitude will occur in a given year using local river gauge information.
What is the probability that a flood of a given magnitude will occur this year?
Years of Record: _________________
Peak Flow: ______________________
Rank of Peak Flow: _______________
Calculate the return frequency (R) using this equation:
R = N+1/M
R is the return frequency
N is the number of years of record
M is the rank of that particular peak flow
Now, take the inverse of R in order to get the probability:
P = 1/R
P is the probability, an estimate of chance. If you want to make it sound like a weather forecast, multiply P by 100 to get the percent chance that a flood of that magnitude will occur this year (or any year).
Suppose you are thinking about purchasing a pretty little house on a floodplain that sits a few feet higher than the bank of a sparkling river. You ask the owners, “How often does this river flood?” They exchange a glance and answer, “We’ve lived here 10 years and never had water in the living room yet!” Before you plunk down your hard-earned cash and buy a bunch of fishing lures, you cleverly figure out the chance that a catfish might swim to your door in any given year. Here’s how:
1. Locate the nearest river gauge as described above. Find out at what gauge height the river will be lapping at your back door (this likely will be an estimate unless you have some pretty advanced gear for determining exact elevations). Suppose your river gauge has 87 years of record and the gauge height for a flood that would swamp your property is 15 feet. Number the peak flows by rank and find the peak flow nearest 15 feet. Suppose a flood that is gauged at 15 feet is a moderately severe one for that river, maybe it is the twenty-fifth-biggest flood on record, or rank 25.
2. Calculate the return frequency: R
R = (N+1)/M:
R = (87 + 1)/25
R = 3.5
Whoa! A flow gauged at 15 feet would be expected to occur every 3.5 years, based on 87 years of record. (I wonder if they are offering owner financing on the house?)
3. Calculate the probability of such a flood: P
P = 1/R
P = 1/3.5
P = .286
4. Multiply P by 100 to get percent chance:
.286 x 100 = 28.6% chance
Now you have some basis for making a foolish decision to buy the house. There is a 28% chance that the river will join you in your living room in any given year. Of course, you should keep in mind that the river could certainly flood this year, next year, the following year, or all three! The fact that it did not flood in the past 10 years does not change the probability one whit. And don’t forget that you almost certainly will not be able to afford flood insurance, if you could even find someone to sell it to you!
In order to get more accurate predictions of great floods, you need long-term data. If you only had a 10-year data set, for example, you would have no idea what was coming!