What is a frequency function?

A frequency function is the relationship between annual peak flood magnitude (flow or stage) and the probability of that flood magnitude being exceeded. The frequency function is a cumulative distribution function. 

Use Computed Probabilities

All hydrologic frequency inputs into HEC-FDA should be based on computed probability with an estimate of equivalent period of record.  The analysis should ensure that expected probability adjustments have not been applied in the engineering analysis.  

What is the purpose of a frequency function?

A frequency function is part of the description of the hazard. In the risk computation algorithm, the level of damage in an impact area is identified using the flood magnitude. With a relationship between the flood magnitude and the probability of that flood magnitude being exceeded, we can identify the probability that a level of damage is exceeded, giving us the function that we need to calculate expected annual damage. 

Analytical versus graphical frequency functions

There are two approaches to developing a frequency function: analytical and graphical. Flow-frequency functions can be developed using either approach. Stage-frequency functions can be developed using the graphical approach only. Below you will find brief descriptions of the two approaches. If an analytical function is reasonable for the channel conditions, an analytical function should be used. An analytical function is considered reasonable if the channel has an unregulated streamflow (a natural, free-flowing channel) at the point of interest, a Log Pearson Type III moments can be derived using regional regression analysis or existing regional equations, or a streamflow record can be modeled using precipitation records. For detailed information on one approach versus the other, please take a look at the below webinar or see EM 1110-2-1619.

Analytical approach

The analytical approach (review Analytical Frequency Function) involves analysis of a time series of peak flow observations or hydrologic modeling to develop a Log Pearson Type III distribution. See USGS Bulletin 17c to learn more about the analytical approach.

Graphical approach

The graphical approach (review Graphical Frequency Function) involves using a set of ordered observations (annual peak flows or annual peak stages) together with the equivalent record length to estimate the uncertainty around stages or flows. The U.S. Army Corps of Engineers uses the Less Simple Method to estimate uncertainty about a graphical frequency function. See the HEC-FDA Technical Reference Manual CPD-72a for more information on the graphical frequency approach.