drainage basins - earth and planetary scienceeps.berkeley.edu/people/lunaleopold/(148) lag time in...

__ _______ _ _ ~ _ _______. ______ V O ~ . 18, p. 157-171 Cremlingen 199 1 1

LAG TIMES FOR SMALL DRAINAGE BASINS

L. 8. Leopold, Berkeley

Summary downstream. Centroid lag is the time

Over a period of ten years, simultane- ous 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 01991 by CATENA VERLAG, W-3302 Cremlingen-Destedt, Germany 0341-8162/91/5011851/US$ 2.00 + 0.25

interval between the center of mass of rainfall and the center of mass of the resulting hydrograph.

The concept of unit hydrograph by im- plication involves lag time, for the shape of the unit hydrograph is a reflection of the intergrated effects of all factors gov- erning 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, for- est clearcutting, overgrazing, channeliza- tion, or other basic alterations decrease lag time for the same reasons. Refor- estation or soil conservation measures increase lag time.

With sufficient data on measured lag time the effects of urbanization may be computed.

2 Empiric relations

These facts have been utilized by several authors to compile empirical relations between lag time and basin characteristics. The most useful of these are the studies by CARTER (1961) and AN- DERSON (1970). Reasoning that lag time must reflect the mean basin slope and the basin length, these authors plotted lag time as a function of & or length over the square root of mean basin gra- dient. On such plots they showed that the degree of urbanization influenced lag time; the greater the degree of development or sewerage, the shorter the lag.

Even more simple is the relation of lag 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.

a .

Leopold .._ ___

3 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 plan- ner 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 pro- cesses.

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) used two quantities, percentage of basin developed and percentage of channels sewered. Again these can usually be stated only roughly. Further, it is logical to suppose that the location of the urban development on the basin relative to the point where stream flow is measured would be important. Development close to the gaging station probably would in- fluencc flow peak more than if the same development were at some distance up- stream.

The percentage of area that is impervious has been used by CARTER and ANDERSON and is discussed in a form useful to computation by DUNNE & LEOPOLD (1978, pp. 301, 324 and 327).

I I I I I I 1 I I I I I l l I 5 10 50 100

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 i s 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 car- ried 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.

At ungaged locations, my students and I at the University of California have collected data by direct observation of gage height and rainfall at various sites. In the simple procedure used by us, a chan-

nel cross section is chosen that is acces- sible 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 two- minute intervals. Observations are made continuously in the hope of experienc- ing a discrete burst of rainfall and i t s associated hydrograph.

In order to determine the quantity of runoff, a discharge rating curve is estab- lished for the chosen cross section. Ve- locity measurements by floats are taken over a range of stages. From the plot

USGS STATION STATION NUMBER NUMBER

4489 1594 1825 4559.5 4640.5 4537 2746

11460600 11460800 11460000

1182400 1 182030

11181008

1181390

NAME

LAG TO RUNOFF CENTROID - LAG Da PERCENT PERCENT DA PEAK L S -

(hours) (mi2) IMPERVIOUS URBANIZED SOURCE 6 (hours) (mi) (ft/mi) COEFFICEhT

1 2 3 4 5 6 7 8 9

10

11 12 13

14 15 16 17 I8 19

20 21 22 23 24 25 26

Highland Creek above Highland Dam 3.25 Green Valley Creek near Corralitos 2.62 San Ramon Creek at San Ramon 1.54 Sulphur Creek near St. Helena 2.36 Dry Creek Tributary near Hopland 1.71 Capell Creek Tributary near Wooden Valley 1.37 Del Pueno Creek Trib. No. 1 in Patterson 1.12 Lagunitas Creek at pt. Reyes Stahon 8.17 Walker Creek near Tomales 4.00 Cone Madera Creek at Ross --

Arroyo del Hambre at Martinez 3.75 0.37 1.33

Rheem Creek at San Pablo Casm Valley Creek at Hayward

Wildcat Creek at Vale Rd, Richmond Wildcat Creek above Alvarado Park Wildcat Creek near Quito Rd. Dry Creek at Mine$ Rd.

5.38 3.70 1 .oo 3.43

Glen Echo Creek, East Oakland 0.7 1 Saratoga Creek at Poweridge 1.45

San Thomas Creek above Williams Rd. 1.3 1 Permanente Creek at Berry Ave. 1.32 Calabazas Cr. nr. Cupertino (Rainbow Dr.) 1.72 San Thomas Creek near Quito Rd. 1.11 Hale Creek near Magdelena Rd. 1.16 Golf Creek near Micabee Rd. 0.92 Ross Creek at Blossom Hill Rd. 0.51-0.68

11.90 7.05 5.89 4.50 1.27 0.87 0.7 1

81.70 37.10 18.00

15.10 1.49 5.50

7.79 7.40 4.13 5.80 1 .oo

15.10

13.40 8.19 3.98 3.63 2.70 2.28 2.20

._

1 1 6

1 25 40

4 ._

13 1

23 16

18 6

16 13 2

15 13

natural n a N a natural natural natural natural natural -_

_ _ ..

Rantz, 1971

USGS Marin Co.

USGS Contra Costa County Flood Control

Alameda Co. Flood Control

McDonald

Santa Clam Co. Flood Control

1.113 - - 5.30 0.690 -- 6.95 0.582 -- 5.72 0.233 -- 4.19 0.047 - - 1.92 0.040 -- 1.96 0.025 -- 1.55

-- 3.25 -- -- 5.42 16.00

2.68 2.32(?) 6.1

1.27 3.00 5.15 0.16 0.32 1.40 0.47 0.88 5.10

0.77 5.13 8.75

0.17 0.75 2.69 0.51 0.92 5.30 0.07 0.46 2.10 1.24 1.20 10.40

1.39 1.13 8.29 0.51 1.07 7.17

-- 1.55 2.75

.. _. --

n it-i 0.85 3.72 . ..

0.21 0.90 2.33 0.16 0.67 1.20 0.10 0.21-0.56 1.51

Tab.1: Basins in the Sun Francisco Bay Area where lag time has been measured.

114 104 102 373 722 476 787

10.9

45 _ _

142

136

103

598 132 236 147

93 254

540

81.9

_ _

._

167 215 522

0.50 0.68 0.57 0.22 0.07 0.09 0.06 4.85

0.91

0.43 0.15 0.44

0.66

0.11 0.46 0.14 0.86

0.86 0.45

0.16 0.18 0.082 0.066

_ -

._

_ _

LAG TO - USGS CENTROID STATION STATION LAG Da PERCENT PERCENT DA PEAK L S 4. RUNOFF NUMBER NUMBER NAME (hours) (mi2) IMPERVIOUS URBANIZED SOURCE a (hours) (mi) (ft/mi) 6 COEFFICIENT

21

28 29 30 31 32 33 34 35 36 37 38 3 0 4( I 41 42 43 44 45 46

41

Cull Creek above Cull Creek Reservoir at 2.30 5.79

Cull Creek 4.3 mi. upsueam of USGS gage 1.30 1.83 Temescal Creek at Lake Temescal 0.37 1.73 Tanglewood Creek 0.50 0.24 Lany's Creek at Woodacre 1.21 1.57 Warner Cr. at Golf Course in Mill Valley 0.53 0.65 Warner Cr. at 48 Catalpa Ave., Mill Valley 0.60 1.00 Utility Creek near Woodacre 1.27 0.36 Smwberry Creek at Oxford Street 0.40 1.29 N. Fork Strawberry Cr. at Haviland Hall 0.42 0.27 N. Fork Strawbemy Creek at Haviland Hall 0.30 0.25 N Fork Strawberry Creek at LeRoy Ave. 0.42 0.20 S Fork Strawberry Creek at Harmon Gym 0.63 1.17 Lower Codomices Creek at Live Oak Park 0.45 0.62 \onh Fork Codomices Cr. nr. Euclid Ave. 0.32 0.12 South Fork Codomices Cr. nr. Euclid Ave. 0.42 0.20 South Fork Codomices Creek 0.37 0.20 Roble Creek near lake Temescal 0.33 0.175 Cemto Creek at Vermont Ave. 0.25 0.067 ('ulvert on golf course, Lincoln Park, 0.17 0.24

rice Creek at Glenhaven Rd. 0.93 3.78

USGS gage

Lands End

5

5

65

12 (est.) 35 (est.)

90 (?) 60 (est.)' 80 (est.) (W?

95 (est.) 85 80

80 (est.) 90 (?)

50 (est.)

._

_ _

._

_ _

_ _ _ _

Loux, Prevetti --

..

Priestof, Rada 0.1 1 Adamsetal. --

P a w 0.065 Larsen 0.04 Larsen 0.07 Paay 0.01 1

Sciocetti, Simmons -- MarangioPoitras --

Broad/Pelke -- MarangidPoitras -- sturman/wiams -- Rogenkamp/Riddle --

Vincent _ _ sturman/wiams --

Adamset al. -- h p o l d _ _

MOe ._

Romo

Leopold 0.0013

_.

_ _ 0.21

0.9 1 0.32 0.58 1.10

._

_ _ _ _

0.23 ._

._

_ _ _.

_ _ _ _ ._

_ _ .-

0.80

.. ..

.. _.

2.46 241

1.66 579 1.36 206 1.89 201 0.99 1220

_ _ ._

.. _ _ _ _ _ _ 1.14 912 _ _ ..

_ _ ..

_ _ _ _ _ _ ..

_ _ _ _ _ _ ..

_ _ ._

_ _ _ _ _ _ _ _ _ _ _ _

_ -

_.

0.16

0.069 0.09 0.13 0.029

.-

_.

_ _ 0.038 _ _ ._

_ _ ._

_.

_ _ _ _ _.

_ _ _.

0.18

0.14 0.24

0.34 0.35

0.18 0.08-0.12 0.1 1

0.07-0.1 1 0.08 0.22

0.42

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.

162 Leopold -

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 ear- lier 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

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 unrepresenta- tive. 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.

Small Drainage Basins, Lag Time 163

____

volume volume peak duration lag to centroid of of Q or

lag rain runoff r u n o r (inches/ rain burst date (minutes) (minutes) (inches) (inches) coefftcient hour) (hour) r- peak -

12130176

01/02/77 03/24/77 02/05/78

0411 6/78

12/17/78 0211 8/79 02/17/80

02/15/82 0 1/26/83

02/l 5/84 0211 4/86

03/04/78

02/18/86

I O 12 5 7 4 9 5 3

17 4 6 9 9

1 1 8 8 6 7 6

10

17 28 18 13 17 13 14 12 20 9

I O 10 18 18 13 12 10 12 I5 20

.16' ,024' .15'

.I5 .03 1 .21

.I8 ,020 . I 1

.64 .014 .02

.10 ,002 .02 ,002

.54 ,019 .04

.18 ,007 .04

.14 ,003 .02

.09 .02 .23

.07 ,014 .20

.35 ,015 .04

.90 ,083 .09"

.7 1 .156 .22

,067 .075 ,050 ,053 ,042 .006 ,025

,045 ,024 ,015 ,018 .057 . I 17

,060 ,043 ,077 ,053 .22

___ .30 .I7 .33 .25 .45 .I7 .I5 . I2 .47 .I7 .11 .33 .20 .42 .33 .I7 .50 .os .I7 .66

Average 8 15

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 immedi- ate response. There is some indication that the peak runoff rates are related to high values of runoff coefficient but ex- ceptions occur.

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 co- eficient of runoff.

Another site, Warner Creek in Mill

CATTENA--An lnierdirciplinnry Journal 01 SOIL SClhNCE HYDROLOGY-. GtOMOKPHOLOGY

164 Leopold

volume volume peak peak lag to centroid of of Q Q peak lag rain runoff runoff (inches/

date (minutes) (minutes) (inches) (inches) coefficient (CFS.) hour)

01/29/86 58 63 .08 ,032 .40 1 I5 ,048 01/30/86 47 52 .26 .089 .34 400 ,165 02/03/86 42 53 .42 ,143 .34 430 ,178 02/ 14/86 47 58 .59 .35 .59 700 .289 02/17/86' 4.19 2.79 .67 800 ,331 0211 8/86 73 980 ,405

Average 48 56 .42

* 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).

volume volume peak duration lag to centroid of of 0 of peak lag rain runoff runoff (inches/ rain burst

date (minutes) (minutes) (inches) (inches) coefficient hour) (hour)

02/07/85, 7 00 am 30 34 0.15 01 1 .07 .016 0 80 02/07/85, 9:OO am 15 24 0.1 1 ,012 .11 025 0 50 03/26/85, 12:30 pm 27 45 0.80 .06 ,075 .044 3.57 03/26/85, 3:OO pm 12 42 0.47 ,0475 .I0 ,059 138 02/12/86, 1 30 pm 21 29 02/12/86, 2:OO pm 42 41 ~ ~

24 02/12/86, 4 10 pm __ 30 02/12/86, 4.40 pm - ~ ~

02/12/86, 5 50 pm - 28 185' 0.142' 077' - ~

02/19/86, 2:OO pm 32 40 0 24 0.020 0 083 .023 0 20 02/19/96, 4.30 pm 16 28 020 00134 ,067 020 0.45

Average 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 rain- imately 0.07. Later in the same storm, fall seasons (1985-1986). Tab. 4 shows the runoff coefficient tends to be on the the tabulated results of the analysis of 11 order of .lo. These data suggest that storm bursts in four storms. In this case, antecedent rainfill1 tends to increase the the runoff coefficient tends to follow a runoff coefficient, as might be expected. pattern. In the early part of a storm, At this station the average centroid lag is the runoff coefficient tends to be approx- 34 minutes with the standard deviation

Small Drainage Basins, Lag Time I65

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.

A N D E R S O N U S G S 0

SAN F R A N C I S C O AREA X

0 0

I I I 0 20 4 0 6 0

P E R C E N T I M P E R V I O U S

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).

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 con- struct 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 ex- act position of the lines in the graph is subject to adjustment as more data be- come 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 esti- mation 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

CATENA-An lntcrdinciplinary Journal of SOIL SCIENCE--HYDROLOGY- 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

Fig. 3 : Dimensionless distribution graph of’ LANG- B E I N ( I 940) showing percent of the total rain- of 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.

CAI t N A An Intcrd4$aplinsry Journal of SOIL S C l t N C t HYDKOLOUY QtOMOKPHOLOliY


___.

time average of interval

time cumulative between times runoff runof rate (percent values of Q in column 1 increment (percent of total

Item of lag) (percent of total) (percent or lag) (percent) runoff pcr lag)

Column: 1 2 3 4 5 6

0 0

20 3.8

40 12.8

60 29.0

80 46.5

100 59.3

120 68.2

140 75.4

160 81.4

180 86.3

200 90.3

220 93.4

240 95.7

260 97.4

280 98.4

300 99.1

320 99.4

1 10 3.8 19.0

2 30 9.0 45.0

3 50 16.2 8 1 .0

4 70 17.5 87.5

5 YO 12.8 64.0

6 1 I O 8.9 44.5

7 130 7.2 36.0

8 150 6.0 30.0

9 I70 4.9 24.5

10 190 4.0 20.0

11 210 3.1 15.5

12 230 2.3 11.5

13 250 1.7 8.5

14 270 1 .0 5.0

15 290 0.7 3.5

16 310 0.03 1.5

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

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 ex- ample, 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:

CATENA-An lnlcrdisciplinary Journal ill SOIL SCI ENCE~-HYDROLOGY C

168 Leopold

25

U 3 2 0 0 I U W a 1 5

z z I -I -I10 U LL z < a : 5

-

2.5

a: 2.0 3

0 I U W

2 I I

1.0 w 0 [r a I

.5 0 2

1.5 a

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

( 1 ) 3.8 100

total volume of runoff (mm) 20% of lag in hours

- - -

3.8 volume of runoff (mm) - (2) Q(y)=5~100~ lag in hours

because 20 percent of lag is one fifth of the lag. To simplify the computation, values of column 5 were multiplied by 5 and written in column 6. To compute average runoff rate at the times shown in column 4,

(3) column 6 x total volume of runoff

100 x lag in hours Q =

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 multiplying values of column 4 by the lag time.

To illustrate the method, an observed runoff event (February 15, 1984) in Cer- rito Creek, California, is used. Fig. 4 shows the observed hyetograph and hydrograph constructed from rainfall readings about every ten minutes and gage-

CATENA-- An Intcrdisciplmury Journal 01 SOIL SCIENCE HYDKOI O G Y GtOMOKI'HOLOCiY


rain data

time mm/hour

Column : 1 2

9:41

9 :49

9:59

10:09

10:19

10:32

10:42

10:52

11:Ol

11.4

9.1

4.6

6.1

3.6

29.6

12.2

8.4

time

3

mm/hour

4

discharge observed

10:36

10:40

10:45

10:50

10:55

11 :oo

11 :05

11:lO

11:15

11 :20

11 :25

11 :30

11 :35

0

.56

1.52

.84

.56

.30

.23

.18

. I 3

. I O

.05

.03

.03

_-__ discharge calculated

lag = .22 hour time mm/hour

5 6

10:36

10:37

10:40

10:42

10:45

10:48

10:50

10:53

10:55

10:58

11 :01

1 1 :03

1 1 :06

11 :08

11:lO

11:14

0

.33

.79

1.42

1.55

1.14

.79

.64

.53

.43

.36

.28

.20

.15

.09

.06

discharge calculated

lag = .47 hour time mm/hour

7 8

10:36

10:39

10:44

10:50

10:56

11.01

11 :09

11:13

11 :I8

1 1 :24

11:30

11 :35

11:41

11 :47

11 :52

11 :58

12:03

0

.15

.37

.66

.71

.52

.36

.29

.24

.20

.16

.13

.09

.07

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

170 Leopold

"., I

cn - n

1 0 : 3 0 1 l : o o TIME-HOUR

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 incre- ments of time beyond that initial point are respectively 10, 30, 50, etc., percent of the 13 minute lag, which added to the

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

C A T t N A A n Inlerdisoplinar~ Joumol o l SOIL S C l t N C I HYDROLOCY GtOhlOKPHOLOGY


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 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 imper- viousness.

A synthetic hydrograph can be constructed by the use of the basin lag time. Such a computation is a useful applica- tion 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 fre- quency of floods in suburban areas U S Geo- logical Survey Professional Paper 424-B, pp B9- B11

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, Califor- nia.

DUNNE, T. & LEOPOLD, L.B. (1978): Water in Environmental Planning W.HG. Freeman Co., San Francisco, 818 pp.

Address of author: Luna B. Leopold Department of Geology and Geophysics

LANGBEIN, W.B. (1940): Channel storage and University of California USA

unit hydrograph studies. Amer Geophysical Berkeley, California 94720 Union Trans. vol. 21, 62&627.

LATtNA-An interdisciplinary 1ourn.d 01 )OIL SClENCb -HYDROLOGY- Gt0MORPHOLOC.Y

drainage basins - earth and planetary scienceeps.berkeley.edu/people/lunaleopold/(148) lag time in...

Documents