Calculate Flood/Rainfall Frequency from cumulative distribution function (CDF) of the distribution

Specifically, we will use the cumulative distribution function (CDF) of the fitted distribution to calculate the annual exceedance probability (AEP), or the probability that the event is equaled or exceeded in any single year. For example, considering a 200,000 cfs level, the exceedance probability is calculated in the following way:
Exceedance_P = P{X≥200} = 1 – P{X<200} = 1 – F(200) = 1 – 0.975 = 0.025 Note: F(200) is the CDF at 200.

To obtain the return period (also known as the recurrence interval) of the event, we should calculate the reciprocal of the exceedance probability:

Return_Period = 1 / Exceedance_P = 1 / 0.025 = 40 years.

F(x) is CDF

F(x) is CDF

The interpretation is that in a very long series, the 40-year flood value would be exceeded every 40 years on the average. For example, about twenty-five 40-year floods can be expected during a 1000 year period (on the average).

Source: http://www.mathwave.com/applications/flood_frequency.html

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Exceedance Probability

Introduction

Sometimes a hydrologist may need to know what the chances are over a given time period that a flood will reach or exceed a specific magnitude. This is called the probability of occurrence or the exceedance probability.

Let’s say the value “p” is the exceedance probability, in any given year. The exceedance probability may be formulated simply as the inverse of the return period. For example, for a two-year return period the exceedance probability in any given year is one divided by two = 0.5, or 50 percent. Continue reading

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