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to represent large-scale, spatially averaged trans-
port of sediment by creep, overland flow and chan-
nel flow processes. This diffusion law has been
used in various forms to study evolution of scarps
(Colman & Watson, 1983; Hanks et  al ., 1984;
Begin, 1988, 1993), hill slopes (Culling, 1960;
Carson & Kirkby, 1972; Hirano, 1975), alluvial
fans, rivers and floodplains (Gessler, 1971; Begin
et  al ., 1981; Green, 1987; Pizzuto, 1987; Begin,
1988; Parker et  al ., 1998; Roering et  al ., 1999;
Pelletier et  al ., 2006), mountains and foreland
basins (Moretti & Turcotte, 1985; Flemings &
Jordan, 1989; Jordan & Flemings, 1991; Sinclair
et al ., 1991; Paola et al ., 1992; Willgoose et al ., 1992;
Tucker & Slingerland, 1994; Chalaron et al ., 1996;
Davy & Crave, 2000; Clevis et al ., 2003; Carretier &
Lucazeau, 2005), or deltas and continental mar-
gins (Kenyon & Turcotte, 1985; Rivenaes, 1988;
Flemings & Grotzinger, 1996). Recent studies based
on flume experiments have also demonstrated that
diffusion laws could be used to simulate time-
averaged transport of sediment (Paola et al . 1992;
Postma et  al ., 2008), although pointing out that
insufficient data are available to verify values of
diffusion laws for real-world prototypes (Postma &
Van den Berg van Saparoea, 2007).
In our model, following the classical approach
used in landscape evolution models (Willgoose
et al ., 1991 a, b; Tucker & Slingerland, 1994), all
processes leading to the movement of sediment
grains are lumped into two large-scale diffusion
processes: a slow slope-driven creeping and a fast
water-driven and slope-driven diffusion transport
(Granjeon, 1996; Granjeon & Joseph, 1999). The
creeping of grains is assumed to be proportional to
the local slope of landscape, leading to a non-linear
slope-driven diffusion equation, mainly active
along hill slopes and continental margin slopes.
and short-term transport processes is assumed to
lead to a large-scale non-linear water-driven and
slope-driven diffusion equation.
Q sw k kkw nm
=
KcQS withQQQ
=
( /)
(2)
w
,
,
w
w
wo
Equation 2: definition of the non-linear water-driven
and slope-driven flux, Q sw , k [m 2 s −1 ], of the grain-size
fraction k, where c k is the surface concentration (−),
Q w the local water discharge (m 3 s −1 ), Q w , is the local
dimensionless water discharge, Q wo =1 m 3 s −1 is the
reference water discharge; S is the basin  slope (−),
K w , k is the water-driven diffusion coefficient of the
grain-size fraction k, defined as a function of water
depth; n and m w are two constants, usually between
1 and 2 (Tucker & Slingerland, 1994).
In classical landscape evolution models, fluvial
water flow is routed across the simulated area using
a single-direction routing method in which water
flows along the steepest slope (Willgoose et  al .,
1991a, b; Tucker & Slingerland, 1994; Tucker,
2004). In our model, a multiple-direction method is
used: water is routed to all the local lower neigh-
bours of a given cell, according to their slope ratios.
This multiple-direction method handles diverging
flow better (Freeman, 1991; Tucker & Hancock,
2010) and is well adapted to simulate overland
sheet flow and braided systems (Murray & Paola,
1994, 1997; Coulthard et al ., 1996).
These two non-linear diffusion equations
define the transport capacity of the system.
Availability of grains is constrained by weather-
ing and incision rate. This rate is highly variable
and is a function of climate, topographic eleva-
tion and slope (Willgoose et  al ., 1992; Tucker &
Slingerland, 1994; Coulthard, 2001; Roering
et al ., 2007). A maximum erosion rate is defined
as a function of the excess of shear stress; that is
the difference between basal shear stress induced
by fluvial water flow and the critical threshold
stress below which no incision can occur. The
actual transport rate is finally defined as the min-
imum of the transport capacity and the grain-size
fraction availability. Sedimentation and erosion
rate of each grain-size fraction at each point of the
basin is computed from the mass conservation
equation and the actual sediment flux. Slope sta-
bility of the depositional profile is then checked
assuming that the angle of the depositional slope
predicted by the long-term diffusion equation
cannot exceed a static angle of repose that
depends on grain-size fractions. At any point of
the basin, if the local slope is higher than the
QKcS
sc k
=
m c
(1)
,
c kk
,
Equation 1: definition of the creeping flux, Q sc , k
(m 2 s −1 ), of the grain-size fraction k , where c k is the
surface concentration of this grain-size fraction
(−); S is the local landscape slope (−); K c , k   is the
creeping diffusion coefficient of the grain-size
fraction k, defined as a function of water depth; m c
is a constant, usually between 1 and 2 (Carson &
Kirkby, 1972).
The second process is the more efficient of the
two as it allows a quick transport of sediment grains
from sources to sinks. At the regional spatial scale
and over geological time, upscaling of local-scale
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