SCS TR-55 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 TR-55 (1986): Urban Hydrology for Small Watersheds

 To:     Precipitation maps for 24-hr duration storms in USA
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Topics on this page:  Introduction    Equations   Runoff Curve Numbers
  Error Messages   References

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Introduction                                                Top of Page
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 (TR-55: SCS, 1986) presents a methodical and reliable approach to predicting peak discharge due to a 24-hr storm event.  (This web page uses TR-55 and SCS (1986) interchangeably; they are the same document.)  TR-55 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 TR-55 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 stand-alone computer programs rather than for programs that run from the world wide web.

Though the TR-55 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, TR-55 only presents rainfall distribution maps for the USA.  Therefore, non-USA users need to determine whether a typical 24-hr rainfall resembles a Type I, IA, II, or III distribution and determine 24-hr rainfalls from local sources.  Our calculation was written in double precision using the Java computer language.

Equations (SCS, 1986)                            Top of Page
TR-55 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:

Runoff Discharge Equations

where: A = total watershed area (mile2).  CN = overall curve number for the watershed.  Fp = pond and swamp adjustment factor from Table 4-2 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.  Ia = initial abstraction (inch); losses before runoff begins (surface depressions, interception by leaves, evaporation, infiltration) - SCS determined the above equation for Ia after numerous studies.  P = precipitation (inch) for 24-hr duration storm of return period for which you are interested.  Q = depth of runoff over entire watershed (inch).  Qp = peak discharge (cfs).  Qu = unit peak discharge (cfs/mile2-inch); computed from equations given in SCS (1986) Appendix F representing its Figures 4-I thru 4-III 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).  Tc = 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 Qp.

Our calculation allows the user to divide a watershed into a maximum of five sub-regions represented by different curve numbers.  Then, the overall curve number and total area are computed.  Alternatively, if there are more than five sub-regions, 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:

Runoff Curve Number Equations

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 sheet-like and more concentrated.  Following shallow concentrated flow, water typically collects in natural or man-made channels.  Each of the flow patterns requires a unique mathematical expression:

Time of Concentration and Travel Times

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).  P2 = 2-yr return period, 24-hr duration precipitation for the geographic region where your watershed is located (inch); click for USA rainfall mapsR = hydraulic radius (ft) of bank full open channel or culvert flowing full; computed automatically if channel cross-section dimensions are input.  S = average ground slope of each flow pattern (ft vertical/ft horizontal).  Tc = 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 QpTt = 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 cross-section 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.

Open Channels and Culverts for Channel Flow

Runoff Curve Numbers                                    Top of Page
The following table of runoff curve numbers (CN) has been condensed from Tables 2-2(a-d) 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 (50-75% 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 over-grazing 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 50-75% 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

*From Chow et al. (1988).

Error Messages given by calculation                            Top of Page
"Tc out of range."  Qp not computed.  The peak discharge calculation is only valid for Tc 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 sub-regions is input, runoff will not be computed.

"Most accurate if Q>0.5 inch."  The runoff and peak discharge calculations using the TR-55 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."  Tt 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 Qp) 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."  Qp not computed.  The total area of the watershed must be greater than zero.  If you are entering sub-region information, at least one of the sub-areas (A1 through A5) must be >0.

"P2 must be >0."  Tt for sheet flow (thus Qp) not computed.   The 2-yr, 24-hr duration rainfall is used for computation of travel time (Tt) for sheet flow.  If you don't want to compute this Tt or sheet flow does not exist, just enter any positive value for P2 and enter L (for sheet flow) as 0.0.

"Manning n must be >0."  Tt 's (thus Qp) 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."  Tt 's (thus Qp) 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 (Qp) not computed.


References  
                                                        Top of Page
Chow, V. T, D. R. Maidment, and L. W. Mays.  1988.  Applied Hydrology.   McGraw-Hill, 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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