Estimating the peak discharge for which highway drainage structures are to be designed is one of the most common problems and biggest challenges faced by the highway engineer. The problem may be separated into two categories: (1) watersheds for which historical runoff data are available, those with gauged sites, and (2) areas for which no data are available. Gauged sites lend themselves to analysis of runoff by statistical methods, whereas ungauged sites rely upon hydrologic equations based on the hydrologic and physiographic characteristics of the watershed.
The runoff data necessary to utilize statistical methods are available through the USGS, which is the primary collector of such data. Additional data sources are given in Chapter 3 of FHWA publication HDS 2 “Highway Hydrology.” Provided that sufficient data are available for a specific site, a statistical analysis may be made that will result in a reasonable determination of the peak discharge. Water Resources Council Bulletin 17B, 1981, suggested that a minimum of 10 years of historic data are necessary to make an accurate estimation based on statistical methods. The USGS has no specific time requirements for historical hydrologic data collection. In the past, however, the recommended time period varied between 10 years for a 10-year design flood to 25 years for a 100-year design flood. HDS 2 should be referenced for different techniques available for determining the inferences of population characteristics from statistics.
Data collection can be categorized and arranged in groups that lend themselves to statistical analysis. The common groupings are by magnitude of peak annual discharge, by time of occurrence, and by geographic location. Of the three, magnitude of peak annual discharge is the most useful in determining peak discharge. Time of occurrence is the most useful in trend analysis or determining the effects of changing land use on runoff. Grouping by geographic location is the most useful when looking at sites that
have insufficient flood data either because they are ungauged or because the historical time frame of the collected data is too short.
There are several standard frequency distributions that have been extensively studied in the statistical analysis of hydrologic data. Three of the most useful are (1) log-Pearson type III distribution, (2) lognormal distribution, and (3) Gumbel extreme value distribution. The log-Pearson type III distribution is popular largely because the distribution very often fits the available data closely and it is flexible enough to be used with many other types of distributions. Because of this flexibility, the U. S. Water Resources Council has recommended that it be used by all governmental agencies as the standard distribution for flood frequency studies. The characteristics of the lognormal distribution are the same as those of the classical normal or Gaussian mathematical distribution except that the flood flow at a specified frequency is replaced with its logarithm and has a positive skew. Positive skew means that the distribution is skewed toward the high flows or extreme values. The characteristics of the Gumbel extreme value distribution (also known as the double exponential distribution of extreme values) are that the mean flood occurs at the return period Tr of 2.33 years and that it has a positive skew.
If runoff data are unavailable for a specific watershed area, one method that may be used to determine the peak stream discharge is a regional flood-frequency analysis. By using historical runoff records from similar drainage basins in the immediate area, estimates of peak discharges may be developed. The USGS is continuously updating the methodology by which the agency performs regional flood-frequency analyses. Recent advances include the use of the “ordinary least squares” and “region of influence” methods for regionalizing historic stream flow data.
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The statistical distributions commonly used for regional flood-frequency analysis result in an equation of the general form:
where Y = dependent variable
a = intercept coefficient Xj, X2,…, Xn = independent variables b1, b2,…, bn = regression coefficients
In practice, the dependent variable is the estimated stream flow for a given return period. The intercept coefficient is a constant used to differentiate the regions used in the analysis and the required return periods. The independent variables are drainage basin characteristics such as drainage area, basin or channel slope, and types of land cover; meteorological characteristics such as annual rainfall; and channel characteristics such as cross-sectional area, active channel width and depth, and flood-plain width and depth.
It is important to note the limitations of regional flood-frequency analyses and the resulting regression equations. In general, independent variables should be determined using the same techniques as were used during the regression analyses. For example, if USGS 7.5-minute quadrangles were used to determine basin characteristics for the regression analysis, then basin characteristics should also be obtained from 7.5-minute quadrangles for peak discharge estimations.
