Geoscience Reference
In-Depth Information
Figure B6.1.3
Use of the function
G
(
A
c
)
to determine the critical value of the topographic index at the
edge of the contributing area given
m
, assuming a homogeneous transmissivity (after Saulnier and Datin,
2004, with kind permission of John Wiley and Sons).
and pattern of deficits in the catchment. This has been incorporated into the TOPDYN version
used, for example, by Vincendon
et al.
(2010).
Another alternative index formulation is provided by the TOPKAPI model of Section 6.5.
This attempts to relax the assumption of instantaneous redistribution of the saturated zone at
each time step in formulating the new index (see Liu and Todini, 2002; Liu
et al.
, 2005). The
MACAQUE model of Watson
et al.
(1999) addresses the same problem in a different way by
introducing a “lateral redistribution factor” that limits the redistribution towards the steady state
water table configuration allowed at each time step.
One of the limitations of the topographic index approach is the assumption that there is
always downslope flow from an upslope contributing area that is constant for any point in the
catchment. Improved predictions might be possible if this area was allowed to vary dynami-
cally. Barling
et al.
(1994) showed that an index based on travel times could improve prediction
of saturated areas for a single time step prediction, but did not suggest how this might be ex-
tended to a continuous time model. A dynamic TOPMODEL can also be derived by an explicit
redistribution of downslope fluxes from one group of hydrologically similar points to another,
where “hydrologically similar” can be based on more flexible criteria than the original topo-
graphic index. In the extreme case of every pixel in a catchment being considered separately,
this approach would be similar to the distributed kinematic wave model of Wigmosta
et al.
(1994). Grouping of similar pixels results in computational efficiency that might be advanta-
geous in application to large catchments or where large numbers of model runs are required to
assess predictive uncertainty. This is the basis for a new, more dynamic version of TOPMODEL
(Beven and Freer, 2001). A simpler way of allowing for changes in upslope contributing area is
suggested by Vincendon
et al.
(2010) in the TOPDYN implemententation, essentially by con-
tinuously recalculating the number of upslope cells that contribute to the topographic index.
