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.

## Flood Hydrograph Estimation Using NFF

The NFF program contains a procedure for computing the average hydrograph for a basin. Because it is the average hydrograph, it does not represent any particular rainfall distribution. The procedure used in NFF is the dimensionless (unit) hydrograph method. In 1932, L.K. Sherman developed the now well known theory of unit hydrographs. The unit hydrograph is defined as a hydrograph of direct runoff resulting from 1 inch of effective rainfall uniformly generated over the basin at a uniform rate for a specified time period or duration. The following basic assumptions apply to the unit hydrograph:

- The effective rainfall is uniformly distributed within its duration.
- The effective rainfall is uniformly distributed throughout the whole drainage basin.
- The base or time duration is constant.
- The ordinates of the direct-runoff hydrograph are directly proportional to the total amount of direct runoff represented by each resulting hydrograph.
- For a given drainage basin, the runoff hydrograph reflects all the combined physical characteristics of the basin.

Figure 1 illustrates a typical unit hydrograph. The dimensionless hydrograph method has three essential parts:

- the peak discharge needed for the basin;
- the basin lag time; and
- the dimensionless hydrograph ordinates

Using NFF, the user computes the peak values, and selects which peak value to use to generate the hydrograph. The user must also estimate the basin lag time. NFF then computes a hydrograph based on the dimensionless ordinates developed by Inman (1987) , which are stored in the program.

Basin lag time is defined as the time that elapses from the center of mass rainfall excess to the center of the mass of the resulting runoff hydrograph. This parameter is the most difficult to estimate for the hydrograph computation. For rural hydrographs, the NFF user must make an estimate of the lag time because there are no lag time equations currently available in NFF.

For small natural drainage basins with simple drainage patterns, the lag time may be very close to the time of concentration. Several empirical formulas have been developed. An example is the formula for computing time of concentration for small agricultural watersheds developed by Z.P. Kirpich.

t_{c} = 0.00013 (L^{0.77} / S^{0.385})

In this formula, t_{c} is the time of concentration in hours, L is the length of the basin in feet
along the watercourse from the point of interest to the farthest point on the basin divide, and S is the
average main channel slope in ft./ft. for the basin.

For large basins, another method must be used to estimate the lag time. Appendix C of the NFF publication contains a summary of lag time equations for several states. However, for urban basins, Sauer, et al., have developed a generalized equation for use nationwide, which is included in NFF. Consult any text on hydrology to find additional information and equations for estimating basin lag time.

Following is an example calculation for a small, rural watershed using NFF.

This is the watershed from the January 2002 NFF Listserv. We will be using the West Virginia equations for our calculations. After we have calculated the rural runoff above, we will move on to the window that asks if we want to calculate a hydrograph by answering "N" to all the intervening prompts that follow.

When we answer "Y" to the hydrograph query, the following window prompts us for the basin length in miles, which we measured at 11,000 feet, or 2.083 miles, from the Hundred, West Virginia, quad map.

The next prompt asks us for the basin lag time in hours, which we will calculate from the Kirpich equation given above. Remember that the length is in feet and the slope in ft./ft. in this formula. To determine the average main channel slope, we will use the method discussed in the September 2001 NFF Listserv, except that we will express the slope in ft./ft.

t_{c} = 0.00013 (L^{0.77} / S^{0.385})

t_{c} = 0.00013 [(11000)^{0.77} / (.0208)^{0.385})]

t_{c} = 0.75 hr.

The next prompt asks us for which peak value we want to calculate the hydrograph. We will choose the 100-year peak.

When we enter "100," NFF displays the hydrograph ordinates as above. The prompt asks if we want to plot the resulting hydrograph. Unfortunately, this version of NFF can only display the resulting graph to the screen. The plot cannot be printed or saved because of the incompatibility between MS DOS programs and the MS Windows environment. Beyond this window in NFF, if you wish to plot, save, and/or print the resulting hydrograph, you must save the ordinates to an NFF file and import them to Excel. (Remember, when saving files in MS DOS format, the file names can only be up to 8 characters long.) Then, using the charting option in Excel, you can plot, save, and print the hydrograph.

The resulting hydrograph from Excel looks like this:

## 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
- Estimation of extreme floods

## Upcoming Bulletin Topics

- Urban Flood Hydrographs Using NFF
- Revised NFF Software

**View the archive page for all Flood Hazard Mapping listservs.**

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