Calibration of Erosion Models - Erosion Modelling - page 41

1 km 2 catchment. The model is a continuous sim-
ulation model that calculates the complete water
balance and sediment detachment and movement.
The best set of parameters found by PEST are ini-
tial infiltration rate, horizontal and vertical K sat
and Manning's n of the slopes and the channel. In
their experience, PEST needs to be run for 2 to 3
times Y 2 , where Y is the number of parameters
allowed to change. It is interesting that a complete
water balance is simulated, enabling the research-
ers to use groundwater wells and TDR soil mois-
ture sensors as extra information for calibration.
They concluded that while the discharge was well
predicted (PEST reported an R 2

Brazier et al ., 2000; see also Chapters 4 and 5).
They applied the GLUE methodology using
Monte Carlo simulations, with uniform parameter
sampling. They compared each simulated and
classified erosion pattern with the observed pat-
tern using a weighted Kappa index (based on the
fraction of correctly classified spatial units;
Congalton, 1991). A Kappa index below 0 shows
no agreement and a value of 1 indicates perfect
agreement between patterns. The results showed
that the parameters most affecting the erosion
patterns were the re-infiltration length in their
model affecting runoff discharge, followed by the
power exponents 0.937 among

other statistics), the groundwater fluctuated more
rapidly in reality than predicted by the model,
while the measured soil moisture fluctuated more
slowly. This led to additional research in the same
area to investigate preferential flow, which appears
to be one of the main soil hydrological processes
(Van Schaik, 2009). Using a tool such as PEST has
strengths and weaknesses: it is easy and powerful
to use, and robust enough to find a best parameter
set in most situations. It provides goodness of fit
statistics and allows the simultaneous use of dif-
ferent measurement series (discharge, groundwa-
ter, etc.) to find a solution. However, the best fit
may not be a realistic parameter set if more then
one best fit exists in parameter space.
Vigiak et al . (2006) assessed the uncertainty of
model prediction and predicted and observed spa-
tial patterns of erosion in a 2 km 2 catchment in
Tanzania. The erosion patterns were assessed
with series of splash cups and Gerlach troughs, as
well as with the Assessment of Current Erosion
Damage method (ACED; Herweg, 1996). This
resulted in a map with five classes of observed
erosion from slight (only splash evidence) to very
severe (large rills and gullies). They then com-
bined the detachment and transport equations
from the MMF erosion model with their own
hydrological model (Vigiak et al ., 2005) to simu-
late erosion. They assumed that the sediment
transport capacity determined the spatial distri-
bution of erosion, and analysed the uncertainty
of distributed model predictions using the
Generalized Likelihood Uncertainty Estimation
(GLUE) methodology (Beven & Freer, 2001;

= used in the streampow-

er-based transport capacity function ( TC

α and γ

= K Q α

sin( ) γ ). Figure 3.3 shows that the best combina-

tions were obtained with

β

0.5, and
a short re-infiltration length L . This resulted in a
Kappa coefficient of above 0.50 (obtained in 277
of 6000 simulations) which can be considered as
moderately good. Table 3.2 shows the contin-
gency between predicted and observed classes.
Methods like PEST and GLUE usually do not
result in one best fit, and therefore may be less
suitable to show directly to decision-makers,
without extensive interpretation. However, they
offer a lot of insight into the behaviour of a model
with a specific dataset, in particular by quantify-
ing the uncertainty.

α = 1.5 and γ =

3.5 Spatial Calibration of Erosion Patterns

From the examples above, a picture emerges
that the largest source of uncertainty is insuffi-
cient knowledge of spatial patterns of sources
and sinks of water and sediment in the area
under observation. Assuming that the calibra-
tions discussed above used a best-possible
parameterization of the model, it seems that
specifying patterns of input parameters based
on land use, landscape and/or geostatistics is
not sufficient to obtain more than moderate
results. This is confirmed by Walling et al .
(2003) who emphasized that a more distributed
approach is needed to provide spatially distrib-
uted predictions of soil erosion and sediment
transport within a catchment. This raises the