Environmental Engineering Reference
In-Depth Information
in general terms, to within 10% ( < 7 cm) or better,
and constituent phases agree on average to within
5%( < 16 ) or better throughout themodel domain.
Figure 16.5 illustrates the calibration process, and
Table 16.1 summarizes the best level of agreement
obtained with k s ΒΌ 0.05.
Values computed by the model were compared
with corresponding values predicted from tide
tables from the British Oceanographic Data Cen-
tre (BODC), and the French Tide Table, (FTT).
Figure 16.6 shows the computed and predicted
tide levels at Felixstowe and Dunkerque.
The model demonstrated the same level of
percentage error against the validation test as in
the calibration. The average error in the phase of
the harmonic constituents is less than 16 ( < 5%)
and the average error in the amplitude of the
harmonic constituents is less than 7 cm ( < 10%).
The calibration and validation procedure provides
an objective means of quantifying the uncertain-
ties in complex model outputs.
This case illustrates how the magnitude of
the uncertainty in a variable (the tidal amplitude)
can be investigated through sensitivity testing
by changing the value of key parameters. It also
shows how a numerical model could be used in a
more formal Level 2 type probability analysis. For
example, wemight be interested in the spring high
tide level at a particular port. The three results for
different values of bed friction coefficient could be
used to estimate the derivative of tide level with
respect to the coefficient, which is needed for the
Mean Value Approximation method (see, e.g.,
Melchers 1999; Reeve 2010) for estimating the
probability of failure.
terrain model (DTM) or model topography was
generated on a staggered finite difference gridwith
a spatial resolution of 1045m. Boundary condi-
tions were specified by imposing the amplitudes
and phases of preselected tidal constituents at
the nodes of the open boundaries. Along the open
boundaries the harmonic constants are available
for five constituents: O 1 ,K 1 ,N 2 ,M 2 and S 2 . The
amplitudes and phases for these constituents were
obtained from Howarth (1990).
A time step of 120 seconds was used and
the model was run for a period of 60 days from
1 January 2001 to cover four spring-neap cycles, in
order to acclimatize the model to the boundary
conditions and to have a good representation of
the flow dynamics in the area. Further details of
the modelling
can be
found in Horrillo-
Caraballo (2005).
Model calibration and validation
The main sources of uncertainty arising in the
model are: numerical errors due to the choice of
grid size and time step; the representation of fric-
tional effects; and errors in the bathymetry and
boundary conditions. To quantify these errors a
process of model calibration and validation is
performed (Horrillo-Caraballo 2005). To calibrate
the southern North Sea model, a range of cases
were studied. First, three different grid resolutions
(2090m, 1045m and 522m) were used to choose
the best grid spacing. The 1045-mgridwas the best
option for these studies giving good results in
reasonable computing time. A second set of tests
was performed in which the bed stress was chan-
ged by altering theNikuradse coefficients (k s ). The
influence of the bottom friction on the model's
ability to reproduce observed data was examined
first. The computed sequences of surface eleva-
tions at each grid node over 60 days were subjected
to harmonic analysis. For each constituent, a grid
map was made in order to compare it with cotidal
maps
Case Study: Statistical Modelling of Beaches
The presence of a healthy beach is often an inte-
gral component of modern coastal flood defence
design. In addition, it is important from a
designer's and shoreline manager's perspective to
be able to predict beach behaviour with some
level of confidence. Numerical models are avail-
able for this but can be difficult to operate.
An alternative to process-based modelling is
derived
from extensive
observations
(Howarth 1990).
According to the calibration for the southern
North Sea, positions of amphidromic points are
well captured and constituent amplitudes agree,
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