Geoscience Reference
In-Depth Information
6.3.5 Dynamic TOPMODEL
While TOPMODEL has been very widely used in rainfall-runoff modelling, it is clear from the above
results and discussion that the assumptions on which it is based are not going to be valid except in a
relatively limited range of catchments, those that are frequently wetted and have relatively thin soils and
moderate topography. It might produce a good fit when calibrated to observed discharges for a wider
range of catchments, but it does not then produce good results for good reasons. It is serving only to
provide fast runoff generation that is a nonlinear function of storage deficit (in much the same way as
other models, such as the PDM model of Section 6.2, the nonlinear filter in the DBM of Section 4.3.2
and the VIC model of Box 2.2).
A particular issue with the classic formulation is the assumption that there is always connectivity over
the whole of the upslope area that underlies the representation of the water table as a succession of steady
states. Barling
et al.
(1994) have shown that a better relationship could be found between saturated area
and a topographic index, if the index was calculated using only an effective upslope contributing area
rather than the full upslope area all the way to the divide. This effective upslope area would be expected
to be small when the catchment was dry and increase as the catchment wets up. In fact, Western
et al.
(1999) show that patterns of near surface soil moisture only show the effects of a topographic control
on downslope flows under relatively wet conditions in the Tarrawarra catchment in Australia. This is, in
fact, another reason why calibrated values of transmissivity in TOPMODEL might be high. Since, in the
soil's topographic index (
a/T
o
tan
β
),
a
and
T
o
appear in ratio, a high value of
T
o
can compensate for an
overestimation of the effective upslope area
a
.
The result is that in environments that are subject to strong drying periods, the application of
TOPMODEL often has difficulties in simulating the first few events during a wetting up period (e.g.
Pi nol
et al.
1997). With this in mind, Beven and Freer (2001a) proposed a modified TOPMODEL, called
“Dynamic” TOPMODEL. This was more flexible in defining the area units for which calculations are
made. In particular, it was possible to separate out areas of different
a
and tan
β
values. Other infor-
mation on catchment characteristics, such as the pattern of
T
o
, can also be taken into account where it
is available. Each elemental area then uses a local numerical implicit kinematic wave solution for the
saturated zone, taking account of local slope angles. Calculated outflows from each elemental area are
then distributed to appropriate downslope elements. The model can be set up without imposing a regular
spatial grid (but the kinematic subsurface solution is otherwise similar to the gridded DVSHM model of
Wigmosta
et al.
, 1999). In this framework, not all elements need to produce downslope flows under dry
conditions, introducing more dynamic hillslope responses than the original TOPMODEL representation
as a succession of quasi-steady states. The unsaturated zone is treated in a similar way to TOPMODEL.
Dynamic TOPMODEL has been successfully used in a variety of applications to catchments in England
(Beven and Freer, 2001; Younger
et al.
, 2008, 2009), Wales (Page
et al.
, 2007), USA (Peters
et al.
, 2003)
and Luxembourg (Liu
et al.
, 2009).
6.4 Case Study: Application of TOPMODEL to the Saeternbekken
Catchment, Norway
In most rainfall-runoff modelling studies, there are generally few internal state measurements with which
to check any distributed model predictions. The potential of making such checks with distributed models
raises some interesting questions about model calibration and validation. One study where distributed
predictions have been checked is in the application of TOPMODEL to the Saeternbekken MINIFELT
catchment in Norway (Lamb
et al.
, 1997, 1998a, 1998b). This small subcatchment of only 0.75 ha
has a network of 105 piezometers and four recording boreholes (Figure 6.7a; Myrabø, 1997; Erich-
sen and Myrabø, 1990). The distribution of the
ln
(
a/
tan
β
topographic index is shown in Figure 6.7b.
