Geoscience Reference
In-Depth Information
general, for both surface and subsurface flow processes, average flow velocities and celerities
will increase with flow in a nonlinear way. Faster flow velocities mean that the runoff will get
to a measurement point more quickly; faster celerities mean that the time distribution of runoff
(e.g. the shape of the unit hydrograph) will change as runoff increases. This was shown for a
small catchment in the classic study of Minshall (1960). Minshall showed a dependence of the
shape of the unit hydrograph derived for a small catchment on the volume of effective rainfall.
Larger storm sizes resulted in a faster time to peak and higher peak discharge in the unit
hydrograph (Figure B2.1.1). In larger catchments, the effects of the routing nonlinearity are
not always easy to distinguish in data analysis. The nonlinearity is not always a greater than
linear increase with increasing inputs. For example, when a river overtops its banks in a flood,
the slow-moving water on the flood plain may lead to a decrease in the average velocity of
the discharge and celerity of the flood wave. In semiarid areas, transmission losses due to
infiltration into a dry channel bed may lead to responses that become more nonlinear with
increasing catchment area (Goodrich
et al.
, 1997).
It is sometimes also difficult to distinguish between simple nonlinear and
nonstationary
re-
sponses, and indeed the difference may only be one of interpretation. A nonstationary response
is one for which the relationship between inputs and outputs is changing over time. One ob-
vious reason for this would be long-term changes in the characteristics of a catchment due to
changes in land use, such as urbanisation or the installation of field drainage. However, the
effects of antecedent conditions might also be considered as a nonstationary effect, especially
if the nature of the processes involved in runoff generation is changing. Such a relationship is
called “nonstationary” if it cannot be represented as a simple nonlinear function of the inputs
or other available variables.
Box 2.2 The Xinanjiang, ARNO or VIC Model
A description of the class of models variously named the Xinanjiang (Zhao and Liu, 1995),
ARNO (Todini, 1996) or Variable Infiltration Capacity (VIC) models (Wood
et al.
, 1992; Liang
et al.
, 1994; Lohmann
et al.
, 1998a) is included here as one example of an explicit soil moisture
accounting (ESMA) or “conceptual” rainfall-runoff model.
ESMA models are typically constructed from connected storage elements, with parametric
functions controlling the exchanges between elements, losses to evapotranspiration and dis-
charges to the stream. In general, all the parameters are effective catchment scale parameters
and are calibrated on the basis of a comparison of observed and predicted discharges, adjusting
the values of the parameters until a best fit is obtained (see Chapter 7 for a discussion of this
type of model calibration). This class of models has been chosen over all other ESMA models
because of one interesting feature: in VIC-type models, there is a function that attempts to allow
for the heterogeneity of fast runoff production in the catchment. Hence the name “variable
infiltration capacity”, although it should be noted that there is no necessary inference that the
fast runoff is produced by an infiltration excess mechanism (but see Zhao and Liu, 1995, for a
process interpretation in this way).
The original idea for this class of models originated in the 1970s in China, where it has
been widely applied (see Zhao
et al.
, 1980; Zhao, 1992). The idea was later adapted for use
in a flood forecasting system for the Arno river in Italy by Todini (1996). Its simplicity has
also seen it used in large-scale hydrological modelling and as the land-surface component in
atmospheric circulation and global climate models (GCMs) (see Dumenil and Todini, 1992;
Liang
et al.
, 1994; Lohmann
et al.
, 1998a, 1998b; Wood
et al.
, 1992) and predictions of
the impacts of future climate changes (Christensen
et al.
, 2004). The essentials of the VIC
hydrological model have also recently been incorporated into a community land surface model
(Wang
et al.
, 2008).
