Estimating Design Discharge for Small Ungaged Watersheds Using the SCS Method

Michael A. Stevens

Introduction
Estimating Runoff
Time of Concentration
Graphical Discharge Method
Appendix
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:

topographic, soil characteristic, and land cover maps of the basin of interest
precipitation data for a given maximum rain event (a 2 year 24 hour storm is the preferred minimum)

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 T_c 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 Description			Hydrological Soil Group
Land Use Description			A	B	C	D
Cultivated land	Without conservation treatment		72	81	88	91
Cultivated land	With conservation treatment		62	71	78	81
Pasture or range land	Poor condition		68	79	86	89
Pasture or range land	Good condition		39	61	74	80
Meadow			30	58	71	78
Wood or forest land	Thin stand, poor cover, no mulch		45	66	77	83
Wood or forest land	Good cover		25	55	70	77
Open spaces, lawns, parks, golf courses, cemeteries, etc.	Good condition: grass cover on 75% or more of the area		39	61	74	80
	Fair condition: 50-75% of the area		49	69	79	84
	Commercial and business areas (85% impervious)		89	92	94	95
	Industrial districts (72% impervious)		81	88	91	93
Residential	Average lot size	Average % Impervious
	1/8 acre or less	65	77	85	90	92
	1/4 acre	38	61	75	83	87
	1/3 acre	30	57	72	81	86
	1/2 acre	25	54	70	80	85
	1 acre	20	51	68	79	84
Paved parking lots, roofs, driveways, etc.			98	98	98	98
Streets and roads	Paved with curbs and storm sewers		98	98	98	98
	Gravel		76	85	89	91
	Dirt		72	82	87	89
Open water			0	0	0	0

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 - I_a)² * [(P + I_a) + S]^-1

(2)

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

Time of Concentration

Next, the time of concentration (T_c) 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 T_t), shallow concentrated flow (T_sc), and channel flow (T_ch).

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

T_t = 0.007 (n * L)^0.8 * (P₂^0.5 * s^0.4)^-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
Grass	Short grass prairie	0.15
	Dense grasses	0.24
	Bermuda grass	0.41
Natural range		0.13
Woods	Light underbrush	0.40
	Dense underbrush	0.80

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

T_sc = L * (58,084.2 * s^0.5)^-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:

T_ch = n * L * (5,364 * R^2/3 * S^1/2)^-1

(5)

where L is the length in feet, R is the hydraulic radius in feet (R = A / P_w), 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 Conduits		Min.	Design	Max.
Earth Channels Earth bottom, rubble sides		0.028	0.032	0.035
Drainage ditches, large, no vegetation	<2.5 hydraulic radius	0.040	0.045	---
	2.5 - 4.0 hydraulic radius	0.035	0.040	---
	4.0 - 5.0 hydraulic radius	0.030	0.035	---
	>5.0 hydraulic radius	0.025	0.030	---
Small drainage ditches		0.035	0.040	0.040
Stony bed, weeds on bank		0.025	0.035	0.040
Straight and uniform		0.017	0.0225	0.025
Winding, sluggish		0.0225	0.025	0.030
Natural Streams	(A) Clean, straight bank, full stage, no rifts or deep pools	0.025	0.033	---
	(B) Same as (A) but some weeds and stones	0.030	0.040	---
	(C) Winding, some pools and shoals, clean	0.035	0.050	---
	(D) Same as (C), lower stages, more ineffective slopes and sections	0.040	0.055	---
	(E) Same as (C), some weeds and stones	0.033	0.045	---
	(F) Same as (D), stony sections	0.045	0.060	---
	(G) Sluggish river reaches, rather weedy or with very deep pools	0.050	0.080	---
	(H) Very weedy reaches	0.075	0.150	---

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

T_c = T_t + T_sc + T_ch

(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.

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 q_u.

log(q_u) = C₀ + C₁ * log (T_C) + C₂ * [log (T_C)]²

(7)

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

Table 4 : Coefficients for Eq. 7²
Rainfall type	I_a/P	C₀	C₁	C₂
I	0.10	2.30550	-0.51429	-0.11750
	0.20	2.23537	-0.50387	-0.08929
	0.25	2.18219	-0.48488	-0.06589
	0.30	2.10624	-0.45695	-0.02835
	0.35	2.00303	-0.40769	0.01983
	0.40	1.87733	-0.32274	0.05754
	0.45	1.76312	-0.15644	0.00453
	0.50	1.67889	-0.06930	0.0
IA	0.10	2.03250	-0.31583	-0.13748
	0.20	1.91978	-0.28215	-0.07020
	0.25	1.83842	-0.25543	-0.02597
	0.30	1.72657	-0.19826	0.02633
	0.50	1.63417	-0.09100	0.0
II	0.10	2.55323	-0.61512	-0.16403
	0.30	2.46532	-0.62257	-0.11657
	0.35	2.41896	-0.61594	-0.08820
	0.40	2.36409	-0.59857	-0.05621
	0.45	2.29238	-0.57005	-0.02281
	0.50	2.20282	-0.51599	-0.01259
III	0.10	2.47317	-0.51848	-0.17083
	0.30	2.39628	-0.51202	-0.13245
	0.35	2.35477	-0.49735	-0.11985
	0.40	2.30726	-0.46541	-0.11094
	0.45	2.24876	-0.41314	-0.11508
	0.50	2.17772	-0.36803	-0.09525

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

Table 5: Pond Adjustment Factor F_p²
Percentage of pond and swamp areas	Fp
0	1.00
0.2	0.97
1.0	0.87
3.0	0.75
5.0	0.72

Once q_u, F_p, Q, and the basin area are found, the peak discharge q_p can be calculated with Equation 8.

q_p = q_u * F_p * Q * A

(8)

where q_p is the peak discharge in cfs, q_u is the unit peak discharge in ^csm/_in , F_p 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 mm	1 mm	0.0394 in
1 ft³	0.0283 m³	1 m³	35.3 ft³
1 mi²	259 ha	1 ha	0.00386 mi²
1 mi²	2.59 km²	1 km²	0.386 mi²
1 acre	0.405 ha	1 ha	2.47 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.