Basic Concepts and Equations

The user-specified unit hydrograph method uses a defined time vs. discharge curve to route excess precipitation to the subbasin outlet using Equation 1. 

1) Q_n=\sum_{m=1}^{n \leq M} P_m U_{n-m+1}

When using this method, all ordinates of the unit hydrograph are explicitly defined by the user.  Modifications to the effective duration of the specified unit hydrograph are required when the rate at which precipitation is applied (e.g. 15-minutes) differs from the effective duration of the derived unit hydrograph (e.g. 6-hours).  S-curves (or S-graphs) are used to change the effective duration of unit hydrographs (Morgan & Hullinghorst, 1939).  Within HEC-HMS, a cubic spline (along with a number of passes) can be used to smooth the S-curve. 

However, in practical applications, shortening the duration of empirically-derived unit hydrographs (i.e. going from a longer duration to a shorter duration) is difficult due to the presence of numerical oscillations within S-curves (Hunt, 1985).

Required Parameters

Parameters that are required to utilize this method within HEC-HMS include the unit hydrograph (which is a paired data object) in addition to a number of passes.  The unit hydrograph paired data object requires the specification of an observation interval [hours] in addition to a duration of uniform excess precipitation [hours].

Estimating the Model Parameters

The unit hydrograph for a watershed is properly derived from observed rainfall and runoff, using deconvolution—the inverse solution of the convolution equation. To estimate a unit hydrograph using this procedure:

  1. Collect data for an appropriate observed storm runoff hydrograph and the causal precipitation. This storm selected should result in approximately one unit of excess, should be uniformly distributed over the watershed, should be uniform in intensity throughout its entire duration, and should be of a duration sufficient to ensure that the entire watershed is responding. This duration, T, is the duration of the unit hydrograph that will be found.
  2. Estimate losses and subtract these from the precipitation. Estimate baseflow and separate this from the runoff.
  3. Calculate the total volume of direct runoff and convert this to equivalent uniform depth over the watershed area.
  4. Divide the direct runoff ordinates by the equivalent uniform depth. The result is the unit hydrograph.

Chow, Maidment, and Mays (1988) present matrix algebra, linear regression, and linear programming alternatives to this approach.  With any of these approaches, the unit hydrograph derived is appropriate only for analysis of other storms of duration T. To apply the unit hydrograph to storms of different duration, the unit hydrograph for these other durations must be derived. If the other durations are integral multiples of T, the new unit hydrograph can be computed by lagging the original unit hydrograph, summing the results, and dividing the ordinates to yield a hydrograph with volume equal one unit. Otherwise, the S-hydrograph method can be used. This is described in detail in texts by Chow, Maidment, and Mays (1988), Linsley, Kohler, and Paulhus (1982), Bedient and Huber (1992), and others.

Application of the User-Specified Unit Hydrograph

In practice, direct runoff computation with a specified-unit hydrograph is uncommon. The data necessary to derive the unit hydrograph in the manner described herein are seldom available, so the unit hydrograph ordinates are not easily found. Worse yet, streamflow data are not available for many watersheds of interest, so the procedure cannot be used at all. Even when the data are available, they are available for complex storms, with significant variations of precipitation depths within the storm. Thus, the unit hydrograph-determination procedures described are difficult to apply. Finally, to provide information for many water resources development activities, a unit hydrograph for alternative watershed land use or channel conditions is often needed—data necessary to derive a unit hydrograph for these future conditions are never available.