Geoscience Reference
In-Depth Information
Once
D
is known, local values of initial storage deficit can be calculated from (B6.1.5). Other
forms of transmissivity function can also be used to derive different forms of index and recession
curves. Lamb
et al.
(1997) show how an arbitrary recession curve can be used in a generalised
TOPMODEL.
B6.1.6 Runoff Routing and Subcatchment Structure
For many catchments, especially large ones, it may be inappropriate to assume that all runoff
reaches the catchment outlet within a single time step. In the original TOPMODEL formulation
by Beven and Kirkby (1979), an overland flow delay function was calculated as a distance
related delay. The time taken to reach the basin outlet from any point was assumed to be
given by:
N
x
i
v
∗
tan
ˇ
i
t
j
=
(B6.1.22)
i
=
1
where
t
j
is the time delay for point
j
,
x
i
is the plan flowpath length and tan
ˇ
the slope of the
i
th segment of a flow path comprising
N
segments between point
j
and the catchment outlet.
If the velocity parameter
v
∗
(m/h) is assumed constant then this equation allows a unique time
delay histogram to be derived on the basis of basin topography for any runoff contributing area
extent. This is, in effect, a variation of the classic time-area routing method (see Figure 2.2),
but developed so as to relate the runoff time delay histogram dynamically to the size of the
source area.
Channel routing effects were considered by Beven and Kirkby (1979) using an approach
based on an average flood wave velocity for the channel network, this being related non-
linearly to total outflow. The approach was an explicit approximation to a kinematic wave
channel routing algorithm and is not recommended, since it is not always stable. Most appli-
cations have been based on a simple constant wave speed routing algorithm, equivalent to the
algorithms based on channel network width function used by Surkan (1969), Kirkby (1976),
Beven (1979b) and Beven and Wood (1993), which has the advantage that it introduces only a
single wave speed parameter. In a single event version of TOPMODEL, Saulnier
et al.
(1997b)
adopted a routing method based on a unit hydrograph derived by the DPFT-ERUHDIT method
of Duband
et al.
(1993). Since the unit hydrograph can be expected to reflect the time response
of subsurface as well as surface flow processes, they show that this choice of routing algorithm
has an effect on the other parameters of the model. Some other linear routing algorithms are
discussed in Section 4.5.
B6.1.7 Recent Variations on TOPMODEL
The simplicity of the TOPMODEL formulation as a way of reflecting the topographic controls
on runoff generation has proven attractive now that digital terrain models for catchments
are more widely available. The simplicity of the ideas has also encouraged both an as-
sessment of the assumptions in relation to perceptions of the processes controlling the
hydrological responses in different catchments and attempts to reformulate and improve
the theory.
The first category of variations on TOPMODEL includes the idea of the reference level for
deeper water tables proposed by Quinn
et al.
(1991), in which the hydraulic gradient is based
on a characteristic water table surface rather than the soil surface. This idea was used with an
exponential transmissivity profile, which may not be appropriate for a depth water table, but
could be extended to more realistic transmissivity profiles. Lamb
et al.
(1997, 1998a) showed
how a generalised transmissivity function could be developed on the basis of a recession curve
analysis (maintaining the simplifying assumption that the pattern of saturated zone hydraulic
