Soil Erosion and Conservation - Environmental Modelling: Finding Simplicity in Complexity - page 351

in Kingdom City, MO, USA in 1981. All of the 40 plots
were cultivated and in other ways treated identically. The
coefficients of variation for the 25 storms ranged from
18% to 91%, with 15 of the storms falling in the range of
less than 30%. The more erosive storms tended to show
the lesser degree of variability. Of the 15 storms withmean
erosion rates of greater than 0.1 kgm − 2 (1.0Mg ha − 1 ), 13
showed coefficients of variation of less than 30%. The
results of the study indicated that 'only minor amounts of
observed variability could be attributed to any of several
measured plot properties, and plot differences expressed
by the 25 events did not persist in prior or subsequent
runoff and soil-loss observations at the site.'
Ruttimann et al . (1995) reported a statistical analysis of
data from four sites, each with five to six reported treat-
ments. Each treatment had three replications. Reported
coefficients of variation of soil loss ranged from 3.4% to
173.2%, with an average of 71%. The authors concluded
by suggesting 'asmany replications as possible' for erosion
experiments.
Nearing et al . (1999) studied erosion variability using
data from replicated soil-loss plots from the USLE
database. Data from replicated plot pairs for 2061 storms,
797 annual erosion measurements, and 53 multi-year
erosion totals were used. They found that the relative
differences between replicated plot pair measurements
tended to decrease as the magnitude of the measured
soil loss increased. Using an assumption that soil-loss
magnitude was the principal factor for explaining
variance in the soil-loss measurements, the authors
were able to calculate the coefficient of variation of
within-treatment, plot-replicate values of measured soil
loss. Variances between replicates decreased as a power
function (r 2

the mean. Zhang et al . (1996) applied the Water Erosion
Prediction Project (WEPP) computer-simulation model
to 290 annual values and obtained an average of 2.18 kg − 2
for the measured soil loss, with an average magnitude of
prediction error of 1.34 kg − 2 , or approximately 61% of
the mean. In both cases the relative errors tended to be
greater for the lower soil loss values. Given these results
and others from similar types of studies (Liu et al ., 1997;
Rapp, 1994; Govers, 1991), the question may be asked:
are the predictions 'good enough' relative to measured
data? What is an acceptable and expected level of model
prediction error?
One manner in which we can address this problem is
to think of the replicated plot as the best possible 'real-
world, physical model' of soil erosion. As such, one might
further consider that the physical model represented by
the replicate plot represents essentially a 'best case' sce-
nario in terms of erosion prediction, which we can use
as a baseline with which the performance of erosion pre-
diction models might be compared. Using, as discussed
above, data from natural runoff plots from the USLE plot
database, Nearing (2000) suggested a basis for an erosion-
model evaluation method using the idea of the replicate
plot as a physical model of the replicated plot. He sug-
gested that if the difference between the model prediction
and a measured plot-data value lies within the population
of differences between pairs of measured values, then the
prediction is considered 'acceptable'. A model 'effective-
ness' coefficient was defined for studies undertaken on
large numbers of prediction versus measured data com-
parisons. The method provides a quantitative criterion
for taking into account natural variability and uncertainty
in measured erosion-plot data when that data is used to
evaluate erosion models.
Nearing (2000) outlines the specific procedures for how
erosion-model evaluation can be done in the presence of
data uncertainty. The method is straightforward, but
requires some detail in the computations. Using similar
arguments with the erosion-plot replicate data, but using
a slightly less complex analysis, we can achieve a rule-
of-thumb measure of model validity simply by looking
at the coefficient of determination for the regression
line between measured and predicted soil-loss values.
Using measured soil-loss data pairs from 3007 storms
(overlapping with some of the same data used in the
previously mentioned studies) Nearing (1998) obtained
a coefficient of determination between measured and
predicted soil loss of 0.77. One certainly would not expect,
(on uncalibrated data) to obtain results between model
predictions and measured data substantively better than

78) of measured soil loss, and were
independent of whether the measurements were event,
annual, or multiyear values. Values of the coefficient of
variability ranged from nearly 150% for a soil loss of
0.1 kgm − 2 to as low as 18% or less for soil loss values
greater than 10 kgm − 2 . One important question for
scientists is: 'How do we know when an erosion model
is working adequately?' Given that the data are highly
variable, when we ask the question about how well a
model works, the answer is not so simple. One cannot just
compare the model output to an erosion rate. One must
simultaneously ask the question: 'How variable is nature?'
Risse et al . (1993) applied the Universal Soil Loss
Equation (USLE) to 1700 plot-years of data from 208
natural runoff plots. Annual values of measured soil loss
averaged 3.51 kgm − 2 with an average magnitude of pre-
diction error of 2.13 kgm − 2 , or approximately 60% of

= 0 .