Ch21 Design Hydrographs

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NATIONAL ENGINEERING HANDBOOK

SECTION

HYDROLOGY

CHAFTER 21. DESIGN HYDROGRAPHS

Victor Mockus

Eydraulic Engineer

Revisions by

Vincent McKeever

William Owen

Robert Rallison

Hydraulic Engineers






SECTION

HY ROLOGY

CHAPTER 21 DESIGN HYDROGRAPHS

Contents

In t roduct ion 21 .1

P r i nc i pa l S p il lways 1 . 1

Runoff cur ve number proc edu re 21.2

S ources of r a in f a l l da t a 1 .2

Areal adjustment of r a i n f a l l amount 1.2

Runoff cu rv e numbers 21 .2

Climatic index 21.3Channel lo ss es 21.5

Q u ic k r et u rn f lo w 2 .5

Upstream re le as e s 1.5

Combination of channel lo ss . quick ret ur n f low.

and upstream re le as e 1.5

Runoff volume maps pr oc ed ur e 21.8

Areas of mapped run of f volume 1.8

Deep snowpack a r e a s 1.8

Cons truc tion of p r in c i p a l spi1lwa;- hydrographs andmass cur ve s 21.9

Development of Table 21.10 21.9

Use of Tab le 21.10 21.10



Figures

Figure

Mass curves of runoff . . . . .ES-1003

. . . . . . . . . . . . . . . . . . . . . . .323-1011 . . . . . . . . . . . . . . . . . . . . . . .ES-1012 . . . . . . . . . . . . . . . . . . . . . .ES-1020 Contiguous s t a t e s

Sheet of 5 . . . . . . . . . . . . . . . . . . . .Sheet 2 of 5 . . . . . . . . . . . . . . . . . . . . .Sheet 3 of . . . . . . . . . . . . . . . . . . . .

heet of

heet 5 of

ES-1021 Hawaii)Sheet of 5 . . . . . . . . . . . . . . . . . . . .Sheet 2 of 5 . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . .heet of

Sheet of 5 . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .heet of 5

ES-1022 Alaska)

Sheet of

Sheet 2 of 5 . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . .heet 3 ofSheet of 5

Sheet 5 of 5

ES-1023 Pu er to Rico)



Table

Tables

Arrangement of increments befo re c on st ruc tio n of

PSHandPSMC 1.11PSH and PSMC f o r example 21.1 21 .14

PSH and PSMC f o r example 21.2 21.16

PSH f o r example 21.3 21.18

S e r i a l numbers of PSH and PSMC 21.19

Time, r a t e , and mass tabu la t ion fo r p r in c ip a l

spillway hydrographs PsH) and mass cu rv es PSMC) 21.20

Equations used i n co ns tr uc ti on of ESH and FH 21.52

Hydrograph comp utatio n 21.54

Hydrograph comp utatio n 21.56R a i n f a l l p r i o r t o e xc es s r a i n f a l l 21.57

R a i n fa l l an d time r a t i o s fo r d e te rmining To

when storm durat ion i s gr ea te r than 6 hours 21.58

Hydrograph fa mi lie s and To/Tp r a t i o s f o r which

dimensionless hydrograph ratios a r e g iv en i n

Table 21.17 .2 1. 59

Time, d is ch arg e, and accumulated runoff :-atios

f o r dimensionless hydrographs 21.60

Ex h ib i t s

Exhib i t






SECTION

HY ROLOGY

CHAPTER 21. DESIGN HYDROGRAPHS

In t roduc t ion

This ch apte r contains a sys tema tic approach t o th e development of

des ign hydrographs fo r use i n propor t ioning ea r th dams and th e i r s p i l l -

ways according t o SCS c r i t e r i a . Include d a re da t a o r sourc e s of da t a

fo r des ign ra i n f a l l amount, dura t ion , and d is t r i bu t io n; methods of

modifying design runoff t o include eff ec ts of channel lo ss es , quick

re tu rn f low, o r ups tream re leases ; and methods fo r rap id con s t ruc t ion

of hydrographs..

The methodology presented i n t h i s chapter i s s u i t a b l e f o r t h e d e s i g n

of many type s of water c ont ro l s t r uc tu re s, inclu ding channel works,

but the emphasis i s on hydrology f o r design of ea rt h dams t h a t pro-

vide temporary s torage f or f lood prevent ion i n a ddi t ion t o permanent

s to ra ge fo r o the r use s. t s chief purpose i s t o c o n tr i bu te t o s a f e

des ign . Although th e methods are based on da ta of a ct ua l s torms and



Any one of four methods of runoff determination is suitable for thedesign of principal spillway capacity and retarding storage. They are

1)the runoff cunre number procedure using rainfall data and the water-shed s characteristics, 2) the use of runoff yolume maps covering

specific areas of the United States, (3) the regionalization and trans-

position of volume-duration-probability analyses made by the SCS CentralTechnical Unit, and (4) the use of local streamflow data with provision

of sufficient documentation on the method and results. The latter two

methods are not discussed in this chapter because they vary in procedurefrom w e to case, due to conditions of local data, and standard pro-cedures have not yet been established.

Runoff Curve Number Procedure

The runoff curve number procedure uses certain climatic data and the

characteristics of a watershed to convert rainfall data to runoff vol-m e. This procedure should be used for those areas of the country notcovered by runoff volume and rate maps. (Exhibit 21.1 through 21.5.

SOURCES OF RAINFALL DATA. Rainfall data for the determination of di-

rect runoff may be obtained from maps in U.S. Weather Bureau technicalpapers

For durations to 1 day.--

TP-40. 48 contiguous States.TP-42. Puerto Rico and Virgin Islands.

TP-43. Hawaii.TP-47. Alaska.

For durations from 2 to 10 days.--

=-49. 48 contiguous StatesTP-51. Hawaii.



Table 21. i . -- ~ at io s f or ar ea l adjustment of r ai n fa ll amount

AreaArea/point ra t io fo r Area/point ra t io fo r

day 10 daysArea

day 10 days

10 o r l e s s

1520

25

30

3 m i .

r a i n f a l l f o r t h e s t r u ct u r e s i t ei s

6 or more inche s, th eN

fo r t he 10-day storm i s taken from table 21.2. If it i s . l e s s th an 6 inches , the CN

fo r the 10-day storm i s th e same as t h a t fo r the 1-day storm. The10-day N i s used only with the t o t a l 10-day ra i nfa l l .

CLIMATIC IIVDEX. The climat ic index used i n th i s part of the chapteri s

where C i=

climatic indexPa = average annual precipitation in inchesTa average annual temperature i n degrees Fahrenheit



Ta ble 21 .2. --Ten-day ru no ff curv e numbers

Runoff curve numbers for:

day 10 days l d a y lo da ys day 10 days



Climatic Maps f o r th e Nation al Atlas . Maps with a scale of one

in t en mi l li on . map fo r ayerage annual pr ec ip it at io ni s

avai l -able but there i s no map f o r avera ge annual temp eratu re.

SCS person nel may ob ta in the se p ub lic at io ns thPough t h e i r Regional

Technical Service Center.

CHANNEL LOSSES. If th e dra inage a rea above a s t ru c tu re has a c l imat ic

index le ss than 1 then th e di re ct runoff from r a i n f a l l may be decreased

t o account fo r channel lo ss es of inf lu en t streams. Channel lo ss es can

be determined from lo ca l dat a but t he lo ss es must not be more than de-termined by use of ta b le 21.3. When adequate lo ca l da ta ar e not a va il-

able , t ab le 21.3 i s t o be used. Example 21.1 gives th e procedure for

making th e channel lo ss reduc tion of d ir ec t runoff.

Channel los ses in areas where the cl im atic index i s 1 or more w i l l

requ ire s pec ial s tudy; r es ul ts must be approved by th e Dir ector ,

Engineering Division, before being used i n f in a l design hydrology.

QUICK RETURN FLOW. Quick retu rn flow (QRF) i s t h e r a t e of discharge th a tPe rs is ts fo r some period beyond th a t f o r which th e 10-day PSH i s derived.

t includes base flow and other flows that become a part of the flood

hydrograph such as ( 1) ra i nf a l l th a t h as i n f i l t ra te d and reappeared

soon afterwards a s sur face flow; ( 2 ) drainage from marshes and potholes;

and 3 ) delayed drainage from snow banks. I f th e dra inage a r ea above

a s t ruc tur e has a c l imat ic index gr ea te r than 1 then QRF must be

added t o the hydrograph o r mass curve of di re ct runoff from ra in fa ll .

QRF can be determined from lo c a l d at a bu t it must not be le ss than the

steady r a t e determined by use of ta b le 21.4. When adequate lo c a l dataare not avai l ab le , ta bl e 21.4 i s t o be used. Example 21.2 give s the

procedure f or adding QRF t o th e hydrograph or mass curv e of d ir e c t run-

off d erived from rai nf al l .



TABLE 21.3--CHANNEL-LOSS FhCTGRS FOR REDUCT ION O f DIR EC T RUNOFF

.......................................................................C L I R A T I C IN DE X C I

O R A l N G t :AREA

1.0 0.9 08 0.7 0.6 0.5 0.4 OR

L E S S

SP. MI .

1 OR LESS

2

3.

4.

5.

20.

SO

40.

SO.

60.



Sable 21 4 Minimum quick return flow f or PSH derived from

r a in fa l l

C i Qm C i RF

in /aax p i n 1 ~



pa rt s by use of a pprop riate CN and then combined, the channel loss re-

duction i s based on th e ar ea of th e semiarid pl ai n and i t s c l imat i c

index, the hydrograph or mass curve of d ir ec t runoff i s cons tructed ,

and QR from th e mountain a re a i s added.

I f th ere are upstream str uc tur es , th ei r releas es a re always added re-

gardless of the downstream climatic index or other considerations.

Rmoff Volume Maps Proced ure

The runoff volume and r a t e maps, ex hib its 21.1 through 21.5, ar e pro-

vided fo r a rea s of th e United S ta te s where measured runoff volumes vary

significantly from those obtained from the curve number procedure forconvert ing r a in fa l l t o runof f. The mapped areas are of two gener,altyp es: (1 ) the are as where runoff from e it h e r snowmelt, dormant season

r a i n f a l l , or a combination of th e two produce gre at er runoff volumes

than growing season rainfall and ( 2 ) the deep snowpack areas of high

mountain elevations.

AREAS OF bIAPPED RUNOFF VOLUME. The 100-year 10-day runoff volume maps,

ex hi bi ts 21.1 and 21.4, repr ese nt regio nalize d value s derived from

gaged streamflow da ta d sup ple me ntk with clim ato log ica l da ta andlo ca l observat ions . These values should be used for estimating flood-

water deten tion sto rag e within th e map a re a where lo ca l streamflow

data ar e not adequate.

Areal reduction should not be made on the 10-day runoff volumes shown

i n th e maps. Since these -amo unts were derived from stream gage da ta ,

base flow nd channel l os s w i l l be automatical ly included i n the map

val ues and i n Table 21.10.

Quick retur n f low i n th i s procedure i s used as th e ra te of discharge

expected t o pe rs is t beyond th e flood period described under th e 10-dayPSH The r a t e s of d ischa rge, ex hi bi t 21.3, were deriv ed by averaging



TIM D YS

Figure 21. la uick Return Flow Combined with Principal Spillway

Hydrograph fo r th e Runoff Volume Maps Pro cedure .

such as seasonal pre cip ita t io n range of elev ation aspe ct cover

geology so il s et c. es t imating equations can be developed witha minimum number of independent variables. Unt i l techniques are

developed t o properly analyze the ef fe ct s of a number of va ria bl es

the selection of homogeneous gaged watersheds with as much similarity

t o t he ungaged watersheds as po ssible i s recommended for estimating

volume-duration-probability data. Sta t i s t i c s from volume-durat ion-

pro ba bil i ty s tud ies of gaged watersheds can al so be used t o a s si s t

i n developing est imating equations.

Construction of Principal Spillway Hydrographs and Mass Curves



rate of flow and then accumulated to form a mass curve, it has theappearance of c m e in figure 21.1. Such a curye is a straightline on log paper and it has the equation:

D Qio ~ ~ / 1 0 1 ~ (21.2)

where QD total runoff at time D in daysQ ~ Qtotal runoff at the end of 10 daysD time in daysa log ( Q ~/ ), in which Q1 is the total runoff at the

end of 1 day

Thus, knowing only the 1- and 10-day runoff amounts, a continuous

mass curve can be developed for the entire lO-day period.

Examination of such mass curves of runoff from streamflow stationsin m ny locations of the United States showed that the exponentvaried from 0.1 to 0.5. Extremes of 0.0458 and 0.699 were chosen forthe standard curves; these extremes correspond to Qi/Qlo ratios of0.9 and 0.2 respectively. The ratio Ql/Qlo is used hereafter in thischapter as a parameter in preference to or Qlo/Ql because Qlo ismore satisfactory as a divisor in preparing PSH and PSMC with dimen-

sionless rates and amounts of flow. Ql/Qlo ratios of 0.2, 0.3, 0.4,0.5, 0.6, 0.7, 0.8 and 0.9 were selected to give representativedegrees of curvature for the runoff curves.

The 10-day on-site runoff for each Qi/Qlo ratio was rearranged as shownin table 21.5to provide a moderately critical distribution of the10-day runoff. This gave a distribution midway between extremes thatare theoretically possible. On figure 21.1, curves A and B show theextremes and c w e shows the rearranged distribution for a Ql/Qlo

ratio of 0.4.

The effects of watershed lag were included by taking increments ofrunoff for each of the eight typical mass curves, making incremental



Table 21.5.--Arrangement of increments before construction of PSHand PSMC

Time Increment

19th largest 1/2 day17th 11 1

15th ,I I,

13th 11 I t

11thI ? 1

9th I I

I t

7th ,,T i t

5th II 11

3rd t t

9th largest 1/10 day

7th I, 1

5th 11 I

3rd I 11

Largest 1/10 day2nd largest 1/10 day

4th II I

6th It i t

th It 11

10th It 1

4th largest 1/2 day



which the t ab le i s prepared, ther efor e choose th at se t having a Q i / Q l o

r a t i o and Tc nea res t tho se of the watershed. I t i s eas i e r t o make

t h e choice on t a b l e 21.9, which gi ve s av ai la bl e PSH and PSMC and t h e i rs e r i a l numbers, and then t o look up th e s e r i a l number i n tab le 21.10fo r th e t abu la t ions.

Examples

The proced ure by which a PSH o r PSMC i s developed w i l l b e i l l u s t r a t e d

by fou r examples. I n example 21.1, channel lo ss es ar e taken from

d i r e c t runoff befo re development of a PSH and PSMC; i n example 21.2,

i s added to a PSH and PSMC; i n example 21.3, ru noff volume andra te maps ex hi bit 21.1through 21.5) are used t o obtain runoff ; and

i n example 21.4, upstream r el ea se s a r e added t o a PSH.

Example 21.1.--Develop t h e 50-year fre quency PSB and PSMC f o r a

watershed located a t la t i tude ongitudeThe watershed has a dra inage a re a of 15 .0 square mi le s, time of

conce ntratio n of 7. 1 hours, average annual pr ec ip it at io n of 22.8

in ch es , ave rage annu al temp eratu re of 61.5OF, and a runoff curve

number CN) of 80. There a re no upstream str uc tu re s.

1. Compile the 1 and 10-day po int r a i n f a l l amounts from U.S.

Weather Bureau maps. For t h i s lo ca ti on TP-40 and TP-49 are used.

The 50-year frequency 1 and 10-day amounts ar e 6 8 and 11.0

inches respectively.

2. Determine th e a re al r a i n f a l l . Get th e adjustment fa ct or s from

table 21.1. For the drainage are a of 15.0 square miles they ar e

0.978 and 0.991 f o r th e 1 and 10-day r ai ns res pec tive ly. Thea r e a l r a i n f a l l i s 0.978 6.8) 6.65 inches fo r th e 1-day ra in

and 0.991 11.0) 10.9 inches f o r th e 10-day rain .



ta b le 21.3 with the drainage area 15.0 square miles and th e C i

of 0.603 and by in ter po lat ion f in d a reduction fa ct or of 0.75.

Multiply Q1 and Qlo of s t ep by the f ac to r t o ge t ne t runof f s

of 3.28 and 4.76 inches res pe cti ve ly. The ne t runoffs w i l l beQ1 and Qlo i n the re s t of t h i s example.

7. Compute th e Q Q O at io . From ste p 6, Q1/Q10 3.28/4.760.689.

8. Find th e PSH and PSMC ta bu la ti on s i n ta b le 21 J.Q . Enterta b le 21.9 with th e ra t i o 0.689 and Tc of 7.1 hours and f ind th a t

t h e PSH with value s nea res t tho se s No. 22. Locate th e appro-

p ri a t e ta bu la ti on s i n t a b le 21.10 by looking up PSH No. 22. Col-umns 1 2, and 4 of ta b l e 21.6 show th e time, r a t e , and mass

tabulat ions taken from table 21.10.

9. Compute PSH disc harg es i n c fs . F i r s t f in d th e product of

drainage area and 810 This i s 15 .0 4 .76) = 71.40 mile2-inches.

Mult iply th e en tr ie s i n column 2, ta bl e 21.6 by 71.40, t o get

th e discharges i n c fs i n column 3.

10. Compute PSMC amounts i n inches. Multip ly t h e en tr ie s i ncolumn 4 table 21.6, by t o get accumulated runoff i n

inches a s shown i n column 5. I f amounts i n acre-fe et or another

un i t a r e des i r ed , conver t Q l o t o th e d esi red u ni t before making

t h e s e r i e s o f m u l t ip l i ca t io n s .

The example s completed with step 10. m e n ex t s t e p i s t h a t of r ou t-

ing th e PSH or PSMC through th e s tru ct ur e; see ch apter 17 fo r rou tin g

methods.

In th e second example t h e s te ps concerning channel lo s s a re omitted

and steps concerning RF are included.



Table 21.6. PSH nd PSMC f o r example 2l.1

cf sTime PSH Acc ppsm

4 0 4

csmlinch fs inches



3. Determine t h e CN fo r th e 10-day ra in . The 10-day amount i n

s t e p 1 i s over 6 inches th er ef or e th e 100-year 10-day amount i s

to o, and t a b l e 21.2 may be used. E nt er t h e t a b l e w i th t h e CN of75 for 1 day and f in d th e N i s 58 a t 10 days .

4. ~ 6 t i m a t e h e d i r e c t r u no ff f o r 1 and 10 days. En t e r f i gu re

10 .1 wi th th e r a i nf a l l amounts f rom s tep 2 and th e approp r ia te

N from step 3 and f ind Q1 = 2.94 and Q l o 6.68 inches. Because

the r e a re no channe l l o s ses , t h e d i r ec t runo ff i s t h e ne t runo f f .

5. Compute t h e QlIQlo at io . F rom s tep 4 Q 1 / Q l o 2.9416.68

0.440.

6. Find th e PSH and PSMC ta bu la ti on s i n ta b le 21.10. Ent er t a b l e

21.9 wi th th e ra t i o of 0 .440 and T of 2 .0 hou rs and f i n d t h a t t he

PSH and PSMC wi th v alu es ne ar es t tho se i s No. 3. Locate the

app rop riate ta bu la t i on s i n ta b l e 21.10 by looking up PSH No. 3.

7. Compute PSH dis ch ar ge s i n c f s . F i r s t f in d th e product of

drainage area and Q l o . This i s 8.0 (6.6 8) 53.44 mile2-inches.

Mul t ip ly th e e n t r i es i n t a b l e 21.10 for PSH No. 3 by 53.44 t oget a i scharges i n cfs . These a r e shown i n column 2 , t ab le 21 .7 ,

under t h e head ing of ~ r e l im in a r yPSH becau se t h e f i n a l PSH must

contain QRF.

8. Compute PSMC amounts i n inch es. Mu ltipl y th e en t r i e s i n t a b l e

21.10 f o r PSMC No. by Q l (6 .68 inches) t o get accumulated

runoff i n inches. The r e s u l t s ar e shown i n column 5 t ab le 21 .7 ,

under t h e hea din g Pr eli mi na ry PSMC bec aus e t h e f i n a l PSMC must

con tain accumulated QBF. I f t h e PSMC i s t o be i n a c r e- f ee t o rano the r un i t , conver t 10 t o t h e d e s ir e d u n i t b e f o re making t h e

s e r i e s of m u l t i p l i c a t i o n s .



21.16

Table 21.7.--PSHand PSM for example 21.2

PrelimPSH

PrelimTime

inary QRF inary Acc.PSMC

PSH PSMC QRF

0

.1

.51.0

2 o

3 0

3.54.04.24.4

4.6

4.74.8

4.95.0

5-15.2

5.35.45.5

5-65.86.o

cfs

0

4860

6978

100118146181

230

259298

3705121992

1039567383302

257

207174154

cf

10

10

10

10

10

10

10101010

10

10

10

10

10

10

10

1010

10

10

1010

cf

10

58

707988

110128

156191240

269308

3805222002

1049

577

393312267

217184164

inches

0

.01

.11-2660

1.001.261.581.721.91

2 132.252.402.603.16

3.844.20

4.42

4.574.69

4.80

4.975 U

inches

0

oo

.02

.04

-09

.14

.16

.18

.I9

.20

.21

-21.22

.22

-22

23-23.24.24

-25

-25.26

-27

inches

0

.01

-13-3069

1.141.421.761.912.11

2.342.462.622.82

3.38

4.074.434.664.81

4.94

5 0055-235.38



In th e th ir d example the use of the runoff volume maps i s i l l u st ra te d.

Example 21.3--Develop t h e 100-year frequency PSH f o r a wa ter -shed loc ate d a t 43 la t i tu de and 77 longitude. The watershed

has a drainage are a of 12 square mile s, time of conc entra tion of

3.5 hours.

1 Estimate 100-year 10-day runoff volumes from exhibit 21.1.

The inte rpo late d value i s 8.8.

2. Sele ct the Q ~ / Q ~ Oa t i o from exh ibi t 21.2. For th i s a r ea

the value i s 0.4.

3 Ca lcu lat e 1-day volume of ru nof f. Q l / Q l o 0.4 , Q i (0 .4)(8.8 ) 3.52 inch es .

4. Find t h e PSH ta bu la ti on s in Table 21.10. Ente r ta b le 21.9

wi th the Q l / Q l c r a t i o of 0 4 and Tc of 3.5 hours and fi n d t h a t

th e PS Ht i th values nea rest i s No. 11 Locate appropriate tabu-

l a t i o n s i n ta b l e 21.10 by look ing up PSH No. 11

5. Compute PSH di sc ha rg es i n c fs . Find t h e product of dr ain age

area and 4 1 0 This i s (12) (8.8) 105.6 mile2-inches. En tri es

f o r PSH No. 11 are mul t ip l i ed by t h i s va lue t o ob ta in d ischarge

i n c fs . These a re shown i n column 2, t a b l e 21.8.

6. Determine the quic k-ret urn flow ra t e . From ex hi bi t 21.3 t h e

in terpola ted value i s 5.3 csm.

7. Extension of quick-return flow r a t e s beyond t h e PSH Thequick-r eturn f low ra t e i s (1 2 ) 5 . 3 ) 63.6 cf s, round t o 64cfs. This constant ra te of discharge i s an extension to the



Table 21.8.--PSH for Example 21.3.

Prelim-inary

Time PSH QRF PSH

cf cf cfs

0 0 0

1 61 61

5 116 116

1 0 134 134

2.0 151 151



2. Flood route the upstream structure releases or outflows to

the lower structure. Chapter 7 discusses flood routing

procedures.

3 Add the routed flows to the preliminary PSB to get the PSHfor the lower structure.

Note that if an upstream structure is itself a lower structure in aseries then the procedure of example 21.4 must be followed for it

first.

Table 21.9. Serial nlahbers of PSH and PSMC

hours

Serial numbers



Table 21.10.--Time, r a t e and mass tabula t ion s f o r Pr i nci pa l Spi l lway

Iiydrographs PSH) and Mass Curves PSMC)

Tc 1.5 hours

S e r i a l No. 1 2 3

Q ~ Q ~ ~ 0 0.3 0.4 0 05

Time PSH PSMC PSH PSMC PSH PSMC PSH PSK

cfS/AQl0 C ~ S / A Q ~a1 fSIOa1 fs/A OeO



Table 21 lo. -- Continued)

T 1 5 hours

Serial No. 5 6 7 8

0 6QJQ lo 0 7 0 8 0 9

Time PSH S PSH P S E PSH PSMC PSH PSMC



Table 21 10. - Continued)

T, ours

Serid No.. 9 10 12

Q o 0 2 0 3 0.4 0 5

Time PSH PSM PSH PSM PSH PSMC PSH P S E



Table 21LO -- continued)

Tc hours

Serial No 3 4 5 6

~ ~ 1 ~0.6 0.7 0.8 0 9

Time PSH PSW PSH PSMC PSH PSMC PSH PSMC



U.24

Table 2 l LO. -- continued)

T 6 hours

S er i a l No. 1 7 1 8 1 9 20

Q ~ / Q ~ o 0 2 Oe3 0.4 0 5

Time PSH PSMC PSH PSMC PSH PEW PSH PSK



Table 21 lo -- continued)

c 6hours

Serial No. 2 23 24

Q I / Q ~ ~ o .6 0 7 0.8 0.9

Time PSH PSMC PSH P SW PSH PSMC PSH PSMC

days

0

2

.51 0

2 0

3.0

3 h4.0

4034.6

4.8

4.9

500

5.1

5.2

593

5 45.5

5.6



21 26

Table 21 10 -- continued)

hours

S e r i a l No 5 6 8

Time PSE PSMC PSH PSH PSB PSMC




T 1 2 hours

S e r i d No. 29 30 31 32

Q ~ / Q ~ ~0 6 0.7 0 8 0.9

T i m e PSH PSI42 PSH PSMC PSH PSW PSH PSMC



Table 21.lo. -- Continued)

i?,18 hours

Serial NO 33 4 35 36

/Bl0 0 2 0 3 0.4 0 5

Time PSR PSMC PSH PSMC PSH PSW PSH PSMC



Table 21.10. --(continued

T = 18 hours

Serial NO 37 38 39 40

Q ~ / Q ~ 0.6 0.7 0.8 0.9

ime PSH PSM PSH PSK PSH PSK PSH PSM

c f s / ~ , ~ l fs/AQIO a1 &lo cfs/A o L ~



Table 21.lo.-- continued)

T, 24 hours

S e r i a l No 4 42 43 44Q ~ Q ~ ~0 2 0 3 0 4 0 5

Time PSH PSW PSH PS E PSH PS E PSH PSM




Tc 4 ours

S e r i a l No. 45 6 7 48

Q l / ~ l o 0 6 0 7 0 8 0 9

Time PSH PSMC PSH PSMC PSH PSMC PSH PSbC



2l.32

Table 21.10a--(Continued)

Tc= 30 hours

Serial No. : 4g

Ql/Qlo50

: 0.2 0*3 51.4 52.5

Time PSH PSI.c PSH PSE PSH PSIE PSH PEW

e. Q/Q-~ -/AQlo Q&o dAQ,o so cf4AQ1.o%o

0

A50.Y55

1.6%l.y55

0

.OOO?

.0103a0407.0747

2.252 .15272-574 -24162.99 .30223.228 -3363

3.579 .3614

3.8%4.124404384.7244.935

5.052

K84:845

0

-0005.0077.0306.0568

0 0

-538 .0057,998 .0233

1.195 .0437

0 0

*067 .0003.425 .0046.764 *0181.937 .Q339

.1201

.lY55-2528.2865

-3133

.32P

.3474

.3682

.m6e4171

.0932

.1567

.2068

:g

1.229 -0738~6% .12632.274 SW322339 .1975

4.249 .2232

.2823

.3032

:gE.3913

5.520

kgi10.535U.666

.2412

.2645443.3299.3708

.444G Y-779 .4266 12.218 .4148

04713 9.730 .4626 12.098 .4597.4982 9a348 .W8 n-502 .5032.5241 8e761 .5312 10.630 .544c



Table 21.lo. -- continued)

T3 hours

Serial NO. 5 54 55 56

QI/Q~O 0 6 0.7 0.8 0.9

Time PSH PSMC PSH PSMC PSH Pix PSH PSMC



Table 21.LO. --(Continued)

T, 36 hours

S e r i d No 57 58 59 6

Q O 0 2 3 Oak 0 5

Time PSH P a PSH PSm PSH PSM PSH PSW



Table 21 . lo. --(continued)

T 36 hours

S e r i a l No. 61 62 63 64

Ql/Q- o 0.6 0.7 0.8 0.9

Time PSH PSMC PSH PSMC PSR PSMC PSH PSW

C ~ ~ / A Q ~ f ~ / ~ ~10fs/A5iOU1 a1



Table 21 10.- continued)

T, 42 hours

erial NO 65 66 67 68

Ql/Ql0 0.2 0.3 0.4 0 5

Time PSH PSMC PSR PSMC PSH PSMC PSH P S K




T, 4 ours

Serial No. 69 70 7 72

Q1/Ql0 0 6 0 7 0 8 0 9

Time PSH P SE PSH P S E PSH P S E PSH PSE

21.38



Table 21.lo.--(continued)

T 8 hours

S e r i a l No. 7374 75 76

Q 0.2 0.3 o 4 0 5

Time PSH PSW PSH PSM PSH PSbE PSH PSW

s.ZL%10 a 1 0 *lo Ql0 cfs/A 30 L5L fs/A 30 &30ays

0

.61.32 0

3 0

4 o

4.8

5.0

5-2

5.4

5.5

5.6

5.7

5.8

5.9

6 o

6 l6.26.3



Table 2120 - Continued)

T, 48 hours

Serial NO 77 78 79 aQl/Qlo 6 0 7 0 8 0 9

Time PSH PSMC PSH PSMC PSB PSKC PSH PSKC




T 5 ours

Serial NO 81 82 83 84

Q ~ / Q ~ o 0 2 0 3 0 4 - 5

Time PSH PSMC PSH PSMC PSH PSMC PSH PSM2



Table 21 -10. -- continued)

T 54 hours

S e r i a l No 85 86 87 88Q1 Q1o 0.6 0.7 0.8 0.9

Time PSH PSMC PSH PSMC PSH P S E PSH PSMC

21 42




T = 6 hours

Serial No. 89 91

Ql/Q l~0 2 0 3 0 4 0 5

Time PSH PSMC PSH PSM: PSH PSM: PSH PSMC



Table 2 .lo. -- Continued)

T = 6 ours

Serial No 93 94 9

Q 0.6 0.7 0.8 0.9

Time PSH PSMC PSH PSMC PSH PSK PSH PSMC



Table 21.lo.-- Continued)

T = 66 ours

d ys

0

.61.32.0

3.0

4.04.8

5.05.25.4

5.65.86.06.26.4

6.56.6

6*76.8

7 0

Serial NO 97 98 99 100

9/Q10 0.2 0.3 0.4 0.5

Time PSH PSM PSH PSM PSH PSM PSH PSMC



Table 21.10. -- continued)

c 66 hours

Serial No 101 102 103 104

Q ~ / Q ~ ~0.6 0.7 0.8 0.9

Time PSH PSMC PSH PSE PSH PSI42 PSH PSMC



Table 21.10.-- continued)

Serial No 105 106 107 108

Ql/ O 0.2 0.3 0.4 0 5

Time PSH PSMC PSH PSMC PSH Psi PSH PSMC

days cfs/AQ10 a1 fs/AQlo



Table 21.10. -- continued)

T 72 hours

S e r i a l No. 109 l l 0 112

Q1/~ 0-6 0.7 0.8 0.9

Time PSH PSMC PSH PSMC PSH PSMC PSH PSMC





R A T ~ O S OR 50 AND 26 -YEAR 10 -DAY RUNO FF VOLUMES

TO ob ta in : M u l l i ~ l y p values b y .

~ r e a A re a 2 A re aW-Y EA R IO-DAY RUN OFF 0.85 0.90 0.92

25-YEAR 10-DAY RUNO FF 0 70 0.80 0.85

JANUARY 1971. REV. APR iL 1976

F IGU R E 2 1 A )

100-YEAR. 10-DAY RUNOFF INCHE S)

PR IN C IPAL SPILLWAY H YD R OGR AP H





L E GE N D

Q1 1-Day Volume Runoff

Il0. 10-Day Volume Runo f f

FIG URE 2 1 El)

R TIOS OF VOLUMES OF RUNOFF Ql/Q1,,)

P RINCIP A L S P IL L WA Y HY DRO G RA P H

-NUARY 1971. R E V . A P R I L 1 9 76







.ANUARY 1971 REV APRIL 1976 P RINCIP AL S P ILLWAY HYDROGRAP H SNOWMELT PRODU CI NG FLOOD ARE AS



Emergency Spillways L/

Flows larger than those completely controllable by the principal spillwayand retarding storage are safely conveyed past an earth dam by n emer-

gency spillway.The emergency spillway is designed by use of an Emergency

Spillway Eydrograph (ESH) and its mi n i m freeboard determined by use ofa Freeboard Hydrograph (FH). Both kinds of hydrographs are constructedby the same procedure. There is a small difference in that procedure de

periding on whether a watershed's time of concentration is or is not oversix hours.

This part of the chapter presents a manual method of developing ESH andFH. The method requires the use of the dimensionless hydrographs given intable 21.17. Methods of routing the ESH or FH through structures are givenin chapter 17.

Alternatives to developing and routihg the hydrographs manually are i)

use of the SCS electronic computer program, in which basic data are inputand the ESH or FH, the routed hydrograph, and reservoir elevations are out-put; and (ii) the Upper Darby or U method, in which no hydrograph is neededbut which uses the hydrograph characteristics of ESH or FH in an indirectrouting procedure with results in terms of spillway elevation and capacity.

The hydrologic criteria given below apply to the manual method and its al-ternatives. The examples that follow apply only to the manual method.



ES -1020, 5 sheets. 48 contiguous States. Supplementary sheetsfor California and Washington-Oregon are also given.

ES-1021, 5 sheets. Hawaii.

ES-1022, 5 sheets. Alaska.

ES-1023, 5 sheets. Puerto Rico.

ES-1024, sheets. Virgin Islands.

The rainfall amounts on these maps are minimums allowed by SCS criteria for

various classes of structures.

DURATION DJUSTMEW OF RAINFALL AMOUNT. If the time of concentration ofthe drainage area above a structure is more than six hours, the durationof the design storm is made equal to that time and the rainfall amount isincreased using a factor from figure 2.2, part (c).

AREPL ADJUS lNEWt OF R INF LL AMOUNT. If the drainage area above a struc-ture is 10 square miles or less, the areal rainfall is the same as the rain-fall taken from the maps of ES-1020 through 1024. If the area is over 10

square miles but not over 100 square miles, the areal rainfall is obtainedby use of a factor from figure 21.2, part (a). If the area is over 100square miles, the adjustment factor for the area is requested from the En-

gineering Division, Washington, D. C. When a request is submitted the

following info-%ion about the area should also be submitted: (lj location,

preferably the latitude and longitude of the watershed outlet; 2) size in

square miles; 3 ) length in miles, following the main valley; 4)time ofconcentration in hours; (5) runoff curve number; 6) proposed value of theadjustment or adjustment factor. If a factor is also needed for a subwater-

shed of that watershed, then similar information about the subwatershed shouldalso be submitted.



the second when i t i s . There i s no dif fer en ce i n procedure f o r ESR and FH.

Equations used i n the examples ar e li s t e d i n tab le 21.11.

Example 2l.5.--Construct an ESH f o r a c la ss (b) s tr uc tu re wi th a dra in-age area of 1.86 square miles , time of c onc ent rati on of 1.25 hours,

CN of 8 2, and l o c a ti o n a t l a t i t u d e , longitude-.

1 Determine th e 6-hour design storm r a i n f a l l amount, P. Fo r th i s

st ru ct ur e c lass t he ESH ra in fa ll amount i s take n from ES-1020, sh ee t

2 of 5. For th e given lo ca ti on t he map shows t h a t P 9.4 inches.

2 . Determine the ar ea l ra in fa l l amount. The ar ea l ra in fa l l i s t h e

same as i n s tep1

because th e drainage area i s not over 10 square miles.Step 2 of example 21.6 shows th e pr oc es s.

3. M e h e d u ra t io n ad ju stment o f r a i n f a l l amount. No ad justme nt i s

made because th e time of co nc en tra tio n i s not over s ix hours. Step 3of example a 6 shows the process.

4. Determine th e -off amount, Q. Enter f ig ure 10 .1 wi th P 9.4

inches and CN 82 and find Q 7.21 inches.

5 Determine th e hydrograph family. Enter fi g ur e 21.3 (ES-1011) withCN 82 and a t P 9.4 read hydrograph family 2.

6. Determine the dur ation of excess ra in fa ll , To. Enter figure 21.4

(Es-1012) with P 9.4 inches and a t CN 82 read by in terp o la t ion

t h a t To 5.37 h o y s .

7 . Compute the i n i t i a l value of Tp. By equation 21.4 t h i s i s O.T(l.25)

0.88 hours.

8. c o m p u t e d % a t io . Th i s i s 5.37/0.88 6.10.



Table 2l.U--Equations used in construction of ESH and FE

Equation No.

Rev. Tp To

I W T p rev

sp484 A

Rev. Tp

where A drainage area in square miles

q hydrograph rate in cfs

9c hydrograph rate in cfs when Q inch

9p hydrograph peak rate in cfs when nch

Q design storm runoff in inches

Rev. Tp revised time to peak in hours

t time in hours at which hydrograph rate is computed

Tc time of concentration in hours

To duration of excess rainfall in hours

To/Tp)rev. revised ratio from table 21 16

Tptime to peak in hours for TU design hydrographs



14. Compute the hydrograph rates. Use equation 21.8 and the qc/qp

column of th e sel ec te d hydrograph in t a b le 21.17. The computed

r a t e s a r e shown i n column 3 of t a b l e 21.12.

The hydrograph i s completed w ith s te p 14 Bow th e hydrograph i s furtherr e t d ~ U h t e d r plot ted f or routing through the spil lway depends on the

rout ing method t o be used. See chapter 17 fo r routing de ta il s.

The mass curve for the hydrograph can be obtained using the Q t / ~ column

of t he se lec ted hydrograph i n ta bl e 21.17. Ratios i n th a t column ar e

mult ipl ied by the Q of s tep 4 t o give accumulated runoff i n inches a t th e

time computed i n s te p 13. For accumulated runoff i n acre -fee t or another

unit , convert Q t o th e desired un it before making the s er ie s of m ult i pl i-

ca t ions .

In the following example th e storm duratio n i s increased because the time

of concentrat ion i s over six hours. Increasing the durat ion als o requires

increas ing the ra in fa l l amount bu t i f the d ra inage area i s over 10 square

miles the increase i s p a r t l y o f f se t b y th e decrease i n a r ea l r a in f a l l .

Example 21.6.- -Con struc t a FH fo r a c lass ( c ) s t ru c tur e wi th a d ra in -age a re a of 23.0 s quare mil es, time of c onc ent rat ion of 10.8 hours,

N of 77, and lo ca ti on a t latitude-, longitude-.

1 Determine t h e 6-hour design storm r a i n f a l l amount, P For th is

s t r u c t u r e c l a s s t h e K ra in fa l l amount i s taken from ES-1020, shee t

5 of 5 For t he given lo ca ti on t he map shows th at P 25.5 inches.

2 Determine th e ar e al r a i n f a l l amount. Use the approp riate curve

on f i g u r e 2l.2.a (Es-1003-a). For t h i s loc at io n th e Humid and sub-humid climate curve app lie s and the adjustment fac tor f o r the drain -

age ar ea of 23.0 square miles i s 0.93. The adjust ed ra in fa ll i s



SCS EIIG 319

Rev. 1 70

File Code ENG 13 14

DATE

OMPUTED BY--YDROGRAPH COMPUTATION CHECKED BY

WATERSHED OR PROJECT zMmm z *)

STATE

STRUCTURE SIT OR SUBAREA

OR. AREA A36 SQ MI. STRUCTURE CLASS^

LZ HR. STOW U R A T I O N R.

POINT RAINFALL N.

ADJUSTED RAINFALL.

AREAL : FACTOR

DURATION: FACTOR

RUNOFFCURVE NO. B

HYDROGRAPH FAMILY NO. 2

7. Compute the i n i t i a l value of Tp.o.T(l0.8) 7.56 hours.

By equation 21.4 t h i s i s



8. Compute the TO/ a t i o . This i s 10.26/7.56 = 1.357.

9. Select a revised T,/T r a t i o from ta bl e 21.16. Enter ta b le 21.16with the ratio from step and select the tabulated ratio nearest it

For t h i s example t he s el ec te d r a t i o , ( ~ ~ / T ~ ) r e v . ,s 1.5.

10. Compute Rev. Tp.i n r a ti o . By equation

This

21.5,

i s a revised Tp usedRev. Tp 10.26/1.5

because of the= 6.84 hours.

change

ll Compute a By equation 21.6 t is i s 484(23.0)/6.84 1627.5cf s. Round to 1628 cf s.

2 Compute Qq Usin@vesw2t: 7 (16287

the Q from step 440,W.6 cfs .

and th e q fromRound to , a 2

s tepcfs .

13. Compute the times for which hydrograph rates w l l be computed.Use equation 21.7 with the Rev. Tp from s tep 10 and th e e nt rie s in

the t /Tp column of the sele ct ed hydrograph i n t ab le 21.17. The com-

puted ra te s ar e shown i n column of t ab le a 13

14. Compute th e hydrograph ra te s . Use equation a . 8 with Qqp of st ep

12 and the qc/q column of th e se le ct ed hydrograph i n Mole 21.17.The computed r a fes a re shown in coLumn 3 of t ab le 21.13.

,;.1-70

l e Code ENG-13-14

DATE



YDROGRAPH COMPUTATION COMPUTED BYHECKED BY

Q =IP /QR

WATERSHED OR PROJECT E x ~ f l P L E L 6

STATEP

STRUCTURE SITE OR SUBAREA

DR. AREA 23.0 SQ. MI. STRUCTU RECL SSC

TcHR. STORM DURATION

POINT RAINFALL 2 5 5 IN.

ADJUSTED RAINFALL:

AREAL : FACTOR

DURATION: FACTOR

RUNOFF CURVE NO. 77

Q Z 7 IN.

HYDROGRAPH FAMILY NO.

CDMPUTEDTp .56 HR.

To 10.26 HR.

Table 21.14.--Rainfall prior to excess rainfall.



inches) inches) inches) inches) inches)

Table 21.15.--Wnfall and time ratios for determining To when the stormduration is greater than 6 hours.



Rain- Time Rain- Time Rain- Time Rain- Timefall ratio fall ratio fall ratio fall ratio

ratio ratio ratio ratio

Change intabulation

increment.

Table 21.16. Hydrograph families and T o / ~ p atios for which dimensionless hydrograph ratios are given in table 21 17



Asterisks signify that dimensionless hydrograph tabulations are given

in table 21.17.

Table 21 17 --Time discharge and accmmlated runoff ratios



Line t/Tp qc/qpNo.

for dimensionless hydrographs

Hydrograph Family 1



Table 21.17 continued)

Line

No.

5

6

78

910

12

131 4

1 5

16

1 718

1 920

Eydrograph Family

T / T ~ 4 To/TP 6



Table 2l. .17 continued)

No.

2

3

45

6

789

10

ll12

1 314

15

16

171 8

1 9X

Hydrograph Family

1.22

2.44

3.664.88

6 .lo

7 728.54

9 76lo . 98

12 2013.4214.64

1517.08

18.30

19 5220.74

u 9623.18



Table 21 17 Continued)

To/Tp 6

Line t/Tp qc/qp Q ~ / QNo.

Hydrograph Family 1

Table 21 17 continued)



T ~ T ~1

Line t T p qc/qp Q ~ QNo.

Hydrograph amily 2

To/Tp 1.5




/TI, 3

Line t / ~ ~

No

1

2

3

45

678910

1112

1314

15

16

1718

1920

Eydrograph Family



Table 21.17 con tinu ed) Hydrograph Family

Line t / ~ ~c/qp t / ~ p qc/qp t/

No



Table 2l 17 (continued) Hydrograph Family 2

To/Tp 36 To/ 5 To/Tp 75

21.68




Line

No.

4

6

78

910

ll

121314

15

16718

1920

Hydrograph Family 3




TO/rp 3

Line t / ~ ~No

1 02 343 .684 1 02

5 1.36

6 1.707 2.048 2.389 2-7210 3.06

11 3.4012 3.7413 4.0814 4.4215 4.76

16 5.1017 5 4418 5.78

19 6.12X 6.46

Hydrograph Family 3

u.70

Table 21.17 ~ontinued) Hydrograph Family 3



LineNo

1

2

345

6

7

910

U

12

1314

15

16

1718

19

20




Line t/Tp qc qpNo.

Hydrograph Family 3




LineNo.

1

4

6

78

910

ll

12

13

14

15

1617

iiydrograph Family



Table 2 l 7 continued) Hydrograph Family

u.74



Table 21.17 continued) EIydrograph amily 4

Line t ~ ~

No.

1 0

2 .50

3 1.00

4 1.505 2.00

6 2.50

7 3.00

8 3 504.00

10 4.50

ll 5.0012 5.50

13 6.00

14 6.50

115 7.00

6 7.50

17 8.00

8 8.50

19 9.002 9.50



Table 21.17 continu ed)

Hydrograph amily

Line t / T p qc/qp

No

Hydrograph amily



Table 2 l 7 continued) Hydrograph Family



Table 21 17 continued) Hydrograph Family 5

Line t/Tp

No

1 0

2 363 -724 1.085 1.44

6 1.807 2.16

8 2.52g 2.8810 3.24

3 60

1 2 3.9613 4.3214 4.6815 5.04

16 5.40



Table 21.17 continued) Hydrograph Family

Line t/Tp q p Q ~ / QNo.

Table 21 17 concluded) Hydrograph Family 5



Line t/TP qc/qP Q ~ / QNo.

TO/T, 5



21.81-HYDROLOGY: CRITERIA FOR DESIGN STORMS USED IN DEVELOPING

EMERGENCY SPILLWAY DESIGN AND FREEBOARD HYDROGRAPHS



DRAINAGE AREA HI SOUARE MILES

1) RAINFALL RATIOS FOR DRAINAGE AREAS OF10 TO 100 SQUARE MILES













































.





T L N T I o C E N





T L T I C C E

INCHES) W R DEVELOPING THE FREEWARD HYDROGRAPH f R CLASS l l STRUPURES

6s 30

T L T I C C E



P _ _ __. .. . .

ES 1 23 Sheet di 5









MIN IMU M SIX.HOUR PRfCIPITAl ION l incherl for de r e l op fnp lh. FREEeOARD HYDROGRAPH or

CLASS 1 1 STRUCTURES or Ih. EMERGENCY SPILLWAY HYDROGRAPH or CLASS b) STRUCTURES

..05

rC A R B B E A N S E A

I 105 I U S SOIL CONSERVATIO N SERVICE JUNE 1V6I

V S 64-d Bl S 6V.0 61.35 6 7

ES 1 24





AS ISLAND

SK JOHN ISLAND



SIX.HOUR PRECIQIIAIION linrh.sJ for d.r.lopinp the fREElOARD HYDROGnArH lo CLASS d SIRUCIURES

Frob. - ax 6-hour Pdp:n tlm ron U.S.W.B. I Pr q

Documents

Ch21 Design Hydrographs