Hydraulic Design of Highway Culverts - DOT On-Line Publications

For gaged sites, statistical analyses can be performed on the recorded stream flow to provide
an estimated peak design flow for a given return period. The accuracy of the estimate improves
as the length of the record increases. For culvert sites significantly removed from the gage, the
peak design flow may have to be adjusted.
Figure II-1--Flood Hydrograph
A typical statistical analysis for data from a gaged site proceeds as follows. First, the annual
peak flows for the site are arranged in descending order. Then, the plotting position is calculated
by one of several available formulas (11). The peak floods are then plotted on a probability
paper to define the frequency relationship for the gage site. If Gumbel paper (Type I external
distribution) is used to plot the data, the mean of the data (mean annual flood) will plot at a
frequency of 0.429. This equates to a return period of 2.33 years. Other return periods can be
read from the frequency plot, because the return period is the inverse of the frequency.
Ungaged sites present more of a design problem. Stream gage data for particular regions have
been utilized to develop statistical regression equations for most areas of the country. These
equations generally require basic watershed parameters such as drainage area and average
stream slope. Using the required data, peak design flows can be determined for ungaged sites
within that region. Deterministic methods are also available which attempt to model the rainfallrunoff
process. The key input parameter in these methods is rainfall which must be related to a
return period. The amount of watershed data required is dependent upon the sophistication of
the model. Table 2 lists some of the commonly employed methods of peak flow generation for
gaged and ungaged sites.
12