The general formula can be expressed as follows:

where

tc = time of concentration,k = constant, and

a, b, y, and z = exponents.

This equation exhibits a linear relationship for the logarithms of thevariables involved.

As indicated in Table 1, all models include the surface slopevariable, S, raised to a negative power ranging from 0.2 to 0.5that is, the slope variable is in the denominator and, therefore, thegreater the surface slope, the less the time of concentration andvice versa. The problem occurs when such empirical models are tobe used for estimating time of concentration on very flat terrainssuch as coastal plains. If existing empirical models are used, as thesurface slope approaches zero the time of concentration approachesinfinity. Engineering judgment suggests that such long times ofconcentration do not represent reality.

METHODOLOGY

Rainfall Test

A rainfall test was conducted using a mobile artificial rainfall sim-ulator (Figure 1) where test surfaces of low slope were prepared.The simulator included a hydroseeder with a 500-gal (1,890-liter)water tank and an 18-in.-high (0.46-m) rain rack with spray nozzlesmounted in a 5-ft (1.52-m) spacing. This rainfall simulator wasdesigned to cover the entire test plot. The hydroseeder pump gener-ated a flow ranging from 15 to 41 gal/min (0.0009 to 0.0026 m3/s).With this range of flow rates, the precipitation rates generated by thespray nozzles ranged from 1.5 to 3.3 in./h (38.1 to 83.8 mm/h).

Each test plot measured 6 ft (1.83 m) wide by 30 ft (9.14 m) long.This size allowed each rainfall test to run for more than 45 min usingthe maximum-capacity 500-gal water tank. A 45-min rainfall durationwas used to ensure that each test would reach the time of concentration.Each rainfall test use the following procedure:

Measure surface soil moisture (except on concrete and asphaltsurfaces),

Determine precipitation rate, Start hydroseeder pump, Observe the first flow of runoff at the outlet of the test plot,

t kL n S ic a b y z= ( )1

Overland Flow Time of Concentration on Very Flat Terrains

Ming-Han Li and Paramjit Chibber

133

Two types of laboratory experiments were conducted to measure over-land flow times on surfaces with very low slopes. One was a rainfall testusing a mobile artificial rainfall simulator; the other was an impulserunoff test. Test plots were 6 ft (1.83 m) wide by 30 ft (9.14 m) long withslopes ranging from 0.24% to 0.48%. Surface types tested include bareclay, lawn (short grass), pasture (tall grass), asphalt, and concrete. Aregression analysis was conducted to construct models for predicting flowtimes. Results predicted with regressed models were compared withthose from empirical models in the literature. It was found that the slopevariable in the regressed model from rainfall test data is less influentialthan that in existing models. Furthermore, the exponent for the slopevariable in the regressed model for the impulse runoff condition is only1/10th of those in existing models. Overall, most empirical models under-estimate overland flow time for laboratory plots with very low slopes.The slope variable becomes insignificant in governing overland flowtime when the slope is small. Antecedent soil moisture, not included inmost empirical models, significantly affects time of concentration, whichis included in the regressed models.

Time of concentration is a primary basin parameter that represents thetravel time from the hydraulically furthest point in a watershed to theoutlet. The accuracy of estimation of peak discharge is sensitive tothe accuracy of the estimated time of concentration (1). Therefore,the importance of an accurate estimate of the time of concentrationcannot be overlooked. For empirical models that estimate time ofconcentration, one of the major variables computed is a nominalvalue of slope for the watershed. Previous literature (25) collectedand listed most of the popular time-of-concentration formulas. Allthese formulas (622) are empirical models and are presented inTable 1. These models share the same general format formed byfour variables:

Length of the watershed, L; Surface roughness (usually Mannings roughness coefficient

for overland flow), n; Slope of the watershed, S; and Rainfall intensity, i.

M.-H. Li, Department of Landscape Architecture and Urban Planning, Texas A&M University and Texas Transportation Institute, 3137 TAMU, College Sta-tion, TX 77843-3137. P. Chibber, PBS&J, 1211 Indian Creek Court, Beltsville,MD 20705. Corresponding author: M.-H. Li, minghan@tamu.edu.

Transportation Research Record: Journal of the Transportation Research Board,No. 2060, Transportation Research Board of the National Academies, Washington,D.C., 2008, pp. 133140.DOI: 10.3141/2060-15

134 Transportation Research Record 2060

TABLE 1 Summary of Time of Concentration Models

Publication and Year Equation for Time of Concentration (min) Remarks

Williams (1922) (6)

Kirpich (1940) (7)

Hathaway (1945) (8), Kerby (1959) (9)

Izzard (1946) (10)

Johnstone and Cross (1949) (11)

California Culvert Practice (1955) (12)

Henderson and Wooding (1964) (13)

Morgali and Linsley (1965) (14), Aron and Erborge (1973) (15)

FAA (1970) (16)

U.S. Soil Conservation Service (1975, 1986) (17, 18)

Papadakis and Kazan (1986) (2)

Chen and Wong (1993) (19), Wong (2005) (20)

TxDOT (1994) (21)

Natural ResourcesConservation Service(1997) (22)

NOTE: 1 mi = 1.61 km; 1 ft = 0.3048 m; 1 in. = 25.4 mm.

tc = 60LA0.4 D1S 0.2L = basin length, miA = basin area, mi2D = diameter (mi) of a circular basin of areaS = basin slope, %tc = KL0.77SyL = length of channel/ditch from headwater to outlet, ftS = average watershed slope, ft/ftFor Tennessee, K = 0.0078 and y = 0.385For Pennsylvania, K = 0.0013 and y = 0.5tc = 0.8275 (LN)0.467S 0.233L = overland flow length, ftS = overland flow path slope, ft/ftN = flow retardance factortc = 41.025(0.0007i + c)L0.33S 0.333 i 0.667i = rainfall intensity, in./hc = retardance coefficientL = length of flow path, ftS = slope of flow path, ft/fttc = 300L0.5S 0.5L = basin length, miS = basin slope, ft/mitc = 60(11.9L3/H)0.385L = length of longest watercourse, miH = elevation difference between divide and outlet, ftIf expressed as Tc = kLanbSyiz format: tc = KL0.77S 0.385K = conversion constanttc = 0.94(Ln)0.6S0.3i 0.4L = length of overland flow, ftn = Mannings roughness coefficientS = overland flow plane slope, ft/fti = rainfall intensity, in./htc = 0.94L0.6 n0.6S 0.3i 0.4L = length of overland flow, ftn = Manning roughness coefficientS = average overland slope, ft/fti = rainfall intensity, in./htc = 1.8(1.1 C)L0.5S 0.333C = rational method runoff coefficientL = length of overland flow, ftS = surface slope, ft/fttc = (1/60)(L/V)L = length of flow path, ftV = average velocity in ft/s for various surfaces(The exponent of S, if converted from Mannings equation, will be 0.5)tc = 0.66L0.5n0.52S 0.31i 0.38L = length of flow path, ftn = roughness coefficientS = average slope of flow path, ft/fti = rainfall intensity, in./htc = 0.595(3.15)0.33kC0.33L0.33(2k)S 0.33i 0.33(1+k)For water at 26CC, k = constants (for smooth paved surfaces, C = 3, k = 0.5. For grass, C = 1, k = 0)L = length of overland plane, mS = slope of overland plane, m/mi = net rainfall intensity, mm/htc = 0.702(1.1 C)L0.5S 0.333C = rational method runoff coefficientL = length of overland flow, mS = surface slope, m/mtc = 0.0526[(1000/CN) 9]L0.8S 0.5CN = curve numberL = flow length, ftS = average watershed slope, %

The basin area should be smallerthan 50 mi2 (129.5 km2).

Developed for small drainage basinsin Tennessee and Pennsylvania,with basin areas from 1 to 112acres (0.40 to 45.3 ha).

Drainage basins with areas of lessthan 10 acres (4.05 ha) and slopesof less than 0.01.

Hydraulically derived formula; values of c range from 0.007 forvery smooth pavement to 0.012for concrete pavement to 0.06 fordense turf.

Developed for basins with areasbetween 25 and 1624 mi2(64.7 and 4206.1 km2).

Essentially the Kirpich (7) formula;developed for small mountainousbasins in California.

Based on kinematic wave theory forflow on an overland area.

Overland flow equation from kinematic wave analysis of runofffrom developed areas.

Developed from airfield drainagedata assembled by U.S. Corps ofEngineers.

Developed as a sum of individualtravel times. V can be calculatedusing Mannings equation.

Developed from USDA AgriculturalResearch Service data of 84 smallrural watersheds from 22 states.

Overland flow on test plots of 1 m wide by 25 m long. Slopes of2% and 5%.

Modified from FAA (16).

For small rural watersheds.

Monitor runoff rate continuously, Shut down hydroseeder pump after the runoff peaked for about

10 min, and Continue measuring runoff rate until runoff ceased.

Impulse Runoff Test

The impulse runoff test measured runoff travel time without artificialrainfall. Both pervious and impervious surfaces were tested. Forpervious surface testing, test plots were kept saturated before testing.The notion was to minimize the effect of antecedent soil moistureand infiltration and focus on the effects of surface type, flow rate, andslope on travel time. Meanwhile, time of concentration was mea-sured as the time for water to travel from the farthest point of the plotto the outlet.

As with the rainfall test, researchers used a hydroseeder as themobile water source. A large reservoir stored water filled by thehydroseeder. This reservoir, during an impulse runoff test, wasplaced on the upstream side of the test plot and as the reservoircapacity was exceeded, water overflowed the weir onto the plot(Figure 2). The hydroseeder pump generated a flow ranging fromabout 15 to 41 gal/min (0.0009 to 0.0026 m3/s). The size of eachtest plot again measured 6 ft (1.83 m) wide by 30 ft (9.14 m) long,as in the rainfall test. Each impulse runoff test used the followingprocedure:

Water pervious test plots, including bare clay and pasture, tocreate a saturated condition;

Determine flow rate; Start hydroseeder pump to generate flow; Record time when water overtopped the weir; and Record travel time when water front reached the outlet.

Li and Chibber 135

Tested Surfaces and Number of Tests

Five surface types were tested in this study. The details of each testtype are described below:

Bare clay (two plots). The texture for the soil tested was 21%sand, 31% silt, and 48% clay. The slopes of these two bare clay plotswere 0.43% and 0.42%, respectively.

Lawn (two plots). The lawn was established using commonBermudagrass (Cynodon dactylon). A grass height of less than 2 in.(5.1 mm) was maintained by mowing. The slopes of these two lawnplots were 0.48% and 0.24%, respectively.

Pasture (two plots). The lawn was also formed using commonBermudagrass (C. dactylon). Grasses of 6 in. (0.15 m) or taller weremaintained to simulate pasture conditions. The slopes of these twopasture plots were 0.48% and 0.24%, respectively.

Concrete (one plot). The plot was built on the taxiway of an oldairport. The slope was 0.35%.

Asphalt (one plot). An asphaltic cold mix was applied on topof an old airport taxiway to simulate the asphalt surface. The slopewas 0.35%.

The number of tests for different surfaces is presented in Table 2.The data and the range of that specific data category collected in thisstudy are summarized in the following list:

Slope: 0.24% to 0.48%; Rainfall intensity (for rainfall test): 1.5 to 3.3 in./h (38.1 to

83.8 mm/h);

FIGURE 1 Rainfall test using artificial rainfall simulator.

Weir for overflow

Reservoir Runoff direction

FIGURE 2 Reservoir used for impulse runoff test.

TABLE 2 Number of Tests

Tested Surface Rainfall Test Impulse Runoff Test

Bare clay 11 15Lawn 13 Not testedPasture 12 13Concrete 10 5Asphalt 7 16

Runoff flow rate (for impulse runoff test): 15 to 41 gal/min(0.0009 to 0.0026 m3/s);

Antecedent soil moisture (bare clay, lawn, and pasture): 8%to 54%;

Infiltration rate: 0.0358 to 0.0598 in./h (0.91 to 1.52 mm/h); Soil texture: 21% sand, 31% silt, and 48% clay (bare clay, lawn,

and pasture plots); and Raindrop size: 0 to 0.07 in. (0 to 1.8 mm) in diameter.

RESULTS AND DISCUSSION

Rainfall Test

A typical hydrograph of the rainfall test observed in this study isshown in Figure 3. A rainfall test began at time zero when the arti-ficial rainfall simulator was turned on. Initially, there was a no-flowperiod at the outlet. Time of beginning was recorded when thefirst flow was observed at the outlet. As the flow plateaued andfluctuated within 5% of the flow rate, the rate was considered asthe peak, which determined the time to peak. Because time of con-centration should involve only hydraulic travel time, the initialloss process (initial abstraction) was not considered as part of thetime of concentration. Therefore, the time of concentration in therainfall test was determined as the time to peak minus the time ofbeginning of runoff.

The results of rainfall tests are presented in Table 3. A linear regres-sion analysis on the rainfall test data was conducted to construct amodel to predict the time of concentration. From a preliminaryanalysis, it was found that the antecedent soil moisture was negativelyassociated with the time of concentration (Figure 4). Therefore, theantecedent soil moisture variable, , was added to Equation 1 tocreate the new model as follows:

where is antecedent soil moisture (percent) and x is an exponentof .

In the new model, the watershed length L is 30 ft (9.14 m), whichis the length of test plots. For the exponent of length L, the mean value,0.5, of several models compiled by Papadakis and Kazan (2) was used.Similarly, regression analysis was conducted to construct modelsfor the time of beginning, tb, and time to peak, tp, using the sameinitial model shown in Equation 1.

The best-fit models for tc, tb, and tp are summarized in Table 4.Signs and values of exponents for each variable in all three models

t kL n S ic a b x y z= ( )2

136 Transportation Research Record 2060

are generally similar. When compared with existing models, expo-nents of variables n, , and i are close to those of existing modelsand they are all statistically significant (P < 0.001). However, expo-nents of the slope variable, S, were found to be insignificant andtheir absolute values are less than those (0.33) from existing models.It appears that S has the least influence on the time of concentra-tion because the absolute values of the exponents for S are theleast among all variables. This could result from the relativelyfew slopes tested in the study (0.24%, 0.35%, 0.42%, 0.43%, and0.48%). Or, if the slope data number is not the cause, the insignif-icant effect of S might indicate that when the slope is very small,the effect from variables n, , and i become dominant on the timeof concentration.

The final regressed model for time of concentration can be expressedas follows:

This model was compared with some existing models developedfrom both overland flow data [Kerby (9), Izzard (10), Hendersonand Wooding (13), and Chen and Wong (19)] and watershed data[Papadakis and Kazan (2) and Natural Resources ConservationService (22)]. Values used for variables in each model are presentedin Table 5. The comparison result is plotted in Figure 5. It is apparentthat all compared models underestimated the time of concentrationfor tested conditions. Note that Izzards model predicted the timereasonably well with the majority underestimated and the minorityoverestimated.

Impulse Runoff Test

The results of impulse runoff tests are presented in Table 6. A linearregression analysis of the impulse runoff test data was also conductedto construct a model to predict the time of concentration. In this case,the time of concentration is the travel time from the farthest side ofthe test plot to the outlet. The initial regression model was modifiedfrom Equation 1 as follows:

where

tc = time of concentration (min),L = watershed length (ft) [30 ft (9.14 m) in this

study],n = Mannings roughness coefficient for overland

flow,Q = flow rate (gal/min), and

a, b, w, and y = exponents.

Again, the exponent (a) of variable L was set as 0.5, which is themean value compiled by Papadakis and Kazan (2) from severalexisting models.

The final model is presented in Table 7. Exponents of n and Q arestatistically significant, whereas the exponent of S is insignificant,similar to the rainfall test result. Furthermore, the exponent for theslope variable in the regressed model for the impulse runoff conditionis only one-tenth of those in existing models. Again, the slope vari-able becomes insignificant in governing overland flow time when theslope is small.

t kL n Q Sc a b w y= ( )4

t L n S ic = 0 553 30 5 0 32 0 277 0 172 0 646. ( ). . . . .

Time to PeakQ

Time

Time of Beginning

0

Time of Concentration

FIGURE 3 Typical hydrograph in a rainfall test.

Li and Chibber 137

TABLE 3 Rainfall Test Results

Time of Time to Antecedent Soil Rainfall Intensity SlopeSurface Beginning (min) Peak (min) Moisture (%) (mm/h) (%)

Bare Clay 1 6 14 41 47 0.43Bare Clay 2 15 27 20 50 0.43Bare Clay 3 6 20 19 54 0.43Bare Clay 4 2 12 53 85 0.43Bare Clay 5 5 15 41 58 0.43Bare Clay 6 22 45 12 43 0.42Bare Clay 7 14 37 17 38 0.42Bare Clay 8 15 37 17 41 0.42Bare Clay 9 10 36 23 41 0.42Bare Clay 10 38 71 9 40 0.42Bare Clay 11 27 61 10 41 0.42Lawn 1 9 34 41 38 0.48Lawn 2 14 54 42 38 0.48Lawn 3 9 34 44 53 0.48Lawn 4 9 38 55 46 0.48Lawn 5 9 36 31 78 0.48Lawn 6 13 32 44 87 0.48Lawn 7 7 24 56 83 0.48Lawn 8 11 55 33 54 0.24Lawn 9 14 47 19 49 0.24Lawn 10 10 40 28 56 0.24Lawn 11 18 57 34 47 0.24Lawn 12 8 34 42 47 0.24Lawn 13 10 39 37 52 0.24Pasture 1 18 50 30 49 0.48Pasture 2 23 63 26 33 0.48Pasture 3 11 39 28 75 0.48Pasture 4 16 49 25 51 0.48Pasture 5 44 91 18 40 0.48Pasture 6 18 60 24 42 0.48Pasture 7 49 95 23 54 0.24Pasture 8 8 46 38 65 0.24Pasture 9 15 44 34 53 0.24Pasture 10 16 51 30 41 0.24Pasture 11 26 61 30 44 0.24Pasture 12 17 47 34 39 0.24Concrete 1 4 12 N.A. 38 0.35Concrete 2 2 18 N.A. 35 0.35Concrete 3 2 15 N.A. 32 0.35Concrete 4 1 16 N.A. 36 0.35Concrete 5 3 10 N.A. 53 0.35Concrete 6 2 10 N.A. 56 0.35Concrete 7 2 14 N.A. 43 0.35Concrete 8 3 12 N.A. 41 0.35Concrete 9 3 9 N.A. 44 0.35Concrete 10 1 11 N.A. 32 0.35Asphalt 1 1 10 N.A. 38 0.35Asphalt 2 1 10 N.A. 41 0.35Asphalt 3 4 14 N.A. 37 0.35Asphalt 4 1 10 N.A. 45 0.35Asphalt 5 1 12 N.A. 43 0.35Asphalt 6 3 10 N.A. 47 0.35Asphalt 7 2 12 N.A. 49 0.35

138 Transportation Research Record 2060

TABLE 4 Regressed Models (Rainfall Test)

N R2 Constant b (for n) x (for ) y (for S ) z (for i)

tc 53 0.86 0.553 0.320 0.277 0.172 0.646(0.115)a (

The observed times of concentration were also plotted against thosepredicted by the new and existing models (Figure 6). Values usedfor variables in each model are presented in Table 8. The Kirpich (7)and Natural Resources Conservation Service (22) models under-estimated the observed times of concentration, the Texas Departmentof Transportation (21) overestimated them. The lower left cluster ofdata in Figure 6 indicates the test results on smooth surfaces (bareclay, asphalt, and concrete), and the higher clusters indicate the resultson pasture. On the basis of comparison results, existing modelscannot correctly predict the time of concentration on flat surfaces.

Limitations

The limitations associated with the laboratory experiment aresummarized as follows:

Data were collected only from laboratory experiments. Fieldstudies are needed to verify the laboratory results.

Only a few flat slopes were tested. The antecedent soil moisture had a significant effect on the time

of concentration; however, changes in soil moisture during testswere not monitored.

CONCLUSIONS

Existing empirical models of estimating the time of concentrationwere mostly developed from data of common watersheds. The abil-ity of these models to predict the time of concentration on very flatterrains has not been fully analyzed. This study used a controlledlaboratory environment to measure times of concentration on testplots 6 ft (1.83 m) wide by 30 ft (9.14 m) long with slopes of lessthan 0.5%. Artificial rainfall tests and impulse runoff tests were

Li and Chibber 139

0

10

20

30

40

50

0 10 20 30 40 50Predicted Tc (min)

Obs

erve

d T c

(m

in)

This studyIzzardKerbyHenderson-WoodingChen-WongPapadakis-KazanNRCS

FIGURE 5 Observed versus predicted time of concentration in therainfall test by seven models: this study, Papadakis and Karan (2),Kerby (9), Izzard (10), Henderson and Wooding (13), Chen andWong (19), and Natural Resources Conservation Service (NRCS) (22).

TABLE 6 Impulse Runoff Test Results

Travel Time Flow Rate SlopeSurface (min) (m3/s) (%)

Bare clay 1 1.28 0.0011 0.43Bare clay 2 1.17 0.0018 0.43Bare clay 3 0.70 0.0023 0.43Bare clay 4 1.02 0.0013 0.43Bare clay 5 1.31 0.0017 0.43Bare clay 6 1.20 0.0016 0.43Bare clay 7 0.73 0.0026 0.43Bare clay 8 1.80 0.0019 0.42Bare clay 9 1.72 0.0015 0.42Bare clay 10 2.27 0.0012 0.42Bare clay 11 1.72 0.0018 0.42Bare clay 12 2.25 0.0020 0.42Bare clay 13 2.23 0.0017 0.42Bare clay 14 2.42 0.0015 0.42Bare clay 15 2.67 0.0011 0.42Pasture 1 5.60 0.0013 0.24Pasture 2 4.88 0.0013 0.24Pasture 3 5.00 0.0013 0.24Pasture 4 4.07 0.0013 0.24Pasture 5 5.50 0.0013 0.24Pasture 6 6.92 0.0016 0.24Pasture 7 5.53 0.0014 0.24Pasture 8 7.00 0.0015 0.48Pasture 9 6.28 0.0009 0.48Pasture 10 5.53 0.0015 0.48Pasture 11 4.33 0.0013 0.48Pasture 12 4.07 0.0019 0.48Pasture 13 5.83 0.0019 0.48Concrete 1 1.32 0.0015 0.35Concrete 2 1.28 0.0015 0.35Concrete 3 1.33 0.0013 0.35Concrete 4 1.35 0.0010 0.35Concrete 5 1.23 0.0009 0.35Asphalt 1 1.02 0.0011 0.35Asphalt 2 1.10 0.0012 0.35Asphalt 3 1.12 0.0007 0.35Asphalt 4 1.33 0.0012 0.35Asphalt 5 1.02 0.0017 0.35Asphalt 6 1.30 0.0011 0.35Asphalt 7 1.02 0.0026 0.35Asphalt 8 1.42 0.0012 0.35Asphalt 9 1.22 0.0008 0.35Asphalt 10 1.08 0.0009 0.35Asphalt 11 1.07 0.0015 0.35Asphalt 12 1.07 0.0015 0.35Asphalt 13 1.15 0.0016 0.35Asphalt 14 1.18 0.0020 0.35Asphalt 15 1.23 0.0023 0.35Asphalt 16 1.63 0.0012 0.35

TABLE 7 Regressed Model (Impulse Runoff Test)

N R2 Constant b (for n) w (for Q) y (for S)

tc 49 0.86 0.779 0.453 0.537 0.037(0.185)a (

be considered in design and a moderate value should be chosenfor risk balancing.

The findings of this study indicate that a direction for future workwould be through field-scale instrumentation and observation of anumber of watersheds with low slopes. The rationale for performingthe laboratory study was the lack of appropriate data as well as thedesire to develop a relationship between the time of concentrationand the explanatory variables without having to collect several yearsof data. In light of the realization that antecedent soil moisture canaffect the time of concentration, some representative soil moisturecontent data would also be useful.

ACKNOWLEDGMENT

This study was sponsored by the Texas Department of Transportation.

REFERENCES

1. McCuen, R. H., S. L. Wang, and W. J. Rawls. Estimating Urban Time ofConcentration. Journal of Hydraulic Engineering, Vol. 110, No. 7, 1984,pp. 887904.

2. Papadakis, C. N., and M. N. Kazan. Time of Concentration in SmallRural Watersheds. Technical Report 101/08/86/CEE. Civil EngineeringDepartment, University of Cincinnati, Cincinnati, Ohio, 1986.

3. Goitom, T. G., and M. Baker, Jr. Evaluation of Tc Methods in a Small RuralWatershed. In Channel Flow and Catchment Runoff: Proc. InternationalConference for Centennial of Mannings Formula and Kuichlings

140 Transportation Research Record 2060

Rational Formula (B. C. Yen, ed.), University of Virginia, Charlottesville,1989, pp. 8896.

4. Mays, L. W. Water Resources Engineering. John Wiley and Sons,New York, 2001.

5. Computer Applications in Hydraulic Engineering, 5th ed. HaestadMethods, Inc., Watertown, Conn., 2002.

6. Williams, G. B. Flood Discharges and the Dimensions of Spillways inIndia. Engineering (London), Vol. 134, 1922, p. 321.

7. Kirpich, Z. P. Time of Concentration of Small Agricultural Watersheds.Civil Engineering, Vol. 10, No. 6, 1940, p. 362.

8. Hathaway, G. A. Design of Drainage Facilities. Transactions of theAmerican Society of Civil Engineers, Vol. 110, 1945, p. 697.

9. Kerby, W. S. Time of Concentration Studies. Civil Engineering, March,1959.

10. Izzard, C. F. Hydraulics of Runoff from Developed Surfaces. Proceedingsof the Highway Research Board, Vol. 26, 1946, pp. 129150.

11. Johnstone, D., and W. P. Cross. Elements of Applied Hydrology. RonaldPress, New York, 1949.

12. California Culvert Practice, 2nd ed. Department of Public Works,Division of Highways, Sacramento, 1955.

13. Henderson, F. M., and R. A. Wooding. Overland Flow and GroundwaterFlow from a Steady Rain of Finite Duration. Journal of GeophysicalResearch, Vol. 69, No. 8, 1964, pp. 15311540.

14. Morgali, J. R., and R. K. Linsley. Computer Analysis of Overland Flow.Journal of the Hydraulics Division, Vol. 91, No. HY3, 1965, pp. 81100.

15. Aron, G., and C. E. Erborge. A Practical Feasibility Study of Flood PeakAbatement in Urban Areas. Report. U.S. Army Corps of Engineers,Sacramento, Calif., 1973.

16. Circular on Airport Drainage. Report A/C 150-5320-5B. FederalAviation Administration, U.S. Department of Transportation, Washington,D.C., 1970.

17. Urban Hydrology for Small Watersheds. Technical Release 55. U.S.Soil Conservation Service, Washington, D.C., 1975.

18. Urban Hydrology for Small Watersheds. Technical Release 55, 2nd ed.U.S. Soil Conservation Service, Washington, D.C., 1986.

19. Chen, C. N., and T. S. W. Wong. Critical Rainfall Duration for MaximumDischarge from Overland Plane. Journal of Hydraulic Engineering,Vol. 119, No. 9, 1993, pp. 10401045.

20. Wong, T. S. W. Assessment of Time of Concentration Formulas forOverland Flow. Journal of Irrigation and Drainage Engineering, Vol. 131,No. 4, 2005, pp. 383387.

21. Hydraulic Design Manual. Texas Department of Transportation, Austin,1994.

22. PondsPlanning, Design, Construction. Agriculture Handbook No. 590.U.S. Natural Resources Conservation Service, Washington, D.C., 1997.

The Hydrology, Hydraulics, and Water Quality Committee sponsored publicationof this paper.

0

2

4

6

8

0 2 4 6 8 10 12 14 16Predicted Tc (min)

Obs

erve

d T c

(m

in)This studyKirpichTxDOTNRCS

FIGURE 6 Observed versus predicted time of concentration in the impulse runoff test by four models: this study, Kirpich (7 ), Texas Department of Transportation(TxDOT) (21), and Natural Resources Conservation Service (NRCS) (22).

TABLE 8 Variable Values Used for Model Comparison (Impulse Runoff Test)

Kirpich Model TxDOT Model NRCS ModeSurface K C (runoff coefficient) Curve Number

Bare clay 0.0078 0.2 89Pasture 0.0078 0.15 80Concrete 0.0078 0.925 98Asphalt 0.0078 0.875 98