CHAPTER 7, APPENDIX A

Transcription

1 CHAPTER 7, APPENDIX A FIELD MANUAL FOR PENNSYLVANIA DESIGN RAINFALL INTENSITY CHARTS FROM NOAA ATLAS 14 VERSION 3 DATA 7A.0 INTRODUCTION Previously used procedures to estimate design rainfall intensities, usually obtained from the U.S. Weather Bureau Technical Paper No. 40 (Hershfield, 1961) or the 1986 Field Manual of PennDOT Storm-Intensity-Duration- Frequency Charts PDT-IDF (Aron et al., 1986), have been updated in this appendix. The regional rainfall design curves in this Pennsylvania field manual were developed from frequency analyses based on hourly records from 278 daily and 139 hourly rainfall gages in Pennsylvania plus gages in surrounding states for a period of record from April 1, 1863 through December 31, The analysis leading to the design curves is fully described in this Appendix. In performing the PDT-IDF analysis, it was found that there were regional differences in rainfall patterns between storm durations. For example, the lowest intensities and amounts for the five (5) minute storms are located in north central PA, whereas the lowest intensities and amounts for the twenty-four (24) hour storm are located in western PA. It was determined that one rainfall region map would not adequately represent the rainfall patterns. Therefore, the maps were developed based upon storm duration and frequency as shown in Table 7A.1. 7A.1 PROCEDURE FOR FINDING DESIGN INTENSITY VALUES A. Objective. To obtain the design rainfall or return periods from 1 to 100-years and durations from 5 minutes to 24 hours and to obtain the 500-year, 24-hour precipitation. Step 1 Step 2 Determine the rainfall duration of the storm that will need to be analyzed. For the rational method, the required storm duration will be equal to the time-of-concentration. From Table 7A.1, determine what Rainfall Region Map should be utilized for the design storm duration of interest. Table 7A.1 Appropriate Rainfall Region Map for each Storm Duration and Frequency Frequency Duration 1 year 2 year 5 year 10 year 25 year 50 year 100 year 500 year 5 min C C C C B B B - 10 min C C C C C C C - 15 min A A A A C C C - 30 min A A A A A C C - 60 min A A A A A C C - 2 hr E E E E E E E - 3 hr E E E E E E E - 6 hr D D D D D D D - 12 hr F F F F F F F - 24 hr F F F F F F F F Step 3 Locate the area of interest on the Pennsylvania map for the Map determined in Step 2 (Figures 7A.1 through 7A.6) and note the region into which this area falls. 7A - 1

2 If a basin should be found to lie on the boundary between two regions, the intensities should be obtained from the two corresponding regional graphs and averaged. In the case that the basin is large enough to be divided into areas A i and A j of measurable size in the adjacent regions i and j, a weighted average intensity may be used. I = Ii A A i + i + IjAj Aj Step 4 From the PDT-IDF curves for that region, determine the rainfall intensity. The rainfall values for the five-minute through six (6) hour storms can be obtained directly from Tables 7A.2(a/b) through 7A.6(a/b) for each of the five regions or from interpolation from the PDT-IDF curves, Figures 7A.7(a/b) through 7A.16(a/b). For the twelve (12) and twenty-four (24) hour storms, the rainfall values can only be obtained directly from Tables 7A.2(a/b) through 7A.6(a/b) for each of the five regions. Table 7A.2(a) Five (5) minute through twenty-four (24) hour storm totals for Region 1 (Metric). Region 1 Rainfall Total 1-Yr Storm 2-Yr Storm 5-Yr Storm 10-Yr Storm 25-Yr Storm 50-Yr Storm 100-Yr Storm 500-Yr Storm Duration (Min) cm cm cm cm cm cm cm cm Table 7A.2(b) Five (5) minute through twenty-four (24) hour storm totals for Region 1 (U.S. Customary). Region 1 Rainfall Total 1-Yr Storm 2-Yr Storm 5-Yr Storm 10-Yr Storm 25-Yr Storm 50-Yr Storm 100-Yr Storm 500-Yr Storm Duration (Min) in in in in in in in in A - 2

3 Duration (Min) Table 7A.3(a) Five (5) minute through twenty-four (24) hour storm totals for Region 2 (Metric). Region 2 Rainfall Total 1-Yr Storm 2-Yr Storm 5-Yr Storm 10-Yr Storm 25-Yr Storm 50-Yr Storm 100-Yr Storm 500-Yr Storm cm cm cm cm cm cm cm cm Table 7A.3(b). Five (5) minute through twenty-four (24) hour storm totals for Region 2 (U.S. Customary). Duration (Min) Region 2 Rainfall Total 1-Yr Storm 2-Yr Storm 5-Yr Storm 10-Yr Storm 25-Yr Storm 50-Yr Storm 100-Yr Storm 500-Yr Storm in in in in in in in in A - 3

7 1. Example. Determine the 10-year rainfall intensity for a drainage area in eastern Schuylkill County that has a time-of-concentration (T c ) of 12 minutes. Step 1 Step 2 The duration would be equal to the time-of-concentration or 12 minutes Since 12 minutes is less than half way between the midpoint between the 10- and 15-minute increment in Table 7A.1, the Map corresponding to the 10-minute duration would be utilized, or Map C. If the T c value falls between values shown in Table 7A.1, one should round to the nearest value in the Table. For example, if a 14-minute T c was obtained, the map shown for the 15-minute duration should be utilized, or Map A. A value of 12.5 would also be rounded to 15 minutes and Map A chosen. Note that rounding is only necessary for map determination. The original T c value should be utilized to obtain the rainfall intensity. Step 3 From Map C, the site would fall in Region 4. Step 4 From the PDT-IDF curve for Region 4, the 10-year, 12-minute storm would be 12.2 cm per hour (4.8 in per hour). NOTE: EQUATION 7.9 FOR THE RATIONAL METHOD IN METRIC UNITS USES mm/hr AS THE RAINFALL UNIT, NOT cm/hr. CHARTS IN APPENDIX 7A ARE IN UNITS OF cm/hr. THE RAINFALL INTENSITIES DERIVED FROM APPENDIX 7A WILL NEED TO BE CONVERTED FROM cm/hr TO mm/hr FOR USE IN THE RATIONAL METHOD, METRIC UNITS. B. Composite Design Storms. In storm runoff modeling, design storms are often needed which are not only appropriate for the entire watershed, but for individual subareas as well. Design storms are typically classified by Average Recurrence Interval (ARI), which is established based upon the frequency of an event or how often an event is statistically likely to occur. The ARI is inversely equivalent to the probability that an event will occur in any given year. For instance, a 100-storm is inversely equivalent to 0.01 which means this event has a 1% chance of occurring in any given year. Similarly, the 25-year storm has is inversely equivalent to 0.04 which means this event has a 4% probability of occurring in any given year. A complete design storm, constructed as described below, will demonstrate the procedures used to obtain precipitation estimates for a given ARI which can then be used for design and analysis. The composite design storm should be generated such that the maximum rain falling over any time span (centered around the storm peak), equals the design storm depth indicated for the corresponding durations. As an example, a 10-year design storm for the same site will be constructed for a location in Map C, Region 4 for the 10-minute duration and Map A, Region 5 for the 20 through 80 minute durations. The storm is to be defined in 10-minute intervals, for a total duration of 80 minutes. The storm peak shall be placed at or right after the center of the storm and that the storm shape be approximately symmetrical. Step 1 From Figures 7A.13(b) and 7A.14(b), obtain 10-year rainfall amounts for the 10 minute duration and from Figures 7A.15(b) and 7A.16(b), obtain 10-year rainfall amounts for the minute durations (the appropriate map and region), and list them as in column (2) in Tables 7A.7(a) and 7A.7(b). Step 2 Compute the incremental rainfall amounts between consecutive durations. Enter into column (3). Step 3 Rearrange the rainfall increments from column (3) to column (4) in a quasi-symmetrical pattern, moving first and largest storm interval time to minutes, the second to minutes, the third to minutes and so forth. Step 4 Compute the rain intensities during the time increments, dividing column (4) by the time step (10 minutes) and multiplying by 60 minutes. Enter the intensities into column (5) and plot the hyetograph. 7A - 7

8 Table 7A.7(a) Composite 10-year storm in Region 5 (Metric). (1) Storm duration (minutes) and Map (2) Rainfall amount (cm) Map C* Map A Map A Map A Map A Map A Map A Map A 5.58 * For region 4 (3) Rainfall increments (cm) (4) Rearranged rainfall inc. (cm) (5) Rearranged rainfall int. (cm/hour) Table 7A.7(b). Composite 10-year storm in Region 5 (U.S. Customary). (1) Storm duration (minutes) and Map (2) Rainfall amount (in) Map C* Map A Map A Map A Map A Map A Map A Map A 2.20 * For region 4 (3) Rainfall increments (in) (4) Rearranged rainfall inc. (in) (5) Rearranged rainfall int. (in/hour) A - 8

9 Figure 7A.1 Map A. 15-, 30- and 60-minute durations for storms occurring with an ARI of 1-, 2-, 5-, 10-years and 30- and 60-minute durations for storms occurring with an ARI of 25-years. 7A - 9

10 Figure 7A.2 Map B. 5-minute durations for storms occurring with an ARI of 25-, 50- and 100-years. 7A - 10

11 Figure 7A.3 Map C. 5- and 10-minute durations for storms occurring with an ARI of 1-, 2-, 5-, and 10-years, 10- and 15-minute durations for storms occurring with an ARI of 25-years and 10-, 15-, 30-, 60-minute durations for storms occurring with an ARI of 50- and 100-years. 7A - 11

12 Figure 7A.4 Map D. 6-hour durations for storms occurring with an ARI of 1-, 2-, 5-, 10-, 25-, 50- and 100-years. 7A - 12

13 Figure 7A.5 Map E. 2- and 3-hour durations for storms occurring with an ARI of 1-, 2-, 5-, 10-, 25-, 50- and 100-years. 7A - 13

14 Figure 7A.6 Map F. 12- and 24-hour durations for storms occurring with an average recurrence interval (ARI) of 1-, 2-, 5-, 10-, 25-, 50-, and 100-years and the 24-hour duration for the 500-year frequency storm. 7A - 14

15 Figure 7A.7(a) Rainfall Intensity for 1- through 100-year Storms for Region 1 (Metric). Figure 7A.7(b) Rainfall Amount for 1- through 100-year Storms for Region 1 (Metric). 7A - 15

16 Figure 7A.8(a) Rainfall Intensity for 1- through 100-year Storms for Region 1 (U.S. Customary). Figure 7A.8(b) Rainfall Amount for 1- through 100-year Storms for Region 1 (U.S. Customary). 7A - 16

25 7A.2 SAMPLE PROBLEMS UTILIZING THE PDT-IDF CURVES AND DATA A. Sample 1. Rational Method Rainfall Intensity Computing Peak Flow (Q) for Storm Sewer and Inlet Sizing. For culvert and pipe sizing where drainage areas are less than 80 hectares (200 acres) and full hydrographs are not required, often the rational method is the most suitable method to compute peak rates of runoff for design. The following example provides the process of obtaining the rainfall intensity for the determination of the rational peak flow value (Q) for the 10-year design storm. Rational Method: 10-year Storm, the center of Armstrong County Determine the Q to an inlet along a road. Drainage Area (A): = 91.4 meters (300 feet) x 15.2 meters (50 feet) pavement width = 1,389.3 square meters (15,000 sf) = 0.14 hectares (0.34 ac) T c = 5 min C = 0.95 from Table 7.6, page 7-27, Chapter 7, Hydraulics Rainfall: Step 1 Determine the appropriate rainfall region map using Table 7A.1. For the 10-year 5 minute storm, Map C would be the appropriate map to determine rainfall region. Step 2 From Figure 7A.3, Map C, the center of Armstrong County would fall within Region 3 Step 3 From Figures 7A.11(a) or 7A.12(a), the 10-year, 5-minute rainfall intensity (I) would be cm/hr (6.2 in/hr). Step 4 Convert cm/hr to mm/hr by multiplying the metric value from Figure 7.A.11(a) by 10 mm/cm to yield 157mm/hr, for use in the rational equation. NOTE: EQUATION 7.9 IN METRIC UNITS USES mm/hr AS THE RAINFALL UNIT, NOT cm/hr. CHARTS IN APPENDIX 7A ARE IN UNITS OF cm/hr. Step 5 From Equation 7.9, Compute the flow (Q) C = 0.95 (Table 7.6) C f = 1 (Table 7.7) I = mm/hr (6.2 in/hr) A = 0.14 hectares (0.34 Ac) METRIC Q = CC f IA/360 = (.95)(1)(157.5)(.14)/360 = m 3 /s (cfs) US CUSTOMARY Q = CC f IA (U.S. Customary) = (.95)(1)(6.2)(.34) = 2.0 cfs 7A - 25

26 B. Sample 2. Rational Samples - Rainfall Intensity Computing Peak Flow (Q) for Storm Culvert Sizing. Using the rational method, determine the Q 25 to size three roadside culverts from three separate contributing drainage areas in central Pike County. Given: Subarea D.A. (ha) D.A. (ac) C (Table 7.6) C f (Table 7.7) T c (min) Step 1 From Table 7A.1, determine the map needed in order to obtain the required rainfall region. Subarea D.A. (ha) D.A. (ac) C C f T c (min) Map B A C Step 2 From each map (Figures 7A.2,1 and 3 respectively), determine what region should be utilized. Subarea D.A. (ha) D.A. (ac) C C f T c (min) Map Region B A C 4 Step 3 From the appropriate PDT-IDF curve, determine the rainfall intensity to be used for each subarea. NOTE: EQUATION 7.9 IN METRIC UNITS USES mm/hr AS THE RAINFALL UNIT, NOT cm/hr. CHARTS IN APPENDIX 7A ARE IN UNITS OF cm/hr. THE RAINFALL INTENSITIES DERIVED FROM APPENDIX 7A WILL NEED TO BE CONVERTED FROM cm/hr TO mm/hr. METRIC Subarea Rainfall Intensity From Figure (cm/hr) Rainfall Intensity Conversion (mm/hr) D.A. (ha) C C f T c (min) Map Region Figure B 3 7A.11(a) A 3 7A.11(a) C 4 7A.13(a) US CUSTOMARY Subarea D.A. (ac) C C f T c (min) Map Region Figure Rainfall Intensity (in/hr) B 3 7A.12(a) A 3 7A.12(a) C 4 7A.14(a) 5.4 7A - 26

27 Step 4 METRIC From Equation 7.9, Compute the flow (Q). Subarea Q = CC f IA/360 Q (m 3 /s) 1 = (.95)(1.1)(177.80)(0.49)/ = (.87)(1.1)(96.52)(4.33)/ = (.79)(1.1)(137.16)(2.31)/ US CUSTOMARY Subarea Q = CC f IA Q (cfs) 1 = (.95)(1.1)(7.0)(1.2) = (.87)(1.1)(3.8)(10.7) = (.79)(1.1)(5.4)(5.7) 26.7 C. Sample hour Storm Total and Composite Design Storms for PDT-IDF 'S' Curve and Hyetograph. In storm runoff modeling, design storms are often needed for a 24-hour storm represented by a typical 'S' curve. A composite 24-hour design storm, constructed as described below, will serve this purpose. The composite design storm should be generated such that the maximum rain falling over any time span (centered around the storm peak), equals the design storm depth indicated for the corresponding durations. As an example, a 50-year design storm for the same site will be constructed for a location in southeast Bucks County. The storm is to be defined in 15-minute intervals, for a total duration of 24 hours (1440 minutes). It is advisable to place the storm peak at or right after the center of the storm and that the storm shape be approximately symmetrical. The process is best set up in an Excel spreadsheet. Since we are obtaining the 50-year Average Recurrence Interval (ARI) storm, the following maps will be utilized for each storm duration rainfall amount. Step 1 From Table 7A.1, Determine which map applies to each duration for the 50-year storm as shown in Table 7A.8(a). Step 2 Find the region the site is located within for each map determined in Step 1. For the 5-minute duration, Figure 7A.2 (Map B) yields Region 3 For the 10-, 15-, 30-, and 60-minute duration, Figure 7A.3 (Map C) yields Region 5 For the 2 and 3-hour duration, Figure 7A.4 (Map E) yields Region 5 For the 6-hour duration, Figure 7A.5 (Map D) yields Region 5 For the 12 and 24-hour duration, Figure 7A.6 (Map F) yields Region 5 To better smooth the curve, it may be necessary to obtain values for storm durations not specified in Table 7A.1, for example the 90, 500, 800, 1000, 1200, 1300, 1350, and 1400 minute durations shown in Table 7A.8 (a) and (b). If a storm duration does not appear in Table 7A.1, the map that should be utilized should be the one for the closest storm duration in Table 7A.1. For instance, a storm duration of 500 minutes is closer to the 6 hour (360 minutes) duration than the 12 hour (720 minutes) duration. Therefore, map D should be utilized for the 50-year storm. For storm durations that fall directly between two storm durations specified in Table 7A.1, the appropriate maps on either side of the selected time can be inspected to obtain the appropriate rainfall region. If the two maps place the site in two different regions the precipitation estimates for both regions should be obtained and the larger of the two precipitation values selected to complete the calculations. For instance, 90 minutes falls midway between the 60 and 120 minute durations. Therefore both maps C and E should be inspected. It should be noted that the values for these intermediate storms not shown in Table 7A.1 may be adjusted slightly to provide for a smoother fitting curve. The values in table 7A.1 may not be modified. 7A - 27

28 Step 3 From Tables 7A.4(a) and 7A.4(b) or Figures 7A.11(b) and 7A12(b) (Region 3), obtain 50-year rainfall amount for the 5-minute duration. (1.65 cm (0.65 in)) From Tables 7A.6(a) and 7A.6(b) or Figures 7A.15(b) and 7A16.(b) (Region 5), obtain 50-year rainfall amounts for the 10-, 15-, 30-, 60-, 120-, 180-, 360-, 720-, and 1440-minute durations (from the appropriate map and region), and list them as in column (2) in Tables 7A.8(a/b) below. The Maps and Regions (columns 3 and 4) may be listed for reference. Therefore, per Table 7A.8 (a/b), the 50-year, 24-hour rainfall total amount would be cm (7.16 inches), which may be utilized for the storm total in TR-55, HEC-HMS or other computations. 7A - 28

29 Table 7A.8(a). Values obtained from 2007 PDT-IDF (Metric) 50-year -24-hour Storm Minutes Amt (cm) Map Region B C C C C C, E E E D D F F F F F F F F 5 Table 7A.8(b). Values obtained from 2007 PDT-IDF (U.S. Customary) 50-year -24-hour Storm Minutes Amt (in) Map Region B C C C C C, E E E D D F F F F F F F F 5 7A - 29

30 Figure 7A.17(a). Initial Plot of the Data (Metric) Rainfall (cm) year Storm Time (minutes) Series1 Figure 7A.17(b). Initial Plot of the Data (U.S. Customary) Rainfall (inches) year Storm Series Time (minutes) Step 4 Step 5 Determine the rainfall distribution, by plotting a curve of the rainfall amount vs. time as shown in Figure 7A.17 (a/b). It has been found that obtaining additional rainfall values for durations not specified in Table 7A.1 (a/b) provides for a smoother curve and a more accurate equation of the curve. Initial values should be obtained from the PDT-IDF curves Figures 7A.7 through 7A.16. Initial rainfall values can be plotted and fitted with a smooth curve to obtain rainfall values for the entire 24-hour event. It is important to not fit an equation to the entire curve, as it will not appropriately represent the center and end portions of the curve. Instead, the data should be divided into two portions, with separate curves and equations developed for the beginning and end portions of the storm, to more accurately estimate the rainfall throughout the event. Split the data into two Tables (halves), as shown in Tables 7A.9(a), 7A.9(b), 7A.10(a), and 7A.10(b). Then develop curves and equations to fit the data, and R 2 values for each half as shown in Figures 7A.18(a), 7A.18(b), 7A.19(a), and 7A.19(b). 7A - 30

31 Table 7A.9(a). Data from Time 0 to 500 Minutes (Metric) Minutes Amt (cm) Table 7A.9(b). Data from Time 0 to 500 Minutes (U.S. Customary) Minutes Amount (in) Figure 7A.18(a). Logarithmic Curve Developed from 0 to 500 Minutes (Metric) Rainfall (cm) y = Ln(x) R 2 = Series1 Log. (Series1) Time (minutes) 7A - 31

32 Figure 7A.18(b). Logarithmic Curve Developed from 0 to 500 Minutes (U.S. Customary) Rainfall (in) y = Ln(x) R 2 = Series1 Log. (Series1) Time (minutes) Table 7A.10(a). Data from Time 500 to 1440 Minutes (Metric) Minutes Amt (cm) Table 7A.10(b). Data from Time 500 to 1440 Minutes (U.S. Customary) Minutes Amount (in) A - 32

33 Figure 7A.19(a). Logarithmic Curve Developed from 500 to 1440 Minutes (Metric) Rainfall (cm) y = Ln(x) R 2 = Series1 Log. (Series1) Time (minutes) Figure 7A.19(b). Logarithmic Curve Developed from 500 to 1440 Minutes (U.S. Customary) Rainfall (in) y = Ln(x) R 2 = Series1 Log. (Series1) Time (Minutes) Step 6 Step 7 Develop a table similar to Table 7.A.11 (a/b) using both curves. This table can be used to determine the time at which the two curves intercept and the development of a composite rainfall curve. The values in column (3) are from Tables 7A.8 (a/b) and based on the maps and the corresponding regional precipitation curves using the procedure discussed in Step 3. The values in Column 4 are calculated from the regression equation representing the curve for the time frame 0 to 500 minutes. Similarly the values in column (5) are calculated from the equation representing the curve for the time frame 500 to 1440 minutes. Negative values at the top of column (5) are not an issue since this portion of column (5) is not used in the composite curve. As can be seen in the Table 7.A.11(a/b), the numbers merge near time 315 minutes, which for this example is considered the intercept of the two curves. Create the composite rainfall curve in column (6) by using the rainfall data from column 4 for the first part of the event (green shading) and use the data from column (5) for the second part (orange shading), or later portion, of the storm. 7A - 33

34 Storm Duration Chapter 7, Appendix A - Field Manual for Pennsylvania Design Rainfall Intensity Publication 584 Table 7A.11(a). Composite Storm Development (Metric) Column Rainfall Rainfall Rainfall Rainfall Rearranged Rearranged Storm From Incremental From From From Rainfall Rainfall Duration Column Rainfall PDM Eqn. 1 Eqn. 2 Distribution Intensity 4 or 5 Fraction of 24-hr Rainfall Hour Minute (cm) (cm) (cm) (cm) (cm) (cm) (cm/hr) (%) A - 34

35 Storm Duration Chapter 7, Appendix A - Field Manual for Pennsylvania Design Rainfall Intensity Publication 584 Column Rainfall Rainfall Rainfall Rainfall Rearranged Rearranged Storm From Incremental From From From Rainfall Rainfall Duration Column Rainfall PDM Eqn. 1 Eqn. 2 Distribution Intensity 4 or 5 7A - 35 Fraction of 24-hr Rainfall Hour Minute (cm) (cm) (cm) (cm) (cm) (cm) (cm/hr) (%)

36 Storm Duration Chapter 7, Appendix A - Field Manual for Pennsylvania Design Rainfall Intensity Publication 584 Column Rainfall Rainfall Rainfall Rainfall Rearranged Rearranged Storm From Incremental From From From Rainfall Rainfall Duration Column Rainfall PDM Eqn. 1 Eqn. 2 Distribution Intensity 4 or 5 Fraction of 24-hr Rainfall Hour Minute (cm) (cm) (cm) (cm) (cm) (cm) (cm/hr) (%) Table 7A.11(b). Composite Storm Development (U.S. Customary) Column Rainfall Rainfall Rainfall Rainfall Rearranged Rearranged Fraction of Storm Storm From Incremental From From From Rainfall Rainfall 24-hr Duration Duration Column Rainfall PDM Eqn. 1 Eqn. 2 Distribution Intensity Rainfall 4 or 5 Hour Minute (in) (in.) (in) (in) (in) (in) (in/hr) (%) A - 36

37 Column Rainfall Rainfall Rainfall Rainfall Rearranged Rearranged Storm From Incremental From From From Rainfall Rainfall Duration Column Rainfall PDM Eqn. 1 Eqn. 2 Distribution Intensity 4 or 5 Storm Duration 7A - 37 Fraction of 24-hr Rainfall Hour Minute (in) (in.) (in) (in) (in) (in) (in/hr) (%)

38 Column Rainfall Rainfall Rainfall Rainfall Rearranged Rearranged Storm From Incremental From From From Rainfall Rainfall Duration Column Rainfall PDM Eqn. 1 Eqn. 2 Distribution Intensity 4 or 5 Storm Duration Fraction of 24-hr Rainfall Hour Minute (in) (in.) (in) (in) (in) (in) (in/hr) (%) Step 8 Step 9 Compute the incremental rainfall amounts in column (7) by subtracting consecutive values entered in column (6). Rearrange the rainfall increments from column (7) to column (8) in a quasi-symmetrical pattern, moving first and largest storm interval time to 720 minutes. Place the second largest incremental rainfall amount at 735 minutes and the third largest incremental rainfall amount immediately preceding the peek, at 705 minutes. Continuing placing the incremental rainfall amounts on either side of the peak until all of the incremental rainfall values fill column 8. This data represents the rainfall distribution for a particular event and could then be input into a hydrologic model such as HEC-HMS for additional hydrologic analysis. Plot the hyetograph from Column 8 as shown in Figures 7A.20(a) and 7A.20(b). 7A - 38

39 Figure 7A.20(a). Hyetograph for the 50-year Storm, Region 5 (Metric) Rainfall (cm) Time (Minutes) Figure 7A.20(b). Hyetograph for the 50-year Storm, Region 5 (U.S. Customary) 1.60 Rainfall (in) Time (Minutes) Step 10 Step 11 (Optional) If incremental intensities are required, divide rearranged rainfall distribution in column (8) by the time step (15 minutes) and multiply by 60 minutes as shown in Tables 7A.7(a/b) to obtain in incremental intensity in units of depth of rainfall/hour. (Optional) To plot the 'S' Curve of the rainfall pattern, the rearranged incremental rainfall values in column (8) can be divided by the total 24-hour storm precipitation of cm (7.16 in) to obtain the fraction of the 24-hour precipitation that has fallen for any given time increment. A running total of each time increment is placed in column (10) to obtain the total fraction of rainfall that has fallen with respect to time. The 'S' Curve is plotted using columns (2) and (10) as shown in Figure 7A.21. Since the 'S' curve is a plot of ratios of a unit of rainfall, the metric and U.S. customary units will plot identical. 7A - 39

40 Figure 7A.21. S-Curve for the 50-year Storm, Region 5 (Metric and U.S. Customary) 24-Hour Rainfall Distribution Fraction of 24-Hour Rainfall Time (Minutes) Note: It should be noted that the values obtained from the equations will vary slightly from the values obtained from the PDT-IDF charts and graphs. The variation is typically not significant enough to have a significant impact on the hydrograph or peak flow results. However, if the engineer sees it justifiable, the columns could be multiplied by the ratio of the difference in values to match the exact number. Also, one may notice in the hyetograph and tables, that there is a slight shift in rainfall difference for each increment near the intercept. This will not significantly affect the peaks. If warranted, the user may readjust the values at each time increment to smooth the curve. 7A.3 REFERENCES Aron, G., D.J. Wall, E.L. White, C.N. Dunn, D.M. Kotz (1986). Field Manual of Pennsylvania Department of Transportation Storm Intensity-Duration-Frequency Charts (PDT-IDF). Department of Civil Engineering and Institute for Research on Land and Water Resources, The Pennsylvania State University. May Hershfield, D. M. (1961). Rainfall Frequency Atlas of the United States for Durations from 30 minutes to 24 hours and Return Periods from 1 to 100 years. Weather Bureau Technical Paper No. 40, U.S. Weather Bureau, Washington D.C. 7A - 40