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Hydrological Theory

Calculating Runoff

Linear Reservoir Response


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.




(c) Copyright 1984-2023 Alan A. Smith Inc.
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