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CHEMICAL ENGINEERING TRANSACTIONS
VOL. 53, 2016
A publication of
The Italian Association
of Chemical Engineering
Online at www.aidic.it/cet
Guest Editors: Valerio Cozzani, Eddy De Rademaeker, Davide Manca
Copyright © 2016, AIDIC Servizi S.r.l.,
ISBN 978-88-95608-44-0; ISSN 2283-9216
Reducing Wildland Fire Hazard Exploiting Complex Network
Theory: a Case Study Analysis
Lucia Russo*a, Paola Russob, Constantinos I. Siettosc
a
Combustion Research Institute,Consiglio Nazionale delle Ricerche, Naples, Italy
b
Department of Chemical Engineering Materials Environment, Sapienza University of Rome, Rome, Italy
c
School of Applied Mathematics and Physical Sciences, National Technical University of Athens, Greece
lrusso@irc.cnr.it
We discuss a new systematic methodology to mitigate wildland fire hazard by appropriately distributing fuel
breaks in space. In particular, motivated by the concept of information flow in complex networks we create a
hierarchical allocation of the landscape patches that facilitate the fire propagation based on the Bonacich
centrality. Reducing the fuel load in these critical patches results to lower levels of fire hazard. For illustration
purposes we apply the proposed strategy to a real case of wildland fire. In particular we focus on the wildland
fire that occurred in Spetses Island, Greece in 1990 and burned the one third of the forest. The efficiency of
the proposed strategy is compared against the benchmark of random distribution of fuel breaks for a wide
range of fuel breaks densities.
1. Introduction
Uncontrolled wildland fires have been the cause of widespread environmental, biota, structural hazards and
significant human loss (Albini and Brown, 1996; Heymes et al., 2013; Vincent et al., 2015). According to the
Food and Agriculture organization of the United Nations (FAO) an average of 19.8 million hectares of forests
were affected by fire annually. During the wildland fire that swept through Victoria, Australia in 2009, caused
the death of 173 people (2009 Victorian Bushfires Royal Commission, 2010), while wildland fires in Greece in
2007 fires resulted in 84 dead (Rosenfeld, 2011). On the other hand, it has been also recognized the
prescribed fires are essential elements in the renewing process of ecological cycle of forests. For example
several species depend on wildfires to improve habitat, and maintain diverse communities (NC Cooperative
Extension, 2002; USGS, 2006).
For this reason, the majority of prevention activities make use of fuel reduction which may be obtained with
prescribed fires or with mechanical treatment of the vegetation. Prescribed fires are run to benefit natural
resources and reduce the risk of unwanted wildfires in the future. Mechanical treatment of fuels means
reducing the amount of vegetation which has built up to dangerous levels, or changing the arrangement of
these fuels in the environment. Mechanical treatments can benefit ecosystems and people by: i) reducing the
probability of catastrophic fires; ii) helping maintain and restore healthy and resilient ecosystems; iii) protecting
human communities.
The allocation of fuel breaks (mainly zones without vegetation) has been demonstrated to reduce the fire
intensities and increase survival of some forest types. This not only reduces the negative impacts on those
forests but the wildfire itself may very well provide benefits in the form of additional fuel management and
ecological process (Finney, 2005; Parsons, 2006; ).
Spatial patterns of fuel treatments can theoretically alter the propagation rate of large fires (Finney, 2001,
2003). By reducing the overall growth rate of a fire, the probability is reduced that a fire will impact a given site
in a given time period as a heading fire. Slower moving fires have reduced intensity and create less negative
net value change for some ecosystem resources. In any case the fuel reduction increases the chance that
suppression action can intervene in fire growth before reaching certain portions of the landscape.
Land managers and decision makers have been using fire behavior and simulation models as a tool to predict
fire potential and identify area with high risk of wildfires. However, the widely used existing simulation models,
such as FARSITE (Finney, 1998), NEXUS (Scott, 1999), FFE-FVS (Reinhardt and Crookston, 2003),
DOI: 10.3303/CET1653004
Please cite this article as: Russo L., Russo P., Siettos C., 2016, Reducing wildland fire hazard exploiting complex network theory: a case study
analysis, Chemical Engineering Transactions, 53, 19-24 DOI: 10.3303/CET1653004
19
BehavePlus (Andrews et al., 2005), and FlamMap (Finney, 2006) use the average attribute values of a forest
for predictions without considering spatial variability in fuels and vegetation within a forest.
To overcome these limitations, recent effort has been put into the development of advanced physics-based
numerical fire behavior models capable of considering spatial variability of fuels within forest as well as fuel
and atmosphere interactions (Penman et al., 2014; Lauret et al., 2014; Platt et al., 2015). The wildland-urban
interface fire dynamics simulator (WFDS), an extension of FDS developed by the US Forest Service and NIST
(Mell, 2010), is one of the models that simulate fire initiation and propagation as a fine-scale, physics-based
process that takes into account size, shape, composition and spatial arrangement of fuel particles.
However, practical applications of the fine-scale fire behavior models have been limited due to the large
amount of data and computation time required to represent detailed variability of fuels within a forest and
model the time-dependent fine scale fire–fuel and fire–atmosphere interactions.
In this work we propose a computational approach introduced in (Russo et al., 2005a), where the landscape is
represented as a (lattice) network whose links reflect the fire spread probabilities (Alexandridis et al., 2008;
2011a). The model may incorporate detailed GIS, landscape and meteorological data (Alexandridis et al.,
2008; 2011a; 2011b; Russo et al. 2013, 2015a,b). For the definition of the spatial distribution of fuel breaks,
the group of nodes through which the fire spreads faster are found. To this aim, the network centralities are
computed and the nodes with the bigger centralities are removed from the network. Finally, as an example we
apply the proposed strategy to a real case of wildland fire that occurred in Spetses Island, Greece in 1990 and
burned the one third of the forest.
2. Methodology
The proposed approach provides a systematic methodology for the spatial distribution of fuel breaks including
the heterogeneity of landscapes and metereological data. The approach consists of three steps (Russo et al.,
2015a): (i) the landscape is represented as a (lattice) network whose links reflect fire spread probabilities, (ii)
the network centralities are computed, and, (iii) the nodes with the bigger centralities (i.e. the nodes through
which the information flows faster within the network) are removed from the network. A detailed Cellular
Automata (CA) simulator (Alexandridis et al., 2008, 2011b) is utilized for the first step, while, for the second
step, the Bonacich centrality is used (Bonacich and Lloyd, 2001). Hence, the spatial distribution of fuel breaks
is reduced to the problem of finding a partition of network nodes that when removed the flow information (i.e.
the fire propagation) goes slower.
2.1 The Cellular Automata model
The CA model (Alexandridis et al., 2008, 2011b) assumes that, at each time step t, each (i, j) cell has one of
the following discrete states: State(i,j,t)=1: a cell is without burning fuel (city, rural areas); State(i,j,t)=2: a cell is
burning; State(i,j,t)=3: a cell has been burned.
The model evolves according to the following rules:
Rule 1: IF state(i, j, t) = 1 THEN state(i, j, t+1) = 1, which implies that a cell with no fuel cannot be burned;
Rule 2: IF state(i, j, t) = 2 THEN state(i, j, t+1) = 3, which implies that burning cells are burned at the next time
step;
Rule 3: IF state(i, j, t) = 3 THEN state(i, j, t+1) = 3, which implies that burned cells do not reignite;
Rule 4: IF state(i, j, t) = 2 THEN state(i±1, j±1, t+1) = 2 with a probability pb, which implies that the fire is
propagated to the neighbour cells with probability pb defined as follows:
(1)
where p0 is a nominal probability of fire spread under no wind condition, flat terrain and certain density and
type of vegetation, that is calculated from experimental data; pden is related to density of the vegetation, pveg to
the type of the vegetation, pw to the wind field (speed and direction), ps to the local slope. The effect of wind,
is modeled as follows:
, (2)
where c1, c2 are constants and θ is the angle between the direction of the fire propagation and the direction of
the wind.
The factor related to the slope-effect is given by:
( )1 10p p p p p pb veg den w s = + +
pw = exp c1V( ) ft ft = exp Vc2 cos θ( ) − 1( )( )
20
,
1 1 2tans
E E
l
θ −
− =
(3)
where E1 and E2 are the altitude of the two cells and l is the length of the square side, while for diagonal cells
−
= −
2
211
l
EE
s tanθ (4)
The above model can integrate GIS, meteorological data as well as vegetation characteristics including
flammability.
2.2 The reconstruction of the network and computation of centralities
The landscape is represented by a network of interconnected patches, , where
is the set of vertices corresponding to the N total cells and E is the set of elements
which are the links between neighbor cells .The weights of links are , where
are the probabilities computed with the CA simulator.
As said before, the spatial distribution of fuel breaks is reduced to the problem of finding a partition of network
nodes that when removed the flow information goes slower. Therefore, for the determination of these nodes
the centrality for each node is computed. Here, we used the Bonacich centrality (Bonacich and Lloyd, 2001)
which for node k is defined as the k-th component of:
1
max
x I eΑ
β
λ
−
= −
, (5)
where e is a vector of ones and is the largest eigenvalue of . For , the above expression
reduces to the degree centrality, while for it reduces to the standard Eigencentrality. Thus a high value of
betweenness centrality implies that the corresponding cell is connected with other cells by relatively shorts
paths and so is central to the information flow (and therefore the fire spread) in the network.
2.3 Hazard Assessment
The hazard intensity R, with respect to the density of fuel breaks df, is defined as follows:
( ) ( )
1
1 rN b
f
ir v
N i
R d
N N=
= (6)
(7)
where df is the ratio of the number of fuel breaks Ne and the total number of nodes that contain flammable
vegetation Nv, while Nr is the number of simulations for a given initial condition and Nb denotes the total
number of burned nodes.
3. Simulation Results
For our analysis we took as paradigm the case of the wildland fire that occurred in Spetses in August, 1990.
The fire ignited near the middle of the island’s forest and was quickly spread to the south by moderate to
strong north winds. The fire was extinguished around 11 hours later, after having burned down a forest area of
8 km2, almost one third of the total area of the island. Figure 1a shows a map of Spetses island with the actual
burned area and the corresponding scaling of the density of vegetation (1 is for sparse and 3 is for dense
vegetation; 0 is for agricultural areas and 4 is for city). Figure 1b shows a typical simulation using the CA
ps = exp aθs( )
( ), G V Ε
{ } , 1, 2, ..., kV v k N= =
k lv v
e { , }k lv v i jv v be p→ = bp
λ
max
A β = 0
β = 1
v
e
f N
N
d =
21
model. The CA simulator approximates adequately the fire spread both in time and space: the wildfire burned
an area of about 590 ha in 11 hours; the CA simulator resulted to a 540 ha burned area (almost equivalent to
the actual burned area) in 11.3 hours (Alexandridis et al., 2008).
Figure 1. (a) A map of Spetses island with vegetation scaling (0-3) and the actual burned area (black). 0 is for
argiculatural areas, 1 for sparse density of vegetation, 3 for dense density of vegetation, and 4 is for city, (b) A
typical simulation using the CA model. The ignition point is marked by the red ellipse.
Figure 2 shows the diagram of the hazard intensity, as obtained using the proposed approach with
and by averaging 50 simulation runs all starting from the ignition point of the real fire incident.
Maximum values of the burned area are also illustrated with bars. The results obtained with the random
distribution tactic are also shown for comparison purposes. All differences were found to be statistically
significant under the t-test criterion with a threshold set at 0.1.
Figure 2. Fire hazard, R(df) over Nr=50 runs. Circles correspond to the fire hazard resulting when distributing
the firebreaks with the proposed approach (Bonacich centrality with ). Squares correspond to the fire
hazard obtained using random distribution of fire breaks. Maximum values of the burned area are also
illustrated with bars.
200 400 600 800 1000 1200
100
200
300
400
500
600
700
800
900
1000
-3
-2
-1
0
1
2
3
4
200 400 600 800 1000 1200
100
200
300
400
500
600
700
800
900
1000
-3
-2
-1
0
1
2
3
4
( )fR d
0 5.β = Nr =
=a
β = 0.5
22
The random distribution tactic has been applied in previous theoretical studies, which have shown that a
random or compartmented distribution of fuel breaks reduce the spread rate of the fire While the contrary,
regular patterns like parallel stripes work affectively just when the direction of fire propagation is perpendicular
to the stripes (Russo et al. 2014).
Simulations results in Figure 2 show that the proposed approach for the distribution of fuel breaks results in
statistically significant lower hazards than that obtained by the random distribution tactic.
4. Conclusions
The majority of activities for forest fire prevention make use of fuel reduction which may be obtained with
prescribed fires or with mechanical treatment of the vegetation. The allocation of fuel breaks to reduce the fire
intensities and propagation velocity is then crucial for the forest fire management. Towards this aim we
propose the adoption of a new methodology introduced in (Russo et al., 2005a). The approach is based on the
complex network theory and a detailed CA modelling, and use the concept of centrality criterion, for the
evaluation of information flow through complex networks. Moreover, the CA model can consider spatial
heterogeneity in both fuel and landscape characteristics and can take as input local meteorological data. The
ability of the CA simulator to adequately approximate the fire spread both in time and space has been shown
by comparison with wildland fire that occurred in Spetses Island, Greece in 1990. The efficiency of the
approach was compared against the typical random tactic of fuel. Simulations results showed that the
proposed approach results in statistically significant lower hazards.
Acknowledgments
Lucia Russo would like to thank Marco Imparato for his technical support.
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