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

unoff, with a negligible amount of additional infiltration. In this context, the runoff coefficient
represents a composite value (Kuichling, 1889, p. 41–42) of the balance between pervious, functionally
impervious surfaces, and functionally pervious “impervious surfaces.” In practice, the runoff
coefficient could be estimated simply from the percent impervious cover of the watershed with
appropriate upper and lower bound restrictions. Kuichling (1889, p. 41–42) uses just this sort of
composite C value with C base = 0.15 and C impervious = 1 and prorated by area weighting.
The runoff coefficient in the engineering literature also is conventionally used to account for watershed
losses, consider for example
“. . . the runoff coefficient can vary with soil moisture conditions and the period of time
and volume of runoff (Wanielista and others, 1997a).”
The quote suggests the idea of composited C values to reflect behavior of different parts of the
watershed to the overall runoff signal. Composite C values, where different portions of a watershed
are assigned different runoff coefficients, exists as early as Kuichling (1889, p. 21). Many tabulated
runoff coefficients associated with land use distinctions available in the engineering hydrology
literature are reported in Appendix A. While these tabulated values are consistent with backcomputed
values the unified rational method described herein dispenses with such tables in favor of
an adaptation of the area weighted functionally impervious approach of Kuichling (1889). Much of
the variability implied in the coefficient tables is instead transferred into the estimation of time in
the unified rational method.
2.1.2. The Drainage Area
The rational method lacks a firm physical loss model, yet initial abstraction exists and increases
with watershed size (Asquith and Roussel, 2007, p. 23). The general phenomenological argument is
that depression storage and channel storage, both in particular, increases as watershed drainage area
increases. The implication for the rational method is that there is a watershed size limit beyond
which the initial abstraction of the watershed can no longer be ignored — that is there is some
upper bound of size for rational method applicability.
The evidence that the researchers have amassed from processing of more than 10,000 storms from
nearly 200 watersheds of considerable size variation 2 is that observed runoff coefficients are smaller
than those in literature. Some of this difference is attributable to satisfaction of abstractions, storage,
and infiltration. Kuichling (1889, p. 24) states “should the solid surface be at all absorbent, the rain
has to furnish the quantity of water necessary to saturate it.” (At saturation, initial abstraction and
arguably infiltration losses are negligible; but it could take considerable time on larger watersheds
to reach this equilibrium.)
The typical recommended upper bound for drainage area for use in the rational method is typically
on the order of 200 – 300 acres. A justification for this bound is that watershed size should be
small enough to ensure a mass balance for the runoff coefficient, in the absence of a loss model, to
faithfully capture any loss processes functioning within the watershed. An additional supporting
2 Many of these watersheds are admittedly larger than usually recommended for rational method application.
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