Investigation on Critical Density in a Fire Spread Model using a Multi-agent Approach

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Dec 1, 2013 (3 years and 8 months ago)

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1

Investigation on Critical Density in a Fire Spread
Model using a Multi
-
agent Approach



Xiaodong Li

RMIT, Department of Computer Science, GPO Box 2476v

Melbourne 3001,Victoria Australia

xiaodong@cs.rmit.edu.au


Abstract.

Small changes in spatial pattern o
n a landscape can sometimes produce dramatic
ecological responses. Such transition ranges are associated with critical environmental
conditions such as tree density. As the landscape becomes dissected into smaller patches
of trees, landscape connectivity

may suddenly become disrupted, which may have
important consequences for the behaviors of forest fire, i.e., how it spreads. Landscape
connectivity depends not only on the tree density but also many other environmental
conditions such as land height, flam
mability, and wind conditions. To determine how the
critical densities are affected by the changes in various landscape conditions, we
developed a bushfire spread simulation model using Swarm, a multi
-
agent simulation
framework developed at Santa Fe instit
ute. The model takes into account some of the
most influential factors contributing to the development and spread of bushfires. These
environmental factors include bush density, bush flammability, heat conditions, land
height, wind direction and wind magn
itude. With different initial conditions, the fire will
either rapidly spread out of control, die prematurely, or survive for moderate periods of
time before being overcome by unfavorable conditions. By varying these variables under
controlled conditions,
this research aims to show how they influence the spread and
growth of a bushfire. The paper will first describe the fire simulation model from a multi
-
agent perspective and the environmental variables that are adopted and implemented in
the simulation mod
el. Some experimental results and analysis will then be presented,
followed by a summary and directions for future research.


1.

Introduction

Every year bushfires across Australia and the rest of the world devastate enormous
areas of land and take a heavy
toll on human life. These fires spread rapidly, and
without adequate models to predict their growth, firefighters are unable to contain
them as efficiently as they would otherwise be able to. One of critical environmental
factors that affect the spread o
f bushfire is bush density. If the landscape is very
densely populated with trees, the fire is likely to spread; if the landscape is only
sparsely populated, then the fire is likely to die out. Now the question is: “what is the
critical density of trees
(between 0.0 and 1.0) that is needed on the landscape for the
fire to spread continuously in a sufficiently large env
i
ronment?”

Questions like these are subjects of study in percolation theory [1] [2]. To illustrate,

consider a two
-
dimensional lattice as t
he landscape where grid cells are randomly
filled. Percolation theory predicts that a uniformly random distribution of filled cells
that comprises at least 0.5928 of the landscape has a very high probability of spanning
the lattice. As the critical densit
y
p
c

is reached, isolated patches of filled cells become
connected to form one continuous (percolating) cluster. Each filled cell of the
perc
o
lating cluster is joined with a neighboring occupied cell along at least one
horizontal or vertical edge (see Fig
. 1). If fire starts from one side of the lattice, it
2

should be able to traverse or “percolate” across this landscape through this formed
cluster. If the lan
d
scape were filled with trees below this critical density (
p
c

<
0.5928), tree clusters would occur

as smaller, isolated patches. The landscape
becomes disconnected as the percolating cluster is broken into many smaller patches.
This would prevent a fire from spreading across the landscape. Small changes in tree
density on a landscape therefore could h
ave discernible impact on the fire spread
behaviors.













2. Multi
-
agent approach

There have been many efforts in modeling fire spread (Mehaffey, 1988; Fowell, 1988;
Andrews, 1991; Beer, 1991; Cheney, 1991). Most of these studies are based o
n
deterministic models. The best
-
known and studied model is Rothermel’s semi
-
empirical model (Rothermel, 1983). It allows the forecast of the rate of spread and the
reaction intensity knowing certain properties of the fuel and environmental conditions
in w
hich the fire will occur. The forecast is based on data of the following variables:
fuel characteristics such as proportion of live and dead material, density, surface
volume coefficients and mineral content; moisture; wind speed and direction; and
topogr
aphic factors such as altitude and slope.

A more recent approach to simulation of fire spread has been using a multi
-
agent
approach (Resnick, 1994). By adopting the multi
-
agent approach, we can describe a
system as a large number of interactive individual
s (mapped to the cells on a 2
-
dimensional CA) with relatively simplistic behavior. When the individuals are
modeled together, their simplistic interactions produce more complex behavior. This
more complex behavior should then match the behavior witnessed

in the system as a
whole in reality. This type of micro
-
simulation involves describing the variables that
define how the individuals themselves act (Stefansson, 1997). The main benefit of
this form of simulation is that once a facet of an individual’s i
nteractions has been
observed then this facet can be incorporated into the simulation without the necessity
of finding a complex mathematical expression that adequately describes how it relates
to the system. To produce the simulation of the whole system,

only the interactions of
the individuals with each other and the environment need to be modeled.

Multi
-
agent approach has been adopted for individual
-
based modeling such as a
prey
-
predator model or an ecosystem (Sutherland & Jacobs, 1994; Forest & Jones,

1994). Landscape can be also represented as a 2
-
dimensional grid (Green, 1994). In
this case, each cell represents a fixed surface area and has attributes that correspond to
environmental features such as bush and land height. This approach has also bee
n


t = 0



t = 40



t = 130 t = 600

Fig. 1.

A simplified forest fire model with 61% tree density. No other environmental
factors
such as land height or flammability are considered here. Fire starts at the left edge,
and it reaches the right edge at t = 600.


3

adopted for modeling fire spread (Green, 1989; Resnick, 1994), but these models are
often very simplistic, lacking detailed description of fire and its environment. This
suggests a need for developing multi
-
agent models that can accommodate more
elabora
te description of fire spread such as those suggested by Rothermel’s model.

In this paper, a CA model for simulating fire spread that takes into account some
major influencing factors from the environment is presented. The model has included
some of the m
ost important variables as suggested in Rothermel’s model. We will
demonstrate how this model can be used to simulate fire spread under various
conditions that are involved with one or more environmental variables. In particular,
the study of fire spread
will focus on investigating
critical density

of bush by
conducting simulation runs under various initial conditions (Green, 1994; Bak &
Chen, 1988). Such critical density determines for example whether a fire starting
from the center of the 2d
-
grid (i.e.
the artificial world) is able to spread to the
boundary of the grid (Resnick, 1994).

The paper is organized as follows: Section 2 presents a detailed description of the
model. The environmental factors that are taken into consideration by the model and
th
eir current implementations are also described here. Section 3 briefly discusses the
implementation issues in general. Section 4 provides discussions on simulation runs
and their analysis. Finally conclusions and future research directions are given in
s
ection 5.

2. Description of the Model

The model consists of a number of basic components. First it has an artificial world
(i.e. a 2
-
dimensional CA) where bushes are placed randomly across the landscape. A
cell's state could correspond to a number of envi
ronmental factors such as fuel and
land height. A fire, which is regarded as an individual in such an artificial world, can
be generated at a particular cell on such a landscape or many fires can be created along
one side of the artificial world. Once sta
rted, fires can then spread into their
neighborhood by looking around locally and following certain local interaction rules
(see Fig. 1), which are defined by some environmental factors, and should simulate
ecological processes such as fire spread. There i
s no global control on how fires
should spread. Macroscopic or system
-
level dynamics will emerge as a consequence
of many such local interactions.









Figure 1
. A fire can spread into its neighborhood on a 2
-
dimensional
artificial world, depending
on some predefined local conditions
(environmental factors) in these neighboring cells.

This model takes into account some of the most influential factors contributing to
the development and spread of fire (Rothermel, 1983; Luke & McArthur, 1977;
A cell's state corresponds to a
number of environmental
factors suc
h as fuel and land
height

4

Cheney, 1
991). The individuals in the model in this case will be spots of fire, or
flames, that spread throughout the bush depending on a number of factors. With
different initial conditions, the fire will either rapidly spread out of control, die
prematurely, or
survive for moderate periods of time before being overcome by
unfavourable conditions. Our goal is to determine how the fire develops in different
manners from those initial conditions. Such conditions will involve the following
factors:



Bush density



Bus
h flammability



Heat conditions



Land height



Wind speed



Wind direction

The above factors are discussed in detail in the following sections. Implementation
of each factor in the current model is also briefly described.

2.1 Bush density

The density of the shr
ubs and trees is perhaps the most important factor of all. No
matter how hot the day, no matter how dry and flammable the growth in the
environment, should the trees be sparse and shrubs and bushes few and far between,
then the fire will be unable to spre
ad over any considerable area. It is really only once
the plant life (the fuel) reaches a suitably high density, that the other factors play a
more important role. This critical density, if the fire is allowed to spread into each of
its four neighboring
squares (north, south, east and west) whenever there is fuel
present there, is about 59 percent (Resnick, 1994). This means that with less than 59
percent of the land being covered with fuel, the fire will tend to starve, while a higher
percentage of fuel

will help ensure that the fire spreads in a healthy manner (for the
fire). Such a density, that does not take into account the flammability of the fuel or
any other factors, is somewhat idealized over an infinitely large area (Resnick, 1994).
In practic
e, the area is most definitely finite. This means the value must be raised


the smaller the area, the greater the critical density will be.

The critical value of 59 percent, which can be approached with a suitably large
area, will alter once other facto
rs are taken into account.

Note also that the restriction of only allowing the fire to spread along the four sides
is an unnecessary one that could be easily alleviated. Indeed, if the fire is allowed to
spread to any one of its eight neighbors (four side
s, four diagonals, see Fig. 1), then
the critical density of an idealized forest is actually only 41 percent. The symmetry
around 50 percent comes from the fact that if the fire cannot move into its diagonal
neighbors then horizontal or vertical sections
of fire are required to reach the edge,
whereas gaps of trees do not have to be so aligned. A diagonally aligned gap of trees
can prevent the fire from growing. If the fire can spread in all eight directions then the
situation is reversed. In this latte
r case, a diagonal section of fire can reach the edge
and must be blocked by a vertical or horizontal gap of trees, but will not be stopped by
a diagonal gap of trees (Resnick, 1994).

5

In the current implementation of the simulation model, bushes are initia
lly
generated and allocated at random on the 2d grid. Bush density can be specified as a
percentage probability of whether or not a particular area of land within the
environment contains bush.

2.2 Flammability

Two factors are considered here to contribu
te to the resulting flammability of the fuel.
The first is the inherent flammability of each bush item. The second are the heat
conditions of the day.

2.2.1 Bush Flammability

The types of growth found in the area best represent the flammability of the bu
sh.
Growth such as leafy vegetation and fire
-
resistant trees are less likely to burn and
would rate as lower fire risks. Items such as dead trees and trees with dry leaves make
for higher fire risks. These latter items are likely to ignite much more rea
dily than the
former items. The critical density of 59% for an idealized forest, not taking into
account factors other than the bush density, assumes the fire will automatically spread
to relevant neighboring areas if there is a presence of fuel. This is

the equivalent of
making all the fuel 100 percent flammable. By modeling nature more realistically, not
all items are equally likely to burn. This method of ranking the fuel in terms of
flammability more naturally models the different growths and differ
ent levels of
ignition that are found in real environments. Clearly this will involve flammability
levels for individual items of fuel being at or less than 100 percent. Since this will
entail the overall fuel flammability to be less than that when model
ing the critical
density of the idealized forest, the critical density will increase. This increase will be
greatest when flammability levels are low, and only small to moderate when the
flammability levels are high. Obviously, as flammability reaches a
uniform 100
percent then there will be no increase, as the simulation models the critical density of
the idealized forest. It would be expected that with a suitably low range of
flammability levels, even a bush density of 100 percent would be insufficient

to
ensure a long life for the fire.

2.2.2 Heat Conditions

The other factor that determines the actual flammability of a piece of fuel, in addition
to its inherent flammability, is the temperature of the day. The temperature, together
with the humidity an
d recent weather conditions (lack of rain, etc) can be grouped
together under the classification of heat conditions. An alternative way of modeling
the heat conditions would be to alter the bush flammability directly, and thus merge
two potential paramete
rs into one. The reason this is not done is because determining
the final flammability value for a piece of fuel by some combination of the two
parameters allows for a richer and more diverse range. Their separation allows the
same area of fuel to be eas
ily tested with a variety of heat conditions. Alternatively,
areas with different ranges of flammable plants could be tested under similar
conditions to see what effect they may have on the growth of the fire.

The bush flammability at a spot in the artif
icial world is represented by a value
randomly selected from a range. For heat condition, a variable termed ignition level is
used. A value of 1 represents standard conditions (and hence no modification of the
chance of a bush igniting) and 0 removes all

chance of ignition. Values can approach
infinity, where the chance of ignition will approach 100%. To accommodate these
)
1
(
)
)
1
(
1
(
2
h
p
p
old
new




6

criteria, nonlinear equations were used (Foster, 1976). Therefore an increase of 0.2
(for example) will not have the same impact if i
t rises from 1.5 that it will if rising
from 1. The equations below show how the probability of a piece of bush catching
fire is modified by the heat conditions. For heat conditions less than or equal to one:


And for heat conditions greater than or equ
al to one:


The heat conditions are represented by
h

and the probability of the bush igniting is
represented by
p
. Both these equations give a new probability that is the same as the
old probability when the heat conditions are set to 1.

2.3 Land Height

T
he height of the surrounding land has an effect on how likely the fuel there is likely
to ignite. Fuel that is on land that is higher up will be more likely to burn. Fuel that is
on lower land will be less likely to burn. This is due to flames rising as

they burn. By
varying how much of an adjustment a set increase or decrease in height makes to the
fuel ignition level, the rise and fall of the land should shape the growth of the fire. In
nature, a greater adjustment may occur for different types of g
rowth. A forest
composed of many tall trees may burn in a different manner uphill to a forest
composed of equally flammable, yet shorter trees. This variable will enable the
simulation to take into account this variable adjustment to the final ignition le
vel
based upon the relative height of the surrounding land.

In the current implementation, user specified minimum and maximum land height
values are used to create different ramps with constant gradients along the Y
-
axis. As
each cell contains its own att
ribute describing the land height, it should be
straightforward to accommodate more complex landscape information. This can be
done by simply mapping land height (depending on the landscape described by a
specific fire scenario) directly onto each cell ind
ividually.

2.4 Wind

There are two aspects to the wind. The first is its direction, the second its strength.
Together, these aspects are able to shape the growth of the fire by adjusting the
ignition level of surrounding fuel. Fuel that is located downwi
nd of the current
location would have an increased likelihood of igniting. On the other hand, fuel that
is located upwind of the current location would have a reduced chance of igniting.
The adjustment to the ignition levels would come from the strength
of the wind. The
wind in this simulation model is able to remain static for the duration of a run, or able
to fluctuate in both direction and strength.

Although the angle and magnitude of wind can be set, it only allows for a single
basic horizontal wind
. Research points to differing wind speeds and flows at the
ground level of forests as compared to its canopy and the open wind (Cheney
et al
,
2000). Under certain weather conditions known as atmospheric instability, inversion
layers that normally inhibi
t vertical air movement are not present. This results in fires
having a vertical structure reaching thousands of meters in the air and is termed a
)
2
(
)
1
1
)(
1
(
2
h
p
p
p
old
old
new




7

‘blow
-
up’ (SECV, 1985). In these situations, fires behave erratically with wind flow
becoming very three
-
di
mensional (Foster, 1976; Luke and McArthur, 1978;
Clark et
al
, 1997). Fires spread much quicker during atmospheric instability than they do
otherwise. Atmospheric instability is not taken into account in this model.

Another important aspect of the wind t
hat is not implemented in this model is that
of spotting. Wind can carry burning materials far forward, starting additional spotfires
that make combating the fire much more difficult (Cheney
et al
, 2000). Various
materials contribute to spotting, such as

branches and light wood, but bark is
especially dangerous since it can travel long distances due to its light weight and can
reflame during flight (Cheney & Gould, 1998). Some reports state that these
firebrands can light fires 10km ahead of the main fro
nt (SECV, 1985). The ability to
model firebrands and their resulting spotfires is important since it would allow for the
crossing of otherwise impassable objects. Roads and rivers are examples of obstacles
that could halt a fire without the ability of fi
rebrands to ‘leapfrog’ into fresh fuel.
Indeed, other research (Sullivan, 1997) has found that such obstacles can often pose
only a moderate firebreak under low intensity conditions, making little impression on
more high
-
intensity fires. Spotting would r
equire a more intricate model of the wind,
probably in three dimensions.

3. Discussion on Implementation

The model was implemented in Swarm,
a general
-
purpose simulation framework that
provides a set of standard tools for simulating and analyzing complex s
y
s
tems
exhibiting highly decentralized architecture such as a multi
-
agent system
(Stefansson,
1997)
.
A user, prior to the start of the simulation run, can set all of the discussed
factors. In addition, the user is able to allow variation in wind magnitud
e and speed
during the run and can set how much variation will occur. Some of the variables do
not set specific instances but instead allow for upper and lower bounds (such as
minimum fuel and maximum fuel). Such ranges will therefore use a random linear

spread between the specified bounds for actual values and hence the same initial
parameters do not guarantee the same (or even similar) results.

None of the parameters use actual units, or have direct comparisons with current
real
-
world systems. Ignition

level, for instance, does not correspond to any real
-
world
systems such as a fire danger index.

4. Experiments and Analysis

The first simulation runs were completed with average values for variables that
needed to be present and the exclusion of ones th
at could be optional. To this end, the
ground remained flat, the forest was of average density, the range of flammability was
average and there was no wind. Table 1 lists the variables used and briefly describes
their function. Note that while
min_fuel
and
max_fuel

vary from 0 to 100, a value of
15 does not equate to a 15% chance of spreading in any particular direction. Due to
the modeling of the fire, including the life of a particular fire as it consumes fuel and
hence its ability to spread almost at

once or before that particular fire exhausts its fuel,
the fuel is not represented in a linear manner, and is actually somewhat higher. This
value is highly dependent on the lifespan of the flame, which is directly related to the
amount of fuel available

at that spot, since longer lived flames have a greater span of
8

time during which they can spread. Thus the values of 2 and 15 for
min_fuel

and
max_fuel

respectively are probably not unreasonably low.


Table 1.

Main variables affecting fire in a simple fo
rest environment.


Model
Parameters

Initial
Value

Description

world_xsize

128

Horizontal size of the world

world_ysize

64

Vertical size of the world

seed_prob

0.5

The percentage of bush randomly allocated to the world

min_fuel

2

The minimum flammabilit
y of any bush

max_fuel

15

The maximum flammability of any bush

ignition_level

1

The heat conditions at the time.



Figure 2.

A forest of moderate density and average flammability spread.
No wind is present and the ground is flat. Three main areas of

fire (red)
remain near the northern and western areas of the picture. Grey denotes
ash from burnt forest and black represents bare ground. Lighter green
denotes more flammable bush than darker green.

Fig. 2 shows a run nearing completion. The fire is d
ying from starvation with only
three areas of fire remaining. The fire has begun in the centre and worked its way out.
Theoretically, in a large forest with favorable fire conditions, the fire would burn
outwards covering an area approximating a circle.

Clearly that is not the case here.
The fire is constrained by its environment. The amount of fuel and its flammability is
perhaps adequate, but if so, then only just. The fire in this example has “thrived”, that
is, it has reached a boundary (the north
ern boundary). The southernmost ash in the
figure probably died from a lack of flammable bushes, as most of the bushes are
darker, and hence less flammable. There were also few trees there, as evidenced by
9

the black gaps. Of the three remaining areas th
at are lit, the topmost will probably
soon die due to lack of fuel, as will the south
-
western fire. The north
-
western one
looks as if it could survive a little longer, but it is difficult to tell.

Also of interest is the number of flames alive during the
run. In conjunction with
the “Fire over Forest” window, areas and times reveal themselves as weak spots for
the bushfire. Three times in Fig. 3 can be seen a significant dip towards 20
-
25 flames.
During these times the bushfire would have been close to
starvation, and a concerted
attack on the flames could have killed the fire. For fires close to the critical density,
we often find the first dip. If the density is too low, the fire cannot recover from its
initial position to spread to more fertile area
s. On the other hand, if the density is
somewhat higher than the critical density, its recovery is swift and it can quickly blaze
out of control. Dips after the initial one are more difficult to predict. The third dip
after 30 steps was likely due to th
e fire reaching the northern boundary. This is akin
to fire reaching the edge of the forest and dying from a lack of fuel. Other dips can
occur from unfavorable topology of the land to a sudden reversal in the direction of
the wind. We will examine the
effects of topology and the wind in later sections but
first we shall look at the chances of a fire surviving around the critical density.


Figure 3.

The number of flames as time progresses. After the starting
area is lit, flames that are close together

compete to break out into the
wider forest, causing some to die off. The number of live flames generally
increases with occasional dips, before the fire eventually starves
(beginning here after about 40 steps).


4.1 Fire Survival near Critical Density

As

stated earlier, a critical density of bush is required before the fire can spread
unchecked. When the environment is small, such as the previous 128x64 example
shown in Fig. 2, not only is the critical density somewhat higher than the ideal, but the
spre
ad of densities at which some fires thrive and others starve is reasonably large. In
environments 512x512 or greater the critical density is found to be lower (closer to the
10

ideal presented by an infinitely large forest) and the density region where some
fires
thrive and others starve is much narrower (Resnick, 1994). Fig. 4 illustrates this with
20 samples taken at approximately the critical density (roughly half the fires thriving
and half starving), at a point somewhere denser where most of the fires t
hrive and at a
point somewhere less dense where most fires starve. As can be seen, the critical
density is somewhat higher for the larger environment and is more constricted than its
smaller counterpart. The values used for the results shown in Fig. 4 ar
e listed in Table
2. They only differ in size, however note that flammability is idealized to 100% to
promote fire spread, hence the critical densities are lower than might be expected from
Fig. 2. The results from Fig. 4 are suggestive of a critical den
sity of around 41% for a
suitably large forest, in concurrence with results obtained by Resnick (1994). The
region of criticality also appears as though it will become much narrower.




Figure 4
. The critical density and the region over which it exten
ds is
influenced by the size of the environment. A small environment of size
128x128 has a critical density of about 38% extending over a region of
about 4%, whereas the larger environment has a critical density of about
40% extending over a region of 2%.

Variables used are listed in Table 2.


Table 2
. Main variables used in the two environments displayed in Fig. 4.


Model
Parameters

Initial
Value

Description

world_xsize

128 / 512

Horizontal size of the world

world_ysize

128 / 512

Vertical size of the w
orld

seed_prob

Varied

The bush density can be found on Fig. 4.

min_fuel

100

The minimum flammability of any bush

max_fuel

100

The maximum flammability of any bush

ignition_level

1

The heat conditions at the time.

Percentage of Thriving Fires at Different Bush
Densities
0
20
40
60
80
100
0.35
0.36
0.37
0.38
0.39
0.4
0.41
0.42
Bush Density
Percentage of Thriving
Fires
128x128
512x512
11


4.2 Effect of the land height on fire

spread

In this experiment, we simulate changes in the land’s topology. With the same
conditions as previously, we divide the map into thirds. The top third ramps upward
to the east, the middle section remains flat and the bottom third slopes down to the

east. This time the fire is started all along the western edge. This run, shown in Fig.
5, demonstrates the effect that topology has on the spread of the fire. Table 3 shows
the initial model parameter values for the simulation run. The upward slope ha
s
clearly facilitated the spread of the fire in the top third, where more spots of fire are
alive and are further advanced than in the other two sections. The middle section of
flat land actually has no remaining fire, which is a little unusual considerin
g there is
fire still remaining in the bottom third. The downward slope of the third section
should hinder the growth of the fire, which indeed is still far behind the top section
and almost level with where the middle section burnt to. Although a number

of
factors likely contributed to the middle section’s possibly premature demise, a close
examination of Fig. 5 a) shows that a low tree density at its point of furthest growth
would have been a major contributing factor. With regard to all three sections
, each
would have been further constrained by the narrowness of their ramps, which are
clearly visible in Fig. 5 b). Even though fire is able to spread from a lower level to a
higher level or vice versa, there are limits in place which prevent it from spr
eading
across what can be considered veritable cliff faces. A more realistic run would use a
considerably larger area, which in turn would be less constricting on the fire.
Nevertheless, the topology of the land can be clearly seen to have an effect on th
e rate
at which the fire spreads.



(a)






(b)

Figures 5.

A forest divided into three sections: a ramp sloping upwards
and eastward, a flat middle section and a ramp sloping down and to the
east. a) shows the grey burnt trees over the green vegetatio
n whilst b)
shows the height of the land (brighter blue is higher). Both are overlaid
with red spots denoting fire.

12

13


Table 3
. Model parameters for fire spread on three ramps with different variations
in slope.

Model
Parameters

Initial
value

Description

world_xsize

64

The horizontal size of the world

world_ysize

64

The vertical size of the world

seed_prob

0.5

The percentage of bush randomly allocated to the world

min_fuel

2

The minimum flammability of any bush


lowest
probability of burning

max_fuel

15

The maximum flammability of any bush


highest
probability of burning

min_height

0

The minimum height of the land

max_height

200

The maximum height of the land

starting_height

100

The starting height for the west end of the land

ignition_level

1

The

heat conditions of the day



4.3 Effect of the wind on fire spread

This simulation run highlighted the effect of the wind. The area was returned to a
state of flatness and all other variables remained at their previous values from Table 3.
The wind wa
s set to 70 degrees with a moderate magnitude. Table 4 shows the
additional parameter values for this run under wind conditions. The fire was returned
to the centre in order to highlight the direction of growth for the fire. The results,
shown in Fig. 6,
show a strong tendency for the fire to follow the direction of the
wind. However, some spread has occurred to the west of its central starting point, as
can be seen in Fig. 6 a), as can a great deal of northerly spread, more than would be
expected from th
e wind’s small northerly component. Subsequent testing with
varying magnitudes of the wind show the flow of the fire follows the wind more
considerably when the wind’s force is increased, and vice versa as one would expect.
These runs used a static wind;

that is, the angle and magnitude of the wind remained
constant throughout each run. A dynamic wind that had changed direction by 90
degrees during a run would make itself clearly evident, assuming it was of reasonable
strength. The amount to which the w
ind randomly changes, or in other words the
fickleness of the wind, is easily altered by the user at the start of each run, as are all
other variables.

14












(a)







(b)

Figure 6.

The effect of a moderate wind blowing 70 degrees from nor
th.
a) shows the grey ash covering the east side of the forest, where the fire
has spread from the centre. b) shows the direction and magnitude of the
wind (magnitude is indicated by the length of the pointer).


Table 4.

Additional model parameters for s
imulating wind conditions.


Model
Parameters

Initial
value

Description

wind_max_magnitude

0.6

Maximum strength of the wind

wind_magnitude

0.4

Strength of the wind

wind_angle

70

Angle of the wind in degrees

wind_fickleness

0

Amount of change in strength

and angle.



5. Conclusion

This paper has presented a method for simulating fire spread by utilizing a cellular
automaton approach within the Swarm simulation framework. A simulation model
has been displayed which will allow for interaction between the
fire and the
environment, taking into account all major environmental factors such as
bush density
,

land height
,
flammability
, and
wind condition

that may affect fire growth and spread.
These factors have undergone testing under some initial conditions, an
d as a
consequence of their combined effect, the fire
-
spread behavior at the landscape level
can be observed to mimic the phenomena of fire spread in nature. In the future, other
environmental factors such as radiation, convection (radiation from and conv
ection
into the advanced flame tends to speed up the movement of flames immediately
15

adjacent to it) and spotting may be incorporated into the current model. More
experiments will be conducted to investigate what impact these factors might have on
fire spre
ad behavior. Another possible extension is to integrate the model with a
Geographic Information System (GIS). This could allow geographic data to be
mapped directly onto the CA during a simulation run.


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