Design Storms for Hydrologic Analysis

Transcription

1 Design Storms for Hydrologic Analysis Course Description This course is designed to fulfill two hours of continuing education credit for Professional Engineers. Its objective is to provide students with an overview of the concepts of design storms used in hydrologic design applications. The course will cover different methods for estimating design rainfall depths and intensities at a specific point and over different areas of drainage basins or catchments. Design charts and tables are presented with detailed descriptions of their usage. Coverage of different methods used to derive storm hyetographs is provided. Chapters Chapter 1: Design Storms and Development of Point Precipitation Data Chapter 2: Intensity-Duration-Frequency Relationships & Design Hyetographs Learning Objectives Upon completion of the course, the participant will be able to: Understand the concepts of design storm and return period Understand how to select a frequency or a return period for a specific design storm Identify different methods for developing design storms Interpret design maps and charts of the National Weather Service (NWS) Explain how to interpolate from standard charts to derive design rainfall for intermediate return periods and storm durations Derive areal rainfall design depths from point values Understand the concepts behind intensity-duration-frequency (IDF) relationships Derive design hyetographs using the triangular method, the NRCS method, and the alternating block method Page 1

2 Chapter One: Design Storms and Development of Point Precipitation Data Overview Introduction Design Frequency and Return Period Design point precipitation depths Areal reduction of point precipitation depths Learning Objectives Understand the concepts of design storm and return period Understand how to select a frequency or a return period for a specific design storm Identify different methods for developing design storms Interpret the different design maps and charts of the National Weather Service (NWS) Comprehend how to extract the design point rainfall values from NWS technical papers and design charts Explain how to interpolate from standard charts to derive design rainfall for intermediate return periods and storm durations Recognize how to derive areal rainfall design depths from point values Introduction What is a Design Storm? A design storm (sometimes called a hypothetical or synthetic storm) is a precipitation pattern defined and used for both design of a hydrological system and planning of hydrologic studies. Design storms are based either on: 1) historical precipitation data at various sites, or 2) analysis of general characteristics of precipitation in a certain region. How is a Design Storm Specified? A design storm can be defined in terms of: 1 a. A value of precipitation depth at a point b. A hyetograph defining time distribution of precipitation during a storm c. An isohyetal map defining the spatial pattern of precipitation Applications of Design Storms There are several design and planning hydrologic applications of design storms: a. Design storms are used in water resources for designing hydraulic structures (e.g., highway culverts), flood control (large spillways), and urban stormwater drainage systems. b. Design storms are used as inputs to standard hydrologic design methods, such as the rational method, to determine peak flows for design of urban storm sewers and culverts. c. Design storms drive rainfall-runoff analyses (e.g., watershed models) that are necessary for design of urban detention basins and large reservoirs. d. Design storms are used to evaluate the effect of urban development projects on flood levels in downstream locations and surrounding areas. e. Design storms are the basis for design of projects when risk of loss of human life or property needs to be assessed and analyzed. Methods for Development of Design Storms Design storms can be defined and developed using the following approaches: a. Point design precipitation depth (covered in this Chapter) 1 Chow, V.T., D. R. Maidment, and L. W. Mays, Applied Hydrology, McGraw-Hill, New York, Page 2

3 b. Intensity-Duration-Frequency (IDF) Relationships (covered in the next Chapter) c. Design hyetographs (covered in the next Chapter) Design Frequency and Return Period Concept of Return Period Design storms are usually specified for a certain design frequency. The term frequency denotes the frequency of occurrence of a certain extreme event (e.g., a storm). The magnitude of an extreme event is inversely proportional to its frequency of occurrence. For example, very severe rainfall storms or floods occur less frequently than moderate events. The frequency of occurrence is closely related to the concept of recurrence interval or return period. If an extreme event is defined to have occurred and if it is equal to or exceeds a certain level (e.g., rainfall larger than a certain depth or flood higher than a certain elevation or magnitude), then recurrence interval or return period specifies the time between occurrences of the event equaling or exceeding the pre-specified level. The return period (or recurrence interval), T, is related to another concept: the probability of exceedance, or p. In fact, T and p are reciprocals of each other: T = 1 1 and p = pequation 1-1 T The following table lists standard design return periods and frequencies: Table 1.1: Standard levels of design return period and probability of exceedance Return Period (T) Probability of exceedance (p) (50%) (20%) (10%) (4%) (2%) (1%) For example, a storm that has a return period of five years (usually called a five-year storm) has a probability of exceedance of 1/5=0.2 or exceedance frequency of 20%. It should be noted that a five-year storm is not the one that will necessarily be equaled or exceeded every five years. Instead, there is a 20 percent chance that the event will be equaled or exceeded in any year. In fact, the five-year event could conceivably occur in several consecutive years, with a 20% probability of recurrence every year. Similarly, there is a 1% probability that a 100-year storm will be equaled or exceeded every year. Selection of Design Frequency or Return Period A hydraulic structure that is designed for a storm with 100+ year return period will likely be safe enough but may not be financially affordable. Therefore, there are two main factors that should be considered when deciding on the adopted design frequency: safety and cost. The safety factor is related to the importance of the structure, and the cost factor is related to available project budget and funding. While it is certainly too costly to design a culvert on a minor highway for extreme events (50- or 100-year return period storms), it is expected that a disaster may occur if a levee around a major city or a large dam spillway were to be designed for too small a storm. The final selection of a design level will be an optimal balance between the two conflicting factors of safety and cost. In certain projects, it is sometimes necessary to perform a risk analysis study to assess the risk associated with the failure of the hydraulic structure. Based on past experience, some generalized design criteria have been developed by different agencies (e.g., US Corps of Engineers or state Departments of Transportation). Based on statistical analysis of long-term rain gauge records, the National Weather Service (NWS) of the National Oceanic and Atmospheric Administration (NOAA) has developed design storm maps (also known as isohyetal or isopluvial maps) which show lines of equal precipitation depths for a given storm duration and frequency (or return period). These maps are developed for the entire United States and are published in several NWS technical papers. Page 3

4 Design Point Precipitation Depths NWS TP 40 maps The NWS technical paper number 40 (commonly called TP 40) includes design maps for storm durations from 30 minutes to 24 hours, and return periods of 1, 2, 5, 10, 25, 50, and 100 years (percent chance of exceedance of 1, 2, 4, 10, 20, 50, and 100). These maps can be interpolated to other durations and return periods. The full technical paper (TP 40) is available from the NWS and can be found at ( oh/hdsc/pf_documents/technicalpaper_no40.pdf). sign rainfall depth can be read from Figure (1.1) as P 100,24 = 13 inches, approximately. NWS TP 49 maps These maps contain precipitation depths for 2 to 100- year return periods (1 to 50 percent exceedance) and 2 to 10-day storm durations. The full version of the TP 49 paper is available from the NWS website at the following website: ( hdsc/pf_documents/technicalpaper_no49.pdf). An example of such maps is shown in Figure (1.2) for a 100-year 10-day rainfall. Electronic copies of the TP 40 maps can be viewed at sites such as ( htm). An example of such maps is shown in Figure (1.1) for a storm duration of 24 hours and a 100-year return period. Figure (1.2): The 100-year 10-day precipitation depth map in inches based on NWS TP 493 Figure (1.1): The 100-year 24-hour precipitation depth map in inches based on NWS TP 40 2 Example Based on TP 40 maps, what is the 24-hour 100-year rainfall design depth for the City of New Orleans in the state of Louisiana? Solution New Orleans is located in the southeastern part of the state of Louisiana. The value of 100-year 24-hour de- 2 Hershfield, David M. U.S. Department of Commerce. Weather Bureau 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 United States Department of Commerce, Weather Bureau. Washington, D.C. NWS HYDRO 35 maps These additional maps provide precipitation depths for the eastern United States for smaller durations (less than 30 minutes; namely from 5, 15, and 60 minutes) which are more desired in some design situations, such as design of storm sewers. The HYDRO-35 maps supersede the 30- and 60-minute TP 40 maps. These maps are based on the Technical Memorandum HYDRO-35; a full version of this publication is available at the following Website: ( PF_documents/TechnicalMemo_HYDRO35.pdf). Two examples of such maps are shown in Figure (1.3) and Figure (1.4) for two cases: 2-year 15-minute and100-year 15-minute rainfall. 3 U.S. Weather Bureau, 1964: Two-to-ten-day precipitation for return periods of 2 to 100 years in the contiguous United States. Weather Bureau Technical Paper No. 49, U.S. Weather Bureau, Washington D.C. Page 4

5 Interpolation from HYDRO-35 Maps to Other Durations and Return Periods 6 The HYDRO-35 maps provide rainfall depths for limited combinations of storm durations and return periods; namely: 5, 15, and 60 minutes, and 2 and 10 years. As specified in the HYDRO-35 document, rainfall depths for two intermediate durations (10 and 30 minutes) can be interpolated as follows: T e e e e 1 X2 X3 X4 Equation Q = ax... X UQ (T=2year) = 2.35 A 0.41 SL 0.17 (RI2+3) 2.04 (ST+8) (13-BDF) IA RQ T=2year e n n Equation 1-3 Figure (1.3): The 2-year 15-minute precipitation depth map in inches based on NWS HYDRO-35 maps4 Similarly, rainfall depths for other return periods, T, can be obtained as follows: Q5 (cfs) = 5.82 (DA) (LK + 3.0) (SL) Equation 1-4 Where a and b are interpolation coefficients that depend on T (Table 1.2). Table (1.2): Coefficients for interpolating design rainfall depths using equation (1.4)7 Return Period (years) a b Figure (1.4): The 100-year 15-minute precipitation depth map in inches based on NWS HYDRO-35 maps5 Example Using HYDRO-35 maps, determine the design rainfall depth for a 10-year 30-minute storm in Houston, Texas. 4 U.S. National Weather Service, 1977: Five to 60-minutes precipitation frequency for eastern and central United States. National Weather Service Technical Memorandum Hydro-35, U.S. National Weather Service, Silver Spring, Maryland. 5 U.S. National Weather Service, 1977: Five to 60-minutes precipitation frequency for eastern and central United States. National Weather Service Technical Memorandum Hydro-35, U.S. National Weather Service, Silver Spring, Maryland. 6 Frederick, Ralph H., Vance A. Myers, and Eugene P. Auciello NOAA Technical Memorandum NWS HYDRO-35 - Five- to 60-Minute Precipitation Frequency for the Eastern and Central United States. Department of Commerce, National Oceanic and Atmospheric Administration, National Weather Service. Silver Spring, Maryland. 7 Chow, V.T., D. R. Maidment, and L. W. Mays, Applied Hydrology, McGraw-Hill, New York, Page 5

6 Solution From the HYDRO-35 maps shown in Figures 1.3 and 1.4, the following rainfall values (inches) can be read for Houston (located in southeast Texas): 15-minute 60-minute 2-year year According to equation (1.3), rainfall depth for a 30-minute duration can be estimated as: Q ( ELEV /1,000) 0.023BSLDEM 10M 100( cfs) = 4.18 DRNAREA Then, the 30-minute 10-year depth can be estimated using equation (1.3) with coefficients a and b taken from Table (1.2) as and 0.449, respectively: Map Rainfall Depth (inches) 2-year 6-hour year 24-hour year 6-hour year 24-hour 5.03 Areal Reduction of Design Point Precipitation Depths The maps introduced earlier (TP-40, TP-49, HYDRO-35, and Atlas 2) are considered point values and should not be applied to areas (e.g., drainage basins) larger than 10 mi 2 in size. For larger areas, the average rainfall design value for an area is less than the maximum value at a point. Therefore, point design depths should be adjusted (reduced) according to the area of the basin under consideration. This adjustment is usually performed using depth-area reduction factors as shown in Figure (1.5). A QT = Q 1 T region Q 2 ( #1) + T ( region#2) At At A NOAA Atlas 2 8 This Atlas contains rainfall design depths for storm durations of 6 and 24 hours and return periods of 2, 5, 10, 25, 50, and 100 years for the western United States. The Atlas also includes equations and interpolation diagrams for determining values for durations less than 24 hours and for intermediate return periods. This Atlas is published in separate volumes for each state in the western United States. An on-line look-up function for extracting design rainfall depths at a certain longitude-latitude location is available at ( The following is an example of various design rainfall depths extracted for a specific site (40 N and W) in the state of Colorado from NOAA Atlas 2 volume 3: 8 Miller, J. F., R. H. Frederick, and R. J. Tracey, 1973: Precipitation frequency atlas of the western United States. NOAA Atlas 2, 11 vols., National Weather Service, Silver Spring, Maryland. Figure (1.5) Depth-area curves for reducing point rainfall to areal average values9 Example If the 1-hour 100-year design rainfall depth extracted for a certain site from the HYDRO-35 maps is found to be 3.46 inches, estimate the corresponding depth for a drainage basin that has an area of 100 mi 2. 9 Miller, J. F., R. H. Frederick, and R. J. Tracey, 1973: Precipitation frequency atlas of the western United States. NOAA Atlas 2, 11 vols, National Weather Service, Silver Spring, Maryland. Page 6

7 Solution From the Depth-Area chart (Figure 1.5), the percent of point rainfall for a 100-mi 2 area is Therefore, the 1-hour 100-year design average depth for this drainage basin is calculated as x 3.46 = 2.5 inches. Summary This chapter introduced some basic concepts about design storms and their use in hydrologic applications. The concepts of return period, frequency, and probability of exceedance were introduced. Selection of design return periods depending on the importance and cost of hydraulic structures was discussed. The chapter proceeded with an examination of the various sources and methods of estimating the point rainfall depth associated with design storms of different durations and frequencies. These sources include charts and curves in the following NWS reports and technical papers TP 40, TP 49, HYDRO 35, and NOAA Atlas 2. Formulas for interpolation of design rainfall depths into intermediate storm durations and return periods were studied. Finally, the concept of point-to-area reduction of rainfall design depths was introduced, along with a method that can be used to calculate the reduction factors. Page 7

8 Chapter Two: Intensity-Duration- Frequency Relationships & Design Hyetographs Overview Intensity-Duration-Frequency (IDF) relationships Design hyetographs Learning Objectives Understand the basic concepts behind intensityduration-frequency (IDF) relationships Understand how IDF relationships can be constructed from point design rainfall information Relate rainfall intensity to total rainfall depth and storm duration Understand how to extract rainfall intensities from IDF curves for certain storm durations and return periods Use IDF equations Derive design hyetographs using the triangular method Derive design hyetographs using the NRCS method Derive design hyetographs using the alternating block method Intensity-Duration-Frequency (IDF) Relationships The IDF relationships define rainfall characteristics for a certain location in terms of: a. rainfall intensity or depth b. duration c. frequency, return period, or exceedance probability Hydrologists can use standard IDF relationships which have been developed by several agencies, such as the National Weather Service (NWS), the United States Geological Survey (USGS), and state departments of transportation. The relationships are developed based on design point rainfall depths for different durations and return periods. Table 2.1 shows an example of such data as available from the Delaware Department of Transportation for Sussex County, Delaware. Table 2.1: Design rainfall intensities (in/hr) for Sussex County, Delaware (source: Delaware Department of Transportation) Duration (T) 2 years Rainfall Intensity I (in/hr) Return Period (Frequency) 5 years 10 years 25 years 50 years 100 years 5 min min min min min hours hours hours hours hours Please print this table. It will be used to answer questions on the quiz and your final exam. It should be noted that the intensity (I) represents average rate of rainfall resulting from a certain rainfall depth (P) during certain duration (D): I = P D Equation 2-1 Page 8

9 For example, from Table 2.1 the design rainfall intensity for a 30-minute 25-year storm is 3.82 inch/hour. The equivalent design depth is P = I x D = 3.82 x 30/60 = 1.91 inches. Rainfall IDF relationships are usually expressed either as graphs or equations, as illustrated on the next pages. Graphical Representation of IDF Relationships For a particular location, IDF relationships can be expressed as a series of curves; each curve is for a specific return period, with duration plotted on the x-axis and rainfall intensity plotted on the y-axis. Figure 2.1 shows an example of IDF relationships developed by the Delaware Department of Transportation based on data from Table Where: c, e, and f are empirical coefficients that vary with the selected return period or frequency (F) and the location (See Table 2.2 for an example). Table 2.2: Coefficients for IDF equation (2.2) for 10-year return period storm intensities at various cities Location c e f Atlanta Chicago Cleveland Denver Houston Los Angeles Miami New York Santa Fe St. Louis Rainfal Intensity (in/hr) year 5-year 10-year 25-year 50-year 100-year Duration (min) Please print this table. It will be used to answer questions on the quiz and your final exam. IDF equations can also be extended to include the return period (T) or frequency (F) as follows: ct I = e D + m f Equation 2-3 Figure 2.1: An example of IDF relationships for Sussex County, Delaware. Each curve represents a certain frequency or return period (source: Delaware Department of Transportation). The curves are constructed based on data in Table 2.1 IDF Relationships as Equations As an alternative to graphical representation, IDF relationships are often expressed using equations to avoid having to use the graphs and interpolate between the values. The equations are commonly expressed as: I c = D e + f Equation 2-2 Where: m is another coefficient. The empirical coefficients are usually provided in tabular format for different geographical locations (e.g., cities or counties) and return periods. Example For a 10-year return period storm, the empirical coefficients of IDF relationships for Houston, Texas, are: c=97.4, e=0.77 and f=4.8. a. Determine the 10-year design rainfall intensity for two storm durations: 20-min. and 1-hour. b. Calculate the corresponding rainfall depth for each of the two durations. Note: in using the IDF equations, the storm duration is in units of minutes and the resulting intensity is in units of in/h. Page 9

10 Solution The design intensity (I) and depth (P) can be calculated as follows: Q T = i = n i= 1 Q T ( region# i) A Ai A QT = Q 1 T state Q 2 ( #1) + T ( state#2) At At Note that the intensity decreases with the increase of storm duration but the accumulated depth increases. Design Hyetographs The methods presented so far provide estimates of a rainfall depth or intensity that is assumed to be constant over a certain storm length. This is useful if the hydrologic designer is concerned with calculating the peak discharge only (e.g., rational method). However, for applications that require information on design hydrographs (i.e., time distribution of discharge), a single value of rainfall design depth is not sufficient. Instead, information of the time distribution of rain depth or intensity (also known as design rainfall hyetograph) is desired. Before a design storm can be constructed from NWS charts, two factors must be decided upon: a. Storm length The storm length selected for the analysis should be at least as long as (preferably in excess of) the time of concentration of the drainage basin or watershed under consideration. A storm shorter than the time of concentration will not allow all parts of the basin to generate runoff during the course of the storm. Note that the time of concentration represents the time required for rain falling on the most hydrologically remote point of a drainage basin to reach the outlet. b. Time interval for each rainfall increment during the storm A t The incremental intervals within the storm should be as small as needed to provide a reasonable representation of the runoff response (i.e., streamflow hydrographs and its peaks) of the drainage basin. There are few common methods for constructing rainfall design hyetographs; the following methods are covered in this chapter: a. Triangular Hyetograph Method b. NRCS (SCS) Method c. Alternating Block Method (also known as Balanced Storm Method) Design Hyetographs using Triangular Hyetograph Method The triangular method is a simple approach for deriving a design hyetograph. It is based on the assumption of a simple triangular shape of the hyetograph (Figure 2.2). For a certain duration (D) and return period, the total rainfall depth (P) can be obtained from the appropriate NWS chart. Then, for a triangular hyetograph, the base can be considered as D and the height (h) can be calculated from the following relationship: 1 P = 2 D h then Equation 2-4 2P h = D The height h represents the peak rainfall intensity within the hyetograph. The time location of the peak intensity can be assumed in the middle of the hyetograph (i.e., a symmetrical distribution). Alternatively, the time location can be offset from the center by introducing a factor known as the storm advancement coefficient, r, which is defined as the ratio of the time before the peak intensity t a to the total duration: ta r = D Equation 2-5 A value for r of 0.5 results in the peak intensity occurring in the middle of the storm hyetograph. A value less than 0.5 will have the peak earlier and vice versa. The difference between D and t a represents the recession time t b : t b =D- t a. Page 10

11 regions of the United States (Figure 2.4) 11. These hyetographs were based on information from available National Weather Service or local storm data. Type IA is the least intense and Type II the most intense short duration rainfall. Types I and IA are for the Pacific maritime climate with wet winters and dry summers. Type III is for the Gulf of Mexico and Atlantic coastal areas, where tropical storms result in large 24-hour rainfall amounts. Type II represents the remainder of the U.S. Figure 2.2: Triangular design hyetograph The storm advancement coefficient for a certain region can be estimated by analyzing a series of storms of various durations 10. Values of this coefficient are available in the literature for different cities in the US. Example: Triangular Hyetograph Method The rainfall design depth for a 15-minute storm with 100-year return period is found to be 2.02 inches. Derive a triangular hyetograph for this storm assuming a storm advancement coefficient of 0.4. Solution According to the formulation of the triangular hyetograph, the peak intensity, h, and its location within the hyetograph, t a and t b can be calculated as follows: LT = 2.79L S The resulting hyetograph has a peak at 6 minutes (earlier than the center of the storm). Rainfall intensities at regular intervals before and after the peak can be calculated by linear interpolation (e.g., at time = 2 minutes, the hyetograph intensity is 2/6*8.08=2.69 in/h). Design Hyetographs using NRCS (SCS) Method The U.S. Department of Agriculture, Natural Resources Conservation Service (NRCS) developed four synthetic hyetographs (Figure 2.3) that vary according to geographical location. The four hyetographs represent 24-hour rainfall distributions (I, IA, II, and III) for four 10 Chow, V.T., D. R. Maidment, and L. W. Mays, Applied Hydrology, McGraw-Hill, New York, Figure 2.3: NRCS (SCS) 24-hour rainfall hyetographs for different regions (I, II, III, and IA), source: US Natural Resources Conservations Service (NRCS) Table 2.3: NRCS (SCS) 24-hour hyetograph rainfall distributions Hour (t) t/24 Type I Type IA Type II Type III Soil Conservation Service, Urban Hydrology for Small Watersheds, U.S. Dept. of Agriculture, Soil Conservation Service, Engineering Division, Technical Release 55, June Page 11

12 Figure 2.4: Approximate geographic boundaries for NRCS (SCS) rainfall distributions.12 Example: NRCS Method The total rainfall depth for a 100-year 24-hour storm in Louisiana is 12.0 inches. Using the NRCS (SCS) method, develop a design hyetograph for this storm in this region, assuming an interval of 1 hour. Solution For Louisiana, a Type-III NRCS (SCS) hyetograph can be used; using the tabular NRCS (SCS) hyetograph distribution for Type III distribution, the following table shows the calculations needed to derive the desired hyetograph. The third column is extracted from the NRCS 24-hour distribution and represents the fraction of the total storm depth that accumulated at the end of each time interval. The fourth column contains the cumulative rainfall depth and is obtained by multiplying the third column by the total depth of the storm (12 in). The last column contains the incremental rainfall depth for each interval and is obtained by taking the difference between consecutive values in the fourth column. Incremental rainfall values from the last column are used to plot the hyetograph of this storm (Figure 2.5). Table 2.4: An example hyetograph rainfall distribution derived using the NRCS method (Example 2.3) Hour (t) t/24 Type III Cumulative rainfall (in) Incremental rainfall (in) Soil Conservation Service, Urban Hydrology for Small Watersheds, U.S. Dept. of Agriculture, Soil Conservation Service, Engineering Division, Technical Release 55, June Figure (2.5): Design hyetograph derived using the NRCS method (Example 2.3) Page 12

13 Design Hyetographs using Alternating Block Method (also known as Balanced Storm Method) The following procedure is outlined to construct a certain design storm using the Alternating Block Method. See Example below for a detailed illustration of this method. a. Select an appropriate length for the storm based on calculation of time of concentration of the drainage basin. b. Select the incremental interval of the storm that is appropriate for the drainage basin runoff response. c. Determine the rainfall intensities from the appropriate IDF curves/equations. d. Adjust the depths for the area of the basin if necessary (basins larger than 10 mi 2 ). e. Calculate cumulative rainfall depths. f. Calculate incremental rainfall depths. g. Re-arrange depths into a balanced storm pattern with a triangular distribution (i.e., largest depth in the center of the storm) with alternating descending depths after and before the largest depth). The resulting time-series of rainfall depths is the desired design hyetograph. h. Calculate hyetograph intensities, if required. Example: Alternating Block Method For a 10-year return period storm, the empirical coefficients of the IDF relationships are: c=97.4, e=0.77 and f=4.8. Develop a design hyetograph for a 10-year, three-hour rainfall storm with an interval of 10 minutes. Solution As shown in the following table, the rainfall intensity for each duration interval is calculated first, using the IDF equation (1 st column in Table 2.5). I c = D e + Then, the calculations proceed according to the steps outlined above for calculating the design hyetograph. The resulting hyetograph is plotted in Figure 2.6. f Table 2.5: Calculations of a design hyetograph using the alternating block method Duration Intensity Cumulative depth Incremental depth Time Interval Distributed rainfall intensity Distributed rainfall depth (min) (in/h) (in) (in) (min) (in) (in) (0-10) (10-20) (20-30) (30-40) (40-50) (50-60) (60-70) (70-80) (80-90) (90-100) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Page 13

14 Figure 2.6: Design hyetograph derived using the alternating block method Summary This chapter introduced two sub-topics that are of vital importance in the development of design storms: 1) intensity-duration frequency relationships; and 2) design hyetographs. Graphic forms and equations of IDF relationships were presented. Different methods for deriving the temporal distribution of rainfall depths within the design storm (i.e., hyetograph) were presented. These methods range from a very simple approach (triangular method) which assumes a simple triangular shape of the hyetograph, to a more involved method such as the alternating block method that makes use of the IDF relationships. The NRCS method, commonly used by hydrologists, and which takes into account geographical location in the U.S., was also presented. The derived hyetographs provide a detailed temporal distribution of the design storms, which can then be used as input to rainfall-runoff analysis to derive design hydrographs. Page 14

15 Final Exam Student Assessment Select the best answer for each question and complete your test online at 1. The magnitude of an extreme event is to its frequency of occurrence. a. Inversely proportional b. Directly proportional c. Unrelated d. Linearly proportional 2. The rainfall design depth for a drainage basin with an area of 80 mi2 is for a drainage basin with an area of 160 mi2. a. Larger than b. Smaller than c. Half of the value d. The same as 3. If the design depth for a 5-year, 20-minute storm is 1.2 inches, the corresponding rainfall intensity is in/h. a. 3.4 b. 3.5 c. 3.6 d The storm length selected for the analysis should be the time of concentration of the drainage basin. a. Shorter than b. Longer than c. The same as d. None of the above 5. In the triangular hyetograph method, the peak intensity will be earlier than the storm center if the storm advancement factor is. a. Less than 1 b. Less than 0.5 c. Larger than 1 d. Larger than If the design rainfall depth for a 100-year, 15-minute storm is 1.8 in, and if the storm advancement factor is selected as 0.4, the recession time of the hyetograph will be minutes. a. 6 b. 7 c. 8 d According to the Natural Resources Conservation Service (NRCS) method, type results in the least intense 24-hour hyetograph distribution. a. I b. II c. IA d. III 8. According to the Natural Resources Conservation Service (NRCS) method, regions dominated with tropical storms are characterized with a type hyetograph distribution. a. I b. II c. IA d. III 9. According to the Natural Resources Conservation Service (NRCS) method, most of the continental U.S. has a type hyetograph distribution. a. I b. II c. IA d. III 10. In deriving the design hyetograph, the alternating block method starts by obtaining rainfall intensities at equal intervals from. a. IDF relationships b. NWS charts c. Storm analysis d. NOAA Atlas Page 15