HYDROLOGICAL PROCESSES
Hydrol. Process. 17, 1711– 1732 (2003)
Published online 15 May 2003 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/hyp.1270
Floodplain friction parameterization in two-dimensional
river flood models using vegetation heights derived from
airborne scanning laser altimetry
David C. Mason,1 * David M. Cobby,1 Matthew S. Horritt2† and Paul D. Bates2
1
Environmental Systems Science Centre, University of Reading, Reading RG6 6AB, UK
2 School of Geographical Sciences, University of Bristol, Bristol BS8 1SS, UK
Abstract:
Two-dimensional (2-D) hydraulic models are currently at the forefront of research into river flood inundation prediction.
Airborne scanning laser altimetry is an important new data source that can provide such models with spatially distributed
floodplain topography together with vegetation heights for parameterization of model friction. The paper investigates
how vegetation height data can be used to realize the currently unexploited potential of 2-D flood models to specify a
friction factor at each node of the finite element model mesh. The only vegetation attribute required in the estimation
of floodplain node friction factors is vegetation height. Different sets of flow resistance equations are used to model
channel sediment, short vegetation, and tall and intermediate vegetation. The scheme was tested in a modelling study
of a flood event that occurred on the River Severn, UK, in October 1998. A synthetic aperture radar image acquired
during the flood provided an observed flood extent against which to validate the predicted extent. The modelled
flood extent using variable friction was found to agree with the observed extent almost everywhere within the model
domain. The variable-friction model has the considerable advantage that it makes unnecessary the unphysical fitting
of floodplain and channel friction factors required in the traditional approach to model calibration. Copyright  2003
John Wiley & Sons, Ltd.
KEY WORDS
distributed friction; segmentation; synthetic aperture radar; River Severn
INTRODUCTION
Two-dimensional (2-D) hydraulic models are currently at the forefront of research into river flood inundation
prediction. Their popularity has arisen partly because of the inability of one-dimensional (1-D) models to
predict certain aspects of out-of-bank flows, and partly because of recent technical advances in two- and
three-dimensional hydraulic modelling, for example the development of algorithms to simulate moving flood
boundaries (Bates and Hervouet, 1999; Defina, 2000). Given that many flood events of practical significance
occur at long reach scales (10–60 km), most models adopt a 2-D finite element approach to minimize the
number of nodes required in the computation. These models solve the shallow-water equations at each node of
an irregular mesh covering the channel and floodplain. Each node of the mesh must be assigned a topographic
height and a (possibly time-varying) friction factor. During a model run, the time-evolving water depths and
flow velocities at each node are calculated in such a way as to satisfy the boundary conditions specified.
The 2-D nature of these models requires spatially distributed 2-D data for their calibration and validation.
Until recently, development of these models was hampered by lack of suitable spatially distributed data.
However, remote sensors carried on satellites and aircraft are now proving to be a rich source of such
* Correspondence to: David C. Mason, Environmental Systems Science Centre, Harry Pitt Building, 3 Earley Gate, University of Reading,
Whiteknights, Reading RG6 6AL, UK. E-mail: [email protected]
† Present address: School of Geography, University of Leeds, Leeds LS2 9JT, UK.
Copyright  2003 John Wiley & Sons, Ltd.
Received 18 April 2002
Accepted 18 November 2002
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D. C. MASON ET AL.
distributed data. For example, synthetic aperture radar (SAR) satellite imagery of flood inundation extent over
large areas can now be used to validate the modelled flood extent (Horritt, 1999, 2001; Horritt et al., 2001).
Because of the complex, shallow topographic gradients found on floodplains, reproduction of the inundation
extent observed should provide a good test of a 2-D model’s capabilities.
Airborne scanning laser altimetry (LiDAR) is a further important new source of data for model parameterization. LiDAR can produce maps of surface height over large areas with a height precision of about š15 cm
(depending on the nature of the ground cover) and a spatial resolution of ¾1 m. The technique has found
applications in many areas of environmental science, including oceanography (Hwang et al., 2000), coastal
mapping (Gutelius et al., 1998), forestry (Naesset, 1997; Magnussen and Boudewyn, 1998), crop height measurement (Davenport et al., 2000) and hydrology (Gomes Pereira and Wicherson, 1999; Marks and Bates,
2000; Bates, 2000). LiDAR data are now routinely collected for UK floodplains by the UK Environment
Agency (EA). The ability of LiDAR to provide suitable model bathymetry has been investigated previously
(Marks and Bates, 2000; Bates, 2000). LiDAR also shows potential in identifying the river channel, because
water generally produces a null return. The channel, together with the LiDAR-derived topography, can be
used in the generation of the model domain and mesh.
Whilst significant advances have been made in the application of 2-D finite element models to river flood
inundation modelling through remote sensing techniques, both in terms of model validation and topographic
parameterization, the specification of flow resistance remains a significant problem. Previous work has used
a calibration strategy, where friction parameters are adjusted to optimize the fit between model predictions
and observations. Owing to computational considerations this generally limits friction parameterizations to
those with uniform floodplain friction or a crude representation of the spatially heterogeneous friction surface
(Horritt, 2000). Furthermore, owing to the paucity of model validation data sets, the same data are often
used for model calibration and validation. This approach is suspect, as shortcomings in model performance
can often be compensated for in the calibration process, and so validation is limited by uncertainty in model
parameterizations. Thus, there is a clear need to move away from the calibration approach used in previous
work (e.g. Bates et al., 1998) to a more scientific method of assigning friction parameters in finite element
models of flood hydraulics. Firstly, this will allow models to be validated in a rigorous fashion by reducing
the need for calibration, which precludes using inundation extent for validation. Secondly, it will allow the
potential spatial complexity of 2-D models to be exploited through the use of distributed roughness values.
The scale and spatial complexity of river reaches prohibits the use of traditional techniques (field survey,
flume studies) to specify roughness properties; hence, remote sensing techniques are a useful starting point to
facilitate such a parameterization.
As well as providing topographic information over the floodplain and the position of the channel, LiDAR
data can be used to generate maps of vegetation height (Menenti and Ritchie, 1994; Cobby et al., 2001). For
floodplains experiencing relatively shallow inundation (<1 m), resistance due to vegetation will dominate the
boundary friction term, and so the ability to map vegetation properties such as height over the floodplain
is essential to any physically based, spatially distributed approach to friction parameterization. Whilst
considerable research has been carried out on flume studies of flow through vegetation (Kouwen and Li,
1980; Kouwen, 1988; Wu et al., 1999; Kouwen and Fathi-Moghadam, 2000), techniques for scaling these
results to river reaches of 10–60 km have yet to be developed and the application of the results to numerical
models of flood flow has not been attempted. The use of LiDAR to generate distributed friction maps is
therefore presented in this paper. The main objectives of the paper are:
1. to investigate how the LiDAR-derived vegetation heights can be converted to friction factors at each node
of the model mesh;
2. to compare modelled and observed flood extents using variable and constant floodplain friction factors;
3. to perform sensitivity tests to investigate the effects of different floodplain vegetation scenarios on flood
risk.
Copyright  2003 John Wiley & Sons, Ltd.
Hydrol. Process. 17, 1711– 1732 (2003)
FLOODPLAIN FRICTION PARAMETERISATION
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Prior to investigating these, the method used to post-process the LiDAR data in order to extract the floodplain
digital elevation model (DEM), vegetation heights and model mesh is outlined.
LIDAR SEGMENTATION
The classic problem in LiDAR post-processing is how to separate ground hits from surface object hits on
vegetation or buildings. Ground hits can be used to construct a DEM of the underlying ground surface, whereas
surface object hits, taken in conjunction with nearby ground hits, allow object heights to be determined. A
LiDAR range image segmentation system has been developed to perform this separation. The system converts
the input height image into two output raster images of surface topography and vegetation height at each
point. The river channel and model flood domain extent are also determined, as an aid to constructing the
model’s finite element mesh. The segmenter is semi-automatic and requires minimal user intervention. Flood
modelling does not require a perfect segmentation as it involves large-area studies over many regions, so a
straightforward segmentation technique able to cope with large (approximately gigabyte) images and designed
to segment rural scenes has been implemented. Detailed descriptions of the segmenter have been published
previously (Mason et al., 1999; Cobby et al., 2000, 2001), and only a summary is given here (Figure 1).
The action of the segmenter is illustrated using a 6 ð 6 km2 sub-image from a large 140 km2 LiDAR image
of the Severn basin. The data were acquired in June 1999 by the EA using an Optech ALTM1020 LiDAR
system measuring time of last return only. At this time of year, leaf canopies were dense, so that relatively
few LiDAR pulses penetrated to the ground. The aircraft was flown at approximately 65 m s1 and at 800 m
height whilst scanning to a maximum of 19° off-nadir at a frequency of 13 Hz. The laser was pulsed at 5 kHz,
which resulted in a mean cross-track point spacing of 3 m. Because current 2-D flood models are capable
of predicting inundation extent for river reaches up to 20 km long (Horritt, 2000), with floodplains spanning
associated large areas, the segmenter has been designed to use LiDAR data with lower resolution than that
used for other applications (Gomes Pereira and Wicherson, 1999). The left-hand side of Figure 2a shows the
raw 3 m gridded sub-image used as input to the segmenter. The sub-image contains a 17 km reach of the
Severn near Bicton west of Shrewsbury. The bright areas are the overlaps between adjacent LiDAR swaths,
which are typically about 550 m wide. The image only appears sensible to the eye when interpolated, as
shown on the right-hand side. However, to avoid loss of resolution in interpolation, the raw data are used in
the segmentation.
The segmenter first identifies water bodies by their zero return (due to specular reflection of the laser pulse
away from the sensor), and agglomerates them into connected regions. To remove low-frequency trends, the
image is subjected to a detrending step that produces an initial rough estimate of ground heights over the
whole image. The detrended height image is then segmented on the basis of its local texture. The texture
measure used is the standard deviation of the pixel heights in a small window centred on each pixel. Regions
of short vegetation should have low standard deviations, and regions of tall vegetation larger values. The
image is thresholded into regions of short, intermediate and tall vegetation, and connected regions of each
class are found (Figure 2b). Short vegetation less than 1Ð2 m high includes most agricultural crops and grasses
and is a predominant feature on floodplains. Intermediate vegetation includes hedges and shrubs, which may
be expected to be significant obstacles to flow over floodplains. Tall ‘vegetation’ greater than 5 m high
includes trees and buildings. No attempt is made to distinguish buildings from trees, as there are generally
few buildings in rural floodplains such as the one used in this study.
An advantage of segmentation is that it allows different topographic and vegetation height extraction
algorithms to be used in regions of different cover type. Figure 2c shows the vegetation height map derived
from the segmentation. Short vegetation heights are calculated using an empirically derived relationship
between the LiDAR standard deviation and measured crop height, which predicts vegetation heights up to
1Ð2 m with an r.m.s. error of 14 cm. In contrast to most LiDAR vegetation height algorithms, this relationship
does not rely on a certain fraction of LiDAR pulses being reflected from the ground (Cobby et al., 2001).
Copyright  2003 John Wiley & Sons, Ltd.
Hydrol. Process. 17, 1711– 1732 (2003)
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D. C. MASON ET AL.
Raw LiDAR data
A dense ‘cloud’ of (x, y, z) points.
Data re-sampling
Heights are sampled onto a 3 m grid. Separate images are constructed using the
minimum and maximum heights in each cell.
Terrain coverage mask
Agglomeration of nearby non-zero pixels identifies continuous land regions. Breaks
in this surface are assumed to be water bodies, which are locally connected.
Detrending
Heights in regions of high standard deviation (e.g. forests) are replaced with a surface
connecting the local minima. Then low-frequency first-order slopes are removed
using bilinear interpolation in non-overlapping 15 × 15 m windows.
Standard deviation of local heights
The detrended surface is subtracted from the original, and the standard deviations (s)
in 15 × 15 m windows centred on each pixel are calculated.
Region identification
The standard deviation image is thresholded to separate regions of short (<1.2 m),
intermediate and tall (> 5.0 m) vegetation. Disconnected segments of intermediate
vegetation (e.g. hedges) are locally reconnected. Each connected region is identified
and processed separately in the following stages.
Short vegetation regions
Vegetation heights (n) are
calculated using
n = 0.87 ln (s) + 2.57
A fraction(f ) of n is subtracted
from the bilinearly interpolated
surface (hb) to give the
topographic heights beneath
the short vegetation (hs), i.e.
Tall and intermediate vegetation regions
The topography (up to a distance dmax from the
regions perimeter) is constructed using an
inverse distance (d ) weighting of the
surrounding short vegetation topography (hs),
and the interior minimum-bilinear surface
(hmb). This latter surface only is used for pixels
lying beyond dmax from the perimeter.
hto = hs
dmax −d
dmax
+ hmb
d
dmax
hs = hb - f n
The topography is subtracted from the raw data
giving the tall and intermediate vegetation
Connected river
bank locations
Topographic
heights
Vegetation
heights
Figure 1. Flow chart showing the main stages of the LiDAR segmentation system
Copyright  2003 John Wiley & Sons, Ltd.
Hydrol. Process. 17, 1711– 1732 (2003)
FLOODPLAIN FRICTION PARAMETERISATION
(a)
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(b)
Raw image
Interpolated image
(c)
(d)
Figure 2. (a) Raw 3 m gridded LiDAR data of a 6 ð 6 km2 area in the Severn Basin, UK (left-hand side). The right-hand side shows an
interpolated region of the raw data. (b) Connected regions identified in the segmentation. Short vegetation is light brown, hedges are green,
tall vegetation dark brown and water regions blue. (c) Vegetation height map. (d) Topographic height map
Copyright  2003 John Wiley & Sons, Ltd.
Hydrol. Process. 17, 1711– 1732 (2003)
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D. C. MASON ET AL.
The topographic height map (Figure 2d) is constructed in regions of short vegetation by subtracting an
empirically determined fraction of the vegetation height from the original data. A comparison with ground
control points (GCPs) gave an r.m.s. height error of 17 cm for the topographic surface in regions of short
vegetation. This is close to the 10 cm r.m.s. error aimed for in DEMs for model bathymetry (Bates et al.,
1997). The figure of 10 cm provides a realistic lower limit for DEM quality, as beyond this the sensor signal
becomes indistinguishable from background ‘noise’ generated by microtopography features such as furrows
in a ploughed field.
In regions of tall and intermediate vegetation, the topographic height map is constructed by interpolation
between local minima (assumed to be ground hits) and topographic heights in nearby short vegetation regions.
However, ground height accuracy falls off in wooded regions due to poor penetration of the LiDAR through
the canopy. Measured over a range of tree canopy densities, the LiDAR-generated topography lay, on average,
64 cm above the corresponding GCPs, with an r.m.s. error of 195 cm. The larger error under trees can be
seen in Figure 2d, though fortunately the example floodplain contains few large areas of woodland. Accurate
calculation of tree height is well documented, and assumes that pulses reflect from both the tree canopy
and the ground beneath (Naesset, 1997; Magnussen and Boudewyn, 1998). Tall and intermediate vegetation
heights are derived by subtracting the ground heights from the canopy returns, and are accurate to about 10%
of vegetation height.
As the LiDAR cannot provide bathymetry within the channel itself, channel bathymetry was generated
using 76 channel cross-sections measured at regular intervals along the 17 km reach. Although the alongreach position of each cross-section was known accurately, there was uncertainty in its across-reach position.
The best fit of a cross-section with the LiDAR topography was found by cross-correlation, allowing the crosssection to be moved along its length to find the position of maximum correlation. The channel bathymetry was
estimated using linear interpolation between adjacent cross-sections, and was then merged with the floodplain
topography. The main channel has an average maximum depth of 5 m and a width of 35–50 m.
The vegetation height map (Figure 2c) is partly corrupted by bands of increased height in areas of overlap
between adjacent LiDAR swaths. These are caused by systematic height errors between adjacent swaths that
increase height texture in overlap regions. The problem can be substantially reduced by the removal of heights
measured at large scan angles (Cobby et al., 2001). Unfortunately, the correction algorithm requires swaths
supplied as individual data files, which were unavailable for this test area. It is hoped that future surveys will
provide data in a format suitable for the correction to be applied.
MESH GENERATION
The flood model chosen for this research was TELEMAC-2D, a 2-D finite element model that has been
extensively tested and that solves the continuous shallow-water equations at each time step at a number
of discrete spatial nodes within the model domain (Bates et al., 1995). Figure 3 shows a typical triangular
finite-element mesh for the reach of the River Severn modelled here. The mesh consists of 5061 nodes and
9962 elements and was generated using the Cheesymesh algorithm (Horritt, 1998, 2000) with the channel and
domain boundaries automatically extracted from the LiDAR topography (Figure 2d). A structured grid is used
to represent the river channel to ensure that the elements are aligned to model effectively the flow physics
and to minimize numerical diffusion. The algorithm inserts a minimum of three elements across the channel
to represent the varying bathymetry and fluid velocity. Since the solution accuracy is strongly dependent on
element size relative to streamline curvature, it also produces channel elements of uniform angular deviation,
with shorter elements around tight meanders (Horritt, 2000). In contrast, the floodplain is represented by a
sparser unstructured mesh. This allows a dense mesh to be used in regions of high process gradient to achieve
solution accuracy while maintaining computational efficiency by keeping the total number of nodes reasonably
small. The only constraints to element size on the floodplain are the channel element size and a parameter
to ensure a smooth increase in element size away from the channel. In this paper, no attempt is made to
Copyright  2003 John Wiley & Sons, Ltd.
Hydrol. Process. 17, 1711– 1732 (2003)
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FLOODPLAIN FRICTION PARAMETERISATION
Figure 3. Finite element mesh. The top inset shows an example polygonal neighbourhood of an interior node (with vegetation class colours
from Figure 2b), and the bottom inset shows a polygon on a mesh edge
decompose the mesh to reflect topographic or structural features in the floodplain, but future application may
have to use meshes developed to reflect hydraulically significant linear features (hedges, ditches and small
channels, dykes) found on the floodplain; see Cobby et al. (in press).
CALCULATION OF NODE FRICTION FACTORS
The potential of 2-D flood models to specify a friction factor at each node of the model mesh is not currently
realized. A single value for the floodplain is generally specified, either by look-up tables or via a calibration
strategy, whereby the friction parameter is adjusted to gain the best fit between model predictions and
observations. LiDAR now offers accurate distributed vegetation height data in floodplains and, therefore, the
possibility of improved model performance by using a more physically based friction parameterization (Horritt,
2001). Flow resistance on a floodplain is a combination of the unvegetated surface roughness and that due to
vegetation protruding into the flow. As it is assumed that the latter will always dominate (Fathi-Moghadam
and Kouwen, 1997), it is the only component considered here.
For each mesh node, an instantaneous friction factor must be calculated at each time step, given the
frictional material in the neighbourhood of the node and the current water depth and flow velocity there. A
node’s neighbourhood is defined as a polygon whose vertices are the centroids of the elements surrounding
Copyright  2003 John Wiley & Sons, Ltd.
Hydrol. Process. 17, 1711– 1732 (2003)
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D. C. MASON ET AL.
the node (Figure 3). For nodes at the edge of the mesh, two additional vertices are positioned at the bisection
points of the lines joining the node with its two neighbouring edge nodes.
Sub-regions of connected regions in the vegetation height map are formed by intersecting the node polygon
map with the vegetation height map. Each sub-region in a polygon may contain either sediment or one of the
three vegetation height classes. If a sub-region contains vegetation then its region’s average vegetation height
is attributed to the sub-region.
A friction factor is first calculated for each sub-region, prior to constructing an average friction factor for
each polygon. Following the approach of Darby (1999), a ‘menu’ approach is adopted whereby a different
equation set is used to model flow resistance in a sub-region depending on the type of material in the subregion. For simplicity the menu was constructed to be specific to the test area being studied. Three different
sets of flow resistance equations were chosen for the menu, the first modelling sediment in unvegetated
channels, the second short vegetation, and the third tall and intermediate vegetation. The only vegetation
attribute required by the latter two equation sets is vegetation height.
Sediment
A channel survey of the River Severn near Montford Bridge (Darby and Thorne, 1996) at the start of the
reach revealed a coarse gravel bed (d84 D 88 mm). Following Darby (1999), the approach of Hey (1979)
based on 93 field data was used to calculate the Darcy–Weisbach friction factor f:
1
as Rh
D 2Ð03 log
3Ð5d
f
84
0Ð314
Rh
as D 11Ð1
Dmax
1a
1b
where as is a dimensionless shape correction factor, Rh is the hydraulic radius and Dmax the maximum depth
of flow in the cross-section.
Short vegetation
Short vegetation on the floodplain includes grasses and cereal crops, which are treated as flexible. When
water flows over flexible vegetation, it may bend and reduce in height. When this occurs its boundary
roughness may be substantially reduced. The drag force exerted on the water flow by the vegetation depends
on its flexural rigidity and stem density. The roughness height is not only related to properties of the vegetation,
but also to water flow velocity and depth. Kouwen and Li (1980), in experiments with flow over flexible
plastic strips, showed that the deflected vegetation height k is given by

1Ð59
MEI 0Ð25




k D 0Ð14 h 
2



h
where h (m) is vegetation height (measurable from the LiDAR), (N m2 ) is local boundary shear stress
and MEI is the product of stem density M and flexural rigidity in bending J, given by J D EI (where E is
the stem modulus of elasticity and I is the stem area’s second moment of inertia). The authors also showed
that Equation (2) was valid for a range of natural grasses up to 0Ð9 m high (see table 2 of Kouwen and Li
(1980)). It is difficult to measure the individual variables M, E and I because of the heterogeneity of natural
vegetation. However, the use of the combined term MEI for natural vegetation has been justified by Kouwen
(1988), who pointed out its compensating effect: if the number of stems M per unit area is increased, then
this causes a similar change in roughness to a corresponding increase in stiffness EI of individual elements.
Copyright  2003 John Wiley & Sons, Ltd.
Hydrol. Process. 17, 1711– 1732 (2003)
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FLOODPLAIN FRICTION PARAMETERISATION
Kouwen and Li (1980) calculate the friction factor f from the roughness height k using a semi-logarithmic
resistance relation:
y 1
n
D a C b log
3
k
f
in which a and b are fitted parameters that are dependent on the ratio of boundary shear velocity Ł (D /1/2 ,
where is water density) to a critical shear velocity Łcrit , where
Łcrit D min0Ð028 C 6Ð33MEI, 0Ð23MEI0Ð106 4
This variation of parameters a and b reflects the fact that, at low shear velocities, natural grasses will bend and
behave elastically; however, once the critical shear velocity is exceeded, they will break and lie prone. Values
of a and b as a function of Ł /Łcrit are given in table I of Kouwen (1988) (reproduced here as Table 1).
Of particular relevance to this study are values for vegetation that remains elastic (i.e. Ł /Łcrit 1), when
a D 0Ð15 and b D 1Ð85.
The product MEI cannot be measured directly using LiDAR. Of great significance for this study, however,
is the fact that MEI has been correlated with vegetation height for a range of growing and dormant grass
species in laboratory experiments carried out by Temple (1987) and Kouwen (1988, 2000):
319 h3Ð3
for growing grass
5
MEI D
25Ð4 h2Ð26
for dormant grass
Vegetation height h measured from LiDAR can thus be used as a surrogate for the product of the stem density
M and flexural rigidity EI. Equation (5) is valid for grasses up to 1Ð0 m high. The correlation between MEI
and grass height is very high (95%) for growing grasses, though somewhat less (83%) for dormant grasses.
Kouwen (1988) found that MEI values based on grass heights using Equation (5) correlated well with MEI
values calculated using the ‘board drop’ test (Eastgate, 1966; Kouwen, 1988). This involves holding a board
vertically with its bottom edge on the ground, then dropping it onto a vegetated surface to deflect the stems in
a manner similar to flowing water. If the height above ground of the top edge of the board is measured when
the board has come to rest, this height can be related to MEI using standard calibration curves (Kouwen,
1988). The method has practical implications, because it may be used to estimate stiffness coefficients for
use in Equation (5) for a range of natural grasses. Currently, Equation (5) is valid only for grasses for which
it has been calibrated. An extension of these calibrations to estimate MEI values for the diverse range of
grasses and cereal crops found on a typical UK floodplain is required. A similar extension is required for
Equation (2) determining roughness height k.
The above treatment is valid only for submerged grasses, but Kouwen and Unny (1973) point out that the
approach can still be used for non-submerged vegetation provided that surface roughness height k is set to
the water depth yn .
Tall and intermediate vegetation
Trees and hedges in the floodplain often have large friction factors and can dissipate a great deal of flow
energy, despite occupying a small proportion of the floodplain area. Whereas hedges, grass and cereal crops
Table I. Values of a and b (after Kouwen (1988) Reproduced by permission of IAHR
Publications)
Condition
Classification
Criteria
a
b
Erect
Prone
Prone
Prone
Ł /Łcrit 1Ð0
1Ð0 < Ł /Łcrit 1Ð5
1Ð5 < Ł /Łcrit 2Ð5
2Ð5 < Ł /Łcrit
0Ð15
0Ð20
0Ð28
0Ð29
1Ð85
2Ð70
3Ð08
3Ð50
1
2
3
4
Copyright  2003 John Wiley & Sons, Ltd.
Hydrol. Process. 17, 1711– 1732 (2003)
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D. C. MASON ET AL.
may be considered a ubiquitous feature of UK floodplains, stands of forest will generally be found above
ground at risk of flooding. However, it is common to find banks of a river lined with trees, a location that
may be hydraulically significant.
Friction factors for trees and hedges were calculated using the method of Fathi-Moghadam and Kouwen,
who investigated flow through non-submerged non-rigid vegetation in the form of coniferous trees (FathiMoghadam and Kouwen, 1997; Kouwen and Fathi-Moghadam, 2000). They showed that the assumption of
rigid vegetation can lead to large errors in the estimation of roughness, and that it was necessary to take
the flexibility of the foliage into account. The authors extended their original study to include a variety of
coniferous trees having a wide range of flexibility, testing small saplings 0Ð3 m high in a flume and full-scale
trees 2–4 m high in air.
They observed that the measured drag force had a linear relationship with flow velocity, unlike the squared
relationship for rigid stems that is often employed. This was due to streamlining of the foliage and, therefore,
a reduction in the momentum absorbing area (MAA) of the vegetation as flow velocity increased. A second
major effect was due to variation in MAA with flow depth. Plant foliage and stems were regarded as being
uniformly distributed in the horizontal plane, but a linear increase of foliage area (and hence MAA) with
height was assumed. In verification of this, the observed drag force was found to increase linearly with flow
depth. Although these two effects were the dominant ones, there were also secondary effects associated with
tree rigidity, shape and MAA varying between different tree species. Stem drag was considered as rigid
roughness, but was much less than the drag due to foliage.
According to Kouwen and Fathi-Moghadam (2000), the friction factor for the non-submerged condition
(where yn /h 1) is


0Ð46


 V 

f D 4Ð06  

 E 
yn
h
6
where V is flow velocity, E is the tree’s modulus of elasticity, accounts for deformation of the tree as a
result of increasing flow velocity and is the density of water.
Although our test area contained mainly deciduous trees and hedges, Kouwen and Fathi-Moghadam (2000)
point out that while application of Equation (6) to tree species other than coniferous trees may have some error,
the estimated friction factor is still expected to be more accurate than available methods that do not consider
the flexibility and deflection of trees. Therefore, values of f for all trees and hedges in our test area were
assumed to be those for white pine, lying in the mid-range of the coniferous tree species considered, and were
calculated using Equation (6), deducing parameters E and from data given by Kouwen and Fathi-Moghadam
(2000). Equation (6) assumes that vegetation just covers the ground in plan view, and this assumption is also
made for the vegetation within tree and hedge regions in the LiDAR segmentation.
Calculation of average friction factor for a node
An average instantaneous friction factor is calculated for each mesh node neighbourhood at each model
time step based on the friction factors of each sub-region contained in the node. The Darcy–Weisbach friction
factor f is linked to the drag force F over an area a of uniform friction for a flow velocity v by
F D fav2 /8
7
Considering a floodplain node’s polygon covered by k regions of area ai and mean height hi (i D 1, . . . , k)
from different vegetation classes, the total force Fe impeding the flow over the area is the sum of the individual
forces Fi due to each vegetation type
n
Fi
8
Fe D
iD1
Copyright  2003 John Wiley & Sons, Ltd.
Hydrol. Process. 17, 1711– 1732 (2003)
1721
FLOODPLAIN FRICTION PARAMETERISATION
Substituting Equation (7) into Equation (8) gives an effective friction factor fe for the node:
n
fe D
fi ai
ae
9
iD1
A channel node would contain only one class, namely sediment. Note that Equation (9) considers only current
strength and ignores the effect of current direction, e.g. emergent vegetation, such as a hedge, oriented in the
direction of the current will have a lower friction factor than one perpendicular to the current due to sheltering
effects (Nepf, 1999).
MODELLING STUDIES
Modelling studies were performed over the Bicton reach of Figure 2 using TELEMAC-2D (Anon, 1998).
The reach has a low longitudinal slope of 2 ð 104 (Darby and Thorne, 1996). The modelling studies were
based on a 50 year flood event from October 1998. The hydrograph for this event at the gauging station at
Montford Bridge at the upstream end of the reach is shown in Figure 4.
A RADARSAT SAR image with pixel size 12Ð5 ð 12Ð5 m2 acquired during the flood at 18:00 hours on
30 October 1998 was used to provide an observed flood extent against which to validate the predicted
flood extent (Figure 5). The SAR flood extent was extracted using the automatic image processing technique
described by Horritt et al. (2001), which uses a statistical active contour model to delineate a flooded region
in the SAR image as a region of homogeneous speckle statistics generally having lower backscatter than the
unflooded surroundings. Horritt et al. (2001) compared the automatic SAR waterline delineation with that
from simultaneously acquired aerial photography, and found that 70% of the SAR waterline coincided with
the aerial photography waterline to within 20 m. This is relatively small compared with the average mesh
node spacing of ca. 70 m. The main error was due to unflooded vegetation giving similar radar returns to
open water. Some error was also due to emergent vegetation at the flood edge. The SAR may place the
flood edge at the boundary between totally submerged and beginning-emergent vegetation because emergent
vegetation may give higher backscatter than open water due to reflection from the canopy. However, the true
flood edge is at the position where the vegetation becomes totally emergent. The RADARSAT flood extent
used in this study was manually edited to remove most segmentation errors, as determined by an experienced
operator’s interpretation of the SAR image.
Model runs were made assuming steady-state conditions over the modelled reach, a reasonable assumption
given its short length and the relatively slowly changing hydrograph. The average wave travel time through
Figure 4. Hydrograph at Montford Bridge for the flood event considered. The vertical line marks the SAR overpass time at 18:00 hours on
30 October 1998
Copyright  2003 John Wiley & Sons, Ltd.
Hydrol. Process. 17, 1711– 1732 (2003)
1722
D. C. MASON ET AL.
Figure 5. SAR image of the flood event in October 1998. (Reproduced by permission. RADARSAT-1 data  Canadian Space Agency/Agence
Spatiale Canadienne 1998. Received and processed by DERA, West Freugh, UK. Distributed under licence from RADARSAT International).
The darker areas around the river channel show the extent of the flood (lighter indicates larger backscatter)
the Bicton reach is about 6–8 h and over such a period around the time of the SAR overpass the flow varies
by less than 10%. This is within the error of the gauging station record for a large overbank flood. Although
the flow rate was monitored at only the upstream end of the reach, the assumption also allowed a downstream
boundary condition to be set. An instantaneous water surface elevation of 51Ð9 m ODN at the downstream end
of the reach was estimated by intersecting the flood extent observed there by the SAR with the LiDAR-derived
topography. The flow rate at the time of image acquisition at the upstream end of the reach was measured as
308 m3 s1 , providing the upstream boundary condition.
A constant viscosity turbulence model was assumed in model runs with a velocity diffusivity of 0Ð1 m2 s1
(Anon, 1998), though results proved fairly insensitive to this parameter. Partially dry elements were detected
and the spurious free-surface gradient terms generated in such areas were corrected using the algorithm
proposed by Hervouet and Janin (1994). For each mesh node, at each time step, a friction factor f was
calculated according to the menu of equation sets described. For short vegetation, at the first time step an
initial estimate of boundary shear stress was made using
D yn S
Copyright  2003 John Wiley & Sons, Ltd.
10
Hydrol. Process. 17, 1711– 1732 (2003)
1723
FLOODPLAIN FRICTION PARAMETERISATION
(where (N m3 is the weight density of water and S is bed slope) to obtain the roughness height k using
Equation (2). On subsequent time steps was calculated using
D fv2 /8
11
where f is the friction factor obtained on the previous time step. For all nodes, the friction factor f was
converted to Manning’s n values for use in TELEMAC-2D using the relation
yn1/3
12
nD f
8g
where g is gravitational acceleration. This is appropriate for uniform 1-D flow in a wide shallow channel,
where the hydraulic radius Rh can be assumed equal to normal flow depth yn (Fathi-Moghadam and Kouwen,
1997) and is assumed valid for this case.
It was found that, for short vegetation, the values of surface roughness height k calculated from Equation (2)
often proved to be greater than the vegetation height h. From the definition of k as deflected vegetation height
this should be impossible. This was probably due to the fact that Equation (2) was derived by Kouwen and
Li (1980) using slopes often substantially greater than the low slope (2 ð 104 ) within the Bicton reach. As
a result, the bed shear stress D yn S is lower for Bicton than for the experimental slopes used, leading
to large values of k. Ideally, a version of Equation (2) valid for such low slopes needs to be derived in
further flume studies. Such studies should also consider developing versions of Equations (2) and (5) valid
for agricultural crops as well as natural grasses. The interim solution adopted here was to limit k to h if
Equation (2) predicted a k value greater than h. This probably underestimates friction somewhat, because,
from Equation (3), if k is limited then f is also limited.
It is known that bankfull discharge at Montford Bridge at the start of the reach is approximately 165 m3 s1
(Darby, 1999). It was assumed that this was also the bankfull discharge for the rest of the reach. An initial
steady-state run with this as the upstream boundary condition confirmed that the model did in fact simulate
this observed behaviour with no significant floodplain inundation. This confirmed that the channel dimensions
and friction factors were approximately correct. The average water surface elevation across the entire reach
for this simulation was 53Ð78 m ODN.
Figure 6a and b shows floodplain water depths and spatially varying bottom friction for a run assuming
steady-state conditions with an input flow rate of 308 m3 s1 (equivalent to the upstream discharge at the time
of the SAR overpass). The average water surface elevation was 54Ð79 m ODN, implying an average floodplain
water depth of 1Ð01 m. Figure 6b exhibits Manning’s n values varying from 0Ð02–0Ð03 in the channel to up
to about 0Ð7 on the floodplain. By comparison with the vegetation height and topography maps of Figure 2c
and d, the higher n values occur where water depths are low (e.g. at the flood edge) and/or where vegetation
is emergent. Few nodes dominated by short vegetation proved to have bottom shear velocities that exceeded
the critical shear velocity of Equation (4), implying that the vegetation was behaving elastically.
Figure 6c shows the model and SAR-derived flood extents superimposed on the bottom topography,
allowing a qualitative comparison to be made. Table II, however, gives a more rigorous quantitative
Table II. Comparison of SAR and model flood edge heights along corresponding sections of waterline, using variable
floodplain friction
Length of SAR pixels Average slope
Model
Model
SAR
SAR
Correlation
combined (equivalent) perpendicular waterline
waterline
waterline
waterline
coefficient
sections
to waterline
average
standard
average
standard
(m)
height (m) deviation (m) height (m) deviation (m)
2375
190
0Ð040
Copyright  2003 John Wiley & Sons, Ltd.
54Ð649
1Ð51
54Ð651
1Ð79
0Ð89
t0
Probability
t > t0
0Ð03
0Ð98
Hydrol. Process. 17, 1711– 1732 (2003)
1724
D. C. MASON ET AL.
BOTTOM
FRICTION
(b)
(a)
WATER DEPTH (M)
2.000000
1.857143
1.714286
1.571429
1.428571
1.285714
1.142857
1.000000
0.857143
0.714286
0.571429
0.428571
0.285714
0.142857
0.000000
318000
317000
316000
315000
314000
0.763627
0.710582
0.657537
0.604493
0.551448
0.498403
0.445358
0.392314
0.339269
0.286224
0.233179
0.180134
0.127090
0.074045
0.021000
318000
317000
316000
315000
314000
342000 343000 344000 345000 346000 347000
342000 343000 344000 345000 346000 347000
(c)
HEIGHT (M)
80.000000
77.247147
318000
74.494293
71.741417
68.988571
66.235718
317000
63.482861
60.730000
57.977139
316000
55.224289
52.471432
49.718571
46.965710
315000
44.212860
41.459999
314000
342000
343000
344000
345000
346000
m3
347000
s1 .
Figure 6. Variable-friction model run outputs for an input flow rate of 308
(a) Floodplain water depth (m) (axes are British National
Grid coordinates in metres). (b) Bottom friction (Manning’s n). (c) Model (black) and SAR (red) flood extents superimposed on bottom
topography
comparison of the SAR and model flood edge heights along selected sections of waterline. These sections are
in areas where the slope perpendicular to the waterline is as low as possible, the SAR extent is unambiguous,
the vegetation is generally short, and the downstream boundary is not close. In these sections (identified by
the letters A–E shown in Figure 6c) one might expect SAR-predicted water surface elevation errors due to
the approximately one pixel inaccuracy in the determination of the SAR waterline position to be minimized.
Each section was 200–740 m in length and contained 16–60 SAR pixels, covering over 2Ð3 km in all. In
order to minimize the effects of inaccuracy in the SAR flood edge heights, SAR and model flood edge heights
at corresponding positions along the reach were compared using a paired Student t-test in which the data from
all five sections were combined into a single statistic for the whole reach. The null hypothesis tested was that
Copyright  2003 John Wiley & Sons, Ltd.
Hydrol. Process. 17, 1711– 1732 (2003)
1725
FLOODPLAIN FRICTION PARAMETERISATION
there was no significant difference between the means of the SAR and model waterline heights. Student’s t
value for a two-sided paired t-test assuming normally distributed samples is given by
13
t D 1 —2 / [s1 2 C s2 2 2s1 s2 /n]
where 1 and 2 are the means of the SAR and model flood edge heights, s1 and s2 are their standard
deviations, is the correlation coefficient between corresponding SAR and model heights, and n is the
total number of pixels considered over the reach. Use of the paired t-test takes into account the fact that
corresponding SAR and model flood edge heights will be correlated due to the gradual drop in height along
the reach. However, the height differences at corresponding points are uncorrelated, as is assumed in the
test. Table II shows that no significant difference between the SAR and model flood edge mean heights was
detectable at the 5% significance level, implying that, for this particular event, the modelled flood extent
agrees in most places with the SAR flood extent.
Figure 7 shows model and SAR-derived flood extents superimposed on the bottom topography for the
parameters of the run of Figure 6, but this time using a temporally and spatially constant Manning’s n value
of 0Ð06 everywhere in the floodplain to allow comparison with the variable friction results. The constant
value was chosen to be representative of that for a UK floodplain containing a typical mix of grasses, crops,
hedges and trees (Chow, 1959; Bates et al., 1998; Horritt and Bates, 2001). Table III compares the SAR
and model mean waterline heights for the positions used in Table II, averaged over the reach. Again, no
significant difference can be detected at the 5% level. However, the average water surface elevation for the
constant-friction model run was 54Ð65 m ODN, which is 0Ð14 m lower than for the variable-friction model
run. It is probably unrealistic to expect a height difference in modelled water surface elevations averaged over
the whole reach to be reflected exactly in the mean height difference between the constant friction model and
HEIGHT (M)
80.000000
318000
77.247147
74.494293
71.741417
68.988571
317000
66.235718
63.482861
60.730000
316000
57.977139
55.224289
52.471432
49.718571
315000
46.965710
44.212860
41.459999
314000
342000
343000
344000
345000
346000
347000
Figure 7. Constant floodplain friction model (black) and SAR flood extents (red) superimposed on bottom topography, for an input flow
rate of 308 m3 s1
Copyright  2003 John Wiley & Sons, Ltd.
Hydrol. Process. 17, 1711– 1732 (2003)
1726
D. C. MASON ET AL.
Table III. Comparison of SAR and model flood edge heights along corresponding sections of waterline, using constant
floodplain friction (Manning’s n D 0Ð06)
Length of SAR pixels Average slope
Model
Model
SAR
SAR
Correlation
combined (equivalent) perpendicular waterline
waterline
waterline
waterline
coefficient
sections
to waterline
average
standard
average
standard
(m)
height (m) deviation (m) height (m) deviation (m)
2375
190
0Ð040
54Ð60
1Ð51
54Ð65
1Ð79
0Ð88
t0
Probability
t > t0
0Ð76
0Ð45
SAR flood edge heights sampled over only 7% of the reach waterline. One reason a difference cannot be
detected is the relatively high slope perpendicular to the waterline (0Ð04 averaged over all five sections) given
the grid cell size of 12Ð5 m onto which the SAR and model heights are mapped. This causes the standard
deviations of both mean heights to be relatively high, reducing the sensitivity of the t-test. This is a somewhat
common problem for this type of modelling, as images and data tend only to be acquired for large floods at
peak discharges when the valley floor is mostly filled. Such data are thus not as discriminatory in terms of
hydraulic models as would be the case with a more modest size event.
The 0Ð14 m fall in average water surface elevation between variable- and constant-friction model runs is
significant in terms of the implied change in flow rate for the floodplain width (up to 500 m) being considered
here and for practical studies involved with calculating the overtopping of structures. As, here, we employ
a steady-state simulation, this is manifest as a change in model predicted velocity. Figure 8a shows that the
variable-friction model run has low floodplain current magnitudes (0Ð1–0Ð4 m s1 that decrease rapidly away
from the channel due to higher friction nearer the flood edge. However, the constant-friction model run has
higher and more uniform floodplain currents of 0Ð2–0Ð6 m s1 across the floodplain (Figure 8b). It should
thus be possible to discriminate between these two model parameterizations using additional validation data
from current meters suitably positioned in the floodplain flow.
Whilst the relatively high slopes at the waterline have reduced the discriminating power of the SAR data
for this particular flood event, the potential of the method can be illustrated using a lower input flow rate.
For this floodplain, the latter implies not only lower water depths (resulting in higher friction) but also lower
slopes at the waterline, as the flood extent lies within the low-lying floodplain rather than towards adjacent
hillslopes and terraces. In this case it is not possible to validate the model waterline heights using the SAR
data, but the waterline heights for model runs using variable and constant (Manning’s n D 0Ð06) floodplain
friction coefficients can be compared directly. Figure 9 shows the variable and constant floodplain friction
model flood extents obtained using an input flow rate of 240 m3 s1 , approximately equivalent to a 5 year
flood discharge (Darby, 1999). The average water surface elevations for variable- and constant-friction model
runs were 54Ð34 m ODN and 54Ð19 m ODN respectively. The average slope perpendicular to the waterline
was 0Ð018, compared with 0Ð040 for an input flow rate of 308 m3 s1 . Differences in the flood extents are
now visible in areas of low slope, such as B. The variable and constant floodplain friction mean waterline
heights are compared in Table IV to quantify differences seen by eye at the positions identified in Figure 9.
A highly significant height difference has been detected.
In the above test using variable floodplain friction it has been assumed that the LiDAR data were collected
at the same time as the SAR. The LiDAR data were actually collected in June 1998, when there was probably
significantly more floodplain vegetation present than at the time of the flood in October 1998. A further
model run was carried out using the parameters of the run of Figure 6, including variable friction, but now
assuming that short vegetation was 0Ð1 m high everywhere. The average water surface elevation was 54Ð65 m
ODN, identical to that of the constant-friction model run. The submerged areas were also similar. If this
reduced short vegetation height is correct, the constant floodplain friction model would appear to be a good
approximation to the variable-friction model for this particular flood event.
Copyright  2003 John Wiley & Sons, Ltd.
Hydrol. Process. 17, 1711– 1732 (2003)
1727
FLOODPLAIN FRICTION PARAMETERISATION
(a)
CURRENT (M/S)
0.710000
318000
0.660000
0.610000
0.560000
317000
0.510000
0.460000
0.410000
316000
0.360000
0.310000
0.260000
315000
0.210000
0.160000
0.110000
314000
0.060000
0.010000
342000
343000
344000
345000
346000
347000
(b)
CURRENT (M/S)
0.710000
318000
0.660000
0.610000
0.560000
317000
0.510000
0.460000
0.410000
316000
0.360000
0.310000
0.260000
315000
0.210000
0.160000
0.110000
314000
0.060000
0.010000
342000
343000
Figure 8. Floodplain current magnitudes (m
Copyright  2003 John Wiley & Sons, Ltd.
344000
s1 345000
346000
m3
347000
s1
for an input flow rate of 308
for (a) variable- and (b) constant-friction model runs.
The arrow shows the direction of water flow
Hydrol. Process. 17, 1711– 1732 (2003)
Copyright  2003 John Wiley & Sons, Ltd.
2560
205
0Ð018
54Ð43
1Ð19
54Ð32
1Ð17
0Ð97
Length of
SAR pixels Average slope
VariableVariableConstantConstantCorrelation
combined
(equivalent) perpendicular
friction model
friction model
friction model
friction model
coefficient
to waterline waterline average waterline standard waterline average waterline standard
sections (m)
height (m)
deviation (m)
height (m)
deviation (m)
6Ð28
t0
<108
Probability
t > t0
Table IV. Comparison of variable- and constant-friction model flood edge heights along corresponding sections of waterline for an input flow rate of 240 m3 s1
1728
D. C. MASON ET AL.
Hydrol. Process. 17, 1711– 1732 (2003)
1729
FLOODPLAIN FRICTION PARAMETERISATION
HEIGHT (M)
80.000000
318000
77.247147
74.494293
71.741417
68.988571
317000
66.235718
63.482861
60.730000
57.977139
316000
55.224289
52.471432
49.718571
315000
46.965710
44.212860
41.459999
314000
342000
343000
344000
345000
346000
347000
Figure 9. Variable (red) and constant (black) floodplain friction model flood extents overlayed on bottom topography, for an input flow rate
of 240 m3 s1
Following Darby (1999), the system may also be used to simulate the effects of different scenarios of
vegetation cover on floodplain inundation for a given input flow rate. Two scenarios of relevance have been
considered for the case of the 50 year flood event. The first involves increasing the height of short vegetation
from 0Ð1 to 2Ð0 m while maintaining its extent as before. Floodplain grasses 2Ð0 m high will be largely
emergent and flooded on average to a depth of 1 m. This is an extreme case, which is probably outside the
bounds of validity of Equation (2) in many areas, but which can serve to provide an upper limit on flood
inundation. It was found that, compared with the previous model run with grass 0Ð1 m high, the average
water surface elevation with 2Ð0 m high grass was 54Ð82 m ODN, a rise of 0Ð17 m, and the area inundated
increased by 3Ð5%, from 259 ha to 268 ha, a relatively small effect.
The second scenario investigated the effect of hedges on floodplain inundation. Whereas field crops
may change on an annual basis, hedgerows remain part of the underlying skeleton of the landscape and
present an (albeit limited) area of relatively high friction to floodwater. The variable-friction model run of
Figure 6 was repeated with all the hedges replaced with 0Ð1 m high grass. However, the resulting change
in the average water elevation was negligible. This is probably due to the fact that hedges occupy such
a small area (5%) of the floodplain. This is not to say that there may not be significant local water level
differences across individual hedges, but these cannot be resolved using the current mesh. This question is
considered in more detail by Cobby et al. (in press), in which a method of decomposing the mesh to reflect
floodplain vegetation structures, such as hedges, having different frictional properties to their immediate
surroundings is developed. Large elements in the floodplain are also decomposed if they contain significant
topographic features having high height curvatures. This approach makes it possible to predict velocity and
depth variations around such features, which may eventually allow the prediction of the subsequent erosion or
Copyright  2003 John Wiley & Sons, Ltd.
Hydrol. Process. 17, 1711– 1732 (2003)
1730
D. C. MASON ET AL.
deposition patterns resulting from these variations. This moves flood models closer to realizing the potential
of the high data density generated by LiDAR. The approach is compared with the computationally more
efficient one used here, of sampling topography and friction values onto relatively large elements in the
floodplain.
CONCLUSIONS
The study has illustrated how vegetation heights can be derived from airborne LiDAR data, and how these
heights can subsequently be converted into spatiotemporally varying friction factors at each node of the model
mesh in the floodplain. The variable-friction model has the considerable advantage that it obviates the need
for the unphysical fitting of floodplain and channel friction factors required in the constant-friction model.
This means that it should be possible to use the same model with different input data to predict accurate flood
extents for different flood events and different reaches; this is not possible with the constant-friction model,
which would, in general, require recalibration.
From the modelling studies it can be concluded that, at least for the flood event studied, the method of
estimating variable floodplain friction using vegetation heights derived from LiDAR data produces a modelled
flood extent that agrees in most places with the extent observed from SAR data. This gives some confidence
that the method works, though it obviously needs to be tested for other flood events and on other floodplains of
different character to the River Severn. The role of floodplain and bank friction may be much more important
for other reaches and events where floodplain flow is more significant, and in those cases the ability to generate
distributed friction maps (e.g. Horritt, 2000) based on vegetation heights will represent a significant advance
in flood inundation modelling.
For this flood event, little difference could be detected between the SAR flood extent and that of the
constant floodplain friction model run, implying that the simpler constant floodplain friction model is already
a good approximation for this reach. This conclusion is reached irrespective of whether the short vegetation
at SAR acquisition time was the same as at LiDAR acquisition time or 0Ð1 m high everywhere. If the former
were true, then the 0Ð14 m difference in average water surface elevation between the variable and constant
floodplain friction model runs could not, in any case, be detected due to the insufficient resolution of the SAR
given the floodplain slopes at the waterline for this event. This uncertainty does highlight the desirability of
acquiring LiDAR data on vegetation close to the time of the flood.
The potential of SAR for validating model flood extents was illustrated using a lower input flow rate, when,
assuming that the constant floodplain friction model extent could be used as a surrogate for the SAR extent,
significant differences could be detected between this and the extent predicted using the variable-friction
model. This suggests that for other events and topographic settings the method may be more significant, and
it is clear that the current practice of only acquiring inundation data for large, valley-filling events is unhelpful
in terms of hydraulic model validation.
From the simulations performed, it can also be concluded that raising the height of floodplain grasses from
0Ð1 to 2Ð0 m has relatively little effect on water elevation or inundation extent, and that, rather surprisingly,
removing the hedgerows has even less effect (at least non-locally).
A number of topics for future work may be suggested:
(1) The use of an airborne rather than a satellite SAR during a flood event would give much higher
spatial resolution and hence improved power for validation. This would also allow the possibility of obtaining
a sequence of SAR images during a flood rather than the single sample typically achieved at present. A
further advantage of an airborne SAR is that it could be made multi- rather than single-frequency, with
polarization information being acquired; this would make possible better flood extent delineation under
emergent vegetation, as different frequencies will be scattered differently by the vegetation canopy. An
airborne LiDAR system that allowed simultaneous acquisition of multi-spectral scanner data would also be
useful for measuring vegetation type and stem density, as well as vegetation height.
Copyright  2003 John Wiley & Sons, Ltd.
Hydrol. Process. 17, 1711– 1732 (2003)
FLOODPLAIN FRICTION PARAMETERISATION
1731
(2) It is important to carry out further experimental flume studies to measure friction factors for the types
of grasses, crops, hedges and deciduous trees found in UK floodplains of low slope, such as that at Bicton, in
an extension of the previous work of Kouwen and Li (1980), Kouwen (1988), Kouwen and Fathi-Moghadam
(2000) and Wu et al. (1999). In addition, although the empirical friction formulation used here is a good
starting point, it can probably be bettered; and the availability of LiDAR data opens the door for further
theoretical and experimental work to determine friction as a function of canopy type and height. Such work
might also include consideration of the theoretical basis of the roughness parameters employed. There is
also a need to understand the contribution of the form friction losses due to microtopography compared with
vegetation friction losses, and the mesh decomposition approach of Cobby et al. (in press) may be appropriate
here. The main aim of this paper has been to illustrate how LiDAR can be used to estimate a spatiotemporally
varying bottom friction, rather than to develop a new friction formulation.
(3) The SAR flood extent is currently determined solely on the basis of the satellite image. As a result, SAR
waterline heights can vary quite substantially locally along the reach. The usefulness of SAR for validating the
model flood extent could be considerably improved by constraining the SAR waterline using the topography
and vegetation heights derived from the LiDAR data. As with the model waterline, the height of the SAR
waterline should be constrained to change only slowly along a reach.
(4) Conditional on obtaining a more discriminating validation data set, one could also explore the extent
to which otherwise redundant sub-grid-scale topographic data could be used to enhance the representation of
dynamic wetting and drying (Bates and Hervouet, 1999; Defina, 2000; Bates, 2000). The key question here
is which topographic features need to be treated explicitly at the grid scale and which, more homogeneous,
features can be treated statistically at the sub-grid scale.
ACKNOWLEDGEMENTS
This work was funded under UK Natural Environment Research Council CONNECT-B grant GR3/CO 030.
Thanks are due to the UK Environment Agency for supplying the LiDAR and RADARSAT data, and to
Infoterra for CASE student support.
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