Ecological Modelling 164 (2003) 1–20
Spatial patterns of lightning-caused forest fires in Ontario,
1976–1998
Justin Podur a,∗ , David L. Martell a , Ferenc Csillag b,1
a
b
Faculty of Forestry, Earth Sciences Centre, University of Toronto, 33 Willcocks Street, Toronto, Ont., Canada M5S 3B3
Department of Geography, University of Toronto, 3359 Mississauga Road North, Mississauga, Ont., Canada L5L 1C6
Received 6 June 2001; received in revised form 22 July 2002; accepted 22 July 2002
Abstract
The spatial pattern of forest fire locations is of interest for fire occurrence prediction and for understanding the role of fire in
landscape processes. A spatial statistical analysis of lightning-caused fires in the province of Ontario, between 1976 and 1998, was
carried out to investigate the spatial pattern of fires, the way they depart from randomness, and the scales at which spatial correlation occurs. Fire locations were found to be spatially clustered. Kernel estimation of the spatial pattern of lightning strikes on days
when the dryness of the forest floor exceeded a designated threshold yielded clusters in the same areas as the lightning fire clusters.
© 2002 Elsevier Science B.V. All rights reserved.
Keywords: Forest fires; Lightning; Fire danger rating; Spatial statistics; K-function; Spatial correlation
1. Introduction
From 1976 to 1998, the province of Ontario in
Canada experienced an average of 1700 forest fires
per year, with an average of 242,000 ha burned.
Fire is a part of the ecology of the boreal forest. It is
one of the primary agents of renewal and succession
in the boreal forest. Many species are adapted specifically to fire-affected habitats. In many ways the boreal
forest is a forest shaped by fire.
Although fire is natural, it often poses a threat to
public safety and can destroy economically and socially valued forests. In Ontario, approximately CAD$
∗ Corresponding author. Tel.: +1-416-978-6960;
fax: +1-416-978-3834.
E-mail addresses: justin.podur@utoronto.ca (J. Podur),
martell@smokey.forestry.utoronto.ca (D.L. Martell),
fcs@geog.utoronto.ca (F. Csillag).
1 Tel.: +1-905-828-3862; fax: +1-905-828-5273.
85 million per year is spent on fire management programs by the Ontario Ministry of Natural Resources
(OMNR, 2001). The OMNR’s fire managers seek to
balance the ecological role of fire, the threat it poses
to public security and property, and the costs of fire
management.
Fire management planning, particularly for the long
term, requires an understanding of the relationships
between fire, weather, vegetation, topography, and
fire-management activities. These relationships can
be investigated from many perspectives. The present
study advances the understanding of the spatial dynamics of lightning-caused fire occurrence. The spatial scale of the study is provincial (landscape) and
the temporal scale is annual.
1.1. Previous research
Lightning-ignited fires contribute 85% of the area
burned and 35% of the fires reported in Canada (Weber
0304-3800/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 3 0 4 - 3 8 0 0 ( 0 2 ) 0 0 3 8 6 - 1
2
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
and Stocks, 1998). Lightning fires burn a disproportionate share of area because they are more likely
to occur in remote areas, where they are harder to
detect and reach, and they arrive in spatial and temporal clusters that can strain the fire organization.
Both of these factors can lead to lightning-caused
fires burning for longer periods of time before they
are extinguished. Because of their important contribution to the total number of fires and area burned,
research into them has been a priority since organized
fire protection arose. Latham and Williams (2001)
review many studies of lightning-caused fires. They
cite Plummer (1912) who summarized research from
Europe and US Forest Service lands. Plummer (1912)
reported that any species of tree is equally likely to
be struck by lightning. Gisborne (1926) studied 2186
fire reports from the US covering a 3-year period and
classified lightning storms as ‘safe’ and ‘dangerous.’
In a subsequent study, Gisborne (1931) found that
‘safe’ storms had both fewer cloud-to-ground (CG)
lightning flashes and a longer duration of rainfall, but
did not resolve whether it was characteristics of the
rainfall or the lightning that made safe storms safe.
Latham and Williams (2001) describe the characteristics of the lightning ground flash:
(Cloud–Ground) lightning is most commonly initiated within the cloud, in the vicinity of the
lower-charge reservoir (usually negative). An ionized path, the stepped leader, is forged through
the air toward ground in a region of high electric
field. This stepped leader carries the large negative
potential of the lower-charge region toward Earth.
As the stepped leader nears the earth, an intense
electric field develops between leader and ground.
The field promotes electrical streamer propagation
upward from elevated points on the ground that can
connect to the approaching leader. When a connection is made, the bright, high-current (10–100 kA)
return stroke is initiated and propagates upward toward the cloud at a speed approaching that of light
(1–2 × 108 m/s) . . .
. . . In the majority of ground flashes, the return
stroke current peaks, in less than 1 ␮s, to values in
the range of 5–30 kA and then promptly decays in
a few hundred microseconds. Despite the extraordinary peak power of such events, both observations
and simulations have shown that the short dura-
tion of the return stroke is inadequate to raise trees
and other flora in the path to kindling temperature
and initiate fire. (Taylor, 1969; Darveniza and Zhou,
1994)
Latham and Williams (2001) describe how 30% of
return strokes lead to a continuing current that is long
enough in duration to ignite vegetation.
Many lightning strikes cause only mechanical damage and do not ignite fires, although no statistics are
available on the proportion of strikes that do so (ibid).
There is anecdotal evidence that ignition takes place
in the fine fuels on the forest floor (ibid).
Morris (1934) studied lightning and fire reports in
Oregon and Washington and reported (1) that fires
were no more likely at higher altitudes than at lower
ones, (2) no reliable ‘danger zones’ for lightning
fires based on historical distributions of fires, (3) no
definite lightning-storm lanes or frequent ‘breeding
spots,’ (4) thunderstorm days can be classified to
indicate fire-starting potential (using a classification
like Gisborne, 1931) and (5) storms with high rainfall
lead to fewer fires. Fuquay et al. (1967, 1972) found
evidence that the cause of lightning ignitions was the
continuing current in the lightning flash. The duration
of the continuing current in lightning flashes varies
significantly (Uman, 1987), and long continuing current (LCC) flashes are the only flashes which ignite
forest fires (Latham and Williams, 2001).
More recent studies, in Canada, utilize the fuel
moisture descriptions of the Canadian Forest Fire
Weather Index System (CFFWIS) (Van Wagner, 1987)
and lightning-locator technology. In the Fire Weather
Index (FWI) system, daily weather observations are
used to calculate numerical ratings representing the
moisture contents of different fuel layers. The calculated numerical ratings of the moisture contents are
combined to generate general indices of potential fire
spread and consumption. Lightning locators detect the
location, time and intensity of lightning strikes. They
have an accuracy of location of 3–4 km and efficiency
of 70% (Flannigan and Wotton, 1991). Using these
technologies, McRae (1992) found no relationship
between elevation, slope, aspect, or topography and
lightning fires in the Australian Capital Territory, but
Van Wagtendonk (1991) found altitude-dependence
for lightning-caused fires in Yosemite National
Park. Renkin and Despain (1992) found no altitude
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
dependence in Yellowstone Park but did find a dependence on fuel type and fuel moisture content.
An approach frequently employed is to study the
lightning efficiency, that is, the number of fires ignited
per lightning strike in different fuel types or areas of
the landscape. Meisner (1993) took this approach for a
small study area in Southern Idaho between 1985 and
1991. He found lightning efficiency to vary by fuel
type. He also found that when there were more than
100 lightning strikes in the study area in a single day,
correlations between fire-weather indices and number
of lightning fires were doubled. Nash and Johnson
(1996) used the lightning-efficiency approach to find
that the Fine Fuel Moisture Code (FFMC) of the FWI
system was the best fuel state predictor for lightning
fires in the Canadian boreal forest, and they also
classified storm days, finding that lightning efficiency
was higher under synoptic high pressure (associated
with low precipitation). Wierzchowski et al. (2002)
studied lightning-fire occurrence in a 183,000 km2
study area in western Canada for 14,000 fires from
1961 to 1994. They found lightning efficiency to be
1/50 in British Columbia and 1/1400 in Alberta. They
found lightning-fire occurrence to be correlated with
the Daily Severity Rating (DSR) component of the
FWI system.
Flannigan and Wotton (1991) used a study area
in northwestern Ontario to examine lightning-ignited
fires. They found insignificant statistical correlations
between the number of lightning strikes and the number of lightning-caused fires. They also found that the
Duff Moisture Code (DMC) component of the FWI
system, a numerical rating of the moisture content
of the loosely compacted moderate-depth duff layer,
was an important predictor of lightning fires and that
positively-charged lightning strikes are not especially
important in fire occurrence. In their tabulation, they
found that positively-charged lightning flashes were
only 5–10% of the total population of ground flashes.
Kourtz and Todd (1991) combined real-time lightning information with fuel, weather, and fire-behavior
information to predict daily lightning ignitions. Their
prediction system has four components. The landscape
is partitioned into grid cells 50 km2 in size. Information on the CG lightning flashes, times and types for
each grid cell is found. In this component of the prediction, the number of LCC flashes is assumed to be
a percentage of the total number. This information is
3
combined with fuel and weather information concerning ignition probabilities in different fuel types to predict the number of ignitions. Next, the probability of
a fire smouldering until detection is assessed based on
fuel density and moisture content. The fourth step is
the assessment of the probability of detection based
on the length of time a fire has been burning, the
fuel conditions, and the weather conditions. In the US,
Fuquay et al. (1979) developed a model for predicting
lightning-fire ignition based on stochastic and physical processes. Ignitions are based on (1) the density
of CG lightning, (2) storm movement, (3) precipitation, (4) the moisture code of fine fuels (corresponding
to the FFMC in the CFFWIS), (5) the lightning-flash
characteristics and (6) the bulk density of fine fuels.
The current study addresses the conclusions of
Morris (1934). In particular, it is relevant to his conclusions that there are no danger zones for lightning
fires nor are there lightning-storm lanes or breeding
zones. This study uses spatial point pattern (SPP)
analysis from the family of spatial statistical tools
(Cressie, 1993) to examine the spatial pattern of
lightning-caused fire occurrence in Ontario and verifies the existence of areas of high lightning and
high-lightning fire activity. The difference between
the conclusions of this study and those of Morris
(1934) are due to important differences in the data
and methodologies that were available to Morris
(1934) and those that are available today. Morris did
not have data on lightning strikes from lightning detectors, but instead had data on storms from lookouts.
He had 6000 records of lightning-storm location and
direction collected by fire lookouts over the period
1925–1931. These storms were analyzed visually,
without the more formal spatial statistical techniques
employed in this study. Even with these differences,
Morris was equivocal in his conclusions about the
presence of persistent ‘danger zones’: “For the two
states as a whole. . . there appears to be practically no
definite ‘breeding zones’ where lightning storms are
formed time after time” (Morris, 1934, p. 8). In this
study, we are not looking for storm ‘breeding zones,’
but for clusters of fire locations. These clusters would,
however, if persistent, be caused by such ‘breeding
zones’ and detected in the same way.
SPP statistical techniques are described in Cressie
(1993). Methodological advances in a related type
of modeling, spatial-point process modeling, have
4
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
been made (Allard et al., 2001) and spatial-point process modeling has been applied to forestry problems
(Stoyan and Penttinen, 2000). Statistical models of
aspects of forest fire other than fire occurrence exist
(Polakow and Dunne, 1999) as do simulation models (Miller and Urban, 1999; Boychuk et al., 1999)
but to date no studies have applied SPP to forest-fire
data in general or to lightning caused forest fires in
particular.
• It is widely recognized as a persistent ‘hotspot’ of
forest-fire activity, as the results below show;
• Fire protection, and hence detection, is quite uniform over this area, making detection bias unlikely
to contribute significantly to the observed spatial
pattern.
2. Study area
3. Data
Two study areas were used. The first was the entire
province of Ontario shown in Fig. 1. The geographic
limits were as follows: 57◦ N, 41.5◦ N, 95.5◦ W,
74.5◦ W. The second area studied was a rectangular
region in northwestern Ontario: the region north of
49◦ N, 52◦ N, west of 89◦ W, and east of 95◦ W. This
subset of Ontario was chosen in order to study spatial patterns of fire occurrence at a finer spatial scale
The data used in this study were provided by the
OMNR. The OMNR fire database is an archive of data
on all reported fires from 1976 to present. The archive
contains fire reports, one of which is completed for
each forest fire in the province. Each fire report contains many variables including fire location, final area
burned, forest type, weather, estimate of cause (lightning or people) and fire suppression information. This
than the all-Ontario scale. Northwestern Ontario was
studied because:
Fig. 1. The study regions are shaded.
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
5
Fig. 2. Lhat function for lightning fires in Ontario, 1992–1995. Note the peak clustering around 3◦ and the regularity beginning at 6◦ .
6
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
study covers the period from 1976 to 1998, during
which a total of 40,000 fires occurred, 17,000 of which
were lightning-caused fires. The records are based on
information compiled by the fire boss after each fire
is extinguished. The fire boss is principally concerned
with fighting the fire—preparing the final fire report
is a secondary concern. It is, therefore, important to
keep in mind that some data (e.g. final fire size) are to
some extent the subjective estimates of the fire boss.
This study is concerned principally with the locations
of the fires. Fire locations are provided in the data to
a precision of 1 m. Error estimates are not provided
with the data. The locations of fires in the database
are determined by the fire boss who identifies fire
Fig. 3. Lhat for lightning fires in Ontario, 1996–1998.
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
locations on a map of 1:50,000 scale. While error in
locations could be quite high, it is unlikely to confound the results of this study. This is because the
size of the study area and the time scale (annual) is
very much larger than the size of the error in fire
locations.
Lightning-strike data were obtained from the
OMNR. The OMNR uses a lightning-location system
that detects CG lightning discharges. This is done
with an electric-field antenna to detect polarity and a
magnetic-field antenna to detect azimuth. The incoming electromagnetic signal is compared with lightning
signature profiles, and if it matches a CG lightning
signature, it is recorded. When two or more sites detect a lightning discharge, the discharge location is
triangulated by a central computer known as a position analyzer. The detection equipment is developed
by Lightning Location and Protection Inc., Tucson,
AZ (Flannigan and Wotton, 1991).
The FWI and DMC, two components of the CFFWIS (Van Wagner, 1987), were assigned to each
lightning strike in the study. The CFFWIS components are measured daily at weather stations across
Ontario. Each lightning strike was assigned the FWI
7
and DMC value measured at the nearest weather station to it. A third component of the CFFWIS used in
this study was the DSR. The DMC is a numerical index representing the dryness of the duff fuel layer of
the forest floor and is calculated using an empirical
model from temperature and humidity measurements.
The FWI is a measure of the potential intensity of a
fire. The DSR is a transformation of the FWI that can
be used to rate the average severity of a set of days
(ibid).
4. Methods
Spatial statistical methods make it possible to determine whether or not fires are more likely in some
places than in others, and whether fires are more likely
to be found in clusters or at some distance from one
another. The spatial statistical techniques used and the
results of the analysis are described below.
SPP analysis is the spatial statistical method best
suited to studying fire occurrence at a provincial scale.
In general, SPP techniques are used to detect patterns
in phenomena occurring at point locations. Important
Fig. 4. Lhat for lightning fires in Ontario, 1976–1998.
8
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
measures in SPP are spatial intensity, defined as the
number of events per unit area, and the nearest neighbour statistic, a measure of how close events are to
one another.
A collection of events is considered to be completely spatially random (CSR) if the intensity is
constant over space and events are neither clustered
nor regularly spaced. If these two conditions are met,
the events are uniformly distributed over space.
There are two ways a point pattern can depart from
randomness. Clustering implies that events are found
nearer to one another than a random distribution
would suggest. Regularity implies points are farther
apart from one another than a random distribution
would suggest.
4.1. Nearest-neighbour statistics
A nearest-neighbour statistic called the K-function
can be used to test the extent to which a phenomenon
is random, clustered, or regular. Let h be the distance
from an event. Let λ be the intensity or mean number
of events per unit area. Define K(h) as
λK(h) = E(number of events within distance
h of an arbitrary event)
where E(·) is the expectation operator. If A is the
size of the study area, then the expected number of
events in the area is λA (the number of events per unit
area multiplied by the area). The expected number of
Fig. 5. Spatial intensity of lightning fires in Ontario, 1992–1995.
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
ordered pairs of events at a distance less than h apart in
the study area, is λA × λK(h) = λ2 AK(h). If dij is the
distance between the ith and jth observed events (fires)
in A and Ih (dij ) is an indicator function, 1 if dij ≤ h
and 0 otherwise, the observed number of ordered pairs
of events
a distance less than h apart in the study area
is i=j
Ih (dij ). An estimate of K(h) is, therefore,
K̂(h) =
1
Ih (dij )
A
×
λ2
i=j
λ is estimated by n/A, where n is the number of events
(Bailey and Gatrell, 1995).
An intuitive understanding of K(h) can be achieved
by imagining an algorithm that ‘visits’ each point in
the study region and ‘counts’ the number of neigh-
9
bouring points within different radii h, and then takes
the average number of neighbours at each radius h.
This function, divided by the intensity (mean number
of events per unit area), is K(h) (ibid).
4.2. Kernel estimation of spatial intensity
The spatial intensity of a point process, or λ as defined above, can be calculated by using Kernel estimation. If s1 , . . . , sn are the locations of the n observed
events then the intensity λ(s) at location s is estimated
by
n
λ̂τ (s) =
1 1
k
στ (s)
τ2
i=1
Fig. 6. Spatial intensity of lightning fires in Ontario, 1996–1998.
s − si
τ
10
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
where k(·) is a bivariate probability density function
symmetric about the origin, known as the kernel (ibid).
A quartic kernel function is often used (Bailey and
Gatrell, 1995). τ is the bandwidth and determines the
radius of a disc centred on s within which points si will
contribute significantly to the intensity λ̂τ (s) (ibid).
The factor
1
s−u
στ (s) =
k
du
τ
τ2
is an edge correction. It is the volume under the scaled
kernel centred on s which lies inside the study area A
(ibid). The estimate of λ can be examined over a grid
over the study area to provide a visual indication of the
variation in the intensity over the area (ibid). Such an
examination can help to identify persistent ‘hotspots’
of high fire or weather activity, for example, and will
be used for this purpose below.
An intuitive or visual understanding of kernel
estimation can be achieved by imagining a threedimensional moving window with a circular base, of
radius τ , and a shape like the kernel function k(·),
moving over the study area. When the window is centred at point s, events within the window contribute
to the intensity at point s, weighted by the value
of k(·).
The K-function was calculated using the spatial
module of S-Plus (Venables and Ripley, 1999). The
K-function itself, however, is difficult to visualize.
It is difficult to look at a plot of the K-function and
determine visually whether an SPP is clustered or
regular. For this reason, a square root transformation
was applied.
For a spatially random SPP, the probability of occurrence of an event is independent of the number of
events that have already occurred and equally likely
to occur anywhere over the entire area. The expected
number of events within a distance h of a randomly
chosen event is, therefore, λπ h2 . So for a random process, K(h) = π h2 , from the definition of K(h) above.
A clustered process would have K(h) > π h2 , and a
regular process would have K(h) < π h2 . To visualize
Fig. 7. Spatial intensity of lightning fires in Ontario, for all the years 1976–1998.
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
this, L̂(h) is plotted against h, where
K̂(h)
L̂(h) =
π
L̂(h) for a random process is πh2 /π = h, the
1:1 line. If L̂(h) is above this line, the SPP is clustered, and if L̂(h)is below this line, the SPP is regular.
As a test of significance, random SPPs can be simulated and their L̂(h) function plotted. The maximum
and minimum L̂(h) values of a large set of simulated
SPPs can be used to form a ‘simulation envelope.’ If
the observed L̂(h) falls outside the simulation envelope, statistically significant clustering or regularity is
indicated.
11
4.3. Hypotheses
The null hypothesis is that forest fires are CSR.
There are reasons to suspect both regularity and clustering.
One reason lightning fires might be clustered is because lightning storms are dynamic, localized phenomena. As was mentioned above, a lightning storm
can ignite multiple fires in a single day. These fires
would be closer to one another than a CSR distribution and would, therefore, be clustered. This is true
for a daily temporal scale, but it is possible this effect
could be reduced over the annual temporal scale of this
study. Since data on lightning strikes is also available,
the spatial pattern of lightning strikes in the study area
Fig. 8. Spatial patterns of lightning, daily severity summed over the fire season, fire and lightning for days DMC exceeded 20 in 1992.
12
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
Fig. 9. Spatial patterns of lightning, daily severity summed over the fire season, fire and lightning for days DMC exceeded 20 in 1993.
was examined and compared to the spatial pattern of
lightning fires. The results are described below.
A second reason for clustering is because vegetation, climate, and daily weather conditions (temperature, humidity and wind) that are conducive to burning
are also localized. Climate and vegetation vary over
the province, and some forest types determined by climate and vegetation are more susceptible to fire than
others.2 Daily weather also varies over the province,
so certain areas are drier, hotter, or more windy than
others at various times. This could potentially result
in the clustering of fires in such areas. Spatial pat2 The type of vegetation in an area can depend on the fire regime.
This means that just as vegetation can determine, to some extent,
the amount of fire activity, fire activity can shape vegetation over
long time scales.
terns were studied on an annual time scale.3 In order
to test the extent to which spatial patterns of weather
were giving rise to spatial patterns of forest fires, a
seasonal severity rating (SSR) was used. This was the
sum of the DSR values, measured at the weather stations in the study area and interpolated to each point
in the study area, over the fire season. These maps of
SSR were then compared with the spatial intensity of
lightning fires. The results are described below.
Weather and lightning are accepted as the most
important causes of lightning fires in lightning-fire ignition models (Kourtz, 1974; Kourtz and Todd, 1991,
and others). Kourtz (1974) suggests a rule of thumb
3 An annual time scale means, in effect, a seasonal time scale,
since almost all forest fires occur during the official fire season
April 1–October 31.
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
for fire occurrence prediction: “An area is most likely
to have lightning fires if the lightning sensor reports
50 or more counts and yesterday’s DMC is 20 or
greater.” This suggests that weather and lightning
should be considered together. Following this rule,
maps of the the spatial intensity of lightning strikes
for all days in each fire season when DMC exceeded
20 were created and compared with the spatial intensity of lightning fires in the study area. These results
are described below.
Third, a detection bias effect might cause clustering in the dataset where clustering does not actually
exist. Fires that start in remote areas and do not ever
grow to large sizes will not be detected with the
same frequency as similarly sized fires in populated
areas. This could mean that detected and reported
13
lightning-caused fires are clustered around these populated areas.
Conversely, it is conceivable that fires ‘repel’ one
another resulting in a regular pattern, because a forest
where the vegetation has burned is unlikely to burn
again for some time. This effect, however, is probably
more prominent over longer temporal scales and finer
spatial scales than those used in this study.
5. Results and discussion
5.1. Clustering
Graphs of L̂(h) versus h for the years 1992–1995 are
plotted in Fig. 2, for 1996–1998 in Fig. 3, and for all
Fig. 10. Spatial patterns of lightning, daily severity summed over the fire season, fire and lightning for days DMC exceeded 20 in 1994.
14
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
the years 1976–1998 combined, in Fig. 4. The graphs
are a maximum distance from the 1:1 line and, therefore, show peak clustering, at a scale of approximately
2.5◦ , which corresponds to approximately 200 km in
the area under study.
As a test of significance, random SPP’s were simulated using a uniform distribution and their K function
calculated. The maximum and minimum K-function
are shown as a ‘simulation envelope’ in Figs. 2–4. The
results show that L̂(h) is much more clustered than
random chance would allow. The graphs also show
regularity at longer spatial scales. An examination of
Figs. 5–7 suggests why this occurs. The areas of high
fire activity, where clustering occurs, are in two areas
(the northwest and the southeast), with areas of low
fire activity in between. This pattern could give rise to
the pattern of clustering at shorter scales followed by
regularity at longer scales in the L̂(h) graphs.
These results suggest that the ‘clustering’ factors
are dominant at scales of 225–375 km or 3–5◦ of latitude/longitude.
5.2. Spatial-intensity results
Kernel estimation of the spatial intensity of lightning fires was conducted using the S-plus spatial
module (Venables and Ripley, 1999). Maps of the
intensity for the years 1992–1995 are shown in
Fig. 11. Spatial patterns of lightning, daily severity summed over the fire season, fire and lightning for days DMC exceeded 20 in
1995.
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
Fig. 5, for 1996–1998 in Fig. 6, and for all the years
1976–1998 combined, in Fig. 7. These show two persistent ‘hotspots’ of fire: one in the northwest and one
in the southeast. The spatial-intensity maps of all the
other years 1992–1998 show the same pattern.
5.3. Spatial-intensity maps of lightning strike and
fire densities, and DSR interpolations
The spatial-intensity maps of lightning-caused fires,
of lightning strikes, and the interpolated sums of the
DSR, for the fire seasons for 1992–1998 (Figs. 8–14)
for the region of Ontario north of 49◦ latitude, south
of 52◦ latitude, and west of 89◦ latitude show no obvi-
15
ous relationship between lightning strike density and
lightning-fire occurrence density over a fire season,
nor do they show any obvious relationship between the
sum of DSR over the season and the fire occurrence
density. The latter lack of a relationship could be a result of a poor quality interpolation due to insufficient
weather stations.
There are numerous models of forest-fire dynamics
in the landscape (e.g. Boychuk et al., 1999; Miller and
Urban, 1999; Polakow and Dunne, 1999). Fire occurrence models (Kourtz, 1974; Kourtz and Todd, 1991)
suggest that the spatial pattern of lightning fires that
arises over a fire season arises over a small number of
intense days when dry weather and lightning strikes
Fig. 12. Spatial patterns of lightning, daily severity summed over the fire season, fire and lightning for days DMC exceeded 20 in
1996.
16
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
Fig. 13. Spatial patterns of lightning, daily severity summed over the fire season, fire and lightning for days DMC exceeded 20 in 1997.
converge optimally on areas with fuels that are conducive to ignition. These few days give rise to the
spatial pattern of ignitions that is left at the end of a
fire season. In order to explain that pattern, then, it is
necessary to look at lightning, weather and fuel during
those particular days. Examining lightning, weather
and fuel over an entire fire season will overwhelm the
signal from these intense days with irrelevant data.
If the lightning, weather and fuel combinations during and just before fire events do show a specific pattern, then that pattern can be searched for on days
and places when no fires occurred, to see how often
it arose.
A preliminary test of the hypothesis was conducted
using the data on lightning strikes on days when DMC
exceeded 20, following the rule of thumb of Kourtz
(1974), quoted above. These are included below in
Figs. 8–14. In Fig. 8, for the year 1992, the lightning density map on DMC >20 days more closely resembles the fire density map than the raw lightning
density. Thus, a kernel estimate of the spatial intensity of lightning strikes on days when DMC exceeded
20 provided a better visual match with the spatial intensity of lightning-caused fires than did weather or
lightning strikes alone, although the evidence of this
test alone is inconclusive. The number of lightning
strikes on days when the DMC exceeded 20 was a
fraction of the total lightning strikes. It is included in
Table 1.
To give an idea of how many days in a fire season are
days in which DMC >20, Table 2 shows the lengths of
the fire seasons in days for the years 1992–1998, and
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
17
Fig. 14. Spatial patterns of lightning, daily severity summed over the fire season, fire and lightning for days DMC exceeded 20 in 1998.
the numbers of days for which DMC >20 for those
years, as measured at a single weather station located
in the northwestern Ontario study region at latitude
51.0273◦ and longitude −93.8698◦ .
The 2 years with the most lightning-fire ignitions
(1995 and 1998) were the years with the most days
DMC >20, while the 2 years with the longest fire
seasons were 1994 and 1998.
Table 1
Lightning strikes on days DMC >20 for Ontario and Northwestern Ontario
Year
Strikes on days
DMC >20 (Ontario)
Total strikes
(Ontario)
Strikes on days
DMC >20 (NW Ontario)
Total Strikes
(NW ON)
1992
1993
1994
1995
1996
1997
1998
57233
151632
85922
169906
119799
70769
154418
282126
411638
373264
440735
456511
242774
366511
2735
4894
15983
48346
32909
12968
19455
63286
64910
87970
114546
108501
49967
53905
18
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
Table 2
Numbers of days DMC >20 and lightning fires
Year
Length of fire season (days)
Number of days DMC >20
Number of lightning fires in Ontario
1992
1993
1994
1995
1996
1997
1998
157
192
211
191
162
162
211
26
42
38
54
48
48
79
262
163
343
1115
648
673
1405
Fig. 15. Topographic map of Ontario.
5.4. Topography and population in lightning-fire
occurrence
It was suggested above that greater forest-fire detection by larger numbers of people could explain higher
recorded forest-fire occurrence in areas of higher population density. The areas of high lightning-fire activity do not, however, coincide with the areas of high
population density. We obtained a map of population
density for Ontario in 1995, based on the World Resources Institute’s Gridded Population of the World
(GPW) data product (World Resources Institute,
2002). It shows northern Ontario to be sparsely populated in general, with small groupings of population
scattered over the province’s area. A topographic map
of Ontario (Fig. 15) shows a belt of high elevation,
into which the areas of high-fire and high-lightning
activity fall. The areas of high elevation correspond
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
essentially to the dry boreal forest belt (lower elevation areas are wetter). The areas of high-fire and
high-lightning activity fall within these high-elevation
areas. Topography is a likely part of the explanation for
these patterns.
6. Conclusions
A spatial statistical analysis of lightning-caused
fires in Ontario from 1976 to 1998 was conducted.
SPP analysis was employed. The results of the analysis are:
• A nearest-neighbour statistic, the K-function,
showed fire locations to be found in clusters at a
scale of approximately 150–200 km (peak clustering at 3◦ ).
• At scales longer than 6◦ , fire locations are regularly
spaced, meaning that they are farther from one another than a random distribution would suggest.
• Kernel estimates of spatial intensity show that these
clusters are located in the northwest and in the
southeastern regions of northern Ontario.
These results conflict with the findings of Morris
(1934), who found no ‘high’- and ‘low’-fire areas.
There are, indeed, ‘high’- and ‘low’-fire areas in Ontario, as the spatial-intensity maps of Figs. 5–7 show.
Kernel estimation of the spatial intensity of lightning strikes on days when DMC exceeded 20 provided
a spatial pattern quite similar to that of lightningcaused fires. This result supports the rule of thumb
used by the OMNR, which is to predict fire based
on lightning strikes in areas where DMC exceeds 20.
These findings support the following conclusion:
Localized dry weather and lightning-storm occurrence are the principal determinants of the spatial clustering of lightning caused fire occurrence.
7. Future research
The use of DMC >20 as a threshold was adapted
from a ‘rule of thumb.’ Future work on this problem could attempt to find a more precise value
of an index at which lightning strikes become far
more likely to cause ignitions. It is known that only
LCC flashes cause ignitions (Latham and Williams,
19
2001). If detector technology were improved to detect LCC flashes, it is highly likely that the spatial
pattern of lightning-ignited fires would be found to
be even closer to the spatial pattern of LCC lightning strikes on dry days. Elevation was not found to
be important to ignition probability in some studies
(McRae, 1992), it was found important in others (Van
Wagtendonk, 1991). The locations of the clusters of
fires and of high-lightning activity areas in the upland
boreal forest regions of Ontario suggest that elevation
is a factor in ignition probability in Ontario. Fires
were found to be clustered in the northwestern and
southeastern regions of the province. The northwestern area was examined in more detail. Spatial intensity
of lightning-ignited fires was found to vary within this
area, likely due to variation in lightning storms and
dry-weather systems. The presence of spatial variation at different scales suggests that different patterns
could be revealed at even finer spatial scales. Finally,
the problem was only examined on the annual temporal scale. The problem could be revisited to search for
spatial patterns for finer and coarser temporal scales.
Acknowledgements
Special thanks goes to Ana Espinoza who did a
tremendous amount of work on the figures. This research was supported by the Natural Sciences and
Engineering Research Council of Canada. J. Beverly,
and B.M. Wotton provided valuable assistance. The
two anonymous referees provided comments that improved the paper considerably.
References
Allard, D., Brix, A., Chadoeuf, J., 2001. Testing local independence
between two point processes. Biometrics 57 (2), 508–517.
Bailey, T.C., Gatrell, A.C., 1995. Interactive Spatial Data Analysis.
Longman Group Limited, Essex.
Boychuk, D., Perera, A.H., Ter-Mikaelian, M.T., Martell, D.L., Li,
C., 1999. Modelling the effect of spatial scale and correlated
fire disturbances on forest age distribution. Ecol. Model. 95,
145–164.
Cressie, N.A.C., 1993. Statistics for Spatial Data. Wiley, New
York.
Darveniza, M., Zhou, Y., 1994. Lightning-initiated fires: energy
absorbed by fibrous materials from impulse current arcs. J.
Geophys. Res. 99, 10663–10670.
Flannigan, M.D., Wotton, B.M., 1991. Lightning-ignited fires in
northwestern Ontario. Can. J. For. Res. 21, 277–287.
20
J. Podur et al. / Ecological Modelling 164 (2003) 1–20
Fuquay, D.M., Baughman, R.G., Taylor, A.R., Hawe, R.G., 1967.
Characteristics of seven lightning discharges that caused forest
fires. J. Geophys. Res. 72, 6371–6373.
Fuquay, D.M., Taylor, A.R., Hawe, R.G., Schmidt Jr., C.W., 1972.
Lightning discharges that started forest fires. J. Geophys. Res.
77, 2156–2158.
Fuquay, D.M., Baughman, R.G., Latham, D.J., 1979. A Model for
Predicting Lightning Fire Ignition in Wildland Fuels. USDA
Forest Service, Research Paper INT-217, Ogden.
Gisborne, H.T., 1926. Lightning and forest fires in the northern
rocky mountains. Mon. Weath. Rev. 54, 281–286.
Gisborne, H.T., 1931. A five year record of lightning storms and
forest fires. Mon. Weath. Rev. 59, 139–150.
Kourtz, P.H., 1974. A System to Predict the Occurrence of
Lightning-Caused Forest Fires. Forest Fire Research Institute,
Canadian Forestry Service, Information Report FF-X-47,
Ottawa.
Kourtz, P., Todd, B., 1991. Predicting the Daily Occurrence of
Lightning-Caused Forest Fires. Petawawa National Forestry
Institute, Forestry Canada, PI-X-112, Petawawa.
Latham, D., Williams, E., 2001. Lightning and Forest Fires. In:
Johnson, E. D., Miyanishi, K. (Eds.), Forest Fires. Academic
Press, San Diego, CA, pp. 375–418.
Meisner, B. N., 1993. Correlation of National Fire Danger
Rating System Indices and Weather Data with Fire Reports.
Forest Fire Laboratory, Pacific Southwest Research Station,
USDA Forest Service, Final Report, Interagency Agreement
No. R500A20021, Riverside.
Miller, C., Urban, D.L., 1999. A model of surface fire, climate and
forest pattern in the Sierra Nevada, California. Ecol. Model.
114, 113–135.
Morris, W.G., 1934. Lightning Storms and Fires on the National
Forests of Oregon and Washington. USDA Forest Service,
Pacific Northwest Forest Experiment Station, Portland.
Nash, C.H., Johnson, E.A., 1996. Synoptic climatology of
lightning-caused forest fires in subalpine and boreal forests.
Can. J. For. Res. 26, 1859–1874.
Ontario Ministry of Natural Resources, 2001. Fire Database.
Plummer, F. G., 1912. Lightning in Relation to Forest Fires. USDA
Forest Service, Government Printing Office, Washington, DC.
Polakow, D.A., Dunne, T.T., 1999. Modelling fire-return interval
T: stochasticity and censoring in the two-parameter Weibull
model. Ecol. Model. 121, 79–102.
McRae, R.H.D., 1992. Prediction of areas prone to lightning
ignition. Int. J. Wildl. Fire 2, 123–130.
Renkin, R.A., Despain, D.G., 1992. Fuel moisture, forest type,
and lightning-caused fire in Yellowstone National Park. Can. J.
For. Res. 22, 37–45.
Stoyan, D., Penttinen, A., 2000. Recent applications of point
process methods in forestry statistics. Statist. Sci. 15 (1), 61–
78.
Taylor, A.R., 1969. Lightning effects on the forest complex.
In: Proceedings of the Annual Tall Timbers Fire Ecology
Conference. Tall Timbers Research Station, Tallahassee,
pp. 127–150.
Uman, M. A., 1987. The Lightning Discharge. Academic Press,
Orlando, 374 pp.
Van Wagner, C.E., 1987. Development and Structure of the
Canadian Forest Fire Index System. Canadian Forestry Service,
Tech. Rep. 35, Ottawa.
Van Wagtendonk, J.W., 1991. Spatial analysis of lightning
strikes in Yosemite National Park. In: Proceedings of the
Eleventh Conference on Fire and Forest Meteorology, Royal
Meteorological Society, Boston, pp. 605–611.
Venables, W.N., Ripley, B.D., 1999. Modern Applied Statistics
with S-Plus. Springer, New York. 500 pp.
Weber, M.G., Stocks, B.J., 1998. Forest fires and sustainability in
the boreal forests of Canada. Ambio 27, 545–550.
Wierzchowski, J., Heathcott, M., Flannigan, M.D., 2002. Lightning
and lightning fire, Central Cordillera, Canada. Int. J. Wildland
Fire 11 (1), 41–51.
World Resources Institute, 2002. Gridded Population of the World,
version 2. http://sedac.ciesin.columbia.edu/plue/gpw/. Accessed
January 16, 2002.