Frequency Functions
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.
Working with Frequency Functions in HEC-FDA
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 CPD-72a for more information on the graphical frequency approach.
Steps for Adding or Editing Frequency Functions
Frequency relationships should be entered for each project condition-analysis year-impact area combination. To access the options for creating, retrieving or importing frequency functions, from the Study Tree, right-click on Frequency Functions and select the desired shortcut command.
The frequency relationships may be one of the three below.
- Analytical flow-frequency function.
- Graphical flow-frequency function.
- Graphical stage-frequency function.
Please see EM 1110-2-1619, HEC-FDA on Discourse, or speak with HEC about choosing one of the three. Recall that uncertainty in EAD is most sensitive to uncertainty in flow, so we want to include flow in our models if the hydrologic and hydraulic conditions permit.
Users can edit, rename or remove frequency functions. To access the options, from the Study Tree, right-click on the function (e.g., Muncie Example LP3) and select the desired command from the shortcut menu.
