1 Spatial Modelling of the Terrestrial Environment - Georeferencial

100 Spatial Modelling of the Terrestrial Environment
a single optimum set of parameters, which produces a maximum value of F 〈2〉 , we identify
a broad region of the parameter space where values of F 〈2〉 are greater than 70%. The
complexity of the parameter space also appears to be a function of model non-linearity.
Thus, Horritt and Bates (2001a) showed that the parameter space for the weakly nonlinear
LISFLOOD-FP model typically contains a single optimum region, whilst the same
parameter space for the more highly non-linear TELEMAC-2D model contained multiple
optima.
Such parameter space mappings do not, however, give information on the distributed
risk of inundation across the floodplain given model uncertainty. The problem here is to
design a measure that both captures distributed uncertainty and, at the same time, contains
information on global simulation likelihood that can be used to condition predictions of
further events for which observed data are not available. Thus, to unearth the spatial uncertainty
in model predictions for the particular flood being modelled, we take the flood state
as predicted by the model for each pixel for each realization, and weight it according to the
measure-of-fitF 〈2〉 to give a flood risk for each pixel i, P flood
i
:
P flood
i =
∑
j
∑
j
f ij F (2)
j
where f ij takes a value of 1 for a flooded pixel and is zero otherwise and F 〈2〉
j
is the global
performance measure for simulation j. Here Pi
flood will assume a value of 1 for pixels
that are predicted as flooded in all simulations and 0 for pixels always predicted as dry.
Model uncertainty (here defined by the interaction of the global performance measure and
spatially distributed probabilities of the event being modelled) will manifest itself as a
region of pixels with intermediate values, maximum uncertainty being indicated by pixels
with Pi
flood ≈ 0.5. When events different from the conditioning event are to be modelled,
the same values of F 〈2〉
j
can be used (these are associated with each parameterization),
but the predicted risk map f ij will differ. Whilst the technique has been developed with
the problem of flood inundation modelling in mind, it should equally well apply to any
distributed model conditioned against binary pattern data. Plots of Pi
flood over the real
space of the Imera and Thames models are shown in Figures 5.7 and 5.8, respectively.
These maps indicate the risk that a given pixel is predicted as wet in the simulations whilst
retaining information on the global performance of the model determined by F 〈2〉 . When
compared to the observed shoreline (solid line), this gives an indication of the degree of
model under- or over-prediction. Figures 5.7 and 5.8 give much more information on the
spatial structure in simulation uncertainty than can be obtained from a global measure
and significant discrepancies between model predictions and the observed shoreline are
indicated at the limits of the parameter space.
Finally, Pi
flood may be updated as more information becomes available and one is thus
able to determine the extent to which additional data act to reduce predictive uncertainty.
Such techniques are thus capable of telling us something about the value of data, and
here further studies are thus required that examine combinations of data, both hydrometric
and inundation extent, and calibration strategies that act to reduce uncertainty in model
predictions.
F (2)
j
(2)