Soil Erosion and Conservation - Environmental Modelling: Finding Simplicity in Complexity - page 352

this, and for all practical purposes expectations of fit must
be less. In the study by Risse et al . (1993) using the USLE
and 1700

loss, R (MJ mmh − 1 ha − 1 a − 1 ) is rainfall erosivity,
K (t hrMJ − 1 mm − 1 ) is soil erodibility, L (unitless
ratio) is the slope-length factor, S (unitless ratio) is the
slope-steepness factor, C (unitless ratio) is the cropping
factor, and P (unitless ratio) is the conservation-practices
factor. Terminology is important here. Note first that the
USLE predicts soil loss (see discussion above) and not
sediment yield. Secondly, the word erosivity is used to
denote the driving force in the erosion process (rainfall in
this case) while the term erodibility is used to note the soil
resistance term. These two terms are not interchangeable.
Thirdly, the model predicts average annual soil loss :it
was not intended to predict soil loss for storms or for
individual years. Conservationists often describe the
predictions as long term, whereas from the geomorphic
perspective the predictions would be referred to as
medium term (Govers, 1996).
The units of the USLE appear rather daunting as writ-
ten (Equation 22.1), but become somewhat clearer with
explanation. The units were originally written, and are
still used in the United States, as Imperial, but conversion
to metric is generally straightforward (Foster et al ., 1981).
The key to understanding the dimensional units lies with
the definition of rainfall erosivity and the concept of the
unit plot . Wischmeier (1959) found for the plot data that
the erosive power of the rain was statistically best related
to the total storm energy multiplied with the maximum
30-minute storm intensity. Thus we have the energy term
(MJ) multiplied by the intensity term (mmh − 1 )inthe
units of R , both of which are calculated as totals per
hectare and per year. The unit plot was defined as a
standard of 9% slope, 22.13m length 1 , and left fallow
(cultivated for weed control). The K value was defined
as A

plot years of data, the overall coefficients
of determination were 0.58 for annual values and 0.75
for annual average soil loss data. In the study of Zhang
et al . (1996), the WEPP model was applied using data
from 4124 storm events, the coefficients of determination
were 0.36 for the individual storms, 0.60 for annual
values, and 0.85 for annual average soil-loss values. The
observation that the fit improves from storm to annual
to average annual predictions reflects the trend that data
variability decreases with increasing soil-loss magnitudes,
as discussed above.
Given that we know, based on the data from erosion
plots, that soil erosion is highly variable, and then using
the information on variability to set limits on the ability
of models to predict soil-erosion rates, the question then
becomes one of utility. Is the model accurate enough to
solve our problems? We will address this question later
in this chapter. But first we need to look at the models
themselves, and look at an example of how an erosion
model might be used to solve a problem.

+

22.2 The approaches

Erosion models used in applications for conservation
planning fall into two basic categories: empirical and
process-based. Undoubtedly the prime example of an
empirically based model is the USLE, which was devel-
oped in the United States during the 1950s and 1960s
(Wischmeier and Smith, 1965, 1978). This equation has
been adapted, modified, expanded, and used for conser-
vation purposes throughout the world (e.g. Schwertmann
et al ., 1990; Larionov, 1993).
The USLE was originally based on statistical analyses of
more than 10 000 plot-years of data collected fromnatural
runoff plots located at 49 erosion research stations in the
United States, with data from additional runoff plots
and experimental rainfall-simulator studies incorporated
into the final version published in 1978 (Wischmeier and
Smith, 1978). The large database upon which the model is
based is certainly the principal reason for its success as the
most used erosion model in the world, but its simplicity
of form is also important:

/

R for the unit plot. In other words, erodibility was
the soil loss per unit value of erosivity on the standard
plot. The remaining terms, L , S , C and P are ratios of soil
loss for the experimental plot to that of the unit plot. For
example, the C value for a particular cropped plot is the
ratio of soil loss on the cropped plot to the value for the
fallow plot, other factors held constant.
The USLE reduced a very complex system to a quite
simple one for purposes of erosion prediction. There are
many complex interactions within the erosional system,
which are not, and cannot be, represented within the
USLE. We will illustrate a few of these interactions below.

1 Most of the early erosion plots were 1.83m (6 feet) wide. A length
of 22.13m (72.6 feet) and a width of 1.83m (6 feet) resulted in a
total area of 1/100 of an acre. Prior to the days of calculators and
computers this was obviously a convenient value for computational
purposes.

A = RKLSCP (22.1)

where A (t ha − 1 a − 1 )

is average annual soil loss

over the area of hillslope that experiences net