Erosion and Sediment Transport: Finding Simplicity in a Complicated Erosion Model - Environmental Modelling: Finding Simplicity in Complexity - page 246

R s = rill spacing (m); Clearly, such an erosion model is highly complicated.

However, it is common; many models that purport to be
process-based share such levels of complexity. The WEPP
is used here as an example. In the following section, the
WEPP is also used to show how the results from such a
model can be simplified, or rather how the model output
(see the topic web site) can be queried, using simple
parameters, to interrogate the complex model results.

W = rill width (m);

and is assumed to occur at a constant rate downslope,
being independent of distance. Any soil detached in the
interrill areas is assumed to be either transported downs-
lope by the uniform unconcentrated flow generated, or
deposited in the adjacent rill area. Potential removal of
material from the rill area is then calculated according
to the dynamic rill-erodibility term when the hydraulic
shear stress of the flow exceeds the critical shear stress of
the soil:

15.4 MIRSED - a Minimum Information
Requirement version of WEPP

D c = K r ( T f − T c ) (15.6)

The MIR modelling approach (Miles et al ., 1996; Quinn
et al ., 1996, 1999) as it is employed in the MIRSED
methodology is detailed in Figure 15.2. Minimum
Information Requirement modelling uses a complex
model - in this case WEPP hillslope - to produce output
for all soil, slope and land-use combinations that occur
in the area to be modelled (see discussion of alternative
approaches to model simplification in Chapters 7, 8
and 28). Detailed data stored in a GIS (see discussion
below) (Figure 15.2a) are used to parameterize WEPP
for all possible hillslopes within each grid cell across a
catchment or region (Figure 15.2b). Within the context of
this chapter, results are generated based upon dominant
soil type, distribution of land use and the use of both
average slopes and slope distributions (Figure 15.2c)
from each grid cell. The hillslopes are then run through
the model, using a representative time series of climate
data (Figure 15.2d), to produce the MIRSED matrix
of soil erosion and runoff output at the hillslope scale
(Figure 15.2e and in detail on the topic web site). The
MIRSED matrix therefore maps the complex model
output from WEPP into a multidimensional parameter
space. This parameter space stores the response of
WEPP in terms of a normalized soil erosion as kg of
sediment per mm of runoff per m width of the hillslope
(kgmm − 1 m − 1 ), which is analogous to an erodibility
term for each combination of soil, slope and land use
and a normalized runoff as percentage of average annual
rainfall. (AAR) for all hillslopes in each grid cell. Runoff
can then be generated as a percentage of AAR across a
region for each grid cell and consequently each hillslope
from the MIRSED matrix (Figure 15.2f). Hillslope soil
erosion is calculated for each hillslope by adjusting the
runoff, as a percentage of AAR relative to that predicted
using the actual climate records used to generate the
MIRSED matrix, and multiplying by the normalized soil
erosion from the matrix (Figure 15.2g). The weighted

where:

D c = detachment capacity of the flow
(kg s − 1 m − 2 );
K r = rill erodibility (s m − 1 );
T f = flow shear stress (Pa);

T c = critical shear stress of the soil (Pa).

Following on from this equation, rill erosion is zero
if flow shear stress is less than critical shear. The actual
detachment (or deposition) rate is calculated from the
potential depending on the amount of sediment load G ,
relative to the flow transporting capacity, TC (Foster,
1982):

D c 1- G D f = (15.7)

TC

where:

D f = net rill erosion or deposition (kg s − 1 m − 2 );
G sediment load (kg s − 1 m − 1 ); =

transport capacity (kg s − 1 m − 1 ). TC =

Therefore, net deposition in rills will occur if eroded
sediment exceeds transport capacity (see Wainwright
et al ., 2008a-c for a discussion of how reasonable this
approximation is). Parameters describing the erodibility
of the soil K i , K r and T c are adjusted from their baseline
values on a daily timestep. These adjustments incorporate
themodification to soil erodibility fromchanges in factors
such as surface roughness, above and below ground
biomass, and canopy cover.
Finally, variation in management is parameterized
using a range of inputs, again bothmeasured and effective.
These parameters include planting and harvesting dates,
above- and below-ground biomass and ground-cover
coefficients.