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This value corresponds to the yield of small modern
rivers such as the Wanganui River, New Zealand,
or  the Homathko and Klinaklini Rivers, Canada
(Syvitski & Milliman, 2007). The yearly-average sedi-
ment concentration in these rivers is around 0.5 g l −1
and 0.7 g l −1 , whilst the sediment concentration in the
XES 02 inflow is 30 g l −1 . The concentration ratio was
set to 0.02, which allowed definition of the upscaled
water discharge; equal to 240 m 3 s −1 .
Using these scaling parameters, a passive margin
model was built. Its characteristic parameters were
defined as 60 km, 20 ka, 4° and 0.6 g l −1 . The simu-
lated area was a rectangular box measuring 60 ×
30 km 2 and the spatial resolution was 300 m. The
total duration of the simulation was around 300 ka
and the numerical time step was 5 ka. The initial
bathymetry was a plane with a gentle slope of
0.01 m km −1 (Fig. 1A). The accommodation was cre-
ated by a downstream-increasing subsidence and
sea-level cycles, as in the XES 02 experiments. The
sea-level curve (Fig. 2) was divided into two stages:
stage 1, with a first smooth long-term cycle (dura-
tion = 108 ka) and a second smooth short-term sea-
level cycle (duration = 18 ka) and stage 2, with
superimposed long and short-term cycles. Water,
240 m 3 s −1 , and sediment supply, 1820 km 3 My −1 ,
were held constant and fed into the basin via a point
source at its western boundary (Fig. 1A).
Transport parameters
The diffusion coefficients used in both experi-
ments were defined using a simple geometrical
rule (see equation 3), assuming that (1) sediment
transport is ruled by a linear slope-driven, non-
linear water-driven diffusion law (m w = 1.0, n = 1.5)
and (2) the fluvial equilibrium slopes, S eq , is
0.3 m km −1 (~0.02°) for sand grains and 0.1 m km −1
(~0.006°) for fine grains.
Q
QS
so
,
K
=
(3)
w
n
m w
wo
,
eq
Equation 3: estimation of the diffusion coeffi-
cients K w (m 2 s −1 ), where Q s,o is the sediment inflow
(m 2 s −1 ); Q w,o is the dimensionless water inflow (−);
S eq is the equilibrium slope (−); n and m w are the
two exponents controlling the non-linear behav-
iour of the transport equation.
The diffusion coefficients obtained from this
geometrical rule were 400 m 2 y −1 for the sand grains
and 1200 m 2 y −1 for the fine grains. Slow creeping
coefficients are usually in the range 10 −4 m 2 y −1 to
10 −2 m 2 y −1 , whilst fast fluvial transport coefficients
are in the range 10 2 m 2 y −1 to 10 4 m 2 y −1 (Flemings &
Jordan, 1989; Avouac & Burov, 1996). Our esti-
mated coefficients are thus in the lower part of the
fluvial transport coefficient range.
Source-to-sink model
A second model was defined to test the influence
of the constant boundary condition imposed in the
flume experiments on the fluvial to sink areas and
in particular on the water flow structure observed
and analysed previously. The passive-margin
model was extended to include a 60 km-long upper
catchment area (Fig. 1C). The initial morphology of
the extended basin was a gentle slope, as previ-
ously. The subsidence (Fig. 1C) was defined using
a tilted plane with uplift of the upper catchment
area and subsidence of the lower catchment and
shelf areas. Two triangle plateaus were added
around the hinge line to force water to focus on a
single point. The downstream part of the extended
basin was identical to the initial passive margin
model. Rainfall was set constant over the full suba-
erial environments. Its value was defined using a
trial-and-error manual inversion used to get nearly
the same final physiography and total sediment
volume, 1820 km 3 My −1 , in the lower catchment
area as in the initial passive margin model. This
constant rain fall was 4000 mm y −1 .
CONTROLS
A direct comparison between the flume tank and
numerical experiments is quite complex due to
the problematic upscaling and inherently cha-
otic results in such experiments. Over basic
snapshots of the geomorphology and stratigra-
phy, quantitative metrics were used to analyse
these numerical experiments and measure the
dispersion of the water flow and the sediment
distribution.
The water flow is the most important parameter
in the experiments as it controls the transport of
sediment. To get an automatic measure of the dis-
persion of the water flow, the number of channels
crossing each strike plane of the simulated domain
was counted. To keep this measure as simple as
possible, the maximum water flow crossing each
strike plane was counted and then a channel was
defined as a cell in which the local water flow
exceeds 10% of this maximum value. In the case
of a uniform water flow, the number of channels is
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