Abstract
We present a shape-oriented data assimilation strategy suitable for front-tracking problems through the example of wildfire. The concept of “front” is used to model, at regional scales, the burning area delimitation that moves, undergoes shape and topological changes under heterogeneous orography, biomass fuel and micrometeorology. The simulation-observation discrepancies are represented using a front shape similarity measure deriving from image processing and based on the Chan-Vese contour fitting functional. We show that consistent corrections of the front location and uncertain physical parameters can be obtained using this measure applied on a level-set fire growth model solving for an eikonal equation. This study involves a Luenberger observer for state estimation, including a topological gradient term to track multiple fronts, and of a reduced-order Kalman filter for joint parameter estimation. We also highlight the need – prior to parameter estimation – for sensitivity analysis based on the same discrepancy measure, and for instance using polynomial chaos metamodels, to ensure a meaningful inverse solution is achieved. The performance of the shape-oriented data assimilation strategy is assessed on a synthetic configuration subject to uncertainties in front initial position, near-surface wind magnitude and direction. The use of a robust front shape similarity measure paves the way toward the direct assimilation of infrared images and is a valuable asset in the perspective of data-driven wildfire modeling.
Highlights
Front-tracking problems arise in many applications, e.g. cardiac electrophysiology [15], tumor growth [36], seismic history matching [62], oil spill [34], precipitation forecasting [4], flaming combustion [44], wildfire behavior [52]
We presented a front shape similarity measure adapted to an eikonal equation solved using an Eulerian level-set front-tracking model
This measure derived from the Chan-Vese contour fitting functional in image segmentation theory is well suited to handle position errors that go beyond the problem of amplitude errors addressed by classical data assimilation framework
Summary
Front-tracking problems arise in many applications, e.g. cardiac electrophysiology [15], tumor growth [36], seismic history matching [62], oil spill [34], precipitation forecasting [4], flaming combustion [44], wildfire behavior [52] Such problems aim at tracking the contour (or “front”) and the motion of an object, which is the indirect shape of, for instance, an electric field, a water saturation, a cloud, a temperature isovalue, etc. The object contour may be subject to strong shape deformations, its motion may be unsteady and present irregularities and topological changes can occur Tracking these changes remains a challenging task from both modeling and observation viewpoint [42, 64]. Observations are subject to instrumental and representativeness errors that are enhanced when the target object becomes partially occluded
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