Use of Rational and Modified Rational Method for ... - CTR Library

the ratio of peak rate of runoff to rainfall intensity for the time of concentration (Wanielista and
Yousef, 1993). However, because the MRM generates a hydrograph and should preserve volumes,
the method implies that the runoff coefficient is conceptually a volumetric runoff coefficient.
The research examined two volumetric runoff coefficients for the application of the modified rational
method. The first is a watershed composite literature-based coefficient ( Cv
lit ), derived using the
land-use information for the watershed and published Cv
lit values for various land-uses. Details of
the examination are presented in Appendix D.
The composite Cv
lit
grid-cell values, using,
value assigned to a watershed is the area-weighted mean value of individual
∑ n
Cv lit i=1
= ∑ C iA i
n
i=1 A , (2.7)
i
where i = i th sub-area with a particular land-use type, n is the number of land-use classes in the
watershed, C i is the literature-based runoff coefficient for the i th land-use class, and A i is the area of
the i th land-use class in the watershed. This runoff coefficient may not necessarily preserve observed
runoff volumes from observed rainfall.
The second runoff coefficient is a back-computed volumetric runoff coefficient, Cv bc , determined
by preserving the runoff volume and using observed rainfall and runoff data. Cv
bc is estimated
by the ratio of total runoff depth to total rainfall depth for individual observed storm events.
The determination and comparison of Cv
lit and Cv
bc are presented elsewhere (Dhakal and others,
2010).
These values were determined for watersheds taken from a larger dataset accumulated by the
researchers and used in a series of past TxDOT research projects (Asquith and others, 2004). The
dataset comprised about 90 USGS streamflow-gaging stations located in the central part of Texas.
The drainage area of study watersheds ranged from approximately 0.8–440.3 km 2 (0.3–170 mi 2 ).
The majority of the watersheds exceed the conventional limit of applicability for rational method
application; however the method, being a subset of the unit hydrograph method was deemed suitable
with some caveats. The rainfall-runoff dataset was comprised of about 1,600 rainfall-runoff events
recorded during the period from 1959–1986. The number of events available for each watershed
varied: for some watersheds only a few events were available whereas for some others as many as 50
events were available.
The cumulative frequency distributions of C lit
v
Figure 2.6. The dashed curve is the distribution of C lit
v
distribution of C lit
v
the solid curve. Values of C bc
v
is 0.49; the median value of C bc
v
and Cv
bc developed for the study are shown on
values. Of particular interest is that the
is limited, ranging from 0.3–0.7. The distribution of Cv
bc values is depicted by
comprise the theoretical domain of 0.0–1.0. The median value for Cv
lit
is 0.29. If the Cv
bc values are assumed to be representative of actual
watershed behavior, then values of Cv
lit from the literature are about two times greater than they
should be. While this finding alone is of interest, the bias in the results is of greater interest.
The peak discharges simulated for real storms were biased high towards the end of the distribution
where the rational method would be anticipated to be valid, that is for the smaller watersheds —
the fact that the bias is reduced for larger watersheds is suggestive that many tabulated runoff
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