Geoscience Reference
In-Depth Information
coming into more widespread use. Such models can predict a pattern of depth-averaged velocities within
the channel and across a flood plain. Examples of such models are TELEMAC 2D, SFV and RMA2
(see, for example, the work of Bates
et al.
, 1992, 1995, and Horritt
et al.
, 2007). Three-dimensional
models of surface flows using general computational fluid dynamics packages are just starting to be used
to study flows in natural channels (see the reviews by Lane, 1998, and Lane
et al.
, 1999) but are still
computationally feasible only for small scale problems. Even then, much remains to be learned about
appropriate representations of turbulence and momentum losses in natural channels for such models.
Some comparisons of 2D models have been provided by Horritt and Bates (2001), Horritt
et al.
(2007)
and Hunter
et al.
(2008).
The increasing availability of detailed topographic data from remote sensing (Lidar, SAR) has also
driven demand for two-dimensional models, not only for fluvial flooding, but also for detailed mapping
of the potential for pluvial flooding in urban areas, and for rapid flood spreading following breaching
or over-topping of flood defences. A number of computationally efficient models have been produced,
based on combining a 1D representation of the channel with a 2D diffusion simplification of the depth
averaged equations on the flood plain (see Box 5.6 for a discussion of simplifications of the St. Venant
equations). These models include the LISFLOOD-FP model of Bates and De Roo (2000) and JFLOW
model of Bradbrook (2006). To speed the calculations further, parallel computing versions of such models
have been produced (e.g. Neal
et al.
, 2010), including implementation of the JFLOW gridded model on
multiple graphics processing units (GPUs) (Lamb
et al.
2009). The advantage of GPUs is that they can
have several hundred individual processors that can each carry out the relatively simple calculations for
the grid elements in the flow domain with near linear speed up of the calculations.
There are a number of numerical issues with these simplified models, including stability issues of
using explicit time stepping, numerical diffusion, mass conservation, and the treatment of wetting and
drying cells at the edges of the flood plain. Recent advances to control these essentially numerical
problems have included the implementation of adaptive time stepping schemes (Hunter
et al.
2006) and
the re-introduction of inertial terms (Bates
et al.
, 2010). However, a number of comparative studies have
suggested that, given all the uncertainties involved in setting up a flood routing model, the simplified
models can reproduce the observed patterns of inundation in past floods as well as the more complex
finite element and finite volume solutions (Horritt and Bates, 2002; Horritt
et al.
, 2007). The advantage
of the faster run times of these simplified models is that they can be run over large areas (such as the
Amazon studies of Wilson
et al.
, 2007) or many times in a given application for use in model calibration
or uncertainty estimation (Aronica
et al.
2002; Di Baldassarre
et al.
2009; Leedal
et al.
2010). Speed
of computation is also an issue if such distributed models might be used for real-time forecasting of
inundation (e.g. Schumann
et al.
, 2010).
Calibration is an important issue in the application of these flow routing models. The parameters that
are required are the patterns of
effective
roughness for the channel and flood plain. It is “effective”
roughness because the values required to produce good simulations of the available observations depend
on which model is being used, the spatial resolution of the discretisation of the flow domain, the way
in which roughness elements on the flood plain (including walls, hedges, trees and buildings) dissipate
momentum, and the accuracy of the available survey information. The data available for calibration is
the change in levels at gauging stations and, in some cases, patterns of maximum inundation elevations
from post-event surveys of wrack marks and marks on buildings (but without any accurate information
on timing). Some studies have used patterns of inundation at specific times when satellite or aircraft
platform sensing images have been available. Some of those images give rather uncertain estimates of
the extent of inundation because of speckle and the effects of emergent vegetation (e.g. Horritt
et al.
,
2003; Di Baldassarre
et al.
, 2009) and there are often important issues about registration of the images
with the representation of flood plain topography that is used in the model (e.g. Romanowicz and Beven,
2003). Such uncertainties interact with other uncertainties in setting up the model, such as the treatment
of the boundary conditions (in particular, the estimates of upstream discharge), the representation of
