SCS TR55 Peak Discharge and Runoff Calculator 
Hydrologic calculations for Peak Discharge, Runoff Depth, Runoff Curve Number, Time of Concentration, and Travel Times 
Based on the USA Soil Conservation Service publication TR55 (1986): Urban Hydrology for Small Watersheds 

To:
Precipitation maps for 24hr
duration storms in USA Topics on this page: Introduction Equations
Runoff Curve Numbers 
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Introduction
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The USA Soil Conservation Service (now called the Natural Resources Conservation Service),
division of the USDA (USA Department of Agriculture) has worked for decades developing
equations and conducting experiments to determine reliable models for predicting peak
discharge from storm events. Relying upon extensive research, Technical Release 55
(TR55: SCS, 1986) presents a methodical and reliable approach to predicting peak
discharge due to a 24hr storm event. (This web page uses TR55 and SCS (1986)
interchangeably; they are the same document.) TR55 is valid for watersheds that
have a time of concentration from 0.1 to 10 hr.
Such watersheds are considered small. Our calculation uses the equations and
graphs (coded into equations) in TR55 chapters 1 thru 4 to solve for peak discharge.
Chapter 5 (titled Tabular Hydrograph Method) also solves for peak discharge but
models more complicated watersheds  watersheds that have several main channels requiring
channel hydrograph routing techniques. Hydrograph routing software is more suitable
for standalone computer programs rather than for programs that run from the world wide
web.
Though the TR55 document mentions specific units (all English) for its equations, our calculation allows a variety of input and output units (English and metric). We have tried to make the calculation useful for the international community. Unfortunately, TR55 only presents rainfall distribution maps for the USA. Therefore, nonUSA users need to determine whether a typical 24hr rainfall resembles a Type I, IA, II, or III distribution and determine 24hr rainfalls from local sources. Our calculation was written in double precision using the Java computer language.
Equations (SCS, 1986)
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TR55 specifies units for its equations. Our calculation allows you to use other
units that may be more convenient. Peak discharge, runoff depth, initial
abstraction, unit peak discharge, and pond/swamp factor are computed as follows:
where: A = total watershed area (mile^{2}). CN = overall curve number for the watershed. F_{p} = pond and swamp adjustment factor from Table 42 in SCS (1986) to which we fit a 3rd order polynomial; input a number in the calculation for the % of watershed area (0 to 5%) occupied by ponds and swamps unless you accounted for ponds and swamps in your curve numbers. I_{a} = initial abstraction (inch); losses before runoff begins (surface depressions, interception by leaves, evaporation, infiltration)  SCS determined the above equation for I_{a} after numerous studies. P = precipitation (inch) for 24hr duration storm of return period for which you are interested. Q = depth of runoff over entire watershed (inch). Q_{p} = peak discharge (cfs). Q_{u} = unit peak discharge (cfs/mile^{2}inch); computed from equations given in SCS (1986) Appendix F representing its Figures 4I thru 4III for various rainfall distribution types; if you are outside the USA, use the rainfall distribution type that best represents your typical storm. s = potential maximum watershed water retention after runoff begins (inch). T_{c} = time of concentration for the watershed (hr); time for runoff to travel from the furthest distance (by time) in the watershed to the location where you wish to determine Q_{p}.
Our calculation allows the user to divide a watershed into a maximum of five subregions represented by different curve numbers. Then, the overall curve number and total area are computed. Alternatively, if there are more than five subregions, you may compute the overall curve number by hand and enter that value into our calculation. Table of curve numbers as a function of land use. Overall curve number is computed from:
After decades of research, SCS (1986) indicates that there are typically three distinct runoff patterns in a watershed  sheet flow, shallow concentrated flow, and channel flow. Sheet flow occurs in the upper reaches of a watershed and persists for a maximum of 300 ft. After flowing in sheets, water then typically becomes less sheetlike and more concentrated. Following shallow concentrated flow, water typically collects in natural or manmade channels. Each of the flow patterns requires a unique mathematical expression:
where: L = length of flow pattern (ft); include all wiggles in channels. n = Manning's n value; for sheet flow, n represents the ground cover to a depth of about 1.2 inches (3 cm); for channel flow, n represents bank full conditions for an open channel or full conditions for a culvert (Manning n's for channel flow were assembled from Manning's n values). P_{2} = 2yr return period, 24hr duration precipitation for the geographic region where your watershed is located (inch); click for USA rainfall maps. R = hydraulic radius (ft) of bank full open channel or culvert flowing full; computed automatically if channel crosssection dimensions are input. S = average ground slope of each flow pattern (ft vertical/ft horizontal). T_{c} = time of concentration for the watershed (hr); time for runoff to travel from the furthest distance (by time) in the watershed to the location where you wish to determine Q_{p}. T_{t} = travel time for flow regime of interest (hr)  sheet, shallow concentrated, or channel flow. V = average velocity of water in each flow regime (ft/s).
For channel flow, our calculation allows you to input the type of channel and the crosssection dimensions. Channel flow information is used for computing channel travel time. SCS (1986) states that bank full dimensions for open channels (or full flow conditions for culverts) should be used for this calculation. The diagrams below indicate the types of channels that are coded into our calculation. The hydraulic radius (R) is calculated by our program, but is provided below for your information. (R is used in the Manning equation to determine flow velocity and then travel time.) If your channel does not match one of the four types shown below, our program can still be used to compute travel time: You should compute R by hand for your channel, then select "Circular Culvert" and enter 4R for the culvert diameter. When our program computes R, it will compute R=D/4=(4R)/4=R, so the R used in the Manning equation will be what you computed.
Runoff Curve Numbers
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The following table of runoff curve numbers (CN) has been condensed from Tables 22(ad)
of SCS (1986), which is an exhaustive listing of runoff curve numbers. The
hydrologic soil group refers to the infiltration potential of the soil after prolonged
wetting.
Group A Soils: High infiltration (low runoff). Sand,
loamy sand, or sandy loam. Infiltration rate > 0.3 inch/hr when wet.
Group B Soils: Moderate infiltration (moderate runoff).
Silt loam or loam. Infiltration rate 0.15 to 0.3 inch/hr when wet.
Group C Soils: Low infiltration (moderate to high runoff).
Sandy clay loam. Infiltration rate 0.05 to 0.15 inch/hr when wet.
Group D Soils: Very low infiltration (high runoff).
Clay loam, silty clay loam, sandy clay, silty clay, or clay. Infiltration rate 0 to
0.05 inch/hr when wet.
Table of Runoff Curve Numbers (SCS, 1986)
Description of Land Use  Hydrologic Soil Group  
A  B  C  D  
Paved parking lots, roofs, driveways  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 
Cultivated (Agricultural Crop) Land*:  
Without conservation treatment (no terraces)  72  81  88  91 
With conservation treatment (terraces, contours)  62  71  78  81 
Pasture or Range Land:  
Poor (<50% ground cover or heavily grazed)  68  79  86  89 
Good (5075% ground cover; not heavily grazed)  39  61  74  80 
Meadow (grass, no grazing, mowed for hay)  30  58  71  78 
Brush (good, >75% ground cover)  30  48  65  73 
Woods and Forests:  
Poor (small trees/brush destroyed by overgrazing or burning)  45  66  77  83 
Fair (grazing but not burned; some brush)  36  60  73  79 
Good (no grazing; brush covers ground)  30  55  70  77 
Open Spaces (lawns, parks, golf courses, cemeteries, etc.):  
Fair (grass covers 5075% of area)  49  69  79  84 
Good (grass covers >75% of area)  39  61  74  80 
Commercial and Business Districts (85% impervious)  89  92  94  95 
Industrial Districts (72% impervious)  81  88  91  93 
Residential Areas:  
1/8 Acre lots, about 65% impervious  77  85  90  92 
1/4 Acre lots, about 38% impervious  61  75  83  87 
1/2 Acre lots, about 25% impervious  54  70  80  85 
1 Acre lots, about 20% impervious  51  68  79  84 
Error Messages given by calculation
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"Tc out of range." Q_{p} not
computed. The peak discharge calculation is only valid for T_{c} between 0.1
and 10 hours.
"Overall CN must be 40 to 100." The runoff and peak discharge calculations are only valid for CN between 40 and 100. If overall CN is input, runoff will be computed. If CN for subregions is input, runoff will not be computed.
"Most accurate if Q>0.5 inch." The runoff and peak discharge calculations using the TR55 method have been found to lose significant accuracy if the runoff (Q) is <0.5 inch (1.3 cm). This is just a warning message; outputs will be computed.
"Sheet length must be 0 to 300 ft." T_{t} for sheet flow not computed. Relying on decades of research, the SCS has found that sheet flow occurs only for flow lengths up to 300 ft. Enter 0.0 if the sheet flow regime does not exist.
"Ponds, Swamps must be 0 to 5%." Pond and swamp factor (thus Q_{p}) not computed. The percent of the total watershed area occupied by ponds and swamps can only be between 0 and 5%. If you have accounted for ponds and swamps in your CN's, then enter 0% for ponds and swamps.
"Total Area must be >0." Q_{p} not computed. The total area of the watershed must be greater than zero. If you are entering subregion information, at least one of the subareas (A_{1} through A_{5}) must be >0.
"P2 must be >0." T_{t} for sheet flow (thus Q_{p}) not computed. The 2yr, 24hr duration rainfall is used for computation of travel time (T_{t}) for sheet flow. If you don't want to compute this T_{t} or sheet flow does not exist, just enter any positive value for P_{2} and enter L (for sheet flow) as 0.0.
"Manning n must be >0." T_{t} 's (thus Q_{p}) not computed. Manning n describes the roughness of the sheet flow terrain and the channel flow material. If either (or both) flow regimes do not exist, just enter any positive value for the n's and enter L=0 for the flow regime(s) that does not exist.
"S must be >0." T_{t} 's (thus Q_{p}) not computed. Average ground slope of each flow regime must be positive. If a certain flow regime (sheet, shallow concentrated, or channel flow) does not exist, just enter any positive value for S and enter L=0 for the flow regime.
"Precip must be >0." Runoff (Q) and Peak
Discharge (Q_{p}) not computed.
References
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Chow, V. T, D. R. Maidment, and L. W. Mays. 1988. Applied Hydrology.
McGrawHill, Inc.
U.S. Soil Conservation Service. Technical Release 55: Urban Hydrology for Small Watersheds. USDA (U.S. Department of Agriculture). June 1986. Available from NTIS (National Technical Information Service), NTIS # PB87101580. Also available on the web in .pdf format at http://www.info.usda.gov/CED/ftp/CED/tr55.pdf .
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