Historic rainfall data is compiled and analyzed to predict storm characteristics. Rainfall data is available from a variety of sources, including governmental organizations and agencies. The data can be presented in various formats, including intensity-duration-frequency (IDF) curves, cumulative rainfall depths, and rainfall hyetographs. In infrastructure design, a synthetic rainfall distribution is often applied to the total rainfall depth for a storm of given duration and recurrence frequency. In the United States, the most frequently applied synthetic rainfall distributions are four 24-hour distributions developed by the Natural Resources Conservation Service, U.S. Department of Agriculture.
Intensity-Duration-Frequency Data
For a selected storm duration, a rainfall intensity exists that corresponds to a given exceedance probability or recurrence interval. A rainfall intensity-duration-frequency (IDF) curve illustrates the average rainfall intensities corresponding to a particular storm recurrence interval for various storm durations (see Figure 2-1). These curves are the result of the statistical analysis of rainfall data for a particular area.
Given the information on the graph shown in Figure 2-1, you can determine that the average one-hour rainfall intensity expected to be equaled or exceeded, on average, once every 100 years is 56.0 mm/hr.
Figure 2-1: Example Set of IDF Curves
Although graphical rainfall curves are acceptable for hand calculations, they are not well-suited to computer analyses. Data are therefore input into hydrologic software either as equations or in a tabular format. Creating a rainfall table from a set of IDF curves is a simple matter of manually picking values from the curves. For example, Table 2-1 can be created from the data presented in the IDF curves of Figure 2-1.
Table 2-1: Example IDF Table
Rainfall Intensities (mm/hr)
Storm Return Period
Durations 2 Years 10 Years 100 Years
5 min 88 135 204
10 min 75 114 168
15 min 65 97 142
30 min 44 66 100
60 min 24 37 56
Computer programs commonly access IDF data in the form of an equation. Several forms have been developed to analytically describe the graphical I-D-F relationships. The most common forms of these equations are:
(
b D)
nwhere i = intensity of rainfall (mm/hr, in/hr) D = rainfall duration (minutes or hours) RP = return period (years)
a, b, c, d, m, and n are coefficients
When applying IDF data to system design, you must use data developed for the specific geographic location where the system is to be constructed. A single set of IDF curves can normally be used for areas as large as a city or small county. Many drainage jurisdictions and agencies such as weather bureaus can provide the engineer with IDF data
recommended for their particular geographical location. Engineers should understand when and by whom the IDF curves were created, as more recently updated resources may be available.
In the United States, such information can be found in several National Weather Service publications. For example, the NWS publication TP 40 (Hershfield, 1961) presents maps showing precipitation depths over the United States for storm durations from 30 minutes to 24 hours and for recurrence intervals from 1 to 100 years. TP 40 was partially superceded by a later publication known as HYDRO-35 for the central and eastern United States (Frederick et al., 1977), and by the NOAA Atlas 2 for the 11 coterminous western states (Miller et al., 1973). Updated atlases for the Midwestern United States (Huff and Angle, 1992) and the northeastern United States and southeastern Canada (McKay and Wilkes, 1995) have also been published.
Temporal Distributions and Hyetographs for Design Storms
Some types of hydrologic analyses require the distribution of precipitation over the duration of the storm. A temporal rainfall distribution, such as the one shown in Figure 2-2, shows the cumulative progression of rainfall depth throughout a storm. The y-axis is represented by a simple rain gauge that fills over the period represented on the x-axis.
Total depth is simply the final depth in the gauge. The average intensity (i) during any time segment is represented by the slope of the rainfall curve during that interval. The steeper the slope, the greater the average intensity is for a given segment.
Figure 2-2: Temporal Distribution of Rainfall
The temporal distribution shown in Figure 2-2 can also be represented using a bar graph that shows how much of the total rainfall occurs within each time interval during the course of an event. A graph of this nature is called a rainfall hyetograph. Hyetographs can be displayed in terms of incremental rainfall depth measured within each time interval as shown in Figure 2-3, or as the average intensity calculated for each interval by dividing incremental depth by the time interval.
Figure 2-3: A Hyetograph of Incremental Rainfall Depth versus Time
The design of stormwater management facilities typically requires a complete rainfall hyetograph. For such situations, engineers commonly use synthetic temporal distributions of rainfall, which are essentially systematic and reproducible methods for varying the rainfall intensity throughout a design event.
The selected length Δt of the time increment between the data points used to construct a temporal rainfall distribution depends on the size (area) and other characteristics of the drainage basin. As a rule of thumb, the time increment should be no larger than about one-fourth to one-fifth of the basin lag time (tl), or about one-sixth of the time of
concentration (tc) of the basin. In any case, the smallest time increment for which rainfall data are generally available is about five minutes. In small urban drainage basins where it is often necessary to use time increments as small as one or two minutes, the data must be extrapolated.
In addition to selecting an appropriate Δt, the engineer must select the total duration to be used when developing a design storm hyetograph. In many cases, the storm duration will be specified by the review agency having jurisdiction over the area in which a stormwater conveyance facility will be built; this approach promotes consistency from one design to another.
Many methods have been proposed for distributing a total rainfall depth throughout a storm to develop a design storm hyetograph. The NRCS developed one of the more commonly used methods in the United States (SCS, 1986). With this method, Table 2-2 is used to find fractions of the total accumulated rainfall depth for storms with 24-hour durations. (Figure 2-4 depicts Table 2-2 graphically.) The storms are classified into various types, with each type being recommended for use in a certain U.S. geographical region, as shown in Figure 2-5. If necessary, interpolation may be used to obtain values not shown in Table 2-2. Nonlinear interpolation methods are recommended for this purpose.
Table 2-2: SCS Dimensionless Storm Distributions (SCS, 1986) t (hr) Type I Type IA Type II Type III
0 0.000 0.000 0.000 0.000
1 0.017 0.020 0.011 0.010
2 0.035 0.050 0.022 0.020
3 0.055 0.082 0.035 0.031
4 0.076 0.116 0.048 0.043
5 0.099 0.156 0.063 0.057
6 0.126 0.206 0.080 0.072
7 0.156 0.268 0.098 0.091
8 0.194 0.425 0.120 0.114
9 0.254 0.520 0.147 0.146
10 0.515 0.577 0.181 0.189
11 0.624 0.624 0.235 0.250
12 0.682 0.664 0.663 0.500
13 0.728 0.701 0.772 0.750
14 0.766 0.736 0.820 0.811
15 0.799 0.769 0.854 0.854
16 0.830 0.800 0.880 0.886
17 0.857 0.830 0.902 0.910
18 0.882 0.858 0.921 0.928
19 0.905 0.884 0.937 0.943
20 0.926 0.908 0.952 0.957
21 0.946 0.932 0.965 0.969
22 0.965 0.956 0.978 0.981
23 0.983 0.978 0.989 0.991
24 1.000 1.000 1.000 1.000
Figure 2-4: Graphical Representation of NRCS (SCS) Rainfall Distributions
Figure 2-5: Coverage of NRCS (SCS) Rainfall Distributions (adapted from SCS, 1986)
Example 2-2: Developing a Design Storm Hyetograph from SCS Distributions Develop a design storm hyetograph for a 50-year, 24-hour storm in Boston,
Massachusetts. Assume that Δt = .1 hr is a reasonable choice for the drainage basin to which the design storm will be applied.
Solution
Figure 2-5 illustrates that a Type III storm distribution is a reasonable choice for Boston.
From TP 40, the total depth of a 50-year, 24-hour storm in Boston is estimated to be 6.0 inches. Table 2-3 illustrates the calculation of the storm hyetograph.
The first column of the table is the time, in hours, since the beginning of the storm, and is tabulated in 1-hr increments for the total storm duration of 24 hours. (In actuality, the Δt used in the calculations would be 0.1 hr; the 1-hr increment is used here for brevity.) The second column is the fraction of the total storm depth that has accumulated at each time during the storm. These values are obtained by interpolation from Table 2-2 for the Type III storm distribution. The third column contains the cumulative rainfall depths for each time during the storm and is obtained by multiplying each fraction in the second column by the total storm depth of 6.0 in. The fourth column contains the incremental depths of rainfall within each time interval during the storm; these values are computed as the difference between the current and preceding values in the third column.
Table 2-3: 50-Year, 24-Hour Storm Hyetograph for Boston, Massachusetts t (hr) Fraction Cum. P (in) Incr. P (in)
The resulting graph of cumulative precipitation is shown in Figure 2-6, and the hyetograph is shown in Figure 2-7. The height of each bar on the hyetograph is the average rainfall intensity during that time interval, and the area of each bar is the incremental rainfall depth during that time interval. Because the time increment is 1 hr (1-hr increment is shown for simplicity; actual Δt is 0.1 hr), the value for the height of the bar (in units of in/hr) is equal to the incremental depth for that time increment (in inches).
Figure 2-6: Graph of Derived Design Storm Cumulative Precipitation
Figure 2-7: Derived Design Storm Hyetograph
2.2 Rainfall Abstractions and Runoff Volume
Only a portion of the total rainfall occurring over a drainage basin contributes to surface runoff and stream flow. In fact, a simple comparison of rainfall and runoff records for most locations in the United States shows that the equivalent depth of runoff is typically about 30 to 50 percent of the precipitation depth.
To obtain the loading information necessary to design and model structures such as storm sewers, culverts, and detention facilities, it is necessary to calculate the runoff volumes and/or flow rates resulting from the storm events of interest. This section presents three techniques for computing total runoff volume: (1) the Horton equation, (2) the runoff coefficient, and (3) the NRCS curve number equation.