Fire Spread Model for Old Towns Based on Cellular Automaton

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TSINGHUA SCIENCE AND TECHNOLOGY
ISSN

1007-0214

25/25

pp736-740
Volume

13,

Number

5,

October

2008


Fire Spread Model for Old Towns Based on Cellular Automaton
GAO Nan (高 楠 ), WENG Wenguo (翁文国 )
**
, MA Wei (马 伟 )

, NI Shunjiang (倪顺江 ),
HUANG Quanyi (黄全义 ), YUAN Hongyong (袁宏永 )


Center for Public Safety Research, Department of Engineering Physics,
Tsinghua University, Beijing 100084, China;
† School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China

Abstract: Old towns like Lijiang have enormous historic, artistic, and architectural value. The buildings in
such old towns are usually made of highly combustible materials, such as wood and grass. If a fire breaks
out, it will spread to multiple buildings, so fire spreading and controlling in old towns need to be studied. This
paper presents a fire spread model for old towns based on cellular automaton. The cellular automaton rules
were set according to historical fire data in empirical formulas. The model also considered the effects of cli-
mate. The simulation results were visualized in a geography information system. An example of a fire spread
in Lijiang was investigated with the results showing that this model provides a realistic tool for predicting fire
spread in old towns. Fire brigades can use this tool to predict when and how a fire spreads to minimize the
losses.
Key words: old town; fire spread; cellular automaton; geographic information system (GIS)

Introduction
Old towns represent the cultural sites having high his-
torical, artistic, and architectural value. Fires are disas-
ters that can burn everything into ashes. Methods are
needed to protect World Culture Heritages sites like
Lijiang. Lijiang is very important to China and to the
world because the style and structure of its buildings
are of great value to scholars. If fire occurred in these
towns, it would result in huge losses to the whole
world. Therefore, methods must be developed to pro-
tect old towns like Lijiang.
Lijiang includes about 20 600 km
2
with 1.12 million
local inhabitants with 23 local minorities. The build-
ings in Lijiang have their own particular style of the
Naxi minority, which follows rules not frequently seen
in other places
[1]
. The Lijiang people usually built their
houses near beautiful scenes, so each house is close to
others (as shown is Fig. 1). The buildings are mainly
made of wood and soil
[2]
. If a fire were to break out, the
fire would spread rapidly to other buildings as the wood
burns and the buildings would collapse due to loss of the
soil that holds the buildings together. Therefore, to pro-
tect old towns like Lijiang from fire damage, the
mechanism that spreads fires in old towns needs to be
studied using computer simulation.
Many scholars have studied the development of city
fires and building fires, but they have mainly investi-
gated fires within only one building or very limited
spaces. Most of these models can only describe the
process and results of fires spreading in one single ma-
terial. There are few studies concerned with large
spaces, e.g., a whole city like Lijiang (including its
nearby mountains)
[3]
. Therefore, another method, the
cellular automaton model, was used here because it not
only can represent the whole process from a macro-
scopic point of view, but can also describe the details
of the fire spreading. This paper presents a fire spread
model for old towns based on cellular automaton.

﹡﹡
Received: 2006-10-24
To whom correspondence should be addressed.
E-mail: wgweng@tsinghua.edu.cn; Tel: 86-10-62796323
GAO Nan (高 楠 ) et al: Fire Spread Model for Old Towns Based on Cellular Automaton

737

Fig. 1 Lijiang photographs
1 Cellular Automaton Model
The cellular automaton (CA) model generally divides
the analysis area into equal-sized grids called cells.
Each cell is a basic unit in the fire spread model, with
its size determined by the situation. Each cell has the
characteristics of the area it belongs to. Each cell has
only one state of several limited states according to the
local circumstances. The state can change with time.
Cells can impact the states of neighboring cells accord-
ing to update rules applied to all the cells in this system,
which are determined from experience.
The cellular automaton method is used in many
fields such as transportation, economy, and chemistry.
It can also be used to understand the complex mechan-
ics of a spreading city fire in terms of its scale, direc-
tion, trends, and so on. This paper presents a fire
spread model for old towns based on cellular automa-
ton, which not only can represent the whole process
from a macroscopic point of view, but also can de-
scribe the specific details of the fire spreading process.
2 Fire Spread Model for Old Towns
2.1 Parameter arrangement
The first step in the cellular automaton method is to
analyze the structure and geography of the city to de-
termine the parameters used in the fire spread model.
Here the old town area of Lijiang is an example.
2.1.1 Cell size
Old areas usually have narrow streets and densely-built
houses. In Lijiang, houses are generally 4 m to 7 m
long and 2 m to 4 m wide. The streets are generally 3
m wide. The streams running through the old town are
about 3 m wide. The numerical accuracy and computa-
tional efficiency were balanced with 3 m by 3 m cells
in this study.
When two or more materials exist in one cell, the
average properties are determined using the area
method or the power method. The area method means
that in one cell the material with the largest area de-
termines the cell characteristics. In the power method,
the cell characteristics are the most important materials
in this cell. This model uses both methods in different
conditions. The area method is used in most parts of
the cities, while the power method is used to cells in
important areas, such as the ancient protected buildings
area and the old central districts.
2.1.2 Cell characteristics
The city fire spread model advanced by Murosaki et
al.
[4]
showed that the building materials, the weather
conditions, and the regional characteristics most
strongly affect the fire spread. These three factors were
defined based on the special characteristics of Lijiang.
(1) Factors of buildings
The buildings in Lijiang are mainly built of wood
and soil and are generally 1 to 3 floors. But as the town
develops, more and more modern buildings are now
being built with many new buildings being built with a
wide variety of materials. The model must include all
these conditions and should be adaptable to future
conditions. The people in Lijiang enjoy their lives un-
der the sun and by the streams. Their houses have lar-
ger windows 4 m to 6 m in size than in other regions.
Thus, they receive more sunshine, but these large win-
dows allow the fire to spread more quickly. The build-
ings in Lijiang were classified as: (1) wooden build-
ings having 1, 2, 3, or 5 floors, (2) earthen buildings
having 1, 2, or 3 floors, (3) brick buildings having 1,
2, or 3 floors, (4) brick and steel buildings having 1 to
7 floors, (5) steel buildings having 2 to 8 floors, and
(6) other buildings like canchas, toilets, and unoccu-
pied buildings. The different buildings have different
Tsinghua Science and Technology, October 2008, 13(5): 736-740

738
building structure parameters S and ratios of wood P.
Besides the structural factors, the different buildings
tend to catch fire in different ways. The equation given
by Wakamatsu
[5]
was used to calculate
( ).
kl
p t

2 1
2 1
1 1
2 1 2 1
2 1
2
1 2
2 1
0.2 4.2
4.0
,
;
5
( )
5.0
( ),
4( )
5
kl
kl
kl
kl
kl
t t
t t
t
t t t
t t t t
p t
t t
t t
t t t
t t



+
+

− −

=



− +
+



≤ ≤
≤ ≤
(1)
1
(3 3/8 8/)/(1 0.1 )t a d D v= + + + (2)
2 f w f
(/5.5)/(/)t w A H A= (3)
where ( )
kl
p t
is the ability of cell [kl] to cause the
fire to spread.
The time
1
t
is defined as the
cell [kl]
starts burning to when it can cause the fire to spread. a
is 3 m, which is the length of one cell. d is an unfixed
variable, which changes according to the time and con-
ditions
[4,5]
. D is the farthest distance that the fire
can spread for a given certain wind speed, calculated
as
[6]

1.15(5 0.5 )
D
V
=
+ (4)
where V is the wind velocity.
The time t
2
is defined as the time from when cell [
kl]
catches fire to when it burns out.
f
w is the fire load.
Based on the authors’ investigations,
f
w for wooden
structures is 60.0, for earthen structures is 45.0, for
brick structures is 20.0, and for others structures that
do not burn is 0.0.
w
A
is the average open area for
doors and windows in each floor.
f
A
and H are the
area and height of each floor in one building.
(2) Weather conditions
The equation for the farthest fire spreading distance
presented by Jirou and Kobayashi
[7]
is a function of
only the wind velocity and direction. The effect of the
west wind is shown in Fig. 2.

(a) 0 to 1 m ∙ s
−1


(b) 2 to 5 m ∙ s
−1


(c) ≥8 m ∙ s
−1

Fig. 2 Effect of western wind
The wind effects have 4 levels and 8 directions for
32 different wind effects
[8]
. The model considers the
effects of each wind effect.
(3) Regional characteristics
Lijiang is in a mountainous area, so the topography
is certainly not smooth. Some buildings were built near
or in the mountains, so the model must consider the
fire spreading from buildings to trees in the mountains
and from trees to the buildings. The fire spread among
trees differs from that among buildings, so the model
must consider the tree characteristics and ground
slopes. The relative topography of two nearby cells are
used to describe the slopes. The topography has 8 di-
rections, including 4 horizontal and 4 vertical direc-
tions
[9]
. The parameter
ij
o shows the effects of the
slope between adjoining cells on the fire spreading.
The value of
ij
o for each cell is depended on topogra-
phy angle with
ij
o = 0.1 for 0
°

-

20
°
, 0.3 for 20
°

-

40
°
,
0.5 for 40
°

-

60
°
, 0.7 for 60
°

-

80
°
, and 0.9 for 80
°

-

90
°
.
Higher values of
ij
o result in larger, stronger fires.
2.1.3 Cell state
The fire states in each cell are: (1) cells are unable to
burn; (2) cells are able to burn, but are not burning; (3)
cells have just begun burning, but are not yet able to
spread; (4) cells are burning strongly and are able to
spread; and (5) cells are burned out. The transitions be-
tween cell states have a fixed order. When the cell
catches fire, the cell state transitions to state (3). Some
time after the cell catches fire, the cell state changes
from state (3) to state (5). If the cell is in state (1) or
state (5), the cell state never changes.
2.2 Simulation and visualization
2.2.1 Simulation
The fire spreading model must determine whether cell
[ij] changes from state (2) to (3). The change probabil-
ity is determined by the fire spreading judgment index
.
ij
F
Cells with different characteristics have different
ij
F
(see Patton and Shaw
[10]
). The indexes for build-
ings and trees are based on the weather and cell
characteristics.
GAO Nan (高 楠 ) et al: Fire Spread Model for Old Towns Based on Cellular Automaton

739
Building rule:
( )
ij ij ij ij kl
F S PW p t w
β
α=
(5)
Tree rule:
( )
ij
x
ij ij ij ij kl ij
F S PW p t o w
β
=
(6)
Here,
ij
S is a building or tree parameter, set to 1.0 for
wooden buildings, 0.0 for steel buildings, and between
0.0 and 1.0 for other structures.
ij
P
is the ratio of
wood in the structures. w is the wind effect in each cell
which varies from 0.0 to 0.5 according to the distance
from the burning cell.
α
⠰(
α

1) is an adjustable
parameter, whose value is changed to wind effects such
as slowing of the spreading velocity.
β
=楳⁡渠ad橵jt-
慢汥⁷ind=灡pame瑥t,⁷h楣h⁤=瑥牭楮敤ith攠牡湧攠e湤n
摩牥d瑩t渠潦⁴h攠晩牥⁳灲敡ei湧n =
ij
o (0<
ij
o <1) is the co-
efficient of ground slope coefficient.
ij
x
is the expo-
nent of slope effect.
ij
W is the combustible loading in
each cell. When
ij
F is larger than a random value (be-
tween 0 and 1, whose value is chosen stochastically), the
state of the cell is changed from state (2) to state (3), and
the cell is defined to have caught fire. When the time af-
ter catching fire is more than
1
t, the cell state is
changed to state (4). When the time is more than
2
t
, the
cell state is changed to state (5). The results show how
the fire spreads in the old town areas.
2.2.2 Visualization with geographic information
system (GIS)
ArcObjects is a technical frame for GIS offered by En-
vironmental System Research Institute, Inc. in America.
We use ArcObject to program GIS applications using
VBA, Visual Basic, and Visual C++.
A city fire spreading dynamic link library was de-
veloped based on the model and connected to the GIS.
The MapControl, a control in GIS, was used to select
the fire start point on the map, with the parameters
such as the wind velocity and direction input into the
simulation.
4 Lijiang Example
The model was used to simulate a fire spreading in
Lijiang as an example of an old town. The parameters
were
α
㴰⸴,=
β
㴱⸰,=
D
=12.0, and
d
=2.0. For
wooden structure
P
=1.0,
f
w
=60.0, for half combusti-
ble materials P=0.8 and
f
w =45.0, for almost no com-
bustible materials P=0.5 and
f
w =20.0, and for no
combustible materials P=0.0,
f
w
=0.0. Figure 3 shows


Fig. 3 Process of fire spreading in Lijiang old town

Tsinghua Science and Technology, October 2008, 13(5): 736-740

740
the process of fire spreading in the Lijiang old town
area. The wind was assumed to be from the east at the
4-5 level. The light gray represents burning cells and
the black represents burned out cells.
Figure 3a shows that the fire has broken out. In Fig.
3b the fire has spread over 1170 m
2
. Here, the fire
spread direction is mainly affected by the wind direc-
tion. In Fig. 3c at t =122 min, the fire has spread from
buildings to trees on the mountain with 1278 m
2
burned out. Once the trees catch fire, the fire spreads
quickly, as shown in Fig. 3d at t=230 min. Thus, the
fire velocity and scope depends on the cell characteris-
tics and some extra conditions.
5 Conclusions
This paper presents a fire spread model for old towns
based on a cellular automaton model. The cell parame-
ters including cell size, cell characteristics, and cell
states are set according to recommended values in the
literature and the building and land characteristics in
Lijiang. Simulation results show that this model pro-
vides a useful tool for predicting fire spreading in old
towns.
Future models will consider more parameters such
as the air temperature and humidity to improve the
model accuracy. Experimental data and historical fire
records will be used to validate the model.
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