Basic Concepts and Equations
The user-specified S-graph (or S-curve) method uses a defined curve that represents the percentage of a summation hydrograph to route excess precipitation to the subbasin outlet. When used in this particular way, the S-curve is defined with the percentage of the watershed lag time, tlag, as the independent variable (x-axis) and percentage of the cumulative runoff volume as the dependent variable (y-axis). tlag [hours] is defined as the length of time between the centroid of precipitation mass and the peak flow of the resulting hydrograph. tlag can either be directly specified or through the use of a regression equation which takes the following form:
| 1) |
t_{l a g}=C\left(\frac{L * L_{c a}}{S^p}\right)^m |
where C = a coefficient that describes the hydraulic efficiency of the stream channel, L = length along the stream centerline from the outlet to the watershed boundary [miles or kilometers], Lca = length along the stream centerline from the outlet to a point on the stream nearest the centroid of the watershed [mi or km], and S = slope of the main watercourse [feet/mile or km/m]. The exponents, m and p, must be derived from gaged data within the region of interest. Computationally, the S-curve is scaled by tlag and successive differences are taken along the curve to compute a unit hydrograph. The resultant unit hydrograph is then used to route excess precipitation to the watershed outlet.
Required Parameters
Parameters that are required to utilize this method within HEC-HMS include the percentage curve (which is a paired data object), a lag time [hours] (when using the Standard method), and/or the aforementioned C, L, Lca, and S coefficients and m and p exponents (when using the Regression method).