Geology Reference
In-Depth Information
temporal support. Erosion measurements empha-
size the high degree of spatial variability (see dis-
cussion in Brazier, 2004), but for the reasons
previously discussed, simple statistical appro-
aches are not valid.
The most widespread use of a statistical scal-
ing approach is that of the slope length and angle
factor (
LS
) in the Universal Soil Loss Equation
(Wischmeier & Smith, 1978). The
LS
factor has
been defined by statistical analysis of the USLE
erosion plot database, by comparing erosion rates
measured on a 'standard' plot length of 22.13 m
and slope of 9%, with observations at different
plot lengths and gradients. One problem with the
statistical underpinning of this approach is that
the vast majority of plots used to calculate the
USLE relationships were of the standard size. The
slope length component (
L
) is defined as:
tinuously increasing erosion rates with increa-
sing slope length (Plate 1). The observation is
contrary to both empirical data (Wilcox
et al
.,
1997; Rejman
et al
., 1999; Parsons
et al
., 2006a)
and the process-based characterization of changes
of rate with scale, which in particular suggests
that there should be a qualitative difference in
the way in which inter-rill erosion scales com-
pared with rill erosion. This example can also be
used to demonstrate the problem with empirical
equations if they are used beyond their measured
range of applicability. In cases where there is no
rill erosion,
b
and thus
m
in Equation (6.7) would
equal zero, and the approach would predict ero-
sion that was independent of scale, which is
clearly contrary to all observations.
Other empirically based methods of regression
(Walling, 1983), or 'semi-quantitative models'
(de Vente & Poesen, 2005) have, of course, been
employed to predict catchment sediment yield,
the latter seeking to predict sediment yields from
distributed catchment properties. Whilst these
models may provide an initial evaluation of the
key catchment properties that contribute towards
sediment yield, they are often subjective in con-
struction and provide no distributed output to
evaluate sediment sources for potential erosion
mitigation, or indeed to evaluate the quality of
predictions in terms of the spatial variability of
erosion processes. Thus, the empirical relation-
ships that underlie such models do not character-
ize the changing erosion rates observed with scale
any more than the aforementioned models.
A further issue relating to scale of data is in the
use of field measurements for the testing and cali-
bration of models. Notwithstanding the usual
caveats about model calibration (see Wainwright
et al
., 2009), if a model is tested or calibrated with
data that have a different data support from that
of the model resolution, then major errors will be
produced. Unfortunately, most erosion models
include some form of this calibration or are tested
against data where the support is different from
that which the model produces, at least implicitly
(see Chapter 3 for a discussion of different data
sources for calibration). For example, Licciardello
et al
. (2009) confused model calibration with
m
l
æ
ö
L
=
ç
(6.6)
÷
è
ø
22.13
where
l
is the length of the plot or slope segment
(m) and
m
is a coefficient. Wischmeier & Smith
(1978) gave values for
m
as a function of slope
steepness, with
m
5%, 0.4 for
slopes of 3.5 to 4.5%, 0.3 for slopes of 1 to 3%,
and 0.2 for slopes <1%. Foster
et al
. (1977) defined
the exponent as:
=
0.5 for slopes
≥
b
m
=
b
(6.7)
1
+
where
b
(dimensionless) is the ratio of rill to
inter-rill erosion. In the revised USLE (RUSLE),
the value of
b
is calculated as a function of slope
angle for soils that are “moderately susceptible to
both rill and inter-rill erosion” (McCool
et al
.,
1997: 105):
sin
q
/ 0.0896
b
=
(6.8)
0.8
3 (sin
q
)
+
0.56
where
q
is the slope angle (°), which predicts val-
ues of
b
from 0.22 to 0.71 for slopes of 1 to 30°.
The effect of the
L
factor is thus to predict con-
