Design Storms for Hydrologic Analysis - Amazon S3 · Design Storms for Hydrologic Analysis Page 1 Design Storms for Hydrologic Analysis Course Description This course is designed

Page 1Design Storms for Hydrologic Analysis

Design Storms for Hydrologic Analysis

Course Description

This course is designed to fulfill two hours of continuing education credit for Professional Engineers. Its objec-tive is to provide students with an overview of the concepts of design storms used in hydrologic design applica-tions. 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


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 vari-ous 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 pointb. A hyetograph defining time distribution of pre-

cipitation during a stormc. An isohyetal map defining the spatial pattern of

precipitation

Applications of Design StormsThere are several design and planning hydrologic ap-plications of design storms:a. Design storms are used in water resources for de-

signing hydraulic structures (e.g., highway cul-verts), flood control (large spillways), and urban stormwater drainage systems.

b. Design storms are used as inputs to standard hy-drologic design methods, such as the rational method, to determine peak flows for design of ur-ban 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 StormsDesign 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, 1988.


b. Intensity-Duration-Frequency (IDF) Relation-ships (covered in the next Chapter)

c. Design hyetographs (covered in the next Chapter)

Design Frequency and Return Period

Concept of Return PeriodDesign storms are usually specified for a certain de-sign 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 oc-cur less frequently than moderate events. The frequen-cy 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 cer-tain 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:

Tp

pT 1and1

==Equation 1-1

The following table lists standard design return peri-ods and frequencies:

Table 1.1: Standard levels of design return period and probability of exceedance

Return Period (T) Probability of exceedance (p)

2 0.5 (50%)

5 0.2 (20%)

10 0.1 (10%)

25 0.04 (4%)

50 0.02 (2%)

100 0.01 (1%)

For example, a storm that has a return period of five years (usually called a five-year storm) has a probabil-ity 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% prob-ability that a 100-year storm will be equaled or ex-ceeded every year.

Selection of Design Frequency or Return PeriodA 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 ex-treme 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 de-signed 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 ex-perience, 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 pub-lished in several NWS technical papers.


Design Point Precipitation Depths

NWS TP – 40 mapsThe 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 interpo-lated to other durations and return periods.

The full technical paper (TP – 40) is available from the NWS and can be found at (http://www.nws.noaa.gov/oh/hdsc/PF_documents/TechnicalPaper_No40.pdf).

Electronic copies of the TP – 40 maps can be viewed at sites such as (http://www.erh.noaa.gov/er/hq/Tp40s.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 (1.1): The 100-year 24-hour precipitation depth map in inches based on NWS TP – 40 2

ExampleBased 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?

SolutionNew 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. 1963. “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.

sign rainfall depth can be read from Figure (1.1) as P100,24 = 13 inches, approximately.

NWS TP – 49 mapsThese 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: (http://www.nws.noaa.gov/oh/hdsc/PF_documents/TechnicalPaper_No49.pdf). An example of such maps is shown in Figure (1.2) for a 100-year 10-day rainfall.

Figure (1.2): The 100-year 10-day precipitation depth map in inches based on NWS TP – 493

NWS HYDRO – 35 mapsThese 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 de-sign 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 fol-lowing Website: (http://xwww.isos.noaa.gov/oh/hdsc/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.


Figure (1.3): The 2-year 15-minute precipitation depth map in inches based on NWS HYDRO-35 maps4

Figure (1.4): The 100-year 15-minute precipitation depth map in inches based on NWS HYDRO-35 maps5

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.

Interpolation from HYDRO-35 Maps to Other Durations and Return Periods6

The HYDRO-35 maps provide rainfall depths for lim-ited combinations of storm durations and return pe-riods; namely: 5, 15, and 60 minutes, and 2 and 10 years. As specified in the HYDRO-35 document, rain-fall depths for two intermediate durations (10 and 30 minutes) can be interpolated as follows:

neneeee

T XXXXaXQ ..........43214321=

Equation 1-2

UQ(T=2year) = 2.35 A0.41SL0.17 (RI2+3)2.04 (ST+8)-0.65(13-BDF)-0.32IA0.15 RQT=2year

0.47

Equation 1-3

Similarly, rainfall depths for other return periods, T, can be obtained as follows:

(SL) 0.339-3.0)(LK (DA) 5.82 (cfs) Q 0.1491.023

5 +=

Equation 1-4

Where a and b are interpolation coefficients that de-pend on T (Table 1.2).

Table (1.2): Coefficients for interpolating design rainfall depths using equation (1.4)7

Return Period (years) a b

5 0.674 0.278

10 0.496 0.449

25 0.293 0.669

50 0.146 0.835

ExampleUsing HYDRO-35 maps, determine the design rain-fall depth for a 10-year 30-minute storm in Houston, Texas.

6 Frederick, Ralph H., Vance A. Myers, and Eugene P. Auciello. 1977. “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, 1988.


SolutionFrom 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-minute2-year 1.22 2.4

100-year 2.02 4.7

According to equation (1.3), rainfall depth for a 30-minute duration can be estimated as:

MBSLDEMELEVDRNAREAcfsQ 10023.0)000,1/(334.0792.0100 72.218.4)( −=

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 0.496 and 0.449, respectively:

t

regionTt

regionTT AAQ

AAQQ 2

)2#(1

)1#( +=

NOAA Atlas 28

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 inter-polation diagrams for determining values for dura-tions 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 (http://www.nws.noaa.gov/ohd/hdsc/noaaatlas2.htm). The following is an example of various design rainfall depths extracted for a specific site (40° N and 105° 16’ 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.

Map Rainfall Depth (inches)2-year 6-hour 1.632-year 24-hour 2.24100-year 6-hour 3.83100-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 val-ues” and should not be applied to areas (e.g., drainage basins) larger than 10 mi2 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 fac-tors as shown in Figure (1.5).

Figure (1.5) Depth-area curves for reducing point rainfall to areal average values9

ExampleIf 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 mi2.

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.


SolutionFrom the Depth-Area chart (Figure 1.5), the percent of point rainfall for a 100-mi2 area is 0.723. There-fore, the 1-hour 100-year design average depth for this drainage basin is calculated as 0.723 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 proba-bility of exceedance were introduced. Selection of de-sign 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 as-sociated 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. For-mulas 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.


Chapter Two:Intensity-Duration-Frequency Relationships & Design Hyetographs

Overview

• Intensity-Duration-Frequency (IDF) relationships• Design hyetographs

Learning Objectives

• Understand the basic concepts behind intensity-duration-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 depthb. durationc. 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)

Rainfall Intensity I (in/hr)Return Period (Frequency)

Duration (T)

2 years

5 years

10 years

25 years

50 years

100 years

5 min 5.06 6.02 6.76 7.67 8.32 8.9610 min 4.04 4.83 5.40 6.11 6.62 7.1215 min 3.39 4.07 4.56 5.15 5.59 6.0030 min 2.34 2.89 3.30 3.82 4.21 4.5960 min 1.47 1.85 2.15 2.54 2.85 3.162 hours 0.91 1.16 1.35 1.61 1.83 2.053 hours 0.66 0.84 0.99 1.19 1.35 1.536 hours 0.40 0.52 0.61 0.74 0.85 0.9712 hours 0.24 0.30 0.36 0.45 0.52 0.6124 hours 0.14 0.19 0.22 0.28 0.33 0.38

Please print this table. It will be used to answer ques-tions on the quiz and your final exam.

It should be noted that the intensity (I) represents av-erage rate of rainfall resulting from a certain rainfall depth (P) during certain duration (D):

DPI =

Equation 2-1


For example, from Table 2.1 the design rainfall inten-sity 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 RelationshipsFor a particular location, IDF relationships can be ex-pressed as a series of curves; each curve is for a spe-cific 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 2.1.

0.10

1.00

10.00

1 10 100 1000 10000Duration (min)

Rai

nfal

Inte

nsity

(in/

hr)

2-year 5-year10-year 25-year50-year 100-year

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 EquationsAs an alternative to graphical representation, IDF rela-tionships are often expressed using equations to avoid having to use the graphs and interpolate between the values. The equations are commonly expressed as:

fDcI e +

=

Equation 2-2

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 fAtlanta 97.5 0.83 6.88Chicago 94.9 0.88 9.04

Cleveland 73.7 0.86 8.25Denver 96.6 0.97 13.90Houston 97.4 0.77 4.80

Los Angeles 20.3 0.63 2.06Miami 124.2 0.81 6.19

New York 78.1 0.82 6.57Santa Fe 62.5 0.89 9.10St. Louis 104.7 0.89 9.44

Please print this table. It will be used to answer ques-tions on the quiz and your final exam.

IDF equations can also be extended to include the re-turn period (T) or frequency (F) as follows:

fDcTI e

m

+=

Equation 2-3

Where: m is another coefficient. The empirical coef-ficients are usually provided in tabular format for dif-ferent geographical locations (e.g., cities or counties) and return periods.

ExampleFor a 10-year return period storm, the empirical coef-ficients 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.


SolutionThe design intensity (I) and depth (P) can be calcu-lated as follows:

∑=

=

=ni

i tiregionTT AAiQQ

1)#(

t

stateTt

stateTT AAQ

AAQQ 2

)2#(1

)1#( +=

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 con-stant 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 hy-etograph) 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 re-quired for rain falling on the most hydrologically re-mote point of a drainage basin to reach the outlet. b. Time interval for each rainfall increment during

the storm

The incremental intervals within the storm should be as small as needed to provide a reasonable represen-tation of the runoff response (i.e., streamflow hydro-graphs and its peaks) of the drainage basin.

There are few common methods for constructing rain-fall design hyetographs; the following methods are covered in this chapter:a. Triangular Hyetograph Methodb. NRCS (SCS) Methodc. Alternating Block Method (also known as Bal-

anced Storm Method)

Design Hyetographs using Triangular Hyetograph MethodThe triangular method is a simple approach for deriv-ing 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 appro-priate 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:

DPhthenhDP 2

21

==

Equation 2-4

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 hyeto-graph (i.e., a symmetrical distribution). Alternatively, the time location can be offset from the center by in-troducing a factor known as the “storm advancement coefficient”, r, which is defined as the ratio of the time before the peak intensity ta to the total duration:

Dtr a=

Equation 2-5

A value for r of 0.5 results in the peak intensity occur-ring 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 ta represents the reces-sion time tb: tb=D- ta.


Figure 2.2: Triangular design hyetograph

The storm advancement coefficient for a certain re-gion can be estimated by analyzing a series of storms of various durations10. Values of this coefficient are available in the literature for different cities in the US.

Example: Triangular Hyetograph MethodThe rainfall design depth for a 15-minute storm with 100-year return period is found to be 2.02 inches. De-rive a triangular hyetograph for this storm assuming a storm advancement coefficient of 0.4.

SolutionAccording to the formulation of the triangular hyeto-graph, the peak intensity, h, and its location within the hyetograph, ta and tb can be calculated as follows:

0.1950.39 -S 2.79L LT =

The resulting hyetograph has a peak at 6 minutes (ear-lier than the center of the storm). Rainfall intensities at regular intervals before and after the peak can be cal-culated by linear interpolation (e.g., at time = 2 min-utes, the hyetograph intensity is 2/6*8.08=2.69 in/h).

Design Hyetographs using NRCS (SCS) MethodThe U.S. Department of Agriculture, Natural Resourc-es Conservation Service (NRCS) developed four syn-thetic 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, 1988.

regions of the United States (Figure 2.4)11. These hyeto-graphs were based on information from available Na-tional Weather Service or local storm data. Type IA is the least intense and Type II the most intense short dura-tion 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 2.3: 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

0 0.000 0 0 0 01 0.042 0.017 0.022 0.011 0.012 0.083 0.035 0.051 0.023 0.023 0.125 0.055 0.083 0.035 0.0324 0.167 0.076 0.116 0.048 0.0435 0.208 0.099 0.156 0.064 0.0576 0.250 0.125 0.204 0.08 0.0727 0.292 0.156 0.268 0.1 0.0898 0.333 0.194 0.425 0.12 0.1159 0.375 0.254 0.52 0.147 0.14810 0.417 0.515 0.577 0.181 0.18911 0.458 0.624 0.623 0.236 0.2512 0.500 0.682 0.664 0.663 0.613 0.542 0.728 0.701 0.776 0.75114 0.583 0.766 0.736 0.825 0.811

11 Soil Conservation Service, Urban Hydrology for Small Watersheds, U.S. Dept. of Agriculture, Soil Conservation Service, Engineering Division, Technical Release 55, June 1986.


15 0.625 0.799 0.769 0.856 0.84816 0.667 0.83 0.8 0.881 0.88617 0.708 0.857 0.83 0.903 0.90418 0.750 0.882 0.858 0.922 0.92219 0.792 0.905 0.884 0.938 0.93920 0.833 0.926 0.908 0.953 0.95721 0.875 0.946 0.946 0.965 0.96822 0.917 0.965 0.965 0.977 0.97923 0.958 0.983 0.983 0.989 0.98924 1.000 1 1 1 1

Figure 2.4: Approximate geographic boundaries for NRCS (SCS) rainfall distributions.12

Example: NRCS MethodThe 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.

SolutionFor Louisiana, a Type-III NRCS (SCS) hyetograph can be used; using the tabular NRCS (SCS) hyetograph dis-tribution for Type III distribution, the following table shows the calculations needed to derive the desired hy-etograph. 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 cumula-tive rainfall depth and is obtained by multiplying the third column by the total depth of the storm (12 in). The

12 Soil Conservation Service, Urban Hydrology for Small Watersheds, U.S. Dept. of Agriculture, Soil Conservation Service, Engineering Division, Technical Release 55, June 1986.

last column contains the incremental rainfall depth for each interval and is obtained by taking the difference between consecutive values in the fourth column. In-cremental 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)

0 0.000 0 0 01 0.042 0.01 0.12 0.122 0.083 0.02 0.24 0.123 0.125 0.032 0.384 0.1444 0.167 0.043 0.516 0.1325 0.208 0.057 0.684 0.1686 0.250 0.072 0.864 0.187 0.292 0.089 1.068 0.2048 0.333 0.115 1.38 0.3129 0.375 0.148 1.776 0.39610 0.417 0.189 2.268 0.49211 0.458 0.25 3 0.73212 0.500 0.6 7.2 4.213 0.542 0.751 9.012 1.81214 0.583 0.811 9.732 0.7215 0.625 0.848 10.176 0.44416 0.667 0.886 10.632 0.45617 0.708 0.904 10.848 0.21618 0.750 0.922 11.064 0.21619 0.792 0.939 11.268 0.20420 0.833 0.957 11.484 0.21621 0.875 0.968 11.616 0.13222 0.917 0.979 11.748 0.13223 0.958 0.989 11.868 0.1224 1.000 1 12 0.132

Figure (2.5): Design hyetograph derived using the NRCS method (Example 2.3)


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 appro-priate IDF curves/equations.

d. Adjust the depths for the area of the basin if nec-essary (basins larger than 10 mi2).

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 descend-ing depths after and before the largest depth). The resulting time-series of rainfall depths is the de-sired design hyetograph.

h. Calculate hyetograph intensities, if required.

Example: Alternating Block MethodFor a 10-year return period storm, the empirical coef-ficients 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.

SolutionAs shown in the following table, the rainfall intensity for each duration interval is calculated first, using the IDF equation (1st column in Table 2.5).

fDcI 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.

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)10 9.11 1.52 1.519 (0-10) 0.086 0.01420 6.56 2.19 0.669 (10-20) 0.096 0.03230 5.26 2.63 0.442 (20-30) 0.110 0.05540 4.44 2.96 0.332 (30-40) 0.128 0.08550 3.88 3.23 0.268 (40-50) 0.154 0.12860 3.45 3.45 0.225 (50-60) 0.194 0.19470 3.13 3.65 0.194 (60-70) 0.268 0.31280 2.86 3.82 0.171 (70-80) 0.442 0.58990 2.65 3.97 0.154 (80-90) 1.519 2.278100 2.47 4.11 0.139 (90-100) 0.669 1.115110 2.31 4.24 0.128 (100-110) 0.332 0.609120 2.18 4.36 0.118 (110-120) 0.225 0.449130 2.06 4.47 0.110 (120-130) 0.171 0.371140 1.96 4.57 0.103 (130-140) 0.139 0.325150 1.87 4.67 0.096 (140-150) 0.118 0.295160 1.78 4.76 0.091 (150-160) 0.103 0.273170 1.71 4.84 0.086 (160-170) 0.091 0.258180 1.64 4.93 0.082 (170-180) 0.082 0.246


Figure 2.6: Design hyetograph derived using the alternating block method

Summary

This chapter introduced two sub-topics that are of vi-tal 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 meth-ods 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 sim-ple triangular shape of the hyetograph, to a more in-volved 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 anal-ysis to derive design hydrographs.

1. The magnitude of an extreme event is __________to its frequency of occurrence.a. Inversely proportionalb. Directly proportionalc. Unrelatedd. 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 thanb. Smaller thanc. Half of the valued. 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. 3.4b. 3.5c. 3.6d. 3.7

4. The storm length selected for the analysis should be _____ the time of concentration of the drainage basin.a. Shorter thanb. Longer thanc. The same asd. 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 1b. Less than 0.5c. Larger than 1d. Larger than 0.5

6. 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. 6b. 7c. 8d. 9

7. According to the Natural Resources Conservation Service (NRCS) method, type ____ results in the least intense 24-hour hyetograph distribution. a. Ib. IIc. IAd. III

8. According to the Natural Resources Conservation Service (NRCS) method, regions dominated with tropical storms are characterized with a type ____ hyetograph distribution. a. Ib. IIc. IAd. III

9. According to the Natural Resources Conservation Service (NRCS) method, most of the continental U.S. has a type ____ hyetograph distribution. a. Ib. IIc. IAd. III

10. In deriving the design hyetograph, the alternating block method starts by obtaining rainfall intensities at equal intervals from _________. a. IDF relationshipsb. NWS chartsc. Storm analysisd. NOAA Atlas

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