Spatial Modelling and Scaling Issues - Environmental Modelling: Finding Simplicity in Complexity - page 77

A

(a)

(c)

(b)

Figure 5.8 The routing of hydrological models according to the steepest topographic slope. (a) The schematic illustrating of runoff
and sediment transport routing. (b) and (c) show sediment transport in the Lake Tanganyika catchment for the second decade of
April 1998. Black polygons are lakes, dark grey indicates high-sediment delivery and white low-sediment delivery. The highest
sediment inputs to the lake occurred in the northern lake region (the River Rusizi subcatchments). (b) Reproduced with permission
from Drake, N.A., Zhang, X., Symeonakis, E. et al . (2004) Near realtime modeling of regional scale soil erosion using AVHRR and
METEOSAT data: a tool for monitoring the impact of sediment yield on the biodiversity of Lake Tanganyika, in Spatial Modelling of
the Terrestrial Environment (eds R. Kelly, N. Drake, and S. Barr), pp. 157-74. and (c) Reproduced with permission from Drake,
N.A., Zhang, X., Symeonakis, E. et al . (2004) Near realtime modeling of regional scale soil erosion using AVHRR and METEOSAT
data: a tool for monitoring the impact of sediment yield on the biodiversity of Lake Tanganyika, in Spatial Modelling of the
Terrestrial Environment (eds R. Kelly, N. Drake, and S. Barr), pp. 157-74.

models at large scales (e.g. Richards, 1993; Pilotti and
Bacchi, 1997).
The sediment yield in Lake Tanganyika (Africa) could
be well explained using the routing process. Drake et al .
(2004) used the concept of sediment-delivery ratio ( Dr )
in each cell in a catchment can be estimated using 'upland
theory' (ASCE, 1975). This theory indicates that steep
headwater areas are the main sediment-producing zones
of a basin and that sediment production per unit area
decreases as average slope decreases with increasing basin
size. When sediment moves through a catchment the
route is primarily controlled by topography. The routed
delivery ratio ( Dr ' i )in ith cell is controlled by the con-
tributing area in the following manner:

sediment yield Ey is estimated using:

n

Dr i E i

E y = (5.8)

i = 1

where yield E i is the soil erosion in i th cell, and n is the
number of cells upstream.
Using this sediment-routing model, the total sediment
transport in the Lake Tanganyika catchment is derived
for the second decade of April 1998 when it received up to
270mm rainfall (Figure 5.8b and c). However, conceptual
evaluations of the sediment-delivery concept suggest that
the success of this approach is as an empirical fitting
procedure, rather than as a representation of the processes
involved in routing sediment through a catchment system
(Parsons et al ., 2004, 2006).

C 2

i

Dr i = C 3

A j (5.7)

5.5.2.6 Frequency-distribution-based method
(expected value or partial transformations)

j = 1

where i represent i th cell with a number of i cells upstream,
A j is the cell size (km 2 ), C 2 and C 3 are empirical coef-
ficients (Richards, 1993). Using the delivery ratio, the

This approach is defined as the calculation of the expected
value of the model output based on the joint frequency
distribution of the variables describing environmental