Environmental Engineering Reference
In-Depth Information
often causing large errors in the predictions of
exchange flows. However, these do not matter if
the time duration of the floodplain filling and
draining processes is small compared to the dura-
tion of the flood. Lastly, the size and location of
floodplain storage cells and links between them
are user defined and therefore require some a priori
understanding of flow pathways in the floodplain,
which may result in circular reasoning within
models.
Two-dimensional modelling of river flood-
plains can be divided into two important classes
of approaches, namely the one where only flood-
plains are modelled in 2D (as part of a combined
1D/2D model) and the one where floodplain flow
and channel flow are modelled as part of the same
2D grid. This latter class of approach is discussed
specifically in the final paragraph of this section.
The main advantage of 2D modelling (over any
other approach for floodplain modelling) is that
local variations of velocity and water levels and
local changes in flow direction can be represented
(Syme 2006). The approach also does not suffer
fromthe limitations of the 1Dand 2D
approaches
detailed in the previous paragraphs. It allows in
principle a better representation of floodplain con-
veyance, but a major limitation of combined
1D/2D models for river and floodplain systems
is that the exchange processes between the river
and the floodplains are still modelled crudely
(momentum transfer is not modelled). A major
drawback of 2D models is their computational
cost (Syme 2006), with a computational run time
typically proportional to
1=
simulations (unlike rivers). However, a casewhere
1D modelling is as close as possible to being
appropriate can be found for example in Lhomme
et al. (2005; deep flooding in a network of well-
defined narrow streets).
In river flooding applications, 1D models of
rivers with cross-section extending over lateral
floodplains are accepted as appropriate for narrow
floodplains, typically where their width is not
larger than three times the width of the main river
channel. An additional condition for such models
to be valid is that no embankment, levee or raised
ground should separate the floodplain from the
main channel. The complicated contribution of
the floodplain to conveyance can then be appro-
priately quantified using recent advances in the
estimation of compound channel conveyance
(HR Wallingford 2003).
However, 1Drivermodels have limitations that
can become significant in many practical applica-
tions. The flow is assumed to be unidirectional
(generally happening in the direction parallel to
the main channel flow), and where this is not true
(recirculation areas), conveyance predictions can
be severely overestimated. Situationswhere flood-
plain flow 'makes its own way' are frequent, but
perhaps an even more significant issue is the fact
that 1D cross-sections will offer a rather crude
representation of floodplain storage capacity in
the case of large floodplains.
The use of 1D
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models, where large
'disconnected' floodplains are modelled as storage
reservoirs (while narrow floodplains can still be
modelled as part of channel cross-sections), allows
a better balance between the correct representa-
tion of floodplain conveyance and the correct
representation of floodplain storage capacity. This
latter modelling approach has its own limitations:
exchange flows between the river and reservoirs
and between the reservoirs are modelled using
equations such as broad-crested weir equations
(Evans et al. 2007), which are not always appro-
priate. Weir equations adapted for drowned (down-
stream controlled) flows are also used, but the
assumption that water levels are horizontal with-
in each reservoir results in incorrect water level
predictions in the vicinity of reservoir boundaries,
L
3
, where L is the grid
resolution.
Mainly through the use of 2D unstructured
grids it is possible to represent a river and adjacent
floodplains in a single 2Dmesh, Fig. 12.4 (see, e.g.,
Sauvaget et al. 2000; Horritt and Bates 2002). This
approach is not particularly common in UK prac-
tice, perhaps because there is a long-established
tradition of 1D river modelling. Surveyed cross-
sections, which are intended primarily for 1D
models, exist for a large proportion of rivers in the
UK. Numerous existing 1D models have been
calibrated usingmeasured data, and 1DManning's
n values are well known for many rivers or river
