Estimating Design Discharge for Small Ungaged Watersheds Using the SCS Method

Michael A. Stevens

Table of Contents

  1. Introduction
  2. Estimating Runoff
  3. Time of Concentration
  4. Graphical Discharge Method
  5. Appendix
  6. Bibliography

An example problem can be found here.

Introduction

The SCS method for determining the unit hydrograph is an easy method that can be used for estimating stream discharge. This method was developed by the US Soil Conservation Service (SCS) for small ungaged streams. It's a fairly easy way to determine maximum discharge for a watershed, and can easily be calculated using a spreadsheet application. This design maximum can then be used as a factor in constructing ditches, culverts, bridges, etc. Since the SCS method was developed using American Customary measurements, they must be used for the calculations. For those who use metric, a conversion table listed in the appendix for your convenience.

In order to use this method, you need to obtain the following:

The particular version of the SCS method used in this discussion uses the Graphical Discharge Method to determine maximum discharge (as opposed to the Tabular Discharge Method). The advantage lies mainly in the relative ease and straightforwardness of calculating the maximum discharge. However, this method does have its limitations and should not be used if the basin is not reasonably homogenous, has several main branches, has large storage reservoirs, has a weighted CN less than 40, or has a Tc less than 0.1 hours, or greater than 10 hours.

Estimating Runoff

The SCS method uses the runoff curve number (CN). This number is a function of soil type and land use, and can be determined from the table below.

Table 1: Runoff Curve Numbers for Selected Agricultural, Suburban, and Urban Land Use1
Land Use DescriptionHydrological Soil Group
ABCD
Cultivated landWithout conservation treatment72818891
With conservation treatment 62717881
Pasture or range landPoor condition 68798689
Good condition 39617480
Meadow30587178
Wood or forest landThin stand, poor cover, no mulch45667783
Good cover 25557077
Open spaces, lawns, parks, golf courses, cemeteries, etc.Good condition: grass cover on 75% or more of the area 39617480
Fair condition: 50-75% of the area 49697984
Commercial and business areas (85% impervious)89929495
Industrial districts (72% impervious) 81889193
ResidentialAverage lot size Average % Impervious     
1/8 acre or less 6577859092
1/4 acre 3861758387
1/3 acre3057728186
1/2 acre 2554708085
1 acre 2051687984
Paved parking lots, roofs, driveways, etc. 98989898
Streets and roadsPaved with curbs and storm sewers98989898
Gravel76858991
Dirt72828789
Open water 0000

The differences in the hydrological soil groups are defined by soil type. This would be a sandy, well-drained soil for type A, a sandy loam for type B, a clay loam or a shallow sandy loam for type C, and a high plasticity clay for type D. For most cases, the entire basin will not consist of a single soil type or land cover. For this situation, a composite CN value can be computed by weighting each CN with its respective area in the basin.

Once the Curve number is found, the potential abstraction S is found with Equation 1.

S = 1,000/CN - 10(1)

where S is the potential abstraction in inches, and CN is the averaged curve number found in Table 1.

This value for S is then used in the general RCN runoff equation.

Q = (P - Ia)2 * [(P + Ia) + S]-1(2)

where Q is the runoff in inches, P is the rainfall in inches, and Ia is the potential abstraction in inches (Ia = 0.2 S).

Time of Concentration

Next, the time of concentration (Tc) is calculated. This value is amount of time it takes from the edge of the watershed to the point of interest, and is a combination of three values: sheet flow Tt), shallow concentrated flow (Tsc), and channel flow (Tch).

The sheet flow time of concentration is calculated by the following equation:

Tt = 0.007 (n * L)0.8 * (P20.5 * s0.4)-1(3)

where L is equal to the length in feet (the maximum value of L for sheet flow is 300 ft), P2 is equal to the 2 year, 24 hour rainfall in inches, s is equal to the slope in ft/ft, and n is equal to the Manning's n for sheet flow, found in the table below:

Table 2: Manning's Roughness Coefficients for Sheet Flow2
Surface Description n
Smooth surfaces (concrete, asphalt, bare soil) 0.011
Fallow (no residue) 0.05
Cultivated Soils Residue cover ≤ 20% 0.06
Residue cover > 20% 0.17
GrassShort grass prairie 0.15
Dense grasses 0.24
Bermuda grass 0.41
Natural range 0.13
WoodsLight underbrush 0.40
Dense underbrush 0.80

The shallow concentrated flow time of concentration can be calculated by:

Tsc = L * (58,084.2 * s0.5)-1(4)

where L is equal to the length in feet, and s is equal to the slope in ft/ft. The maximum value of L for shallow concentrated flow is 300 ft.

The channel flow time of concentration is calculated by a derivation of Manning's equation, which is shown below:

Tch = n * L * (5,364 * R2/3 * S1/2)-1(5)

where L is the length in feet, R is the hydraulic radius in feet (R = A / Pw), s is equal to the slope in ft/ft, and n is the Manning's number (see table below).

Table 3: Typical Manning's Roughness Coefficients3
Type and Description of ConduitsMin.DesignMax.
Earth Channels Earth bottom, rubble sides0.0280.0320.035
Drainage ditches, large, no vegetation<2.5 hydraulic radius0.0400.045---
2.5 - 4.0 hydraulic radius0.0350.040---
4.0 - 5.0 hydraulic radius0.0300.035---
>5.0 hydraulic radius0.0250.030---
Small drainage ditches0.0350.0400.040
Stony bed, weeds on bank0.0250.0350.040
Straight and uniform0.0170.02250.025
Winding, sluggish0.02250.0250.030
Natural Streams(A) Clean, straight bank, full stage, no rifts or deep pools0.0250.033---
(B) Same as (A) but some weeds and stones0.0300.040---
(C) Winding, some pools and shoals, clean0.0350.050---
(D) Same as (C), lower stages, more ineffective slopes and sections0.0400.055---
(E) Same as (C), some weeds and stones0.0330.045---
(F) Same as (D), stony sections0.0450.060---
(G) Sluggish river reaches, rather weedy or with very deep pools0.0500.080---
(H) Very weedy reaches0.0750.150---

Once these three values are found, add them together to get the time of concentration for the basin.

Tc = Tt + Tsc + Tch(6)

Graphical Discharge Method

Now that the runoff and the time of concentration are known, we can calculatethe max discharge using the graphical peak discharge method. This is one of the two methods specified by the SCS method, and is the easiest to compute. This is done by first determining the SCS type that best describes the maximum precipitation event in the desired basin. Figure 1 shows a graphical representation of the SCS types, with type IA being the least intense, on to type III which is the most intense.

SCS 24 hour rainfall distributions
Figure 1: SCS 24 hour rainfall distributions2

Once the SCS type is determined for the basin, the next step is to calculate the unit peak discharge qu.

log(qu) = C0 + C1 * log (TC) + C2 * [log (TC)]2(7)

where qu is the unit peak discharge in csm/in, Tc is the time of concentration in hours, and C0, C1, and C2 are coefficients from Table 4.

Table 4 : Coefficients for Eq. 72
Rainfall typeIa/PC0C1C2
I0.102.30550-0.51429-0.11750
0.202.23537-0.50387-0.08929
0.252.18219-0.48488-0.06589
0.302.10624-0.45695-0.02835
0.352.00303-0.407690.01983
0.401.87733-0.322740.05754
0.451.76312-0.156440.00453
0.501.67889-0.069300.0
IA0.102.03250-0.31583-0.13748
0.201.91978-0.28215-0.07020
0.251.83842-0.25543-0.02597
0.301.72657-0.198260.02633
0.501.63417-0.091000.0
II0.102.55323-0.61512-0.16403
0.302.46532-0.62257-0.11657
0.352.41896-0.61594-0.08820
0.402.36409-0.59857-0.05621
0.452.29238-0.57005-0.02281
0.502.20282-0.51599-0.01259
III0.102.47317-0.51848-0.17083
0.302.39628-0.51202-0.13245
0.352.35477-0.49735-0.11985
0.402.30726-0.46541-0.11094
0.452.24876-0.41314-0.11508
0.502.17772-0.36803-0.09525

Next is the swamp and pond adjustment factor Fp. This is found from Table 5 :

Table 5: Pond Adjustment Factor Fp2
Percentage of pond and swamp areasFp
01.00
0.20.97
1.00.87
3.00.75
5.00.72

Once qu, Fp, Q, and the basin area are found, the peak discharge qp can be calculated with Equation 8.

qp = qu * Fp * Q * A(8)

where qp is the peak discharge in cfs, qu is the unit peak discharge in csm/in , Fp is the pond and swamp adjustment factor , Q is the runoff in inches, and A is the basin area in square miles.

Appendix

Appendix A: Common SI equivalents
Customary to SI SI to Customary
1 in 25.4 mm1 mm0.0394 in
1 ft30.0283 m31 m335.3 ft3
1 mi2259 ha1 ha0.00386 mi2
1 mi22.59 km21 km20.386 mi2
1 acre0.405 ha1 ha2.47 acre

Bibliography

1 Bedient, P.B., Huber,W.C., Hydrology and Floodplain Analysis, Addison-Wesley (1992) p.129.
2 Urban Hydrology for Small Watersheds (TR-55), US Department of Agriculture, ftp://ftp.wcc.nrcs.usda.gov/downloads/hydrology_hydraulics/tr55/tr55.pdf (1986).
3 2.0 Basic Concepts of Open Channel Flow Measurement, US Environmental Protection Agency, http://www.epa.gov/ORD/NRMRL/Pubs/600R01043/600R01043chap2.pdf (posted as of 2004), p. 3.