Geoscience Reference
In-Depth Information
Figure 9.3
(a) Saturated area ratio (SAR) against relative water content (RWC) for a five-year simulation period
of the Reno catchment at the Calcara river section (grey dots); the steady state curve (SS) was obtained as a
set of SAR-RWC values for different simulations relative to precipitation events of different intensity and after
the equilibrium state has been reached; the drying curve (DC) represents the SAR and RWC values for the
drying down transition phase only; (b) Schematic diagram showing how the hysteretic relationship is used in
the lumped TOPKAPI model (after Martina et al., 2011, with kind permission of Elsevier).
can then be related to the characteristics of the area being modelled, including slope lengths, hydraulic
conductivity and porosity. Figure 9.3 shows the relationship between relative water content and saturated
area derived for the whole of the Reno catchment in Italy (4000 km
2
). Martina
et al.
also show that
different subcatchments, with different characteristics, exhibit somewhat different hysteretic behaviour.
Relationships were also developed for return flow as a function of saturated area.
These two studies do not represent a complete solution to the closure problem because of the simplifying
assumptions that are made (constant hydraulic conductivities in relatively shallow flow pathways, etc.)
but they point to the way in which the forms of better closure schemes mught be developed. They also
do not attempt to predict the residence times of water in the system, which would be a useful additional
attribute to include in a next generation of rainfall-runoff model.
9.6 Representing Water Fluxes by Particle Tracking
Another way of implementing a closure scheme based on velocity distributions is to treat the water as
particle masses of different velocities (and therefore energy and momentum). The sample of particle
velocities is then a representation of the assumed velocity distribution. As the system wets and dries, the
particles can change state and velocity accordingly. There is some overlap here with stochastic storage
models since the mean residence time of a water particle within a storage volume will be a function of both
its point of origin and the
Lagrangian velocity
along its pathway to the outlet. Stochastic storage models
have a long history in hydrology. This type of model was first implemented by Jay Bagley working at
Stanford University at the same time as Norman Crawford was developing the Stanford Watershed Model.
At the catchment scale, stochastic storage assumptions also underly the concepts of the geomorphological
unit hydrograph (see Section 4.7.2). Many other conceptual storage models can be interpreted in this
way. This approach is considered in more detail when we discuss residence time distribution models
in Chapter 11.
