Full text: Mapping without the sun

a result, the process no longer describes a global birth-and-death 
but regional expansions and shrinkages of the sets under study 
namely the front, the seats and the scar of the spread. We draw 
from the model instructive simulations and a precise predictor of 
scars that actually occurred in the State of Selangor during the 
period 2000-2004. 
For the moment, fire daily predictions were not tested. This will 
be a future work to undertake. 
Figure 8: Cumulative number of hot spots from 2000 to 2004, 
during the periods April-June (a), July-September (b), and 
October-December (c). 
a) b) c) 
ACKNOWLEDGEMENTS 
The authors would like to thank The Cilix Corp. for having al 
lowed them to use their maps of fuel combustion and spread rate. 
REFERENCES 
Abdullah, M.J., M.R. Ibrahim, and A.R. Abdul Rahim : The inci 
dence of forest fire in Peninsular Malaysia: History, root causes, 
prevention and control. Workshop on prevention and control of 
fire in peatland, Kuala Lumpur, Malaysia, 19-21 March 2002. 
Figure 9: a) cumulative number of hot spots from 2000 to 2004, 
during the period January to March, b) and c) two simulations 
based on the input set a) with two values of k in the ratio 1.5. 
Selangor area a(S) is equal to 79, 969 pixels, and in the simula 
tion of Figure9c, the average number of Poisson points over the 
set S of Selangor is 500. On the other hand, the sum of the fuel 
amount over S equals 304,130, in dimensionless units. There 
fore, by integrating Equation(20) over S, we find numerically 
J s 0{x)d(x) = 7 g°g 6g = k f fw{x)d(x) 
from which we draw 
304,130 
79,969 k 
k = 1.64 x 10~ 3 
(21) 
4.2 Fire spread simulations 
If Io stands for the input set, then each point x of Io is replaced 
by one of the discs of Figure7, according to the value r(x) of the 
spread rate map at point x, which results in 5(x). Then, the simu 
lated new seats I\ = /3(/o) are obtained by intersecting each S(x) 
by a realization J of Poisson points, as indicated in Relation(2), 
with intensity 6 = kf w , and by taking the union for all x of Io- 
Finally, each point y of the set of new seats I\ is replaced in turn 
by S(y), and the dilation X2 = S(I\), as given by Relation(3), 
consists in the union of the discs S(y). 
Figure 9b and c depict two propagation simulations <5(/i) when 
we take a winter input set Io (Figure 9a), and when we use the 
two maps r and / of Figure 2. The two simulations differ by 
their coefficients k, which are taken such that kb/ k c = 1.5. The 
values chosen for kb amplifies the phenomenon. One will notice 
that most of the small hot spots of Figure 9a do not develop fires. 
5 CONCLUSIONS AND FUTURE WORK 
This paper proposes a new Random set model, the random spread. 
More than the classical spatial birth-and-death processes, random 
spread depends strongly on the heterogeneity of the space, which 
appears via two functions of intensity (9) and extension (6). As 
ADB (Asian Development Bank) and BAPPENAS (National De 
velopment Planning Agency). Causes, extent, impact and costs of 
1997/98 fires and drought. Final Report, Annex 1 and 2. Planning 
for Fire Prevention and Drought Management Project. Asian De 
velopment Bank TA 2999-1NO July 1998 - March 1999. Fortech. 
Pusat Pengembangan Agribisnis, Margueles Poyry. Jakarta, In 
donesia. 
P. Bak, K. Chen, C. Tang : Phys. Letters A 147, 297. 1990. 
P. Bak, K. Chen, M. Paczuski : Solitons in the one-dimensional 
forest fire model, Physical Review Letters, The American Physi 
cal Society, vol. 86 no. 11, March 2001. 
R. Blanchi, M. Jappiot, D. Alexandrian : Forest fire risk assess 
ment and cartography. A methodological approach. Forest Fire 
Research and Wildland Fire Safety, Viegas Ed. Millpress Rotter 
dam, 2002. 
M. Bilodeau, F. Meyer and M. Schmitt (Edts) Space, Structure, 
and Randomness Lecture Notes in Statistics, Springer, 2005 
P. Carrega : Relationship between wind speed and the rate of 
spread of a fire front in field conditions : an experimental example 
from the Landes forest. Forest Fire Research and Wildland Fire 
Safety, Viegas Ed. Millpress Rotterdam, 2002. 
W.R. Catchpole, E.A. Catchpole, A.G. Tate, B. Butler, R.C. Rom 
mel : A model for the steady spread of fire through a homoge 
neous fuel bed. Forest Fire Research and Wildland Fire Safety, 
Viegas Ed. Millpress Rotterdam, 2002. 
Colin, Colin, P.-Y., and Al., 2002. Saltus program-spot fires: 
knowledge and modelling, in Proc.ofthe IV international conf.or 
Fire Research, Luso, Portugal, 2002. 
FAO An Overview of Forest Products Statistics in South and 
Southeast Asia. Information and Analysis for Sustainable For 
est Management: Linking National and International Efforts 
in South and Southeast Asia (Qiang, M. & J.S. Braodhead. 
eds.). Food and Agriculture Organization of the United Nations, 
Bangkok. 177 p., 2002. 
Fire Detection and Monitoring using Remote Sensing, in 
Hotspots Interpretation Manual, Asian Specialized Meteorologi 
cal Centre, Singapore intranet, 2003. 
Forestry Canada 1 
ture of the Canad 
Forestry Canada, 1 
Gantz, D.: Framin 
est and land fires 
Union, pp. 92. 20( 
M.D. Hairi Sulims 
dom Simulations 
Chen Ed., AIT Ba 
Mastura Mahmud, 
East Asia National 
12 Nov. 1999, Bar 
G. Matheron: Rar 
York, 1975. 
I. Molchanov, Ran 
149, 2005. 
C. J. Preston, Spati 
46,1977, pp371-3< 
J. Serra, Image c 
II: theoretical adx 
1988. 
J.Serra, Random S 
March 2006. 
0. Sero-Guillaum 
a complete set of e 
modynamics. Int. 
pp 1705-1722. 
D. Stoyan, W. S. K 
its Applications, 2 
S. Tahir Qadri Ed. 
Strategy Asian De 
J.A. Turner, B.D. 
Danger Rating Sy 
practices. Environ 
Victoria, BC, BC- 
W. S. Wan Ahmac 
pp. 66-74, 2002. 
Zhang, Y.-H., Wo 
Monthly burned a 
for the Russian Fe 
Environment, 87,2
	        
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