Modelling Landscape Evolution - Environmental Modelling: Finding Simplicity in Complexity - page 298

equation, which relates the temporal change in elevation
h [L] to (potentially spatially and temporally varying)
rock uplift U [L T − 1 ] and the divergence of sediment flux
Q s [L 3 T − 1 ]:

The relationship between sediment flux and controlling
state parameters (slope, curvature, discharge, etc.) for
different processes is defined by the geomorphic transport
laws included in the model (see next section). Short-range
hillslope processes distribute sediment between a cell and
its direct neighbours, whereas long-range processes pass

∂ h

= U −∇ Q s (19.1)

∂ t

Glacial
erosion

Soil
production

Hill-slope
diffusion

Landsliding

Fluvial incision

(a) (b)

(c) (d)

Figure 19.1 (a) Conceptual sketch of different processes taken into account in most landscape-evolution models (Reproduced with
permission from Schlunegger, F. (2002) Impact of hillslope-derived sediment supply on drainage basin development in small
watersheds at the northern border of the central Alps of Switzerland. Geomorphology , 46, 285-305). (b) Division of landscape into
interconnecting cells (here rectangular) and topology of fluvial system along steepest slopes. Grey shading represents available mobile
regolith or sediment in each grid cell (Modified with permission from Tucker, G.E. and Slingerland, R.L. (1994) Erosional dynamics,
flexural isostasy, and long-lived escarpments: a numerical modeling study. Journal Geophysical Research , 99, 12229-43). Lower panels
show drainage networks predicted by the Cascade model for erosion of an initial 1000-m high, 100

100 node plateau using (c) a
regular rectangular mesh and d) an irregular mesh connected by Delauney triangulation (Adapted with permission from Braun, J.
and Sambridge, M. (1997) Modelling landscape evolution on geological time scales: a new method based on irregular spatial
discretization. Basin Research , 9, 27-52). (d) Adapted with permission from Braun, J. and Sambridge, M. (1997) Modelling landscape
evolution on geological time scales: a new method based on irregular spatial discretization. Basin Research , 9, 27-52.

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