Geoscience Reference
In-Depth Information
However, because no direct link could be established between the parameters and the
physical mechanisms in the catchment, like any other unit hydrograph they suffer from a
lack of generality and they must always be calibrated to be of any use. For this reason the
quest has continued for better formulations of the catchment scale processes involved in
the transformation of precipitation into runoff.
One of the more active lines of endeavor has made use of stochastic concepts to
describe the instantaneous unit hydrograph as the distribution of the arrival times of
water at the catchment outlet. These approaches have typically consisted of linear rout-
ing of precipitation through topologically random channel networks with various prob-
ability distributions for the channel segments and with different assumptions regarding
the holding time or travel time distributions of the water in the channel segments. As
different concepts have matured, the width function has gradually emerged as the tool
of choice to describe the structure of the channel network (Snell and Sivapalan, 1994;
Marani
et al
., 1994; Veneziano
et al
., 2000), and has replaced earlier methods based on
Horton-Strahler stream ordering (see Figure 11.1) and the resulting order ratios. Simi-
larly, different attempts have been made to improve the formulation of the holding times
from exponential distributions (Rodriguez-Iturbe and Valdes, 1979; Gupta
et al
., 1980)
to more realistic response functions, such as obtained from the complete linear solution
(5.72) (see Kirshen and Bras, 1983; Troutman and Karlinger, 1985), or from the dif-
fusion approximation (5.95) (see Troutman and Karlinger, 1985; Rinaldo
et al
., 1991).
The inclusion of hillslope outflows into the channel network has also been explored
(see VanderTak and Bras, 1990; Robinson
et al.
, 1995) with different hillslope response
functions. Note that the assumption of an exponential distribution of residence times
in a channel segment is equivalent with the assumption of a linear storage element as
formulated by Equation (12.28). An overview of advances in this stochastic approach
has been presented by Rodriguez-Iturbe and Rinaldo (1997).
With the growing complexity of such representations and the increasing number of
the required parameters, these approaches are gradually evolving into direct simulation
models; however, in the process the appeal of parsimony of the unit hydrograph is being
lost, while its main limitations, namely linearity and time invariance are being kept. Also,
although the description of the channel network is becoming increasingly realistic, the
simulation of some critical processes at the catchment scale, involving the inclusion of
hillslope mechanisms, with such thorny aspects as preferential flow and simultaneous
transport of new and old water (see Chapter 11), has not received much attention so far;
its inclusion in linear theory remains an elusive goal and will require more research.
12.3
STATIONARY NONLINEAR LUMPED RESPONSE
It is generally recognized that the transformation of precipitation and other inputs into
streamflow can be quite nonlinear and non-stationary, so that the unit hydrograph is not
always the proper method of approaching this problem. This is especially true in the
case of extreme deviations, such as catastrophic floods, when rainfall-runoff systems
tend to exhibit considerable nonlinearities, as manifested by the fact that runoff fails
