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Simulations of Forest Fires by Cellular Automata
Modelling
ERMINIA BENDICENTI*, SALVATORE DI GREGORIO*, FRANCESCO
M. FALBO# and ANGELA IEZZI*
*Department of Mathematics, University of Calabria, Arcavacata, 87036 Rende, Italy;
#Comando Provinciale Vigili del Fuoco CS, viale Repubblica 56, 87100 Cosenza, Italy
ABSTRACT
Forest fires represent a serious environmental problem, whose negative
impact is becoming day by day more worrisome.
Forest fires are very complex phenomena; that need an interdisciplinary
approach. The adopted method to modelling involves the definition of local
rules, from which the global behaviour of the system can emerge. The
paradigm of Cellular Automata was applied and the model ABBAMPAU
was projected to simulate the evolution of forest fires.
First simulations account for the main characteristics of the phenomenon
and agree with the observations. The results show that the model could be
applied for the forest fire preventions, the productions of risk scenarios and
the evaluation of the forest fire environmental impact.
KEYWORDS: Forest Fire, Cellular Automata, Complex Systems.
1. INTRODUCTION
Cellular Automata (CA) are a paradigm of parallel computing; they are
good candidates for modelling and simulating complex dynamical systems,
2 Erminia Bendicenti et al.
whose evolution depends exclusively on the local interactions of their
constituent parts (Di Gregorio and Serra, 1999).
A CA involves a regular division of the space in cells, each one
characterised by a state that represents the actual conditions of the cell. The
state changes according to a transition function that depends on the states of
neighbouring cells and of the cell itself; the transition function is identical
for all the cells. At the time t=0, cells are in states, describing initial
conditions, and the CA evolves changing the state of all the cells
simultaneously at discrete times, according to the transition function.
The CA features seem to match the system “forest fire”; the parameters,
describing globally a forest fire, i.e. propagation rate, flame length and
direction, fireline intensity, fire duration time et c. are mainly depending on
some local characteristics i.e. vegetation type (live and dead fuel), relative
humidity, fuel moisture, heat, territory morphology (altitude, slope), et c..
The only global characteristic is given by wind velocity and direction, but
wind velocity and direction is locally altered according to the morphology;
therefore wind has also to be considered at local level.
The fundamental studies of Rothermel (1972, 1983) point out these
characteristics; its forest fire spread model is based on dynamic equations,
that allow the forecast of the rate of spread and the reaction intensity
knowing certain properties of the fuel matrix (fuel particle, fuel
arrangement) and environmental conditions (slope, wind, fuel moisture) in
which the fire occurs.
Some models were previously developed in terms of CA: Green (1983a,
1983b) considered a two-dimensional square CA, where each cell is
identified by fuel content and its combustion duration. The fire-spread
mechanism is shortly the following: each burning cell generates an ellipse
with a focus at the cell centre; the ellipse dimension and orientation is
depending on the wind direction and strength. If a cell with fuel content is
inside an ellipse, it will burn at the next steps.
Gonçalves and Diogo (1994a, 1994b) developed a more complex
probabilistic CA model based on the Rothermel’s (1972, 1983) equations of
fire rate spread. A burning cell determines, according the fire rate spread
toward the direction of neighbouring cells, an ignition probability.
Malamud and Turcotte (2000) developed a statistical model of
comprehensive effects in a forest for the two opposite phenomena of trees
taking root in free areas and trees burnt by the fire.
The proposed CA model ABBAMPAU (Iezzi, 2000) is deterministic, it is
related to Rothermel’s studies (1983) and is based on an empirical method
(Di Gregorio and Serra, 1999) that may be applied to some macroscopic
phenomena in order to produce a proper CA model. The main points of the
method are here illustrated shortly:
1. The state of the cell must account for all the characteristics, relevant to the
evolution of the system and relative to the space portion corresponding to
Simulations of Forest Fires by Cellular Automata Modelling 3
the cell; e.g. the altitude. Each characteristic must be individuated as a
substate. The substate value is considered constant in the cell.
2. As the state of the cell can be decomposed in substates, the transition
function may be also split in many components. We distinguish two types
of components: internal transformation, depending on the substates of the
cell and local interactions, depending on the substates of the cells in the
neighbouring. Local interactions may be treated in terms of flows of some
quantity or propagation of properties towards the neighbouring cells, in
order to reduce “unbalance” conditions, e.g. fire propagation.
3. Special functions must supply the history of “external influences” overall
on the CA cells and direction.
4. Some cells represent a kind of input from the “external world” to the CA;
it accounts for describing an external initial influence, which cannot be
described in terms of rules; e.g. the fire starting points.
This paper illustrates in the next section the model ABBAMPAU, the CA
transition function is described in the successive section; the fourth section
treats the model implementations and first results of applications; at the end
comments conclude the paper.
2. THE CA MODEL ABBAMPAU
A CA was developed for simulating forest fire; its was named
ABBAMPAU (ABating Burning danger through A Model Provided by
cellular AUtomata - to be read “ahb-bahm-‘pah-oo”, as the acronym was
devised to mean “it blazed up” in Calabrian and Sicilian language).
A first release of ABBAMPAU was developed (Iezzi, 2000);
improvements have been added in order to better simulate real events. The
following model represents our more complete version that was partially
implemented on a real case.
ABBAMPAU is a two-dimensional CA with square cells:
ABBAMPAU = <R, X, S, P, σ, I, Γ>
where
• R = {(x, y)| x, y ∈ N, 0 ≤ x ≤ lx, 0 ≤ y ≤ ly} is the set of points with integer
co-ordinates in the finite region, where the phenomenon evolves; N is the
set of natural numbers; each cell corresponds to a territory portion.
• The set X = {(i, j)| x, y ∈ N, 0 ≤ x ≤ lx, 0 ≤ y ≤ ly} identifies the geometrical
pattern of the cells (Moore neighbouring), which influences the change in
the state of each one (respectively the central cell and the surrounding
ones).
• The finite set S of the states of the cell is:
S = SA × SV × ST × SH × SC × SD × SWD × SWR × (SFS)8
o SA, substate “altitude”, takes the altitude value of the cell;
4 Erminia Bendicenti et al.
o SV, substate “vegetation”, specifies the type of vegetation, relatively to
the properties of catching fire and burning;
o ST, substate “temperature”, takes the temperature value of the cell;
o SH, substate “humidity”, takes the relative humidity value of the cell;
o SC, substate “combustion” for the two possible fire types in the cell:
“surface fire” and “crown fire”; it takes one of the values “non-
inflammable”, “inflammable”, “burning” and ”burnt” for each type.
o SD, substate “duration”, takes the value of the duration rest of the fire in
the cell;
o SWD, substate “wind direction”, takes the values of the wind directions
(the eight directions of the wind rose) at ground level (that could be
different from the free wind direction);
o SWR, substate “wind rate”, takes the values of the wind rate (Km 0-60) at
ground level (that could be different from the free wind rate);
o SFS, substate “fire spread”, accounts for the fire spread from the central
cell to the other neighbouring cells; SFA , substate “fire acquire”, is just a
renaming of SFS and individuates the fire propagation to the central cell
from the other neighbouring cells.
• P is the finite set of global parameters, which affect the transition function;
they are constant overall in the cellular space:
o pe, the size of the cell edge; in this case the size of the cell is m.20.
o ps, the time corresponding to an ABBAMPAU step; the step of
ABBAMPAU is 3 minutes.
o Pv, the set of parameters concerning catching fire and burning,
depending on the type of vegetation; they are also constant in time. Other
parameters are
o pt, the current time (month, day, hour and minute),
o pw, the weather conditions depending on the sun and concerning a fixed
characteristics: exposure and characteristics, varying during the day
according the season: reference values of humidity and temperature
(such values are correct considering the type of vegetation, the wind and
in the case of a previous raining episode as far as a month
o pwd, the free wind direction
o pwr, the free wind rate;
Note that the function γ1 keeps pt up-to-date, the function γ2 supplies the
history of pw, pwd and pwr at each CA step.
• σ:S9→S is the transition function, that will be sketched in the next section;
it accounts for the following aspects of the phenomenon: effects of
combustion in surface and crown fire inside the cell, crown fire triggering
off; surface and crown fire spread, determination of the local wind rate and
direction.
• I⊂ R individuates the cells, where the fire starts.
• Γ = {γ1, γ2, γ3, γ4} is the set of functions representing an external influence
Simulations of Forest Fires by Cellular Automata Modelling 5
on ABBAMPAU. They are computed at each step before the application of
σ.
o γ1:ps×pt→pt determines the current time of the CA step;
o γ2:N→pw×pwd×pwr supplies the weather conditions related to sun, the
external wind direction and rate, N is the set of natural numbers
identifying the ABBAMPAU steps;
o γ3:N×I→SC accounts for external setting fire to cells of I at prefixed
steps;
o γ4:N×R→SC accounts for firemen intervention at prefixed steps.
3. THE TRANSITION FUNCTION
The transition function involves the following internal transformation,
concerning the effects of combustion in surface and crown fire inside the
cell:
o σT1 : SV×ST×SH×SC×SD×SWD×SWR×Pv×pw×pt → ST×SH×SC×SD.
The following local interactions that compute, in order, the wind
direction and rate at the cell altitude, the change of combustion conditions
cell, the fire spread toward the neighbouring cells:
o σI1: (SA)9 × pw × pt × pwd × pwr → SWD × SWR
o σI2: (SFA)8 × SC → SC
o σI3: (SA)9 × SV × SC × SH × ST × SD × SWD × SWR × ps × pe × Pv → (SFS)8
The internal transformation and the local interactions are computed in the
same order of the presentation. the transition functions is computed
T1) When the substate S
C is not “burning”, then it doesn’t change
together the substate SD, while the substates SH and ST vary their previous
values on the basis of the weather change (pw), the day hour (pt), the wind
(SWD and SWR) and the vegetation type (SV and Pv). When the substate SC is
“burning”, then the substates S
T, S
H, S
C and S
D depend on the previous
values of SH, SD and ST. The value 0 for SD determinates the change of SC to
“burnt”. The conditions for the ignition from fire surface to crown fire are
applied in T1.
I1) The computation of the substates SWD and SWR, “wind direction and
rate” depends on pwd and pwr that represent the values of the free wind. Such
values are reduced in relation to the altitude of the cell according to an
empirical table of Rothermel (1983), obtaining the wind vector, related to the
cell altitude. A corrective vector wind is computed, considering the angle
between the slope relative to the cell and the free wind direction. It accounts
on that, in absence of free wind, convective currents form along the
maximum slope directions; their rate depends also on the weather and the
hour of the day. Empirical tables of Rothermel (1983) indicate the value of
6 Erminia Bendicenti et al.
such vector. The new values of SWD and SWR are obtained adding the altitude
vector to the corrective vector.
I2) This functions tests if the fire is spreading toward the central cell from
the other cells of the neighbouring. If the combustion substate S
C is
“inflammable”, then it changes to “burning”.
I3) Three computation steps are considered, if the state SC is “burning”:
a) It is calculated a circle, whose radius is proportional to the fire intensity,
depending on substates S
V, S
H, S
T, S
D and the set of parameters P
v; of
course the time corresponding to the step of ABBAMPAU ps and the size
of pe effect also the size of the circle.
b) Such circle is transformed in ellipse with a focus in the centre of the cell,
considering the effects of the wind (substates SWD and SWR).
c) The fire can propagate towards the neighbouring cells inside the ellipse,
i.e. SFS takes the value “true”.
4. IMPLEMENTATION AND PRELIMINARY
APPLICATIONS
The implementation of ABBAMPAU was developed in the programming
language Delphi. Minor features of the model were not implemented: cells
are considered burning indefinitely (lack of substate SD and value “burnt” of
SC), but this absence does not affect the simulation; the parameter pw, is not
considered to be influenced by the wind (SWD and SWR), because a satisfying
more precise correlation is not significant at this level of the model.
A first validation of this new release of ABBAMPAU was tested on a real
case of forest fire (fig.1) in the territory of Villaputzu, Sardinia island,
August 22nd, 1998, (SALTUS, 1998-2000). This forest fire was a case
treated and monitored in the milieu of European Research Program
SALTUS, Environment and Climate, (1998-2000). The beginning time was
very nearly 12.30 and lasted less than 9 hours. The wind was in direction SE
at a rate 20-30 Km/h. The burnt area is approximately Km2 3.
The forest fire area in Fig. 1 is well evidenced by colours specifying the
different type of burnt vegetation:
- light-blue colour represents a vegetation of cistus, (on the left top, at the
starting point of forest fire);
- light-green colour represents the prevalent vegetation, maquis with cistus,
phillyrea and lentiscus;
- dark-green colour represents a forest of conifers with some oaks;
- chestnut colour represents a vegetation of maquis with junipers
The dotted lines individuate the roads. The roads on the left and on the
right of the initial area of the fire represents a barrier, because the human
Simulations of Forest Fires by Cellular Automata Modelling 7
intervention to limit the fire spread is easily performed in the zones adjacent
to roads.
Figure 1. The forest fire of Villaputzu, August 22nd, 1998.
The simulated area (fig. 2 A, B, C, D, E, F) is visualised at each
simulation step by a square matrix with 168 rows and 131 columns; the cell
edge is m 20; the contour lines are blue, the sea is blue-grey, the burning
cells are red and natural or artificial fire barriers (also determined by the
firemen intervention) are black.
The forest fire started in the light-blue area on the left top of fig. 1; the
third step of the simulation (fig.2-A, less than 10 minutes) individuates the
first cells burning. In the matrix of simulation, a barrier is introduced in the
flat area on the right of the fire beginning area, because an easy human
intervention was performed there.
In the step 70 (fig.2-B, 3.5 hours), the fire is reaching rapidly the peaks of
mountain; a fire jump is introduced after the central peak in order to account
for the strict gorge that cannot be well relieved because of the precision lack
of our morphological data. The strict gorge permits an easy fire spread.
8 Erminia Bendicenti et al.
The fire is propagating according the wind direction. The positive slope
enlarges also the fire toward E, NE (fig.2-C, 6.5 hours; fig. 2-D, less than 7.5
hours). Then the propagation toward the wind direction is almost exhausted,
its rate slows with negative slope (fig. 2-E, almost 8 hours). The only
propagation directions are now toward SW and the fire died out (fig.2-F, less
than 9 hours).
Figure 2. Sequence of six simulation steps: figures A, B, C, D, E, F correspond respectively
to steps 3, 70, 130,147, 162, 175.
Fig. 3 and 4 represent respectively the superimposition of the figures of
simulated fire on real fire and vice versa. The result of simulation looks
good, few areas of the real fire don’t appear to be burnt in the simulation and
few areas, which were not burnt, are computed to be “burnt” in the
simulation.
Simulations of Forest Fires by Cellular Automata Modelling 9
5. CONCLUSION
The results of the simulations show a phenomenon development that fits
significantly with real data but it is necessary to stress some problems:
- standard fire records don’t account for all the data necessary to the
simulation; e.g. firemen intervention was inserted in simulation according
to good sense considerations;
- vegetation data are usually incomplete;
- Rothermel tables [1972, 1983] must be modified and completed according
the features of European vegetation; they must be improved in
consideration of local humidity;
- the spurious symmetries of the square tessellation can effect negatively the
simulation in flat areas; our final results are good because the presence of
flat areas is not relevant.
A first improvement of the model involves the introduction of hexagonal
cells; the wind directions must be increased; fires with more complete data
must be considered.
Figure 3. Simulated forest fire vs real forest fire of Villaputzu.
10 Erminia Bendicenti et al.
Figure 4. Real forest fire vs simulated forest fire of Villaputzu.
ACKNOWLEDGEMENTS
The authors thank the components of European Research Program
SALTUS, Environment and Climate, (1998-2000) for the precious data
utilised in this research.
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