Environmental Engineering Reference
In-Depth Information
depend on the correct prediction of flood dis-
charge (flowing through or over the failed defence)
much more than on the floodplain friction param-
eterization. The possibility to calibrate floodplain
friction in such circumstances using real event
data has not been exploited to the present date. It
could only exist if (i) the inflow was accurately
measured, and (ii) appropriate hydrometric data
were collected on the floodplain, i.e. during the
transient phase of the inundation process (not
after the flood has settled on the floodplain). It
can be concluded that inundation extent and
floodplain water level measurements alone can-
not usually be used to calibrate 2D floodplain
models in the same way as river levels are used
to calibrate 1D river models (Hunter et al. 2005;
Werner et al. 2005; N
ยด
elz et al. 2006). In the same
way as calibrating 1D models usually involves
tuning friction parameter values to yield an opti-
mal match between predicted and measured wa-
ter level hydrographs, an appropriate approach for
2D floodplain models should at the very least
concentrate on the prediction of features of the
flow that depend primarily on the processes mod-
elled by the 2D solver (perhaps velocities), and the
flow conditions at the boundaries of the flood-
plain should be known accurately as part of the
calibration data. An additional difficulty if mea-
sured velocities are to be used as calibration data
is that these must be measured in a form that is
consistent with what models predict, i.e. depth-
averaged velocities.
The above paragraphs focus either on the
modelling of floodplains only or on the modelling
of floodplains in 2D as part of combined 1D/2D
models (see 'Hybrid 1D/2D methods' below). Ap-
proaches to calibration for fully-2Dmodels, where
floodplains as well as river channels are modelled
in 2D, is somewhat different (see, e.g., Sauvaget
et al. 2000). However, issues of over-parameteri-
zation and equifinality affect fully-2D models in
a similar manner.
Elaborate approaches to floodplain friction pa-
rameterization that do not involve calibration
have been suggested in recent years. These are
detailed under 'Representation of surface rough-
ness and energy loss' below.
modelling, although it should be borne in mind
that the formulation of friction is different in 2D
models, because (i) bed friction only concerns the
interaction of the flowwith the river or floodplain
bed while in 1D models it concerns the entire
wetted perimeter, and (ii) viscosity is explicitly
represented in the 2D shallow water equations
whereas it is effectively taken into account as part
of the friction parameterization in 1D models.
Theoretically this should result in lower values
(assuming that lower values are used for less rough
beds, as is the case withManning's n) of friction in
2D models compared with 1D models (Morvan
et al. 2008), but in practice the friction parameter
is scale dependent and is used to compensate for
varying conceptual errors in the model.
The process of parameterizing models of com-
bined river and floodplain systems is made diffi-
cult by the problem of over-parameterization.
Predictions of flood levels bymodels of compound
channels have been shown to be sensitive primar-
ily to the channel friction values used, with the
sensitivity to floodplain friction values being
much less significant (see, e.g., Pappenberger
et al. 2005). This reflects the fact that many
floodplains act as lateral storage reservoirs where
water depths and velocities remain small com-
pared to those in the main channel (it may be
argued that this is the case, e.g., in the UK more
than in southern regions of Europe where floods
can be more extreme). The main consequence is
that it is not straightforward to calibrate flood-
plain friction using measured flood levels (or in-
undation extent maps; Hunter et al. 2005). A
more compelling argument for not adopting this
approach is the problem of equifinality (see, e.g.,
Aronica et al. 1998; Beven 2006), or the non-
uniqueness of calibrated parameter values in
over-parameterized problems. In the above con-
text it implies that an agreement between model
predictions and any observed flood level or inun-
dation extent is achievable by calibrating channel
friction values only. In the distinct context where
floodplain flow results from some form of failure
of flood defences (and continues until flood waters
recede or until the floodplain has been completely
filled), correct model predictions are then likely to
