Geology Reference
In-Depth Information
or constant parameters) is also cumulative, as not
only are key hydrological parameters such as
hydraulic conductivity highly heterogeneous
(Beven, 2004), but they also control infiltration
and therefore overland flow rates, which then
interact with equally heterogeneous erodibility
parameters. If neither the spatial variability of
fundamental hydraulic parameters nor their soil
structural counterparts are well represented in
erosion models, and therefore models represent
process as spatially lumped, then it is unlikely
that meaningful (and scaleable) predictions will
be forthcoming.
The consequences of the conceptual and meth-
odological problems highlighted above are that
improved representations of subgrid scale varia-
bility of the parameters that control soil erosion
are required in erosion models. Representation of
variability can then be used to model the proc-
esses that dominate at each scale of interest, in
theory allowing the erosion model to 'scale' its
predictions appropriately. Understanding scale is
thus more than just representing and (hopefully)
understanding variability; critically, it must have
an underlying process basis in order to support
the possibility of being transferable between dif-
ferent areas and environments.
¶
hv
¶
h
sd
,
sd
,
sd
,
+
-
e
+
d
=
0
(6.9)
d
d
¶
t
¶
x
where
h
s
,
d
is the equivalent depth of sediment of
size
d
in transport (m),
v
s
,
d
is the virtual velocity
of sediment in movement (m s
−1
),
e
d
is the rate of
particle entrainment of the surface (m s
−1
),
d
d
is
the rate of deposition (m s
−1
),
t
is time (s) and
x
distance (m) along the slope. MAHLERAN is coupled
with a pseudo-2D flow-routing model so that
x
can represent distance in both dimensions on the
surface (see Scoging, 1992; Parsons
et al
., 1996;
Wainwright
et al
., 1999). In this form the model
scales erosion explicitly in two ways: firstly,
d
d
at
any point on the slope is a function of entrain-
ment at all points upslope and the probability
function of deposition of that sediment, and sec-
ondly,
v
s
,
d
scales the speed of the movement of
the sediment. Transport by splash, unconcen-
trated overland flows and concentrated overland
flows are considered separately, and movement
can be by bedload or suspension, or a mixture of
mechanisms. For simple slopes, the patterns of
sediment flux are similar to the analytical results
presented above, with the most significant change
downslope occurring where the process regime
changes to include concentrated flows, and thus
erosion rates start to increase again (Fig. 6.3). The
location of this change was found to be most
strongly dependent on rainfall intensity, and thus
will vary both during and between events.
Wainwright
et al
. (2008b) tested MAHLERAN on
a 35-m downslope × 18-m across-slope runoff plot
which had been subjected to rainfall simulation
events with a constant intensity of 80 mm h
−1
.
Sediment fluxes had been measured both at the
plot outlet, and at two cross-sections located
12.5 m and 21 m from the upper plot boundary.
Rill heads were located between the lower cross-
section and the plot outflow. The results of this
test demonstrate that MAHLERAN was able to rep-
resent the plot sedigraph well (NRMSE
6.5 A Travel-distance Approach
to Scaling Erosion Predictions
As has been shown, in complex modelling situa-
tions, numerical approaches are required to
account for the variability in initial and boundary
conditions, and for the high degree of variability
in real-world applications. Wainwright
et al
.
(2008a,b,c) have developed the Model for
Assessing Hillslope-Landscape Erosion Runoff
And Nutrients (MAHLERAN) methodology, as a
numerical, expanded version of the analytical
approaches to scaling erosion rates discussed
above. MAHLERAN employs an explicit process
basis for scaling in that it uses the travel-distance
approach to provide an explicit scaling of deposi-
tion rates, and estimates fluxes of sediment using
the continuity equation:
=
18.74%,
Nash-Sutcliffe index
0.79), as well as the total
fluxes at the cross-sections and the particle-size
characteristics of the observed eroded sediment
(Plate 2). In a further test, the model was applied
=
