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I would like to calculate the bankfull flow for a certain point on a river. The recurrence interval of bankfull flow varies for different rivers, but is typically always found to be between 1 and 2 years. Let's imagine I decide to set the recurrence interval at 1.67 years, which gives me an exceedance probability of approximately 60% ($\rm Pr(X\geq0.60) = Pr(X\leq0.40)$).

Supposing I have a stream gage at the point I am interested in estimating bankfull flow for, and I recorded hourly discharge values for 20 years, which set of values should I use to calculate the recurrence interval? Should I determine the value associated with this exceedance probability using all hourly flows, the daily mean flows, the annual high flows (what the USGS calls instantaneous peak flows), or some other subset of values?

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I think you should just follow the guidelines provided by the USGS for this calculations (http://water.usgs.gov/osw/bulletin17b/dl_flow.pdf). From there you can read:

"Flood events can be analyzed using either annual or partial-duration series. The annual flood series is based on the maximum flood peak for each year. A partial-duration series is obtained by taking all flood peaks equal to or greater than a predefined base flood".

They also provide a list of FAQs (http://water.usgs.gov/osw/bulletin17b/bulletin_17B.html) and a way to calculate them.

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