International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
resurgence or misclassified pixels of the SAR imagery. The
latter can be partially removed after confronting the classified
image with photographs taken during the event. A further
evaluation of the flood map can be achieved by combining the
resulting image with a high resolution digital elevation model in
order to derive the water elevation at each cross section. By
comparing the profile of the water line with the elevation of the
river bed, doubtful values can be outlined and eventually be
removed from the reference data used during calibration.
d.
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Figure 3. Three probability classes of flooding are defined
3.2 Flood propagation modelling
It is nowadays commonly accepted that, once riverbank
overtopping occurs, river flow becomes two-dimensional. As
2D inundation models become more readily available, the
calibration based on flood maps derived from earth observation
data will become more popular. It is somewhat surprising that
despite the obvious limitations in ID model formulation, it has
been shown that in some river reaches simple 1D models and
the more sophisticated 2D models performed equally well
(Horritt and Bates, 2002). Computational advantages therefore
suggest that ID models should be used whenever the
topography of the floodplain allows considering the 1D river
flow hypotheses.
The widely used 1D HEC-RAS model is used in the present
study. This model requires a minimal amount of input data and
computer resources and is thus very easy to use. The unsteady
flow model UNET, which is part of HEC-RAS, solves the full
ID St Venant equations for unsteady open channel flow. The
required input data comprises the topographical description of
adjacent river and floodplain cross sections, the dimensions of
hydraulic structures and the boundary conditions at the
upstream and downstream end of the river reach. The
description of the flood propagation is based on the commonly
used Manning-Strickler formula which means that three
roughnesses (one for the channel and two for the floodplains)
are the free parameters that need to be calibrated in order to
minimise the difference between simulations and observations.
Nearly all one-dimensional and quasi two-dimensional flood
propagation models use Manning's equation to estimate
empirically the friction slope (Pappenberger et al., in press).
Downstream of Luxembourg-city, the HEC-RAS model was set
up using 74 cross-sections that describe the channel and
floodplain geometry. These data are extracted in GIS based on a
high resolution, high accuracy DEM. The latter was obtained by
combining the data describing the ground surveyed cross-
sections and the floodplain data obtained by airborne laser
altimetry. The inflow hydrograph of the January 2003 flood
event constitutes the upstream boundary. At the downstream
end of the river reach, the friction slope is set to the average
channel slope. Assuming normal flow, the Manning equation
then allows calculating for each time step the water height
which is used as downstream boundary condition.
Nowadays, connections between 1D hydraulic models and
Geographical Information Systems (GIS) allow for the accurate
2D mapping of simulated inundations. Hence, the comparison
of these modelled flood extents with remotely sensed flood
areas has become straightforward. However, the needed export
of the model results into GIS makes that this remains a very
time consuming task. As a matter of fact, in the present study,
where a large number of computational runs were carried out,
the distributed 2D inundation data are therefore processed in
order to become compatible with 1D model calibration and
evaluation. Therefore, the x and y coordinates at the
intersection of the digitised flood boundary and each of the
river cross sections considered in the model formulation, are
extracted in the GIS environment. Next, for each model run and
at each cross section, the distance between the simulated and
the radar derived flood extent is computed and used to
determine the likelihood of the underlying parameter set. Point
measurements of stage and travel time do not need to be
transformed prior to ID model calibration and evaluation.
3.3 Model calibration
Remote sensing data sets (ERS-2 SAR and Envisat ASAR) and
high water marks are used for calibration. These reference data
have in common that they are relatively uncertain. Hence, fuzzy
measures are most appropriate to reflect this noise in the data
sets. The only condition a fuzzy membership function
describing the likelihood of a given parameter set must satisfy
is that it must vary between 0 and 1 (Freer at al., 2004). Al
those cross sections where high water marks are available, a
fuzzy product definition of the performance measure (PM) was
used, having the following form of trapezoidal membership
function (Equation 1):
: 3t a<x<h
L|w (ejr, .w, )]- L bsrse (1)
fe! m e&x&d
Oi xlsx
where M(a|v,.w,.) indicates the model, conditioned on input
data Y and observations Wy. For each cross section i, x is the
distance between the simulated water level and the surveyed
high water mark. The parameters a, b (in this study -0.5 and 0.5
meters) define the core and the parameters c, d (in this study
-1.5 and 1.5 meters) define the support of the trapezoidal
membership function. The core defines the range of simulated
water levels where the parameter set is credited with the highest
possible likelihood value. The support is the range of water
levels where we have a non-zero membership value. The
performance measure of this model is given by the product of n
fuzzy measures (n is the number of cross sections where HW is
available). The maximum possible PM is I.
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