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FLOW PEAK RISING LIMB ~ ~ . A 4 ~ FALLING LIMB 4 , ..I . 'I oj l . ~ 4 l 1 . i j ~ A ~ ~ TIME ~ l ~ I ~ I GROUNDWATER CONTRIBUTION period is the inverse of the frequency. . l ~ Figure II-l.--Flood hydrograpb. 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. A typical statistical analysis for data from a gaged site proceeds as fol- lows, First, the annual peak flows for the site are arranged in descending or- der. 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 extremal 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 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 equa- tions generally require basic watershed parameters such as drainage area and average stream slope. Using the required data, peak design flows can be determined for un gaged sites within that region. Deterministic methods are also available which attempt to model the rainfall-runoff 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 em- ployed methods of peak flow generation for gaged and ungaged sites, l , 1 i t , l i j 14 1 ~