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Mapping without the sun
Zhang, Jixian

Jean Serra 1 , Mohd Dini Hairi Suliman 2 , and Mastura Mahmud 2
1 Laboratoire A2SI, Groupe ESIEE, BP 99, 93162 Noisy-le-Grand Cedex France. Email: serraj@esiee.fr
2 Earth Observation Center, Universiti Kebangsaan, 3600 Bangi, Selangor Malaysia
KEY WORDS: Selangor, risks maps, random sets, forest fires, mathematical morphology, random spread
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The paper proposes a stochastic model to study forest fires from risk maps and to predict the location of the scar zones. This model
holds on both the process (the fire front) and on the result (the scars)of a fire. A new set operator, called ’’random spread” /3, describes
the front of the fire at each daily step. Under iteration, operator /3 provides the time evolution of the process. Average sizes, and the
probabilities of extinction at each step are derived. The random spread model is applied to analyse the fires that occurred in the State of
Selangor (Malaysia) from 2001 to 2004. It proves to able to predict all places where burnt scars actually occurred, which is a strongly
significant verification. Finally, the model is used for simulating forest fires.
In a large number of wild forests, such as typically in South East
Asia, forest fires propagate less under the action of the wind, as
in Mediterrenan countries, than under almost isotropic irregular
causes. For instance, the fires that occurred in the state of Selan
gor (Malaysia, see Figure 1) from 2000 to 2004 seem to evolve
randomly: the initial seats vanish sometimes, but may also give
birth to new seats at some distance.
Figure 1: Malaysia and State of Selangor.
The foresters use to describe the fire progress by means two key
maps (Hairi Suliman et al.2005), namely the daily spread rate
of the fire, i.e. the radius r of the daily circular propagation of
the fire, and the fuel consumption f w , (a weighted version of
the vegetation map). Both are depicted in Figure 2. Clearly, a
straightforward use of such key maps does lead to a pertinent
description. By starting from any point seat, one always arrives
to bum the whole country in a finite time, under iteration, as both
maps are positive. Indeed, one must use the rate information in
some restrictive way, to be able to reach actual events. It is the
purpose of the present paper.
Figure 2: a)map f w of the fuel consumption; b)map of the spread
rate, i.e.of the radius r of the daily circular propagation of the
1.1 State of the art
The literature about quantitative modelling of Malaysian type for
est fires, can be split into two groups. Firstly, the behaviour of a
forest fire is often described from what is actually observed (Car-
rega2002), (Wan Ahmad2002). The research centres of forestry,
in the countries where such fires occur, have analyzed the situa
tion over long periods of time. They define series of pertinent pa
rameters, coming either from permanent sources (fuel maps, soil
nature) or from variable ones (typically weather observations:
temperature, relative humidity, wind, rain) (Forestry Canada2003).
Then they propose complex systems for managing this informa
tion, which result in behaviour predictions of the rate of spread,
of the fuel consumption, of the temperature at the front of the fire,
etc. (Colin et al.2002), (Turner et al. 1985), (Zhang et al.2003).
Their predictions yield daily maps which are often synthesized in
an overall risk map (Blanchi et al.2002).
Such descriptions cooperate with satellite data, not only for the
land cover classification they need, but also because their maps
have to be read in association with those of the hot spots which
are detected daily by satellite.
From a second point of view, the heart of the description lies in
the equations that underlay a fire. Several phenomena are in
volved, such as heat transfer (Catchpole et al. 2002), gas proper
ties (Catchpole et al. 2002), turbulence phenomena (Bak et al. 1990),
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