The purpose of the NFF mailing list is to provide information on the U.S. Geological Survey (USGS) National Flood Frequency (NFF) program. NFF is a computer application that is used to estimate peak discharges for unregulated streams. Values (discharges) derived by the program often serve as input for other applications (such as hydraulic computer models) that are used to technically support end-products (map revisions) of the National Flood Insurance Program (NFIP).

## Discussion on USGS Regression Equations and the NFF Program

The USGS developed a computer program titled "National Flood Frequency" or "NFF" that estimates the flood frequency and magnitude for ungaged sites through the application of the appropriate regional regression equations. NFF was released in 1993 and does not incorporate any revisions to regional regression equations that occurred after September 30, 1993. Since 1993 a significant number of the regression equations have been revised. The USGS is in the process of revising the NFF computer program to incorporate the updated regression equations. The revised version of NFF will be released soon.

The regional regression equations are currently being used for National Flood Insurance Program (NFIP) purposes. Therefore, FEMA would like to continue with this listserv and discuss issues of interest in the application of the regional regression equations for NFIP purposes. Upon the release of the revised NFF program, the focus of this listserv will shift to assist users in becoming familiar with the revised NFF program and its application for NFIP purposes.

## Estimation of Extreme Floods

Extreme floods can be thought of in several different ways. Probably the most familiar is the flood having a 0.2% chance of being exceeded in any given year, (500-year flood). This flood is usually included in Flood Insurance Studies (FISs) where detailed analyses have established the 1% annual chance of exceedance or, base (100-year ) flood elevations. When dealing with dam design or evaluation, the Probable Maximum Flood (PMF) is a familiar extreme flood. It is based on the assumption of the most severe hydrologic and meteorologic conditions considered to be reasonable at a site. The National Weather Service has published Probable Maximum Precipitation reports on which PMF estimates are based. For other design projects, the U.S. Army Corps of Engineers Standard Project Flood (SPF) is also a familiar extreme flood. Neither the PMF nor SPF have any associated probability of exceedance associated with them.

In general, the largest flood having an associated exceedance probability used commonly for planning, floodplain management, and design is the 0.2% annual chance of exceedance flood. It is also the largest flood discharge computed in the USGS and Bulletin 17B flood frequency programs. The 0.2% annual chance of exceedance flood is used in FEMA FISs and by the National Park Service for defining floodplains in the National Parks. In addition, recent bridge failures caused or exacerbated by scour damage during floods have prompted the Federal Highway Administration to advise State Departments of Transportation to evaluate the risk of bridges from scour damage during floods in the 1% to 0.2% annual chance of exceedance year range. Clearly, there is a practical application for discharges on the order of the 0.2% annual chance of exceedance.

When NFF was published in 1994, only 15 of the 50 States, Southwestern United States, and Puerto Rico equations included an equation for the 0.2% annual chance of exceedance event. Therefore, a methodology was provided to enable the extrapolation of NFF results to provide 0.2% annual chance flood values. The procedure consists basically of fitting a log-Pearson Type III curve to the 50% through 1% annual chance flood discharges resulting from the NFF calculation and extrapolating to the 0.2% annual chance flood value. The following five steps are involved in the procedure:

- Determine the flood peak discharges using NFF
- Fit a quadratic curve to the NFF points on log-probability paper using least squares computations. The quadratic curve is an approximation of the log-Pearson Type III curve that will be computed
- Determine the skew coefficient of the log-Pearson Type III curve that passes through the 50%, 10%, and 1% annual chance floods defined by the quadratic curve. The skew coefficient is defined approximately by the formula: G = –2.50 + 3.02 log(Q100/Q10) / log(Q10/Q2)
- Re-plot (conceptually) the selected discharges for the return periods using a log-Pearson Type III probability scale such that it is a straight line
- Fit a line by least-squares regression to the points plotted in step 4 and extrapolate it to the 500-year discharge

Figure 1 is an example of using this procedure on the Fenholloway River near Foley, Florida. The solid triangles are the values computed by NFF. The solid circle (12, 800 cfs) is the result of the extrapolation procedure described above. The solid triangle (11, 500 cfs) for the 0.2% annual chance (500-year) value is the result of the NFF calculation, since Florida is one of the 15 States having 0.2% annual chance equations published with NFF. The difference between the two values is 11.3 percent, which is typical of several comparisons of extrapolated and 0.2% annual chance regional regression results. Those comparisons indicated that the differences usually fell within plus or minus 15 percent.

Generally, one would expect the extrapolated 0.2% annual chance discharge to be less than the envelope-curve values. This is because several watersheds in a given region have probably experienced at least one flood exceeding the 0.2% annual chance value. In addition, the comparison with the curves is meant to be qualitative only because there is no frequency of occurrence associated with the envelope curves.

## Previous Bulletin Topics

- Introduction to the NFF Program and USGS regression equations, the applicability of the regression equations, and the advantages and limitations of the regression equations
- Use of USGS regression equations in the NFIP and criteria for using USGS regression equations in the NFIP
- Revisions to the USGS regression equations since the NFF software was released
- Part 1. Unusual parameters of USGS regression equations and how to obtain them
- Part 2. Unusual parameters of USGS regression equations and how to obtain them
- Part 3. Unusual parameters of USGS regression equations and how to obtain them
- Examples in which USGS regression equations are used for NFIP purposes
- How to treat State Line faults (basins lying in more than one state)
- Estimating drainage area and cross sections from USGS topo maps
- Measures of accuracy in NFF
- Weighting NFF results with observed data

## Upcoming Bulletin Topics

- Flood Hydrograph Estimation Using NFF
- Revised NFF Software

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Last Modified: Monday, 25-Jun-2007 11:57:20 EDT