Assessing the uncertainty in distributed model predictions using observed binary pattern information within GLUE

Abstract

Abstract:In this paper we extend the generalized likelihood uncertainty estimation (GLUE) technique to estimate spatially distributed uncertainty in models conditioned against binary pattern data contained in flood inundation maps. Untransformed binary pattern data already have been used within GLUE to estimate domain-averaged (zerodimensional) likelihoods, yet the pattern information embedded within such sources has not been used to estimate distributed uncertainty. Where pattern information has been used to map distributed uncertainty it has been transformed into a continuous function prior to use, which may introduce additional errors. To solve this problem we use here 'raw' binary pattern data to define a zero-dimensional global performance measure for each simulation in a Monte Carlo ensemble. Thereafter, for each pixel of the distributed model we evaluate the probability that this pixel was inundated. This probability is then weighted by the measure of global model performance, thus taking into account how well a given parameter set performs overall. The result is a distributed uncertainty measure mapped over real space. The advantage of the approach is that it both captures distributed uncertainty and contains information on global likelihood that can be used to condition predictions of further events for which observed data are not available. The technique is applied to the problem of flood inundation prediction at two test sites representing different hydrodynamic conditions. In both cases, the method reveals the spatial structure in simulation uncertainty and simultaneously enables mapping of flood probability predicted by the model. Spatially distributed uncertainty analysis is shown to contain information over and above that available from global performance measures. Overall, the paper highlights the different types of information that may be obtained from mappings of model uncertainty over real and n-dimensional parameter spaces.

Impact of the timing of a SAR image acquisition on the calibration of a flood inundation model

“…This problem of being unable to properly constrain the parameter space is closely linked to the equifinality problem, i.e. different 60 parameter sets yield similar model results with respect to the objective function used in the calibration (Beven and Binley, 1992;Aronica et al, 1998Aronica et al, , 2002Horritt and Bates, 2002;Pappenberger et al, 2005;Werner et al, 2005). The parameter sets that lead to the same optimal solution for the calibration problem are often defined as 'behavioural' parameter sets (Beven, 1996).…”

“…Among alternatives to evaluate the model's performance distributedly, are the use of post-flood field survey data (Aronica et al, 1998;Hunter et al, 2005;Neal et al, 2009), aerial photos or airborne and spaceborne Synthetic Aperture Radar (SAR) data (Bates and De Roo, 2000;Aronica et al, 2002;Horritt et al, 20 2007; Di Baldassarre et al, 2009a). Especially, radar, with its day, night and cloud penetrating capacity, is a promising technology for supporting flood inundation modelling (Bates, 2004;Montanari et al, 2009;Schumann et al, 2009b;Tarpanelli et al, 2012).…”

“…One aspect concerns the fact that the parameter space is often restricted to the Manning coefficients as these parameters are considered to be the most important parameters controlling the flow characteristics (Romanowicz et al, 1996), even though it is recognized that several parameters (related to roughness, channel cross section dimensions, initial con- presented by Aronica et al (2002) and Hunter et al (2005) are the measures most commonly used to evaluate flood inundation models with SAR-extracted binary flood maps. Essentially, these measures are based on the confusion ma-35 trix.…”

2D Finite Element Inundation Modelling in Anabranching Channels with Sparse Data: Examination of Uncertainties

“…Five parameters were identified as the primary sources of uncertainty (Table 2) We used a GLUE-based framework to quantify the predictive uncertainty in TELEMAC2D outputs by employing two types of observed inundation maps for conditioning the likelihood weights. The deterministic binary inundation maps (Fig 5) were used following the method proposed by Aronica et al (2002), and the possibility of inundation maps (Fig 4) were used to incorporate uncertainty in satellite-observed flood extents following the methodology of Di 13 . As both approaches produce probability maps of predicted inundation, we compared the differences in their spatial patterns.…”

“…With the increased availability of remotely-sensed data to capture the extent of inundation, binary flood maps have been used to quantify the distributed uncertainty of inundation models under the GLUE approach (Aronica et al, 2002). Recognizing the possibility of error in these 4 maps, Schumann et al (2009) proposed 'possibility of inundation' maps rather than deterministic binary flood maps.…”