Bushfire propagation speed: Combining the effects of wind and slope
Dr. Stefan Berres 1 and Noemí Cárcamo 2
1, Universidad del Bío-Bío, Chile
2, Universidad Católica del Maule, Talca, Chile
Stefan.Berres@gmail.com
Abstract: In this contribution the effect of slope inclination on the bushfire propagation speed is studied. The slope effect is estimated in an inverse problem setup. As observation data, real fire scenarios are given in terms of maximum fire expansions. With the knowledge of the initial ignition location, the front perimeters can be determined in any direction. The direct problem is formulated as a mathematical model of surface bushfire. It is expressed in a functional form, where the front propagation speed depends on wind and slope. The fuel material as predominant factor is given as a constant, i.e. no heterogeneous combustible effects are considered, and the effects of humidity are neglected. The observation data are given as radial front propagation perimeter. As model and data are two dimensional, the wind impact is decomposed in speed and direction; the speed is the maximal speed in wind direction, such that in the orthogonal direction to the wind there is zero speed and negative maximum speed in the opposed wind direction. In the model, the speed parameters are fixed for the overall domain, whereas the inclination is known from topographical data. The parameter identification problem is formulated as a nonlinear optimization problem, where the distance of the parametric model to the data is minimized by the optimal parameter set. The observation data give the distance reached by the propagation front. Though the radial perimeter data are two dimensional, covering all 360 degree directions, the model decouples the directions, establishing for each direction a one dimensional model. In this model simplification it is assumed that the fire spreads in each direction separately, without cross-directional interference. The mathematical model describes the propagated pathway simultaneously for each direction by a differential equation, where the change of position in time is given by the velocity model, that expresses the velocity in terms of wind and slope. In general, the model solution at given time points can be compared with the measured advance of the propagation front of a particular fire. The measurement data of final bushfire perimeters is provided by the National Forest Corporation of Chile (CONAF). The used experimental data is implemented manually from a shapefile type file using Google Earth tools. The methodology of solving the inverse optimization problem is implemented computationally on the Matlab/Octave, with plans to migrate to Python. The sensitivity analysis gives only a weak validation of the slope dependence. As a conclusion, more data than the final perimeter data are required. In standard situations, satellite images have been available only once a day, and firefighters are not yet by default equipped with GPS sensors that might enable local fire-front tracking. The expectation is that in the context of the big data paradigm, i.e. within the omnipresence of ubiquitious computing, a denser data coverage is going to be available, that might be coordinated by corresponding projects. Regarding the model, certainly the simplification of a two-dimensional scenario by simultaneous one-dimensional models is restrictive, especially in the perspective that the interaction with meteorological aspects requires a three-dimensional model, that even might be enhanced by multiple scales. Yet, the different model types might contribute to the discussion in the context of the availability of data and different comprehension levels of involved users or stakeholders. Thus, the presented model is going to be still valid for didactic purposes and as an intermediate parameter identification approach, that goes fine within an open modelling methodology.
