1 Spatial Modelling of the Terrestrial Environment - Georeferencial

94 Spatial Modelling of the Terrestrial Environment
processes in fixed grid models (e.g. King and Roig, 1988; Defina et al., 1994; Bates and
Hervouet, 1999; Defina, 2000) using proportionality coefficients based on the sub-grid
topography, lack of data has usually meant that these coefficients are assumed rather than
parameterized from actual measurements. Unlike ground survey data, which are frequently
unavailable at even the grid resolution, LiDAR data are typically available at a much higher
resolution than most model grids. It is therefore possible to use the redundant, sub-grid
scale data to directly parameterize these sub-grid scale algorithms and better correct for
wetting and drying effects in two-dimensional Shallow Water models (Bates and Hervouet,
1999; Bates, 2000). Both areas of model development are still in their infancy and further
research is required.
5.3.2 Spatially Distributed Friction Data
The traditional method of parameterizing bottom friction in hydraulic models involves
specifying friction factors for floodplain and channel. These are treated as free parameters
to be adjusted to provide the best fit between model predictions and observations. As
noted above, use of sparse hydrometric data for model calibration means that the assigned
parameters are typically spatially and temporally lumped so that one value is used to
represent the channel and one to represent the floodplain. A more physically-based friction
parameterization can now be obtained using the vegetation height data generated from
airborne LiDAR as described in section 5.2.3, which can be used (see Figure 5.3) to specify
an ‘effective’ individual friction factor at each node of a computational model (Mason
et al., 2003). A different equation set can be used to model flow resistance at a node
depending on the vegetation within the node neighbourhood. Thus, for in channel areas
flow resistance is calculated as a function of bed material size using the relationship of Hey
(1979). For short vegetation, such as floodplain grasses and crops, the Darcy-Weisbach
friction factor f is modelled using the approach of Kouwen (1988) described above with the
term MEI determined using an empirical correlation with vegetation height determined by
Temple (1987). Finally, tall vegetation is treated using the method of Fathi-Moghadam and
Kouwen (Fathi-Moghadam and Kouwen, 1997; Kouwen and Fathi-Moghadam, 2000). This
calculates the hydraulic resistance of such vegetation as a linear function of velocity. The
surface properties in the vicinity of each node are then integrated to give a value for f which
then varies in time as a function of the local hydraulics. Specifically, Figure 5.3 shows the
computational mesh of a two-dimensional finite element hydraulic model of the 17 km
reach of the River Severn upstream of Shrewsbury, UK. This uses data from the LiDAR
survey described in section 5.2.3 and shown in Figures 5.1 and 5.2, along with data from the
flow gauging station at Montford Bridge to assign an upstream boundary condition to the
model. This was then used to simulate a dynamic 1-in 50-year flood event, which occurred in
October 1998 for which a RADARSAT SAR image was available for model validation. Use
of the Mason et al. parameterization generated a reach-average 16 cm difference in water
levels over a control simulation with a spatially lumped and calibrated friction surface. This
is a significant difference, however, both parameterizations fitted the available satellite SAR
validation data equally well given its resolution and error. This was because the floodplain
slope at the waterline (∼0.03 m m −1 ) for this 50-year event means that a 16-cm elevation
change does not generate a 1 pixel change in inundation extent and is thus undetectable. An
essential requirement is, therefore, the acquisition of a benchmark model validation dataset