Geology Reference
In-Depth Information
related to soil structure (Boiffin & Monnier, 1986;
Torri
et al
., 1999). Apart from these more obvious
reasons, the predictive quality of the erosion mod-
els is strongly determined by spatial and temporal
variability of the input parameters. Beven (2002)
pointed out that surface and subsurface hydrology
are largely dominated by local geometry and bound-
ary conditions, rather than by the dynamics of the
fluid itself. Consequently the influence of variabil-
ity in the soil (surface) characteristics may be very
large. Many studies have been done on the effects
of spatial variability and error propagation, using
sensitivity analyses based on Monte Carlo simula-
tion and other methods (see e.g. De Roo
et al
., 1992;
Brazier
et al
., 2000). The results show that most of
the model parameters are stochastic in nature, and
measurement errors and uncertainty as a result of
spatial interpolation add considerable uncertainty
to the model results (see Chapter 4 for further dis-
cussion, and Section 14.4 on the realism of cali-
brated parameter values).
able in reproducing the observed behaviour of that
system”. They called this equifinality. This can
simply be shown with a sensitivity analysis of two
parameters that influence runoff:
K
sat
and a surface
resistance parameter (such as Manning's
n
).
A higher resistance slows down the runoff and
permits more time for infiltration. It therefore
influences the shape of the hydrograph. In order to
show this, the model LISEM was run 100 times for
a single event in the 1 km
2
Ganspoel catchment in
Belgium (Van Oost
et al
., 2005), changing the
K
sat
and Manning's
n
from 0.2 to 2.0 with steps of 0.2
around best calibrated values. Fig. 3.2a shows the
sensitivity of LISEM for combinations of
n
and
K
sat
for the total discharge (which varies non-
linearly from 0 m
3
in the lower right corner to
2300 m
3
in the upper left corner). The black iso-
line connects all combinations of
K
sat
and
n
that
give a runoff total close to the measured value
of 253 m
3
. The central point (2) is the best fit.
There is, however, a catch to this analysis, one
that increases the equifinality unnecessarily.
The same total runoff can be achieved with
many different hydrographs. Fig. 3.2b shows three
hydrographs for points 1 to 3 and the measured
hydrograph. While none of the simulated graphs
gives an exact fit, it is clear that the central
point resembles the observed hydrograph most
closely. This suggests that by considering only
lumped values of total runoff or peak values
without considering the shape of the hydrograph,
uncertainty is unnecessarily added and the prob-
lem of equifinality is seemingly increased. This
may have caused unnecessary scatter in the data
when comparing model predictions with meas-
ured values.
3.3
Sensitivity of Process Models
Models used in catchment-scale predictions are
often calibrated using saturated hydraulic con-
ductivity (
K
sat
) and, for event-based models, ini-
tial soil moisture. This is logical as these
parameters directly determine the infiltration
excess and amount of runoff. The most common
strategy is to calibrate the total runoff (without
attempting to fit a hydrograph) (De Roo
et al
.,
1996; Quinton, 1997; Hessel
et al
., 2003a;
Takeuchi
et al
., 2009). Sometimes a single param-
eter set can be used to calibrate all events in a
season, but sometimes different values have to be
used for each event.
This difficulty in finding the right combination
of parameters to calibrate a series of events stems
mostly from the fact that a different combination
of input parameters can give the same result.
Beven and Freer (2001) argued that “in mechanis-
tic modelling of complex environmental systems,
there are many different model structures and
many different parameter sets within a chosen
model structure that may be behavioural or accept-
3.4
Calibration Examples Based on Automatic
Parameter Estimation
The difficulty in finding the right combination of
input parameters to simulate a given output invites
the use of automatic methods of finding the cor-
rect combination, based on statistical goodness-
of-fit criteria between predicted model output and
observed data. One of the advantages of such
