Use of the Rainfall Hyetograph
A rainfall hyetograph is a graphical representation of the variation of rainfall depth or intensity with time. Rainfall-runoff hydrograph methods require a description of this variation. It is possible to use actual rain gauge data in rainfall-runoff models if the data are recorded using a small enough time period (such as 15-minute increments). Often such data are not readily available.
For design, the use of a single measured rainfall event without consideration of other events is not practical because storms vary considerably from event to event with no probability of occurrence established.
Storm Distributions
In the Rational method the intensity is considered to be uniform over the storm period. Unit hydrograph techniques, however, can account for variability of the intensity throughout a storm although the overall depth for a storm will be the same for a given duration for each method. Therefore, when using unit hydrograph techniques, determine a rainfall hyetograph or distribution. The NRCS Type II and II distributions are examples of standardized
distributions that are available for use. These two distributions are typically described in either an incremental or accumulative rainfall format, usually in 15-minute increments. In addition, they are also considered to be dimensionless. That is, they represent a distribution of one inch of rainfall over a 24-hour period to which a design (frequency) rainfall depth can be applied. The distribution itself is arranged in a critical pattern with the maximum
precipitation period occurring just before the midpoint of the storm.
The table below represents the NRCS 24-hour Type II and III distributions.
NRCS 24-Hour Rainfall Distributions Time, t
(hours)
Fraction of 24-hour Rainfall
Type II Type III
0 0.000 0.000
2 0.022 0.020
4 0.048 0.043
6 0.080 0.072
7 0.098 0.089
8 0.120 0.115
8.5 0.133 0.130
9 0.147 0.148
9.5 0.163 0.167
9.75 0.172 0.178
10 0.181 0.189
10.5 0.204 0.216
11 0.235 0.250
11.5 0.283 0.298
11.75 0.357 0.339
12 0.663 0.500
12.5 0.735 0.702
13 0.772 0.751
13.5 0.799 0.785
14 0.820 0.811
16 0.880 0.886
20 0.952 0.957
24 1.000 1.000
The duration and temporal arrangement of the NRCS 24-hour Type II and III distributions may not always be statistically appropriate for some local conditions or basin sizes, in which case a site-specific rainfall distribution and duration may be necessary. For some sites it may also be necessary to relocate the maximum period of rainfall intensity within the distribution to reflect local conditions such as orographic effects.
Storm Duration
Selecting storm duration is the first step in storm modeling. The determination of
appropriate rainfall duration depends on several factors. The first consideration is technical.
Except for historical analysis, the minimum required storm duration for a basin model must be equal to or greater than the time of concentration of the total (undivided) watershed. (This is the fundamental basis of the Rational method.) This requirement is necessary to assure that a full runoff response from the basin is achieved.
The second consideration is statistical. Although more formal research is required, shorter duration rainfalls are generally more appropriate for application with smaller basins than longer duration storms. Some correlation may exist between storm duration and standard frequencies--that is, short storms may be responsible for producing the runoff for 2- and 5- year events, mid-length storms for the 10- and 25-year events, and longer storms for the 50- and 100-year flood events.
A third consideration is related to standard practice and regulatory preference. A local entity, for example, may prefer the use of specific storm duration based on local experience or a purely arbitrary duration that typically covers all the basin sizes in their jurisdiction.
Likewise, a design office may simply prefer a standardized storm for simplicity. The NRCS 24-hour Type II and III distributions generally fall into this category.
A fourth consideration is based on engineering judgment relative to the critical nature of the project and the consequences of failure. Due to the consequences of failure, dams are typically designed to withstand relatively extreme conditions. Therefore, twenty-four hour storm duration is a more appropriate design consideration for a high hazard dam than a three-hour duration event that meets the minimum technical requirement based on the time of concentration.
For TxDOT use the NRCS 24-hour storm is a starting point for analysis. However, if the analysis results appear inconsistent with expectations, site performance, or experience, consider an alternative storm duration.
Consult the Bridge Division Hydraulics Branch for advice.
Depth-Duration-Frequency
The primary and current sources for rainfall depth-duration-frequency (DDF) relationships are:
♦ Technical Paper No. 40, Rainfall Frequency Atlas of the United States for Durations from 30 minutes to 24 hours and Return Periods from 1 to 100 Years, U.S. Weather Bureau, 1961.
♦ NOAA Technical Memorandum NWS HYDRO-35, Five to 60 minute Precipitation Frequency for the Eastern and Central United States, NWS, 1977.
♦ Technical Paper No. 49, U.S. Weather Bureau, 1964.
Intensity-Duration-Frequency
If only intensity information is available, you can determine the IDF relationships either from IDF curves or by equations typically taking the form of Equation 5-4, where the storm duration (Td) in minutes is used in place of Tc.
The rainfall depth for the selected intensity and duration is simply:
Equation 5-22: D = I Td /60 where:
D = rainfall depth (in.)
I = design rainfall intensity (in./hr) td = storm duration (min.)
Example: Determine the 3-hour, 2-year rainfall depth for Coleman County.
From the 24-Hour Rainfall Depth Versus Frequency Values: e = 0.767, b = 40, and d = 7.6 for the 2-year frequency; Td = 3 hours or 180 minutes and Equation 5-4.
Therefore: I = 40/ (180 + 7.6)0.767
= 0.72 in/hr
…and from Equation 5-22, D = 0.72 x 180 / 60
= 2.16 inches
Standardized Rainfall Hyetograph Development Procedure Use the following steps to develop a rainfall hyetograph:
1. Determine the rainfall depth (Pd) for the desired design frequency, location, and storm duration.
2. Determine the distribution type. Use Figure 5-8 to determine the distribution type.
3. Select a time increment that divides equally into an hour. Use the same time increment as that used for hydrograph generation. For storm durations of 1 to 24 hours, the increment should not exceed 15 minutes. The storm duration for most TxDOT projects will not exceed 24 hours.
4. Create a table of time and the fraction of rainfall to total td rainfall. Interpolate the Rainfall Distributions table for the appropriate distribution type.
5. Calculate the cumulative depth. Multiply the cumulative fractions by the total rainfall depth (from step 1) to get the cumulative depth.
6. Determine the incremental rainfall for each time period by subtracting the cumulative rainfall at the previous time step from the current time step.
A plot of the resulting incremental rainfall versus times represents the rainfall hyetograph.
Standardized Rainfall Hyetograph Example
The following is an example of a rainfall hyetograph for a 25-year, 24-hour storm duration in Harris County using a one-hour time increment for demonstration only.
From the 24-Hour Rainfall Depth Versus Frequency Values: e = 0.724, b = 81, d = 7.7 From Equation 5-4: I = 81 / (1440 + 7.7 )0.724 = 0.417 in./hr
From Equation 5-22: rainfall depth = 0.417 in./hr. x 1440 min. / 60 min./hr. = 10.01 in.
Distribution type (from Figure 5-10) = III For time = 1 hour:
1. Determine the cumulative fraction by interpolating the NRCS 24-Hour Rainfall Distributions table: P1/P24 = 0 +(0.02 - 0) * (1 - 0)/(2-0) = 0.01.
2. The cumulative rainfall is the product of the cumulative fraction and the total 24-hour rainfall: P1 = 0.01 * 10.01 = 0.10 in.
3. The incremental rainfall is the difference between the current and preceding cumulative rainfall values: 0.10 – 0 = 0.10 in.
Repeating the procedure for each time period yields the complete hyetograph ordinates.
The following table presents the calculations. Figure 5-11 shows the resulting hyetograph.
Example of Incremental Rainfall Tabulation (English)
Time Cum.
Fraction
Cum. Rain Incr. Rain (hours) Pt/P24 Pt (in) (in)
0 0 0 0
1 0.01000 0.10 0.10
2 0.02000 0.20 0.10
3 0.03150 0.32 0.12
4 0.04300 0.43 0.12
5 0.05750 0.58 0.15
6 0.07200 0.72 0.15
7 0.08900 0.89 0.17
8 0.11500 1.15 0.26
9 0.14800 1.48 0.33
10 0.18900 1.89 0.41
11 0.25000 2.50 0.61
12 0.50000 5.01 2.50
13 0.75100 7.52 2.51
14 0.81100 8.12 0.60
15 0.84850 8.49 0.38
16 0.88600 8.87 0.38
17 0.90375 9.05 0.18
18 0.92150 9.22 0.18
19 0.93925 9.40 0.18
20 0.95700 9.58 0.18
21 0.96775 9.69 0.11
22 0.97850 9.79 0.11
23 0.98925 9.90 0.11
24 1.00000 10.01 0.11
0.00 0.50 1.00 1.50 2.00 2.50 3.00
1 3 5 7 9 11 13 15 17 19 21 23 25
Time (hours)
Rainfall (in)
Figure 5-13. Example of Rainfall Hyetograph
Balanced Storm Method for Developing Hyetographs
The Balanced Storm Method (also called alternating block) is a straightforward way of developing hyetographs, especially for rainfall duration of less than 24 hours. You can use the method for the design of storm water detention and retention facilities as well as to investigate the effects of development on runoff volumes and discharges for different scenarios. The method employs the department’s intensity-duration-frequency relationship (Equation 5-4).
1. Determine the rainfall intensity coefficients (e, b, and d) for the desired frequency.
2. Establish the desired rainfall duration.
3. Establish a duration interval that divides equally into an hour.
4. Tabulate the duration in increasing values of the interval.
5. Use Equation 5-4 to calculate and tabulate the rainfall intensity.
6. Calculate the cumulative depth for each duration. Multiply the rainfall intensity by the duration.
7. Calculate the incremental rainfall depth for each time period by subtracting the cumulative rainfall at the previous time step from the current time step.
8. Distribute the incremental depth values. Use time blocks that correlate with the duration intervals. Assign the highest incremental depth to the central time block, and arrange the remaining incremental depth blocks in descending order, alternating between the upper and lower time blocks away from the central time block. This is demonstrated in the example that follows.
You may then use the resulting ordinates of the hyetograph as a design rainfall in rainfall- runoff models such as the NRCS dimensionless unit hydrograph method covered earlier in this section. For an example of this distribution method, see Hyetograph Using the Balanced Storm Method.
Section 9