SCS Curve Number Loss Model

Basic Concepts and Equations

The Soil Conservation Service (SCS) Curve Number (CN) model estimates precipitation excess as a function of cumulative precipitation, soil cover, land use, and antecedent moisture, using the following equation:

1)	$\begin{array}{l}\displaystyle P_{e} = \frac{(P-I_{a})^2}{(P-I_{a})+S}\end{array}$

where Pe = accumulated precipitation excess at time t; P = accumulated rainfall depth at time t; Ia = the initial abstraction (initial loss); and S = potential maximum retention, a measure of the ability of a watershed to abstract and retain storm precipitation. Until the accumulated rainfall exceeds the initial abstraction, the precipitation excess, and hence the runoff, will be zero. From analysis of results from many small experimental watersheds, the SCS developed an empirical relationship of Ia and S:

2)	$\begin{array}{l}\displaystyle I_{a}=0.2 * S\end{array}$

Therefore, the cumulative excess at time t is:

3)	$\begin{array}{l}\displaystyle P_{e}=\frac{(P-0.2*S)^2}{(P+0.8S)}\end{array}$

Incremental excess for a time interval is computed as the difference between the accumulated excess at the end of and beginning of the period. The maximum retention, S, and watershed characteristics are related through an intermediate parameter, the curve number (commonly abbreviated CN) as:

4)	$\begin{array}{l}S = \begin{cases} \frac{1000-10CN}{CN} &\text(foot-pound\;system)\\ \frac{25400-254CN}{CN} &\text{(SI)} \end{cases}\end{array}$

CN values range from 100 (for water bodies) to approximately 30 for permeable soils with high infiltration rates. Publications from the Soil Conservation Service (1971, 1986) provide further background and details on use of the CN model.

Since no means for extracting infiltrated water is included, this method should only be used for event simulation.

Required Parameters

Parameters that are required to utilize the SCS curve number method include a curve number and directly connected impervious area [percent]. Optionally, I_a [in or mm] can be entered as well.

The curve number that is entered should be a “composite” curve number that represents all of the different soil group and land use combinations in the subbasin. This value should not include any impervious area that will be specified separately as the percentage of impervious area. Typically, curve numbers are derived from soils maps. I_a defines the amount of precipitation that must fall before excess precipitation results. If this value is not entered, it will be automatically calculated using:

5)	$\begin{array}{l}\displaystyle I_{a}=0.2*S\end{array}$

The CN for a watershed can be estimated as a function of land use, soil type, and antecedent watershed moisture, using tables published by the SCS. For convenience, Appendix A of this document includes CN tables developed by the SCS and published in Technical Report 55 (commonly referred to as TR-55). With these tables and knowledge of the soil type and land use, the single-valued CN can be found. For example, for a watershed that consists of a tomato field on sandy loam near Davis, CA, the CN shown in Table 2-2b of the TR-55 tables is 78. (This is the entry for straight row crop, good hydrologic condition, B hydrologic soil group.) This CN is entered directly in the appropriate input form. For a watershed that consists of several soil types and land uses, a composite CN is calculated as:

6)	$\begin{array}{l}\displaystyle CN_{composite}=\frac{\sum A_{i}CN_{i}}{\sum A_{i}}\end{array}$

in which CNcomposite = the composite CN used for runoff volume computations; i = an index of watersheds subdivisions of uniform land use and soil type; CNi = the CN for subdivision i; and Ai = the drainage area of subdivision i.

Users of the SCS model as implemented in the program should note that the tables in Appendix A include composite CN for urban districts, residential districts, and newly graded areas. That is, the CN shown are composite values for directly-connected impervious area and open space. If CN for these land uses are selected, no further accounting of directly-connected impervious area is required.

Finally, the percentage of the subbasin which is directly connected impervious area can be specified. Directly connected impervious areas are surfaces where runoff is conveyed directly to a waterway or stormwater collection system. These surfaces differ from disconnected impervious areas where runoff encounters permeable areas which may infiltrate some (or all) of the runoff prior to reaching a waterway or stormwater collection system. No loss calculations are carried out on the specified percentage of the subbasin; all precipitation that falls on that portion of the subbasin becomes excess precipitation and subject to direct runoff.

A Note on Parameter Estimation

The values presented here are meant as initial estimates. This is the same for all sources of similar data including Engineer Manual 1110-2-1417 Flood-Runoff Analysis and the Introduction to Loss Rate Tutorials. Regardless of the source, these initial estimates must be calibrated and validated.