We often speak of the selected return period for design as "the 50 year flood" or "the 100 year flood." Many who hear this understand it to mean that this is a flood expected to occur once every 50 or 100 years. By speaking this way we imply a level of protection which is seldom achieved. For example, if we design for a 100 year storm event many people would believe that would mean the system should function for 100 years without ever being over capacity.
Unfortunately, this is not true. Because flood probabilities are based on historical records, their accuracy depends on the length and completeness of those records. Many reporting stations have only a few years of record so that the probabilities calculated from them are less reliable than stations with a record of 40, 50 or more years. Recently NOAA has updated their precipitation frequency records adding an additional 30 years of record to the data. This should improve the accuracy of the published data and make our estimates more reliable. Even so, they will remain "estimates" only. That is, they are simplified ways of stating the probability of an unpredictable event occurring.
A possibly better way of viewing these events, and speaking about them, is to refer to them by their annual probability of occurrence. The so called 100 Year storm is, by definition, the storm which has a 1 percent probability of occurring in any one year. If we want to know how frequently such a storm might occur over a longer period of time, that probability can be calculated by:
Px = 1 - ( 1-1/N)^x
Where: Px is the probability of occurrence in x number of years
1/N= the Probability of Occurrence in any one year
For example, if we want to calculate the probability of occurrence of the 100 year flood over 100 years the calculations would be:
Px = 1 - ( 1-1/100)^100
Px = 1 - ( 1- .01)^ 100
Px = 1 - ( 0.99)^100
Px = 1- 0.366
Px = 0.634
In other words, there is a 63 percent probability that the 1 Percent storm will occur one or more times over the next 100 years.
This kind of calculation can be done for any selected range of frequencies and time periods.
I'm not sure you will find any standard conversions, and it also varies depending on if you are concerned with total storm runoff or peak flows. I would guess that if there are any "standard" relationships, they will vary from one region to the next depending upon the local climate. They will also vary from one watershed to the next depending on the specific characteristics of the watershed including land slope, soil types, vegetation, storage, flood conveyance, etc.
