Environmental Engineering Reference
In-Depth Information
Model performance based on water levels
it allows one to express one's belief in a pixel being
flooded and assign a performance value to a sim-
ulation that predicts the pixel as flooded accord-
ingly (Matgen et al. 2004; Pappenberger
et al. 2006). Additionally, such an approach may
give insights into the effects of different model
parameters on acceptability of model performance
(Schumann et al. 2007b).
Visually illustrating uncertainty in model
performance may be a difficult task given the
'fuzziness' of the information content and the com-
plex model parameter interactions when dealing
with multiple model simulations. Nevertheless,
there have been a few notable attempts to output
uncertain flood maps. Romanowicz et al. (1996) pro-
posed to derive a 'probability' map by:
Despite the fact that some authors have demon-
strated that water depth might constrain the
uncertainty in flood inundation models more
efficiently than binary patterns (e.g. Werner
et al. 2005; Mason et al. 2009; Schumann
et al. 2008b), studies that refer to the use of
remote-sensing water levels in the model calibra-
tion or validation processes are at present very
limited (Schumann et al. 2007b, 2008b; Hostache
et al. 2009; Mason et al. 2009). Possible reasons for
this include the greater data-processing
skills involved in water level retrieval and also
the lack of precision often associated with indi-
rectly retrieved water levels. Moreover, although
directly retrieved water levels may possess the
desired accuracy, they often lack the required
spatial resolution. In the case of indirect measure-
ments the inaccuracy has largely been the result of
a combination of uncertain flood boundary
position and DEMs that are inappropriate for the
scale of the river reach under study. However, this
situation has considerably improved with the
availability of LIDAR and recently developed in-
novative stage retrieval techniques (as described
earlier), and this improvement is likely to contin-
ue with the newly launched higher-resolution
SAR sensors.
Water stages may be used to define additional
flood model parameter classes according to differ-
ent magnitudes of model error (Schumann
et al. 2007b). This highlights the importance of
model evaluation at the local scale. In a similar
approach, Mason et al. (2009) used the Student's
t-test on the error information between SAR-
derived waterlines and modelled ones to define
model performances with an a priori defined
uncertainty level. Another useful implementation
is to use the uncertainty associated with water
levels to set a spatially continuous acceptability
interval (Beven 2006) inside which model simula-
tions are required to fall (see Schumann
et al. 2008b; Hostache et al. 2009). This evaluation
procedure allows the modeller to gain insights of
the model functioning at different spatial scales
(Schumann et al. 2008b).
X
L
i
w
ij
X
i
RCM
j
¼
ð
11
:
1
Þ
L
i
i
in which L
i
is the weight for each simulation i,and
the simulation results for the j
th
model element
(e.g. computational cell or node) is w
ij
¼
1forwet
and w
ij
¼
0 for dry. The weight can be based on
normalized performance measures, which are de-
rived from maps conditioned on remotely sensed
information. RCM
j
is the relative confidence mea-
sure for each cell j, which expresses a belief that an
uncertain prediction is a consistent representation of
the system behaviour.
Horritt (2006) addressed the issue by exploiting
the spatial nature of floods and computing model
precision and accuracy over the model domain. A
precise map will contain large areas that are clas-
sified as definitely dry or wet, and few areas of
probability around 0.5. The precision of the map
can therefore bemeasured by the entropy - defined
as C in Horritt (2006). For an accurate uncertainty
map, the regions with probability 0.5, for example,
will contain equal areas of wet and dry observa-
tions. The accuracy can therefore be visualized by
the reliability curve, which plots the model prob-
ability against the proportions of wet and dry areas
in the observations (Fig. 11.6). An accurate model
will exhibit a 1:1 relationship, and the deviation
from this (e.g. the RMS error) can be used as a
measure of the accuracy (Schumann et al. 2009).
