Uncertainties in the base flood discharge create uncertainties in the calculated base flood elevation and in the delineation of the floodplain boundary. For a given base flood discharge, uncertainties in hydraulic modeling and parameters create uncertainty in the BFE. For a given BFE, uncertainties in terrain elevation and boundary delineation methods create uncertainties in the location of the floodplain boundary. Although the discharge, elevation, and extent of inundation are interrelated, uncertainty increases with each step of the mapping process. The purpose of this chapter is to define the magnitude of these uncertainties in relation to the nature of the data and methods used in flood mapping.

UNCERTAINTY OF THE BASE FLOOD ELEVATION AT STREAM GAGES

A large number of factors have an effect on flood map uncertainty. It is helpful to have a benchmark measure of uncertainty to determine with some level of objectivity what is or is not significant. The BFE is a useful benchmark because it separates the hydrology and hydraulics analysis from the mapping step.

USGS stream gage sites are the principal places in the country where flood elevations have been measured precisely and consistently over many years. Each year of streamflow record includes the stage height (water height relative to a gage datum elevation) recorded every 15 minutes as well as the maximum stage height and corresponding maximum discharge for the year. The USGS publishes these peak stage heights and discharges for more than 27,000 stream gages as part of its National Water Information System.2 This includes data from the approximately 7,000 USGS gages presently operational, as well as approximately 20,000 gage sites that were operational for some period in the past but are now closed. Frequency analysis of peak discharges is the standard approach for defining extreme flow magnitudes. Peak stage heights can also be subjected to flood frequency analysis using the same approach. Although this approach is unconventional, the uncertainty in the peak stage revealed by frequency analysis forms a lower bound on the uncertainties inherent in BFE estimation by normal means.

It is true that frequency analysis of stage height is not the same thing as frequency analysis of base flood elevation because the BFE is defined relative to an orthometric datum, the North American Vertical Datum of 1988 (NAVD 88; see Chapter 3), and the stage height is defined relative to an arbitrary gage elevation datum. However, it is not necessary to reconcile these datums because what we are seeking is not the elevation itself, but rather the uncertainty of the elevation. The difference between the stage height and the flood elevation is the fixed datum height that is the same for all measurements and thus does not affect their variations from year to year. It should be understood that the purpose of this exercise is to gain insight into the sampling variation of extreme water surface elevations around a statistically determined expected value, not to statistically determine the base flood elevation. Indeed, because the BFE depends on the land surface elevation, which is different at each gaging station on a river, and on drainage area and other factors that vary from one location to another, it is not possible to regionalize the computation of the BFE as it is to regionalize the corresponding base flood discharge. However, as the following analysis demonstrates, there is a great deal of commonality among the sampling uncertainties around statistically estimated extreme stage heights. It is this commonality that lends insight into the corresponding uncertainties in the BFE estimated at the same locations. The sampling uncertainties of extreme stage heights are a lower bound on the corresponding and larger uncertainties in the base flood elevation.

The committee analyzed peak flow records in three physiographic regions in North Carolina to determine whether the uncertainty in the BFE is influenced by topography. The stations evaluated included six gages around mountainous Asheville in Buncombe County, seven gages in the rolling hills near Charlotte in Mecklenburg County, and eight gages distributed along the flat coastal plain (Figure 4.1). The average land surface slope, computed from the National Elevation Dataset, is 26.7 percent in Buncombe County, 6.1 percent in Mecklenburg County, and 0.304 percent in Pasquotank County in the coastal plain. On average, a 1-foot rise in land elevation in Buncombe County corresponds to a horizontal run of 3.7 feet, while in Pasquotank County a 1-foot rise corresponds



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