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0.05 x(t)
0.60 x(t)
0.35 x(t)
Fig. 12.16 A tank model representation of the Kitakami
River in northern Honshu by Sugawara and
Maruyama (1956). Both tanks are linear storage
elements with a unit response function given by
Equation (12.28). The bottom part of the fast
response tank represents 20 mm of initial loss.
Loss
Slow
Fast
y(t)
Fig. 12.17 A tank model representation of daily flows consisting of
baseflow (BF) and interflow (or subsurface stormflow SSF) by
Sugawara and Maruyama (1956). All three tanks are linear
storage elements with unit response functions given by
Equation (12.28) but different storage coefficients K .
x(t)
SSF
y(t)
BF
In the earliest description of this approach, now also known as the tank model,
Sugawara and Maruyama (1956) and Sugawara (1961) gave a number of examples
of combinations of linear storage elements, which had been used to describe basin out-
flows. For instance, Figure 12.16 shows the arrangement used to describe flood flows of
the Kitakami River in northern Honshu; the basin was represented by two elements in
parallel, one with K
9 h that
receives 35% of the input; 5% of the total input and 20 mm of the initial input into the
fast response tank were assumed to be “lost.” Unlike in flood flows, in the description
of daily flows, interflow and baseflow are more important; to simulate these, a differ-
ent arrangement was used, which is illustrated in Figure 12.17. Initially after a drought
period, precipitation flows out of the first tank into groundwater storage, from which the
water flows out as baseflow. Only after the first tank has become full, does the overflow
into the second tank result in subsurface stormflow runoff. Several arrangements were
also proposed by Sugawara and Maruyama (1956) to accommodate spatial variation of
the input characteristics of the basin. One of these is considered in the following example.
=
33 h that receives 60% of the input, and one with K
=
2
.
Example 12.7. Tank model allowing for spatial variability
Figure 12.18 illustrates an arrangement by which each storage element represents a
subarea of the basin. Thus each tank receives as input the output from the upstream tank,
in addition to the rainfall on the subarea it represents. Let
α 3 be the fractions
of the total area represented by each tank. Then, for an input into the first tank given
α 1 2 and
 
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