Environmental Engineering Reference
In-Depth Information
crudely (water is transferred instantaneously from
one end of the storage cell to the other), and
calculated inter-cell flows may be significantly
in error (because of the lack of appropriate spill
discharge equations). The 1D þ approach is also
referred to as 'pseudo-2D' (Evans et al. 2007) or
'quasi-2D'.
Simplified 2D approaches not based on the full
2D shallow water equations are referred to as
'2D-'. This class of models encompasses mainly
2Dmodels based on a simplified version of the 2D
shallow water equations where some terms are
neglected, resulting in the kinematic and diffusive
wave representations (Bradbrook et al. 2004;
Hunter et al. 2007). However, it also includes
models relying on square-grid digital elevation
models and a simplified 1D representation of the
flow between the raster DEM cells (Bates and
De Roo 2000). In effect the latter approach is
similar to 1D þ approaches but usually with a
much finer regular discretization of the physical
space. As with the 1D þ approach, momentum is
not conserved for the two-dimensional floodplain
simulation in 2D- models.
1D, 2D and 3D modelling approaches can also
be combined with one another. Many commer-
cially available software packages now offer the
possibility to link a 1D river model to 2D flood-
plain models. This allows modellers to benefit
from the advantages of 1Dmodels (computational
efficiency, established tradition of 1Dmodelling),
while representing floodplain flows more appro-
priately in 2D. However, the modelling of the
1D/2D linkage is an area where further research
and development is needed, as most approaches in
application represent exchange processes rather
crudely (see 'Hybrid 1D/2D methods' below).
Combined 1D/2D modelling approaches where a
1D sewer systemmodel can be linked to 2D flood-
plain models are also commercially available.
Finally, some existingmodels that do not strict-
ly fall in any of the above categories should be
mentioned. This is the case of the rapid flood
spreading methods (Gouldby et al. 2008), which
are the subject of research and application in the
context of national scale flood risk assessment
(for which simulation run times are required to
Hervouet 2007). A solution to these equations can
be obtained from a variety of numerical methods
(e.g. finite difference, finite element or finite vol-
ume) and utilize different numerical grids (e.g.
Cartesian or boundary fitted, structured or
unstructured) all of which have advantages and
disadvantages in the context of floodplain model-
ling. Further detailed considerations are provided
below.
One-dimensional approaches based on some
formof the one-dimensional St-Venant or shallow
water equations (Barr ´ de St-Venant 1871) are
predominant in river flow studies. Over the years
their use has been extended to the modelling of
flow in compound channels, i.e. river channels
with floodplains. In this case floodplain flow is
part of the one-dimensional channel flow, and
simulation of inundation is an integral part of the
solution of the St-Venant equations. The tech-
nique has at least two disadvantages, namely that
(i) floodplain flow is assumed to be in one direc-
tion parallel to the main channel, which is often
not the case, and (ii) the cross-sectional averaged
velocity predicted by the St-Venant equations has
no physical meaning in a situation where large
variations in velocity magnitude exist across the
floodplain. The approach has been enhanced in
recent years thanks to significant advances in
parameterization through the development of
the conveyance estimation system (Samuels
et al. 2002).
Approaches that combine the 1D approach ap-
plied to the main channel flow and storage cells to
represent floodplains are referred to as '1D þ '.
These storage cells can cover up to several square
kilometres and are defined using a water level/
volume relationship. The flow between the 1D
channel and the floodplain storage cells is mod-
elled using discharge relationships (such as weir
flowequations), whichmay be used to link storage
cells to each other. The water level in each storage
cell is then computed using volume conservation.
Unlike the 1D approach, the 1D þ approach does
not assume that flow is aligned with the river
centre line, and thereforemay bemore appropriate
to model floodplains of larger dimensions. How-
ever, these models represent wave propagation
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