NATIONAL ENGINEERING HANDBOOK SECTION HYDROLOGY CHAFTER 21. DESIGN HYDROGRAPHS Victor Mockus Eydraulic Engineer Revisions by Vincent McKeever William Owen Robert Rallison Hydraulic Engineers Reprinted with minor revisions 1972 NEH Notice 4-102 August 1972
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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.
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-
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
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
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 .
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
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
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.
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