- Introduction
- Estimating Runoff
- Time of Concentration
- Graphical Discharge Method
- Appendix
- Bibliography

An example problem can be found here.

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.

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 Use^{1} | ||||||

Land Use Description | Hydrological Soil Group | |||||

A | B | C | D | |||

Cultivated land | Without conservation treatment | 72 | 81 | 88 | 91 | |

With conservation treatment | 62 | 71 | 78 | 81 | ||

Pasture or range land | Poor condition | 68 | 79 | 86 | 89 | |

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 | |

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 (

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

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

T = 0.007 (_{t}n * L)^{0.8} * (P_{2}^{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), *P _{2}* is equal to the 2 year, 24 hour rainfall in inches,

Table 2: Manning's Roughness Coefficients for Sheet Flow^{2} | ||

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}*),

Table 3: Typical Manning's Roughness Coefficients^{3} | ||||

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) |

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 distributions ^{2} **

Once the SCS type is determined for the basin, the next step is to calculate the unit peak discharge *q _{u}*.

log(q) = _{u}C + _{0}C * log (_{1}T) + _{C}C * [log (_{2}T)]_{C}^{2} | (7) |

where *q _{u}* is the unit peak discharge in

Table 4 : Coefficients for Eq. 7^{2} |
||||

Rainfall type | I_{a}/P | C_{0} | C_{1} | C_{2} |

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_{p}^{2} | |

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}*,

q = _{p}q * _{u}F * _{p}Q * A | (8) |

where *q _{p}* is the peak discharge in cfs,

Appendix A: Common SI equivalents | |||

Customary to SI | SI to Customary | ||

1 in | 25.4 mm | 1 mm | 0.0394 in |

1 ft^{3} | 0.0283 m^{3} | 1 m^{3} | 35.3 ft^{3} |

1 mi^{2} | 259 ha | 1 ha | 0.00386 mi^{2} |

1 mi^{2} | 2.59 km^{2} | 1 km^{2} | 0.386 mi^{2} |

1 acre | 0.405 ha | 1 ha | 2.47 acre |

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.