Bayesian calibration of a flood simulator using binary flood extent observations

Abstract

Abstract. Computational simulators of complex physical processes, such as inundations, require a robust characterization of the uncertainties involved to be useful for flood hazard and risk analysis. While flood extent data, as obtained from synthetic aperture radar (SAR) imagery, have become widely available, no methodologies have been implemented that can consistently assimilate this information source into fully probabilistic estimations of the model parameters, model structural deficiencies, and model predictions. This paper proposes a fully Bayesian framework to calibrate a 2D physics-based inundation model using a single observation of flood extent, explicitly including uncertainty in the floodplain and channel roughness parameters, simulator structural deficiencies, and observation errors. The proposed approach is compared to the current state-of-practice generalized likelihood uncertainty estimation (GLUE) framework for calibration and with a simpler Bayesian model. We found that discrepancies between the computational simulator output and the flood extent observation are spatially correlated, and calibration models that do not account for this, such as GLUE, may consistently mispredict flooding over large regions. The added structural deficiency term succeeds in capturing and correcting for this spatial behavior, improving the rate of correctly predicted pixels. We also found that binary data do not have information on the magnitude of the observed process (e.g., flood depths), raising issues in the identifiability of the roughness parameters, and the additive terms of structural deficiency and observation errors. The proposed methodology, while computationally challenging, is proven to perform better than existing techniques. It also has the potential to consistently combine observed flood extent data with other data such as sensor information and crowdsourced data, something which is not currently possible using GLUE calibration framework.

The Cost of Imperfect Knowledge: How Epistemic Uncertainties Influence Flood Hazard Assessments

“…The topography was obtained from stereophotogrammetry at a 50 m scale with a vertical accuracy of ±25 cm, obtained from large-scale UK Environment Agency maps and surveys. This reach has also been study previously in G. Aronica et al (2002), J. W. Hall et al (2011), andBalbi andLallemant (2023).…”

“…(2018) for dynamical hydrological models or in J. W. Hall et al. (2011) and Balbi and Lallemant (2023) for hydraulic inundation models.…”

“…More complex procedures to include model uncertainty can be used to include uncertainty in the model structure. For example, a formally probabilistic calibration procedure that includes model structural uncertainty as an additive Gaussian Process is discussed in Balbi and Lallemant (2023).…”

“…The details of the calibration procedure using the GLUE framework can be found in Balbi and Lallemant (2023), but they can be summarized in four steps:…”

“…It can, typically, be represented through uncertainty in the parameters that describe the models as data is not sufficient to perfectly identify them. Limited knowledge, on the other hand, is usually represented through simplifying assumptions, such as the ones in the HPP model, the distribution family chosen for 𝐴𝐴 𝐴𝐴(𝑥𝑥|𝜃𝜃) , or the particular physics-based model chosen for S. These can be harder to represent mathematically, although it can been done through averaging model ensembles, such as Bayesian Model Averaging (Madadgar & Moradkhani, 2014), or via statistical representations of model deficiencies as developed in Abbaszadeh et al (2019) and Pathiraja et al (2018) for dynamical hydrological models or in J. W. Hall et al (2011) and Balbi and Lallemant (2023) for hydraulic inundation models.…”