Technical Note: A measure of watershed nonlinearity II: re-introducing an IFP inverse fractional power transform for streamflow recession analysis
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English
OPEN
Ding, J. Y.
(2013)
This note illustrates, in the context of Brutsaert–Nieber (1977)
model: −d<i>Q</i>/d<i>t</i> = <i>aQ<sup>b</sup></i>, the utility of a newly rediscovered inverse
fractional power (IFP) transform of the flow rates. This method of
streamflow recession analysis dates back a half-century. The IFP
transform Δ<sub><i>b</i></sub> on an operand <i>Q</i> is defined as Δ<sub><i>b</i></sub> <i>Q</i> = 1/<i>Q<sup>b-1</sup></i>.
Brutsaert–Nieber model by IFP transform thus becomes:
Δ<sub><i>b</sub>Q(t)</i> = Δ<sub><i>b</sub>Q(0)</i> + (<i>b</i>−1) at, if <i>b</i> ≠ 1.
The IFP transformed recession curve appears as a straight line on
a semi-IFP plot. The method has both the advantage of being
independent of the size of computational time step, and the
disadvantage of being depending on the parameter <i>b</i> value. This is
used to calibrate the Brutsaert–Nieber recession flow model in which
<i>b</i> is a slope (or shape) parameter, and <i>a</i> is an intercept (or
a scale parameter). It is applied to four observed events on the
Spoon River in Illinois (4237 km<sup>2</sup>). The results show that the IFP
transform method gives a narrower range of parameter <i>b</i> values than
the regression method in a recession plot. Theoretically, an IFP
transformed recession curve for large watersheds falls between those
performed by the reciprocal of the cubic root (RoCR) transform and
the reciprocal of the square root (RoSR) one. In general, the
forgotten IFP transform method merits a fresh look, especially for
hillslopes and zero-order catchments, the building blocks of
a watershed system. In particular, because of its origin in
hillslope hydrology, the 1-parameter RoSR transform need be
falsified or verified for application to headwater catchments.