The RiverSim environment has an optional watershed runoff and snow melt model. The runoff model is based upon the SCS curve and unit hydrograph methods as described in National Engineering Handbook Section 4B, USDA, Soil Conservation Service, 1993. The snow melt model is based upon an equation developed by F.A. Bertle, Effect of Snow Compaction on Runoff from Rain on Snow, US Department of the Interior, Bureau of Reclamation, 1966.

Determination of Runoff

The SCS method determines direct runoff consisting of surface runoff and subsurface flow, but not including baseflow using accumulated precipitation. The basic equation is :

F / S’ = R / P

Where F is actual retention, S’ is potential maximum retention, R is actual runoff and P is potential maximum runoff. If we introduce initial abstractions, the equation becomes:

[(P – Ia) - R] / S = R / (P – Ia)

or:

R = (P – Ia)² / [(P – Ia) + S]

NEH 4B develops the equations for determining initial abstractions depending on antecedent moisture conditions upon a watershed:

S = 1000 / CN – 10

Where S is retention, and CN is a curve number. Hence, the greater the curve number, the less water is retained in the watershed. The SCS uses an empirical equation to relate abstraction to retention:

Ia = 0.2 S

Now, substituting the initial abstractions into the formula for runoff and simplifying:

R = (P – 0.2S)² / (P + 0.8S)

R = (P – 200 / CN + 2)² / (P + 800 / CN – 8)

The curve number to use depends upon the antecedent moisture of the watershed. Typically, three curve numbers are chosen, one for dry conditions, one for moist or normal conditions and one for saturated conditions. They are designated as AMC 1, 2, and 3.

The runoff is in units of depth and must be multiplied by the basin area to get volume.

A dimensionless unit hydrograph is defined as a hydrograph having unit flow at unit time and subtending a unit volume of runoff. While RiverSim allows any shape of unit hydrograph, the SCS method is generally used with a triangular graph having one third of its volume on the rising limb and two thirds on the receding limb. RiverSim will accommodate this type of hydrograph as well.

To use a unit hydrograph, it must be scaled up to match the basin characteristics. RiverSim uses three parameters to accomplish this scaling. These three parameters are: 

• D duration of excess rainfall,

• Lag the time from the midpoint of the excess rainfall to the peak of the hydrograph.

• Base Time the time from the beginning of excess rainfall until the hydrograph is substantially complete (for a triangular hydrograph as shown below, this point is known with certainty, for an asymptotic hydrograph, it must be estimated).

For each time step, the runoff model calculates cumulative excess runoff. It then routes the change in runoff through the unit hydrograph.