Geoscience Reference
In-Depth Information
(a)
h(t)
t
(b)
h(t)
t
(c)
Figure 2.6
The unit hydrograph as (a) a histogram; (b) a triangle; (c) a Nash cascade of N linear stores in
series.
where
). For different values
of
N
and
K
, the Gamma distribution has quite a flexible range of forms (Figure 2.6c). Mathematically,
N
does not have to be an integer number of stores but can also take on fractional values to give a wider
range of shapes in fitting the observed data. Dooge (1959, reproduced in Loague, 2010) provided a
summary of a number of other simple linear models that could be used, including those with time delays
(see also Dooge and O'Kane, 2003).
The advantage of these functions is that, in general, much more stable estimates of the parameters are
obtained, while retaining a flexibility in shape for representing a variety of different catchment hydro-
graphs. Attempts have been made to relate the resulting parameters to different variables representing
catchment characteristics, but it must be remembered that the parameter values will be dependent on the
(
N
) is the Gamma function (
(
N
)
=
(
N
−
1)! for integer values of
N
