Abstract
A continuous time function with two parameters for a curvilinear dimensionless unit hydrograph (CDUH) is derived from the unit hydrograph in the form of a gamma probability density function. This equation is then applied to the Natural Resources Conservation Service [formerly, Soil Conservation Service (SCS)] curvilinear dimensionless unit hydrograph [NRCS (SCS) CDUH]. The values of the parameters are slightly different for the rising and recessing limbs of the unit hydrograph. The NRCS unit hydrograph that expresses the time distribution of runoff of unit depth is shown to be a two-parameter gamma probability density function. Its mass curve is, therefore, an incomplete gamma function. This technical note explains mathematically that what was originally called the mass curve of the ratio of runoff volume to the total volume of the NRCS CDUH is shown to be, in fact, the mass curve of the unit hydrograph. The equations of continuous time functions derived in this study can be used in place of the NRCS CDUH tabulation and the NRCS linear triangular unit hydrograph. An example is shown to illustrate the application.
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