__
_
_____
_
_
__ _______ _
__~_
V O ~ .18, p. 157-171
Cremlingen 1991 1
LAG TIMES
FOR SMALL DRAINAGE BASINS
L. 8. Leopold, Berkeley
Summary
Over a period of ten years, simultaneous measurement of storm rainfall and
resulting runoff during individual storms
were made in small basins in the San
Francisco Bay Area, California. By simple measurement, without any recording
devices, data collected define a relation
of basin lag time to drainage area. This
lag time, expressed as time between center of mass of rainfall and center of mass
of runoff, is a specific measure of some
basin characteristics including the effect
of urbanization.
Using lag time relations, synthetic hydrograph construction shows the effect of
urbanization on peak discharge from a
given storm. The method applied to one
storm shows that urbanization increased
the peak discharge by two fold.
1
General statement
Lag time refers to the hours or minutes elapsing between a burst of rainfall and the resulting hydrograph downstream. There are two common ways of
measuring it. Lag to peak is the term
applied to the time interval between the
center of mass of rainfall and the peak
of the resulting hydrograph at a point
ISSN 0341 -8162
0 1 9 9 1 by CATENA VERLAG,
W-3302 Cremlingen-Destedt, Germany
0341-8162/91/5011851/US$ 2.00 0.25
+
downstream. Centroid lag is the time
interval between the center of mass of
rainfall and the center of mass of the
resulting hydrograph.
The concept of unit hydrograph by implication involves lag time, for the shape
of the unit hydrograph is a reflection of
the intergrated effects of all factors governing the translation of a precipitation
hyetograph into a resulting hydrograph.
The principle of the unit hydrograph is
that rainfall events having the same time
duration will result in respective hydrographs differing in the ordinate values
of discharge but the time distributions
will be the same. In other words, precipitation events similar in time duration
but differing in rainfall rates will produce
hydrographs that differ in discharge values but have similar time distributions of
those discharge values. Regardless of the
total rainfall in the event, the time between the center of mass of the rain and
the peak or center of mass of resulting
runoff tends to be constant.
The generalization that lag time is constant is limited. It is intended as a hydrologic planning tool for moderate size
basins and moderate sized rainfall events,
not as a tool for describing extreme rainfall events.
The lag time is an integrated measure
of the speed with which rainfall appears
downstream as a runoff hydrograph. If
water collects rapidly and moves down-
158
stream swiftly, lag time is short. If sufficient channel storage releases the water
slowly and the travel velocity is low, the
lag time is long.
In a sense the lag time is a fingerprint
of the drainage basin, reflecting the storage and velocity of water in its travel
over the basin and down channel.
It is clear, then, that disturbance of thc
basin surface and its channels will alter
lag time. Urbanization tends to speed
water downstream by eliminating channel and surface storage and increasing
mean velocity in channels. Simularly, forest clearcutting, overgrazing, channelization, or other basic alterations decrease
lag time for the same reasons. Reforestation or soil conservation measures
increase lag time.
With sufficient data on measured lag
time the effects of urbanization may be
computed.
___
3
.._
Leopold
Needed extensions
The empiric relations cited above need to
be extended to include relationships for
small basins and to include more data on
lag time changes which result from land
disturbance, in particular, urbanization.
In this regard, the study of small
basins is important. The land planner may be interested in the hydrologic effects in a basin the size of a
housing development or even a single
house. Similarly, the hydrologic effects
of disturbance in small basins is important to foresters, engineers for small-scale
projects, and geologists of surficial processes.
ANDERSON had three classes of
land disturbance: natural, developed
basin partly channelled, and completely
sewered. These are understandable but
difficult to apply because the word “developed” is not quantitatively defined.
LEOPOLD (1968) and RANTZ (1971)
2 Empiric relations
used two quantities, percentage of basin
These facts have been utilized by sev- developed and percentage of channels
eral authors to compile empirical rela- sewered. Again these can usually be
tions between lag time and basin char- stated only roughly. Further, it is logical
acteristics. The most useful of these are to suppose that the location of the urthe studies by CARTER (1961) and AN- ban development on the basin relative to
DERSON (1970). Reasoning that lag the point where stream flow is measured
time must reflect the mean basin slope would be important. Development close
and the basin length, these authors plot- to the gaging station probably would inted lag time as a function of & or length fluencc flow peak more than if the same
a .
over the square root of mean basin gra- development were at some distance updient. On such plots they showed that stream.
The percentage of area that is imperthe degree of urbanization influenced lag
vious
has been used by CARTER and
time; the greater the degree of developANDERSON
and is discussed in a form
ment or sewerage, the shorter the lag.
useful
to
computation
by DUNNE &
Even more simple is the relation of lag
LEOPOLD
(1978,
pp.
301,
324 and 327).
time of a natural or unaltered basin to
drainage areas as used by DUNNE &
LEOPOLD (1978), who found that for
most basins the introduction of slope and
length did not improve the correlation.
I
I
I
I I I 1
5
10
I
I
I
I I l l
50
D R A I N A G E R R E A - S O . MtLES
Fig. 1: Centroid lag time in hours in relation to basin drainage area. The position of
each plotted point is designated by a number which is the estimated percentage of’ the
basin area that is imperuious. A series of parallel lines on the graph represent various
values of percent impervious area.
4
California measurements
The measurement of lag time can be carried out in the field with simple observations. What is required is the continuous
measurement during a storm of the rainfall and the resulting runoff at a channel location. Over the past two decades
such data have been collected in the San
Francisco Bay Region. One source is the
recorded hydrographs at gaging stations
maintained by U.S. Geological Survey
and county flood control agencies. The
measured discharge is compared with a
nearby recording rain gage.
nel cross section is chosen that is accessible for observation during rainstorms.
A staff gage is installed and the cross
section is surveyed. A rain gage, usually a portable plastic gage, is installed
in a location near the chosen channel
cross section. During a rainstorm, observations are recorded of the rainfall
quantity at intervals of about ten minutes. Simultaneously, the stage at the
channel cross section is recorded at twominute intervals. Observations are made
continuously in the hope of experiencing a discrete burst of rainfall and i t s
associated hydrograph.
ungaged locations, my students and
In order to determine the quantity of
At
I at the University of California have col- runoff, a discharge rating curve is establected data by direct observation of gage
height and rainfall at various sites. In
the simple procedure used by us, a chan-
lished for the chosen cross section. Velocity measurements by floats are taken
over a range of stages. From the plot
I
100
USGS
STATION STATION
NUMBER NUMBER
4489
1594
1825
4559.5
4640.5
4537
2746
11460600
11460800
11460000
NAME
CENTROID
LAG
Da
(hours)
(mi2)
PERCENT
PERCENT
IMPERVIOUS URBANIZED
Highland Creek above Highland Dam
Green Valley Creek near Corralitos
San Ramon Creek at San Ramon
Sulphur Creek near St. Helena
Dry Creek Tributary near Hopland
Capell Creek Tributary near Wooden Valley
Del Pueno Creek Trib. No. 1 in Patterson
Lagunitas Creek at pt. Reyes Stahon
Walker Creek near Tomales
Cone Madera Creek at Ross
3.25
2.62
1.54
2.36
1.71
1.37
1.12
8.17
4.00
--
11.90
7.05
5.89
4.50
1.27
0.87
0.7 1
81.70
37.10
18.00
Arroyo del Hambre at Martinez
Rheem Creek at San Pablo
Casm Valley Creek at Hayward
3.75
0.37
1.33
15.10
1.49
5.50
Wildcat Creek at Vale Rd, Richmond
Wildcat Creek above Alvarado Park
16 Wildcat Creek near Quito Rd.
17 Dry Creek at Mine$ Rd.
I8 Glen Echo Creek, East Oakland
19 Saratoga Creek at Poweridge
5.38
3.70
1.oo
3.43
0.7 1
1.45
7.79
7.40
4.13
5.80
1.oo
15.10
13
1
23
16
13.40
8.19
3.98
3.63
2.70
2.28
2.20
18
6
16
13
2
15
13
1
2
3
4
5
6
7
8
9
10
1182400
1182030
11181008
11
1181390
14
15
12
13
San Thomas Creek above Williams Rd.
1.31
Permanente Creek at Berry Ave.
1.32
22 Calabazas Cr. nr. Cupertino (Rainbow Dr.) 1.72
1.11
23 San Thomas Creek near Quito Rd.
1.16
24 Hale Creek near Magdelena Rd.
0.92
25 Golf Creek near Micabee Rd.
0.51-0.68
26 Ross Creek at Blossom Hill Rd.
20
21
._
1
1
6
1
25
40
natural
naNa
natural
natural
natural
natural
natural
-_
__
.
.
DA
SOURCE
6
Rantz, 1971
1.113
0.690
0.582
0.233
0.047
0.040
0.025
(ft/mi)
5.30
6.95
5.72
4.19
1.92
1.96
1.55
16.00
114
104
102
373
722
476
787
10.9
__
0.50
0.68
0.57
0.22
0.07
0.09
0.06
4.85
_-
45
0.91
--
------
--
S
-
RUNOFF
COEFFICEhT
USGS Marin Co.
--
USGS Contra
Costa County
Flood Control
2.68
5.42
3.25
-2.32(?) 6.1
1.27
0.16
0.47
3.00
0.32
0.88
5.15
1.40
5.10
142
81.9
136
0.43
0.15
0.44
0.77
5.13
8.75
103
__
0.66
598
132
236
147
0.11
0.46
0.14
0.86
93
254
0.86
0.45
Alameda Co.
Flood Control
4
._
LAG TO
PEAK
L
(hours) (mi)
McDonald
Santa Clam Co.
Flood Control
--
--
0.17
0.51
0.07
1.24
.
.
0.75
0.92
0.46
1.20
1.13
1.07
-1.55
n it-i
0.85
. ..
0.21
0.90
0.16
0.67
0.10 0.21-0.56
1.39
0.51
Tab.1: Basins in the Sun Francisco Bay Area where lag time has been measured.
_.
2.69
5.30
2.10
10.40
8.29
7.17
2.75
3.72
2.33
1.20
1.51
._
540
167
215
522
._
__
0.16
0.18
0.082
0.066
USGS
STATION STATION
NUMBER NUMBER
21
28
29
30
31
32
33
34
35
36
37
38
30
4(I
41
42
43
44
45
46
41
NAME
CENTROID
LAG
Da
PERCENT
PERCENT
(hours)
(mi2) IMPERVIOUS URBANIZED
Cull Creek above Cull Creek Reservoir at
USGS gage
Cull Creek 4.3 mi. upsueam of USGS gage
Temescal Creek at Lake Temescal
Tanglewood Creek
Lany's Creek at Woodacre
Warner Cr.at Golf Course in Mill Valley
Warner Cr. at 48 Catalpa Ave., Mill Valley
Utility Creek near Woodacre
Smwberry Creek at Oxford Street
N. Fork Strawberry Cr. at Haviland Hall
N. Fork Strawbemy Creek at Haviland Hall
N Fork Strawberry Creek at LeRoy Ave.
S Fork Strawberry Creek at Harmon Gym
Lower Codomices Creek at Live Oak Park
\onh Fork Codomices Cr. nr. Euclid Ave.
South Fork Codomices Cr. nr. Euclid Ave.
South Fork Codomices Creek
Roble Creek near lake Temescal
Cemto Creek at Vermont Ave.
('ulvert on golf course, Lincoln Park,
Lands End
rice Creek at Glenhaven Rd.
2.30
5.79
1.30
0.37
0.50
1.21
0.53
0.60
1.27
0.40
0.42
0.30
0.42
0.63
0.45
0.32
0.42
0.37
0.33
0.25
0.17
1.83
1.73
0.24
1.57
0.65
1.00
0.36
1.29
0.27
0.25
0.20
1.17
0.62
0.12
0.20
0.20
0.175
0.067
0.24
0.93
3.78
5
DA
SOURCE
Loux, Prevetti
5
._
65
__
12 (est.)
35 (est.)
._
__
90 (?)
60 (est.)'
80 (est.)
(W?
95 (est.)
85
80
80 (est.)
90 (?)
50 (est.)
__
__
a
-.
.
Priestof, Rada
0.1 1
Adamsetal.
-Paw
0.065
Larsen
0.04
Larsen
0.07
Paay
0.01 1
Sciocetti, Simmons -MarangioPoitras
-Leopold
0.0013
Broad/Pelke
-MarangidPoitras --
sturman/wiams
Rogenkamp/Riddle
Vincent
sturman/wiams
Adamset al.
hpold
MOe
Romo
LAG TO
PEAK
L
S
(hours) (mi) (ft/mi)
_.
.
.
__
.
.
0.21
._
0.9 1
0.32
0.58
1.10
__
__
0.23
._
._
__
__
__
__
__
._
.-
---
__
---
_.
._
0.80
2.46
__
.
.
4
.
6
RUNOFF
COEFFICIENT
_-
_. _.
241
0.16
.-
0.18
1.66 579
1.36 206
1.89 201
0.99 1220
0.069
0.09
0.13
0.029
0.14
0.24
.
.
_.
__
1.14
__
__
__
__
__
__
__
__
__
__
._
__
__
912
.
.
.
.
__
__
.
.
.
.
._
__
__
__
__
0.038
__
__
._
0.18
0.1 1
0.08-0.12
._
_.
__
__
__
0.07-0.11
0.08
0.22
_.
_.
Stations 1-26 are gaging stations maintained by the US. Geological Survey or by County Flood Control District. Stations 27-47 are temporary staff
gages observed by the author and students during rainfall events. Original data are on file in the Water Resources Archives, University of California.
Berkeley. Analyses of stations 1-7 were made by S.E. RANT2 (1971); of stations 8-14 and 19-26 by J. PATRY: of stations 14-18 by L. McDONALD.
No data indicated by dash "-".
Tab. 1: Continuation.
0.34
0.35
0.42
162
of channel cross section area, and the
mean velocity at various stages, a rating
curve of discharge versus stage may be
constructed.
With the collected runoff data, rating curve, and rainfall measurements, a
hydrograph and hyetograph are plotted.
When these graphs are plotted together,
the lag time may be determined.
Of the data in tab. 1 , about half were
collected in this manner. The remaining
data were plotted from records at gaging stations and rainfall stations. The
lag to peak and centroid lag were determined by measuring the time interval
between the centroid of rainfall and the
peak or centroid of the resulting hydrograph. Length, L, is the length of the
main channel measured from the basin
outlet to the basin boundary. Slope, S, is
the average slope between points of 10
and 85 percent of L measured from the
basin outlet. The length-slope ratio and
the drainage area-slope ratio are computed using the values defined above.
The relation of centroid lag time to
drainage area for the sites in tab. 1 is
plotted in fig. 1. For each site where percentage impervious area was estimated,
that percentage is written over the plotted point. The line drawn through the
points for natural or unurbanized basins
conforms to the relation determined earlier by DUNNE & LEOPOLD on the
basis of far fewer data (1978, fig. 10-36).
The values of percent impervious are
estimates and a uniform criterion is
needed. In some small basins my students and I have mapped in the field
areas of sidewalks, streets, and roofs to
determine the relation of house density
to percent of the basin that is impervious. This method was possible in only
a few small basins, but our estimates
and measurements generally agree with
-
Leopold
those of RANTZ (1971). He states that
a low density of urbanization defined as
three to six houses per acre had 15 percent impervious area, and medium density, seven to ten houses per acre, had
20 percent impervious area. Even in the
city of Berkeley, California, where houses
are quite crowded together, we estimated
only about 25 percent of the area was
impervious.
5
Variance among
measurements of lag time and
runoff coefficient
Some of the small basins included in
tab. 1 were measured only in a few
storms. It is necessary to have some indication of the reliability of those data.
At one measuring site, Cerrito Creek in
Berkeley, observations of rainfall and resulting runoff were made by the author
during 20 events in a ten-year period.
In some of these events, several individual bursts of rain and consequent hydrographs were observed. In some but
not all, the volume of rainfall and resulting runoff could be computed. The
measurements are compiled in tab. 2.
The average value of centroid lag was
15 minutes with a standard deviation of
5.7. This variance is understandably high
considering the fact that only a single
rain gage was used and it was located
at a point near the stream measurement
position and in many cases does not
fairly represent the rain over the whole
basin. In some storms, the rain measured
must have been local and unrepresentative. Nevertheless, all storms measured
are included in the table, though some
do not exhibit the desired characteristic
of a well-defined burst of rainfall and a
simple hydrograph.
163
Small Drainage Basins, Lag Time
rlag to
date
12130176
01/02/77
03/24/77
02/05/78
03/04/78
04116/78
12/17/78
0211 8/79
02/17/80
(minutes)
peak
IO
12
5
7
4
9
5
3
17
4
6
9
9
____
volume
of
rain
(inches)
duration
or
(inches)
(inches/
hour)
.16'
,024'
.15'
13
.10
.031
,020
.014
,002
,002
.21
17
.I5
.I8
.64
,067
.075
,050
,053
,042
.006
,025
.54
.18
.14
,019
,007
,003
.04
.04
.02
rain burst
(hour)
___.30
.I7
.33
.25
.45
.I7
.I5
.I2
.47
.I7
.02
,014
.23
.20
.057
. I 17
.90
,015
,083
.04
.09"
.7 1
.156
.22
,060
,043
,077
,053
.22
17
28
18
13
14
12
20
9
IO
10
18
11
18
13
12
.35
02/18/86
8
8
6
7
6
10
10
12
I5
20
Average
8
15
02/l 5/84
02114/86
peak
runor
coefftcient
.09
.07
02/15/82
0 1/26/83
volume
of
Q
centroid
lag
(minutes)
runoff
.I1
.02
.02
,045
,024
,015
,018
.11
.33
.20
.42
.33
.I7
.50
.os
.I7
.66
Tab. 2: Lug time und storm data, Leopold Residence, Cerrito Creek. Berkeley, Cali,fornia. ( D A = ,068 mi2).
What is confusing in these data are
the values of runoff coefficient. Nearly
half the values are of the order of 2 to
10 percent whereas several are of the order of 15 to 23 percent. This variation
is not explained by antecedent rainfall
data. Clearly, the runoff is due to saturated overland flow, not to Hortonian
runoff production. No doubt, the single
rain gage does not represent the whole
basin, and a burst of rainfall near the
gage falling on that part of the basin
already saturated would cause immediate response. There is some indication
that the peak runoff rates are related to
high values of runoff coefficient but exceptions occur.
CATTENA--An lnierdirciplinnry Journal 01 SOIL SClhNCE
Some insight into this problem may
be obtained from the exceptionally useful data obtained by Mrs. Pam Romo
on Tice Creek, drainage area 2,420 acres
(979 hect.), during the unusual storms
of January-February 1986. These data
are shown on tab. 3. The rainfall events
had a recurrence interval of 20-40 years,
and the measured data show a runoff
coefficient of 3&60 percent despite the
fact that only a modest portion of the
basin is actually covered with houses.
As we are discovering, golf courses and
mowed grassed areas, as in the case of
Tice Creek, have a surprisingly high coeficient of runoff.
Another site, Warner Creek in Mill
HYDROLOGY-. GtOMOKPHOLOGY
164
Leopold
lag to
peak
(minutes)
centroid
lag
(minutes)
01/29/86
01/30/86
02/03/86
02/ 14/86
02/17/86'
02118/86
58
47
42
47
63
52
53
58
Average
48
date
*
volume
of
rain
(inches)
volume
of
runoff
(inches)
peak
runoff
coefficient
.08
.26
.42
.59
4.19
,032
.089
,143
.35
2.79
.40
.34
.34
.59
.67
73
peak
Q
Q
(CFS.)
(inches/
hour)
1 I5
400
430
700
800
980
,048
,165
,178
.289
,331
,405
.42
56
Discharge was high and constant for 9.6 hours. Runoff volume is for that period;
rain is for 19 hour period.
______
Tab. 3: Lag time and storm data January-February 1986. Tice Creek ut Rumo
Residence, 1929 Glenhuven Rd., Walnut Creek, CA. (2420 acres).
date
02/07/85,
02/07/85,
03/26/85,
03/26/85,
02/12/86,
02/12/86,
02/12/86,
02/12/86,
02/12/86,
02/19/86,
02/19/96,
Average
*
7 00 am
9:OO am
12:30 pm
3:OO pm
1 30 pm
2:OO pm
4 10 pm
4.40 pm
5 50 pm
2:OO pm
4.30 pm
lag to
peak
(minutes)
centroid
lag
(minutes)
30
15
27
12
21
42
__
34
24
45
42
29
41
24
30
28
40
28
-
32
16
volume
of
rain
(inches)
volume
of
runoff
(inches)
0.15
0.1 1
0.80
0.47
01 1
,012
.06
,0475
peak
of
runoff
coefficient
(inches/
hour)
rain burst
(hour)
.07
.11
,075
.016
025
.044
,059
0 80
0 50
3.57
138
.I0
-
-
~
~
~
~
185'
0 24
020
0.142'
0.020
00134
duration
0
077'
0 083
,067
-
.023
020
~
~
0 20
0.45
34
Values for total storm of February 12, 1986.
Tab. 4: Lug time and storm data at Larsen Residence, 1985-1986, Warner Creek,
Mill Valley, CA. ( D A = 1.0 mi2).
Valley, has been observed for two rainfall seasons (1985-1986). Tab. 4 shows
the tabulated results of the analysis of 11
storm bursts in four storms. In this case,
the runoff coefficient tends to follow a
pattern. In the early part of a storm,
the runoff coefficient tends to be approx-
imately 0.07. Later in the same storm,
the runoff coefficient tends to be on the
order of .lo. These data suggest that
antecedent rainfill1 tends to increase the
runoff coefficient, as might be expected.
At this station the average centroid lag is
34 minutes with the standard deviation
I65
Small Drainage Basins, Lag Time
of 7.6 minutes.
From an analysis of those few stations
where runoff of many storms has been
measured, the data from the seldom measured basins are generally acceptable as
measures of the relation of lag time to
basin area.
ANDERSON
USGS 0
S A N F R A N C I S C O AREA X
0
0
0
I
I
I
20
40
60
PERCENT IMPERVIOUS
Fig. 2: The ratio of observed lag timellag
time,for a natural basin of the same area,
is plotted against the percent of basin
estimated as impervious. Data are from
observations made in the Sun Francisco
Bay Area of California and data from
ANDERSON (1970).
CATENA-An
lntcrdinciplinary Journal of SOIL SCIENCE--HYDROLOGY-
6
Effect of urbanization and
land disturbance
More difficult is the measure of land
alteration, as mentioned previously.
Clearly, there is a difference in lag time
for a given basin area among stations
draining areas of different land use.
As an approach toward quantifying
this relation, I have plotted on fig. 2 the
data on impervious area of tab. 1 versus the ratio between observed centroid
lag and centroid lag for a natural or
unurbanized basin of the same size. The
data are understandably scattered due to
the nature of the estimates of impervious
area and to the variation in observed lag
time from one storm to another. I have
drawn, by eye, a line through the data
in fig. 2 and used that relation to construct on fig. 1 a series of parallel lines
representing the lag time as a function
of drainage area for various percentages
of impervious area of the basin. The exact position of the lines in the graph is
subject to adjustment as more data become available. Certainly, the order of
magnitude of lag time reduction due to
increasing impervious area is correct and
has some advantage over those methods
involving “percent of area urbanized” or
“percent of area served by sewers”.
It is possible that the relation of
present lag time to unurbanized or natural lag is a better expression of degree of
landscape alteration than any field estimation of percentage of impervious area.
7
Use of lag time for
computation of effect of land
disturbance
The effect of urbanization or other land
change can be computed from lag time
GEOMORPHOLOGY
166
Leopold
Time (percent of centroid lag)
by the development of a synthetic hydrograph. The computation suffers from its
inability to deal with the effect of location or areal distribution of the urbanization or the land disturbance. Therefore,
this method treats merely the total effect
of the disturbance and as a result is useful primarily for small drainage basins.
The procedure is to develop a synthetic
hydrograph for existing conditions that
checks or agrees with an observed hydrograph. Then using the same volume of
runoff and a different lag time, another
synthetic hydrograph is constructed representing the changed condition.
If the basin is already urbanized, a
hydrograph of longer lag time representing natural conditions may be constructed, giving, therefore, the estimated
pattern for the original, unknown condition. Alternatively, if the basin is natural,
a shorter lag time is used to give an estimated hydrograph representing the new
urbanized condition for the same runoff
CAI t N A
Fig. 3 :
Dimensionless
distribution graph of’ LANGB E I N ( I 940) showing
percent of the total rainof as a function of time
when time is expressed in
percent o f centroid lag.
volume. The first step is to synthesize
a hydrograph under observed conditions
as a demonstration that the synthesis
agrees with observation.
A variant of the unit hydrograph
principle was published by LANGBEIN
(1940). He found that if the time scale
of the distribution graph were expressed
in terms of lag rather than hours, the
resulting dimensionless graph fitted most
hydrographs for large as well as for small
basins. This graph is shown in fig. 3. The
S shaped curve is the usual distribution
graph showing the percentage of runoff
accumulated with passage of time. The
peaked curve is the slope of the distribution graph and is in the form of a
hydrograph.
On that graph several important traits
of hydrographs are shown. Practically
all the water has runoff in a time period
equal to 3.5 times the lag. The peak
discharge should occur at a time after
runoff begins equal to 0.60 lags.
An Intcrd4$aplinsry Journal of SOIL S C l t N C t
HYDKOLOUY QtOMOKPHOLOliY
Small Drainage Basins, Lag Time
167
___.
Item
Column: 1
time
(percent
of lag)
cumulative
values of Q
(percent of total)
time average
of interval
between times
in column 1
(percent or lag)
2
3
4
5
6
0
0
10
3.8
19.0
20
3.8
30
9.0
45.0
40
12.8
50
16.2
8 1 .0
60
29.0
70
17.5
87.5
80
46.5
YO
12.8
64.0
100
59.3
1IO
8.9
44.5
120
68.2
130
7.2
36.0
140
75.4
150
6.0
30.0
160
81.4
I70
4.9
24.5
180
86.3
190
4.0
20.0
200
90.3
210
3.1
15.5
220
93.4
230
2.3
11.5
240
95.7
250
1.7
8.5
260
97.4
270
1.0
5.0
280
98.4
290
0.7
3.5
300
99.1
310
0.03
1.5
320
99.4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
runoff
increment
(percent)
r u n o f rate
(percent of total
runoff pcr lag)
Tab. 5 : Summation graph in terms of lag time.
To express the LANGBEIN dimensionless hydrograph in tabular form,
tab. 5 was prepared. Column 2 is the
time unit chosen which is 20 percent of
lag. At each point chosen, the cumulative percent of runoff was read from his
graph and tabulated in column 3. The
time representing the midpoint of the
CATENA-An
lnlcrdisciplinary Journal ill SOIL SCI ENCE~-HYDROLOGY C
time interval is tabulated in column 4,
and the increment of the runoff in percent of total experienced in that time
interval is shown in column 5. For example, in the time interval of 0 20 percent of lag, the runoff was 3.8 percent of
the total runoff. To compute the average
runoff rate during the interval in mm/hr:
Leopold
168
2.5
25
a:
U
2.0 3
320
0
I
U
0
I
U
W
W
1.5 a
a15
2
z
z
I
I
-I
I
1.0 w
-I10
U
0
LL
[r
a
z
-
I
<
.5
a : 5
0
2
a
9:30
1o:oo
10:30
11:oo'
TIME-HOUR
Fig. 4: Hyetograph and hydrograph observed in the storm of February 15, 1984, on
Cerrito Creek, Berkeley, Calfornia, that has a drainage area of .O68 mi2 (17.6 hect.).
Rate of runoff Q
- -3.8 total volume of runoff (mm)
20% of lag in hours
100
(1)
As can be seen, column 6 is merely
five time the values in column 5 so that
the denominator contains the lag time in
hours.
The 16 points used to plot the hydrograph are, for the ordinate value, Q as
written in Equation (3); the abscissa values are positions in time computed by
because 20 percent of lag is one fifth of multiplying values of column 4 by the
the lag. To simplify the computation, lag time.
values of column 5 were multiplied by
To illustrate the method, an observed
5 and written in column 6. To compute
runoff event (February 15, 1984) in Ceraverage runoff rate at the times shown
rito Creek, California, is used. Fig. 4
in column 4,
shows the observed hyetograph and hydrograph constructed from rainfall readcolumn 6 x total volume of runoff
Q=
(3) ings about every ten minutes and gage100 x lag in hours
volume of runoff (mm)
- (2)
Q(y)=5~100~
lag in hours
3.8
CATENA-- An Intcrdisciplmury Journal 01 SOIL SCIENCE
HYDKOI O G Y
GtOMOKI'HOLOCiY
Small Drainage Basins, Lag Time
rain data
time
mm/hour
Column : 1
2
9:41
169
discharge
observed
time
mm/hour
_-__
discharge
calculated
lag = .22 hour
time
mm/hour
discharge
calculated
lag = .47 hour
time
mm/hour
3
4
5
6
7
8
10:36
0
10:36
0
10:36
0
10:37
.33
10:39
.15
10:40
.79
10:44
.37
10:42
1.42
10:50
.66
10:45
1.55
10:56
.71
10:48
1.14
11.01
.52
10:50
.79
11 :09
.36
10:53
.64
11:13
.29
10:55
.53
11 :I8
.24
10:58
.43
1 1 :24
.20
11 :01
.36
11:30
.16
1 1 :03
.28
11 :35
.13
11:41
.09
.07
11.4
9 :49
9.1
9:59
10:40
.56
4.6
10:09
6.1
10:19
10:45
1.52
3.6
10:32
29.6
10:42
10:50
.84
12.2
10:52
8.4
11:Ol
10:55
11 :oo
11 :05
11:lO
.56
.30
.23
.18
11:15
.I3
11 :20
.IO
11:25
.05
11:30
.03
11 :35
.03
1 1 :06
.20
11 :47
11 :08
.15
11 :52
11:lO
.09
11:58
11:14
.06
12:03
Tab. 6: Cerrito Creeks, storm of February 15, 1984. Basin area .068 mi2 (17.6 hect.).
CATENA
An Inlerdisctplmmry Journal uf SOIL SCIENCE~-IIYDROI.OGY~~GEOMORPHOLOOY
Leopold
170
".,
I
-
cn
n
1l:oo
TIME-HOUR
10:30
11:30
Fig. 5 : Observed hydrograph on Cerrito Creek, February 1 5 , 1984, and synthelic
hydrograph computed from the observed lag time of' 0.22 hours. Another computed
hydrograph computed with u lag time of 0.47 hours represents the discharge from the
same storm before urbanization or under natural conditions.
height readings made each five minutes.
In tab. 6 the observed rainfall rate in
this storm is shown in columns 1 and
2; the data are used to plot the hyetograph in fig. 4. The discharge values and
times of observation are in columns 3
and 4, the observed gage heights have
been converted to discharge rates by use
of a rating curve developed by flow measurements during various storms.
The observed lag time in this storm, 13
minutes (0.22 hours) was used to compute a synthetic hydrograph from equation ( 3 ) and tab. 5. Zero discharge was
assumed to be at 10:36 a.m. The increments of time beyond that initial point
are respectively 10, 30, 50, etc., percent
of the 13 minute lag, which added to the
CATtNA
initial time as shown in column 5, tab. 6.
Corresponding values of computed discharge are in column 6, tab. 6.
The observed hydrograph, columns 3
and 4, are plotted on fig. 5 as the solid
line. The hydrograph computed from lag
time, columns 5 and 6, are plotted on
fig. 5 as a dashed line. The two agree
reasonably well.
The Cerrito Creek basin is urban and
in fairly steep hill country. The little valley in which the creek flows is densely
wooded. The basin is estimated as 20
percent impervious. The drainage area
of .068 mi2 (17.6 hect.), would have a lag
time of 0.47 hours if unurbanized or natural. Its observed lag time is 0.22 hours.
To compute the peak flow for the storm
A n Inlerdisoplinar~Joumol o l SOIL S C l t N C I
HYDROLOCY GtOhlOKPHOLOGY
Small Drainage Basins, Lag Time
of February 15, 198, had the basin been
in natural condition, the computation is
repeated in columns 7 and 8 using a lag
time of 0.47 hours. This new hydrograph
is plotted in fig. 5.
Note that when the lag time is
changed, the abscissa values of time
for the computed discharge values have
changed.
The computation showed that the effect of urbanization was to increase
the peak discharge of this storm from
0.76 mm/hour to 1.55 mm/hour, or by a
factor of 2.
8
171
LEOPOLD, L.B. (1968): Hydrology for Urban
Land Planning. U.S. Geological Survey Circular
554.
RANTZ, S.E. (1971): Suggested criteria for hydrologic design for storm-drainage facilities in
the San Francisco Bay Region. U.S. Geological
Survey Open File Report, Menlo Park, California.
Concluding statement
Simple observations of rainfall and
stream flow in a small drainage basin
can be used to determine the lag time between rainfall and resultant runoff. This
lag time is a finger print of the conditions of the basin for it integrates many
aspects of water runoff such as storage,
channel efficiency, and degree of imperviousness.
A synthetic hydrograph can be constructed by the use of the basin lag time.
Such a computation is a useful application of the unit graph principle.
References
ANDERSON, D.G. (1970): Effects of urban development on floods in northern Virginia US.
Geological Survey Water Supply Paper 2001-C
CARTER, R.W. (1961): Magnitude and frequency of floods in suburban areas U S Geological Survey Professional Paper 424-B, pp B9B11
DUNNE, T. & LEOPOLD, L.B. (1978): Water
in Environmental Planning W.HG. Freeman
Co., San Francisco, 818 pp.
LANGBEIN, W.B. (1940): Channel storage and
unit hydrograph studies. Amer Geophysical
Union Trans. vol. 21, 62&627.
LATtNA-An
interdisciplinary 1ourn.d 01 )OIL SClENCb -HYDROLOGY-
Address of author:
Luna B. Leopold
Department of Geology and Geophysics
University of California
Berkeley, California 94720
USA
Gt0MORPHOLOC.Y