Hydrological Theory
Calculating Runoff
Linear Reservoir Response |
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From the MIDUSS Version 2
Reference Manual - Chapter 7
(c) Copyright Alan A. Smith Inc. |
Figure 7-20 - The Single
Linear Reservoir IUH
A more complex
response function was suggested by Pederson (see references) and is
currently in use in the URBHYD routine of the OTTHYMO model. The
shape of the Instantaneous Unit Hydrograph (IUH) is obtained as the
response of a single linear reservoir to a rectangular pulse of
rainfall of unit volume and duration
Dt.
The storage coefficient
K
of the linear reservoir is taken to be
0.5
tc
where
tc
is computed by equation [7-41] in which the maximum rainfall intensity
is used since this intensity tends to dominate the subsequent
convolution process. The resulting IUH is illustrated in Figure 7-20
and comprises a steeply rising limb over the time step
Dt
followed by an exponential decay. Most applications of this method
have used a procedure in which the IUH is
discretized at intervals of
Dt
and then convoluted with the effective rainfall.
Because
tc
is assumed to be constant in this method, both the response of the
linear reservoir and the convolution are linear processes and it is
therefore immaterial in what order they are carried out. The
essential equivalence of the alternate methods is illustrated in
Figure 7-21.
Figure 7-21 ‑
Alternative implementations of a linear reservoir response.
MIDUSS uses the
alternate approach of convoluting the effective rainfall with a simple
rectangular response of duration
Dt
and height
umax
= A/Dt.
The resulting 'instantaneous' runoff hydrograph is then routed through
the linear reservoir. This approach reduces the computational time by
at least an order of magnitude and improves the accuracy.
The routing process is
carried out using a time step of
Dt/2
in order to improve the accuracy in the vicinity of the peak runoff
but the results are presented only at intervals of
Dt.
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