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LIGHTNING-IGNITED WILDFIRE OCCURRENCES INT A CENTRAL-FLORIDA
LANDSCAPE MANAGED WITH PRESCRIBED FIRE
DARRELL L. FREEMAN
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
Darrell L. Freeman
Research presented in this document is dedicated to the Southwest Florida Water
Management District, Brooksville, and to the School of Forest Resources and
Conservation at the University of Florida
I am especially thankful to Loukas G. Arvanitis, my graduate committee chair, for
urging me to "perservere" and for the opportunity to pursue graduate studies under his
guidance. I thank Alan Long and Alexandre Trindade, my other committee members, for
their valuable suggestions which resulted in a more focused analysis.
I thank the Southwest Florida Water Management District for providing tuition
assistance during my graduate career. I am grateful to my supervisor, Kevin Love, and
department director, Fritz Musselmann, for providing a flexible work schedule which
allowed me to continue my full-time career while pursuing a graduate education. I also
thank my co-worker Paul Elliott for collecting quality data, Amy Poxson for organizing
the data, and Carol DaLeo for archiving and protecting the data through the years.
Special gratitude goes to my family, particularly my mother-in-law, Janet Weis,
and my cousin, Barry Brown, who provided encouragement and logistical support. Most
of all, I thank my wife, Trish, for accepting with grace the many evening hours and
weekends devoted to this thesis.
TABLE OF CONTENTS
ACKNOWLEDGMENT S ................. ................. iv.............
LIST OF TABLES ................ ..............vii .......... ....
LI ST OF FIGURE S ................. ................. viii............
AB STRAC T ................ .............. ix
1 INTRODUCTION ................. ...............1.......... ......
Types of Wildfire Occurrences............... ...............
Predicting Lightning Ignitions ................. ...............2............ ....
Wildfire Mitigation .................. ...............3.................
Prescribed Burn Applications ................. ...............4............ ....
Prescribed Burning Effects on Wildfires ................. ...............................4
Wildfire Occurrence Probability .............. ...............5.....
W ildfire Impacts .............. ...............6.....
Fire Regim e .............. ...............7.....
Study Obj ectives ................. ...............8............ ....
2 METHODOLOGY .............. ...............10....
Study Area ................. ...............10.......... .....
Decision Process ................. ...............10.................
Site Description .............. ...............10....
Data Collection ................ ........... ...............13.......
Prescribed Burn Records ................. ......... ...............13......
W ildfire Reports ................. ...............14.......... .....
Fire Return Interval .............. ...............16....
Landscape Type ................. ...............16.................
R ainfall .............. ...............17....
Lightning .............. ...............18....
Statistical Analysis............... ...............18
Descriptive Statistics .............. ...............18....
Landscape Type Proportion............... ...............1
Fire Return Interval .............. ...............20....
Multiple Linear Regression .............. ...............20....
3 RE SULT S .............. ...............22....
Prescribed Burns ................. ...............22.................
General Description............... ..............2
Lightning-season Burns ................. ...............23.................
Lightning-Fires .............. ...............24....
Fire Interval .............. ...............25...
Multiple Linear Regression .............. ...............27....
Variable Selection ................... ...............28..
Correlation among variables .............. ...............28....
Data transformations .............. ...............30....
Model Selection--FI................ .... ..........3
Model Selection--Lightning-fire Acres .............. ...............32....
Model Selection--Number of Lightning-fires .....__.___ ........._. ..........._...3 3
4 DI SCUS SSION ........._.__....... .__. ...............3 5...
Prescribed Burns ........._.__....... .__. ...............35....
Lightning-fires ........._.__........_. ...............36....
Re gre ssion Analyses ........._.__....... .__. ...............3 8...
Fire Interval .............. ...............38....
Size of Lightning-fires............... ...........3
Suggestions for Future Research .............. ...............40....
5 MANAGEMENT IMPLICATIONS .............. ...............42....
LIST OF REFERENCES ........._.__....... .__. ...............44...
BIOGRAPHICAL SKETCH .............. ...............48....
LIST OF TABLES
1-1. Causes of wildfires in Florida during 1995-2001 by percent of total acreage .............2
2-1. Description of landscape types ................. ...............17......_... ..
2-2. Description of weather variables used in the study ................. ................. ...... 18
2-3. Description of variables, excluding weather-related, used in the regression .............21
3-1. Composite transformed landscape type proportions of burn units ................... ..........22
3-2. Fire interval distribution Goodness-of-fit statistics ................. ................ ...._..27
3-3. Correlation matrix of variables used in the regression analyses .............. ..............29
3 -4. Variables used in the regression analysis s of NUMFIRES ................. ............... ....30O
3-5. Regression models for FI ranked by AICc ...._ ......_____ ..... ..._ ........3
3-6. Regression models for ACRES ranked by AICc. ....._____ ... ......_ ................32
LIST OF FIGURES
2-1. Green Swamp Wilderness Preserve location map with generalized habitats .............12
3-1. Total acres prescribed burned by year ......___ ... ..... __ ...................2
3 -2. Prescribed burn units and lightning-fire locations in the GSWP ............... .... ........._..24
3-3. Total annual lightning-fire acres by year............... ...............25..
3 -4. Fire interval frequency distribution of lightning-fires ........__. ........ _.._.............26
3-5. Annual acres prescribed burned by annual acres of lightning-fires. ........._...............34
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
LIGHTNING-IGNITED WILDFIRE OCCURRENCES INT A CENTRAL-FLORIDA
LANDSCAPE MANAGED WITH PRESCRIBED FIRE
Darrell L. Freeman
Chair: Loukas G. Arvanitis
Major Department: Forest Resources and Conservation
Lightning-ignited wildfires (lightning-fires) in the Green Swamp Wilderness
Preserve (GSWP), Florida, were characterized and modeled in relation to acreage burned
and time since last burn (Fire Interval) as a function of weather, prescribed burn history,
and other predictor variables. Data associated with lightning-fires and prescribed burns
dating back to 1981 were organized in a geographic information system. A total of 31
lightning-fires were recorded during the study period and 20 of those occurred in
prescribed burn units with known histories. An annual average of 1.4 lightning-fires
ranged from 1 ac to 267 ac with a median of 7.0 ac. Landscape type composition of
lightning-fires was predominately pine flatwoods and was significantly different than the
GSWP (p-value<0.000) as a whole and burn units combined (p-value = 0.002). The
proportion of planted pine was greater in lightning-fires than in burn units or the GSWP.
Mean fire interval (FI) for lightning-fires was 37.1 mo; however those data best fit a
Size of prescribed burns averaged 435.7 ac and the total area involved was 50, 158
ac, or 76.2% of the GSWP. An average of 7,258 ac/yr were prescribed burned.
Landscape type composition was primarily pine flatwoods but included more cypress
systems than lightning-fires.
Multiple linear regression was used to model FI and size of lightning-fires
(ACRES) as a function of a set of predictor variables and the resulting models were
ranked by use of Akaike's Information Criterion (AICc). The "best" model of FI
predicted that FI increased as the size of lightning-fires increased. The implication was
that the longer an area remains unburned, the larger the resulting wildfire will be when it
occurs. ACRES was best predicted as a function of greater 30-day rainfall totals and
longer FI. This model supported the conclusion indicated by the FI model; however, the
inclusion of increased near-term rainfall was contradictory to established empirical fire
behavior and spread models. An additional regression model indicated that the annual
number of lightning-fires decreased as annual prescribed burn acres increased. Overall,
models had low predictive value (R2 < 32%), likely due, in part, to fire suppression
activities which prevented lightning-fires from coming to their natural conclusions.
Compared to a similar study in north Florida the GSWP experienced fewer
average annual number of lightning-fires which burned a smaller proportion of the study
area. Managers of the GSWP should continue the active program of prescribed burning
to reduce lightning-fire occurrence rates and acreages by maintaining fire intervals to 3 yr
or less. Burns should be conducted during the May-August lightning-season if mimicking
the historic timing of lightning-fires is a management goal.
Wildfires occur in every state of the U. S. and annually cause the loss of human
lives, property, and natural resources. Nationwide, during the latest 10-year reporting
period (1992-2001) an average of 103,112 fires burned 4,215,089 acres each year (NIFC,
2003). The annual trend has been toward larger fires and greater acreages burned as
evidenced by the 2002 fire season in which 88,458 fires consumed 6,937,584 acres. A
total of 835 homes and 46 commercial buildings were lost in 2002 and the suppression
costs were estimated at $16 billion, including only federal expenditures.
Although the maj ority of the acreages burned are located in the western U. S. and
Alaska, Florida suffers its share of wildfires. In 1998 a total of 4,899 fires burned across
506,970 acres causing an estimated $620 million in damages, primarily to timber
resources (FDOF 2003; Mercer et al. 2000). During the period from 1999 through 2001
an annual mean of 5,724 fires resulted in 323,276 acres consumed each year. As an
apparent result of increased rainfall amounts, 2002 was a relatively mild year with 3,065
wildfires scorching only 56,835 acres.
Types of Wildfire Occurrences
Wildfires may be initiated by a number of different ignition sources. The Florida
Division of Forestry (2003) maintains records for ten different categories of wildfire
causes. Table 1-1 lists the causes of wildfire ignitions with their average annual percent
of the total acreage burned in Florida for the period 1995 2001.
Table 1-1. Causes of wildfires in Florida during 1995-2001 by percent of total acreage
Cause Average annual percent of total acreage burned
Debris burning 7.6
Lightning stands out as a major source of wildfire ignitions and is the only category
of wildfire not caused by humans (excluding Unknown). During the period from 1995
through 2001 lightning-ignited wildfires accounted for over one-third of the annual
acreage burned in Florida and 20% of the number of total fires reported.
Predicting Lightning Ignitions
Florida's geographic location and subsequent climate lead to intense and numerous
thunderstorms, accompanied by frequent lightning strikes, particularly during the summer
rainy season (Trewartha 1981). An individual storm may produce over a thousand strikes
of varying intensity and charge (Hildebrand pers. comm.). Under the appropriate
conditions of fuel moisture, humidity, and temperature, vegetative fuel may ignite and
become a wildfire. The Lightning-Caused Fire Occurrence Prediction system was
developed by Anderson (2002) based upon a model which uses the number of lightning
strikes detected, weather, and fuel conditions. An additional conceptual model was also
developed to predict the probability of a wildfire ignition as:
pfire(t) = plcc~pignition "psurvival(t)*"parrival ,
where Icc is long continuing current (type of lightning strike), survival is the smoldering
phase of combustion, and arrival is flaming combustion. This model suggests that
wildfire ignition probability is a function not only of weather and fuel conditions, but also
of lightning strike variables. Polarity of lightning flashes may also be a determining
factor in the likelihood of an ignition. Fuquay (1980) found a correlation between
positively charged flashes and wildfire occurrences. However, this association was not
detected for fires in a different study which found no statistically significant correlation
with positively-charged flashes or negative flashes and wildfire occurrence (Rorig and
Ferguson, 1999). Strike density, or the number of strikes per unit area, may also not
contribute to the prediction of ignition probability. An investigation of fires which
occurred in the northwest U. S. during the active fire season of 2000 revealed that high
atmospheric instability and high dewpoint depression were much more significantly
correlated with wildfire ignition than strike density (Rorig and Ferguson 2002).
Geographic location may be a factor in the significance of strike density with
wildfire occurrence. In Alaska, strike density was a significant variable in a regression
model which included elevation and percent tree cover (Kasichke et al. 2002). Their
model explained 84% of the variation in fire return interval (R2 = .84). Similarly, strike
density was a significant variable in Canada's lightning wildfire occurrences
(Wierzchowski et al. 2002). Interestingly, they found that fewer strikes in British
Columbia resulted in more fires than in Alberta which experienced a greater number of
flashes during the study period.
Heat, fuel, and oxygen are basic ingredients of all fires (Pyne 1996). In wildlands
only the fuel variable is readily manipulated by man. Vegetative fuels may be reduced or
removed by a) mechanical methods such as logging or machine clearing, b) livestock
grazing, c) herbicide application, or d) prescribed burning. Prescribed burning, the
application of fire to a designated location, under specific conditions, to achieve a pre-
determined obj ective, is probably the most commonly utilized fuel management tool in
Prescribed Burn Applications
Humans have used fire as a tool in the U.S. since before European settlement.
American Indians were known to use fire to drive game, attract game, increase berry
production, prepare planting sites, and to create fire-safe boundaries around settlements
(Pyne 1997; Lewis and Ferguson 1988). In modern times, prescribed fire is used in much
the same way, with the exception of driving game. Prescribed fire has been used for
decades by forest plantation managers for the purpose of protecting stands against
wildfire damage (Wade 1983). Wildfire hazard reduction has continued to be a maj or
reason for the application of prescribed burns in recent years (DOF 2003). Florida is a
leader in total annual acres prescribed burned with an average of approximately 500,000
acres per year during the period 1993-1999 (Butry et al. 2002).
Cleaves et al. (2000) surveyed U. S. Forest Service prescribed burners to determine
costs, reasons for burning, and the constraints on accomplishing bum objectives. A
similar survey was conducted on prescribed burners of private lands and public lands in
the South (Haines and Busby, 2001). In both surveys the reduction of wildfire hazard
was listed as one of the main purposes for conducting prescribed burns.
Prescribed Burning Effects on Wildfires
Investigations of the effects of prescribed burns on wildfires generally involve one
of two questions: 1) Does prescribed burning reduce the probability of wildfire
occurrences, and if so, for how long? ; 2) Are wildfire impacts, intensity, or aerial size
reduced by prescribed burning? Femandes and Botelho (2003) conducted an exhaustive
literature review to analyze the premise that prescribed fire is a valuable tool for forest
protection and wildfire mitigation. The general conclusion was that prescribed fire
reduced the size, intensity, and damage ofwildfires, all types included. Prescribed fire
effectiveness was reported to extend only for a period of 2-4 yr. The authors indicated
that the need exists for more properly designed experiments. A more detailed
examination of those studies' results is presented next.
Wildfire Occurrence Probability
In north Florida and south Georgia wildfire occurrence rates were somewhat higher
in areas which had not burned in over three years ("three-year rough"), however this
difference was described as "not very great" (Davis and Cooper, 1963). Expressed as
wildfires per 10,000 acres per year, rates of lightning ignitions ranged from 0.303 in age
0 roughs to 0.607 in age 5+ roughs. No statistical tests of significant difference between
the means were reported.
Prescribed burning may either reduce wildfire ignition probability or increase it. In
an African savanna system, prescribed burns were conducted on a large conservation area
in a random pattern and allowed to burn unaltered for up to seven days (Brockett et al.
2001). This program was monitored for several years and resulted in smaller, but more
numerous wildfires than before the prescribed burns were incorporated into the
management of the area. Conversely, Butry et al. (2002) found a negative correlation
between the number of prescribed burn permits and wildfire ignitions in Florida. Their
analysis relied upon the Prescribed Burn Authorization permit process administered by
the Florida Department of Forestry. Records of burn permits issued for each cadastral
section were compared with the locations of wildfires. Sections in which no permits
were issued during the study period experienced roughly 75% of all the wildfires, while
sections with >1 permit had only 4% of the total number of fires.
Davis and Cooper (1963) calculated wildfire burn acreage per 10,000 acres for
lightning-ignited wildfires, indicated no significant correlation, and values ranged from
1.42 for age 0 roughs to 2.09 in age 5 roughs. All of the large fires (> 200 ac), however,
occurred in areas which had not been prescribed burned in over five years. Wildfire
intensity was examined as a function of height of crown scorch line on trees and the
height of bark char. Variation in crown scorch line height was related more to ambient
temperature than to age of rough. Bark char height, however, was determined to be a
positive and significant correlate with age of rough. Martin et al. (1988), in a study of the
same geographic area, found that the average size of wildfires was 20.4 ac in areas
prescribed burned within the previous three years and 60.5 ac in untreated areas.
Koehler (1993) concluded that prescribed burn programs in central Florida, which
had been ongoing for an adequate time, resulted in fewer and smaller wildfires. He also
suggested that consistent annual wildfire acreages indicated a reduction in fire intensity,
despite severe weather conditions. Contradictory to those conclusions, over 24,000 acres
in the Osceola National Forest in north Florida burned in one extreme drought year,
despite an active prescribed burn program (Outcalt and Wade, 2000).
A reduction in wildfire intensity as a result of a previous prescribed burn has been
documented in the U.S.(Pollet and Omi, 2002) and in Europe (Femandes et al. 1999). In
Portugal, an average reduction in fireline intensity of 98%, as a result of prescribed bums
in pine (Pinus spp.) stands, was reported by Fernandes et al. (1999). The effectiveness of
prescribed burning on fireline intensity may be quite variable, as low as 10%, depending
upon the percentage of fuel-load reduction, which is affected by weather parameters at
the time of the burn (Omi and Kalabokidis 1998).
Variables such as precipitation, temperature, fuel moisture and fuel age have been
utilized in regression analyses to predict variation in wildfire burn acreage (Turner and
Romme 1994; Larsen 1996). Those relationships may not be linear. In Los Angeles
County, California, wildfire burn area increased steadily as fuel age and temperature
increased and precipitation and fuel moisture decreased. Above a certain threshold,
however, fire risk did not increase (Schoenberg et al. 2003).
Fire regime describes the parameters associated with fire in an ecosystem or region
and may include burn area extent and fire intensity, as well as fire frequency, burn
seasonality, and fire interval (Pyne et al.1996). Fire effects on vegetation are also
considered part of a fire regime (Glitzenstein et al. 1995). Bravo et al. (2001) defined fire
frequency as the recurrence of fire throughout time. Fire frequency was calculated as a
ratio of the number of fires in a given area to the time interval, in years, between the first
recorded fire and the last. Fire interval was defined as the interval, in years, between two
fires occurring in the same location. Bravo et al. (2001) reported a fire interval with a
median of four years for a savanna in Argentina which fit the Weibull frequency
distribution, a commonly used model in fire studies (Reed 1994; Johnson and Gutsell
1994). The Weibull distribution of fire interval is derived from a model which assumes
that flammability, or probability of ignition, is a power function of time since last burn.
However, McCarthy et al. (2001) argue that basing fire interval distributions on the
Weibull model may be unnecessarily restrictive and may not make sense from a
The goal of this study was to further investigate the effects of prescribed burning
on lightning-ignited wildfire occurrence in terms of size, number, and fire interval on the
Green Swamp Wilderness Preserve (GSWP) in central Florida. The GSWP is a relatively
large public landholding of roughly 72,000 acres owned and managed by the Southwest
Florida Water Management District (SWFWMD). Prescribed fire has been utilized as a
management tool there for over 20 years to reduce wildfire hazard and to restore and
enhance ecosystem processes (Love pers. comm.). Despite the frequent and widespread
use of prescribed Gire, the GSWP has periodically experienced lightning-ignited wildfires
in addition to anthropogenic fires. A detailed analysis of the wildfire occurrences in
relation to the prescribed burn program and other variables may serve to improve
empirical knowledge of those phenomena and to increase predictive modeling accuracy.
Specifically, the obj ectives were as follows:
* 1. Describe the prescribed bum program: a) bum unit acres; b) acres burned per
year; c) landscape type proportions burned versus the GSWP as a whole; d)
seasonality of bums; e) burn frequency.
* 2. Describe lightning-ignited wildfire occurrences: a) acres burned; b) fire interval;
c) fire frequency distributions; d) landscape type proportions versus prescribed
burns and versus the GSWP as a whole.
* 3. Model the influence of key variables on the acres burned in individual lightning-
* 4. Model the influence of key variables on the fire interval of individual lightning-
* 5. Model the influence of key variables on the annual number and total acreage of
The obj ectives were designed to assist in testing the following hypotheses:
* H1: Annual lightning-ignited wildfire acreage is inversely proportional to annual
prescribed bum acreage.
* H2: Landscape type has greater influence on lightning-ignited wildfire size than
fire interval which has greater influence than climate variables.
* H3: The fire interval distribution of lightning-ignited wildfires is best modeled by
the Weibull frequency distribution.
The Green Swamp Wilderness Preserve (GSWP) was chosen as the study area
because of its relatively large size (65,820 ac), and the data records existed for prescribed
burns and wildfires dating back over 20 years. The occurrence of wildfires on a property
with an active prescribed burn program made the GSWP attractive as a site for the study
of the relationship between the two phenomena. In the literature review no studies of this
type were located which were conducted in central Florida. It is possible that research
findings in other parts of the U. S. or elsewhere may be different from those found in
The GSWP-East is roughly 72,000 ac in total area and is located in west-central
Florida. The property encompasses parts of eastern Pasco County, southwestern Lake
County, southern Sumter County, and northern Polk County. A portion (6,140 ac) of the
northeast extension of the property is managed by the Florida Division of Forestry as the
Little Withlacoochee Flood Detention Area. Due to a different management regime and
data collection effort, that area was excluded from the analysis resulting in a study site
comprised of 65,820 ac, referred to hereafter as GSWP (Figure 2-1).
The GSWP was purchased and is managed by the Southwest Florida Water
Management District (SWFWMD) to a) protect the region's water supply and water
quality, b) reduce flooding, c) conserve native ecosystems, and d) for public recreation
and other benefits. Management activities on the property include prescribed burning,
exotic plant and animal control, and timber production from designated plantation sites.
Recreational uses include passive activities such as hiking, bicycling, birdwatching,
camping, Eishing, frogging, and hunting. Hunting is administered by the Florida Fish and
Wildlife Conservation Commission through a Wildlife Management Area agreement.
Several species of small game and large game, including feral hog (Sus scrofa) are
hunted on GSWP.
Historical, long-term rainfall averages about 53 in yearly though the average during
the study period was 51.2 in, and ranged from 37.5 in to 77.3 in. A matrix predominated
by pine flatwoods, dotted with cypress wetlands, and bottomlands lining creeks and
rivers, defines the maj ority of the GSWP landcover. Pine flatwoods consist of an
overstory of longleaf pine (Pinus palustris) and slash pine (Pinus elliottii) and an
understory mostly of saw palmetto (Serenoa repens), gallberry (Ilex glabra), and
wiregrass (Aristida spp.). Cypress wetlands occur in depression ponds and strands, lake
and river shorelines, and are dominated by pond cypress (Ta-xodium a~scendens) with bald
cypress (Taxodium distichum) confined to the lakes and rivers. Bottomlands are in the
floodplains along streams and rivers. These are densely forested, mixed landscapes of
cypress, laurel oak (Quercus laurifolia), sweetgum (Liquidambar~~~dddd~~~~ddd styraciflua), and red
maple (Acer rubrum). The GSWP is regionally important as the headwater source for the
Oklawaha River, Myakka River, Peace River and the Withlacoochee River. Turpentining
of old-growth pines, followed by logging of cypress and pines, and, later, cattle ranching
were the historic land uses on the GSWP (Richards pers. comm.).
Green Swamp Wildernless Preserve
Plne F$Latw ad
-lpre66 tly arrlL raeeman2~
Psaure Dat a source : SElftYBF#9t alia Water Managemnent IlEhldt
Figure 2-1. Green Swamp Wilderness Preserve location map with generalized habitats
Prescribed Burn Records
The SWFWMD archived all executed burn documents for all of the lands under its
management. All bum records for the GSWP, dating back to 1981, were pulled from
archives and examined for this study. Burn plans were written in advance for all
prescribed burns conducted on the GSWP as directed by the Florida Prescribed Bumner
Act (F.S. 590). Each burn plan included: 1) the specific location of the burn [both the
Section(s), Township(s), and Range(s), and a map], 2) season of the burn, 3) habitats or
landscape types to be burned, 4) acres, 5) weather parameters such as wind speed and
direction, relative humidity range, temperature range, and smoke dispersion range, 6)
smoke plume proj section map, 7) purpose and obj ectives of the bum, 8) bum manager' s
name and Florida Prescribed Burner certification number.
At the conclusion of each burn additional data were collected in a post-burn
evaluation and added to the plan prior to being archived: 1) date of the burn, 2) duration
in hours, 3) weather parameters, as described above, observed during the burn, 4) acres
burned, 5) names of personnel involved, 6) tree crown-scorch percent estimate, 7)
number of spotovers, or escapes, and any damage, 8) positive or negative assessment of
whether the obj ectives were met, and 9) comments. In most cases the burn manager also
marked on the map included in the plan the specific area which was burned. This was
important because many burn units were divided into smaller blocks and completed over
a period of weeks or months. A number of burn units were only partially completed due
to unforeseen constraints, while others were adjusted in area by logistical considerations.
Temporal and spatial resolution of burn area was therefore increased by those records.
Burn plans generated during the 1970s through the early 1990s contained maps consisting
of blue-line aerial photos with hand-drawn fire boundaries while those from the mid-
1990s through 2002 utilized maps created in a Geographic Information System (GIS)
with relatively current digital ortho quarter-quadrangle (DOQQ) images. Data quality of
plans executed before 1990 were judged as poor due to incompleteness or indiscernible
mapping of fire perimeters. Burn plans of questionable quality were excluded from the
analysis and only those dating from 1990 through December 2002 were utilized.
Each useable prescribed bum plan for the GSWP through 2002 was thoroughly
inspected for specific burn dates and fire perimeters. The boundary of each burn was
digitized over a DOQQ developed from aerial images taken in 1999. ArcGIS software
(ESRI 1999) was utilized for all digitizing work and spatial data analysis. Burn perimeter
mapping accuracy was judged as "high" since burn units were typically bounded by
existing roads, firebreaks, streams or other water features which were readily visible on
the DOQQ. Where the burn evaluation map indicated that fire perimeters differed from
the proposed boundary, those changes were followed as closely as possible during the
digitizing process and often aligned with dirt roads, old fencelines, or landscape type
borders which were readily visible on the DOQQ. A total of 186 burn perimeters were
digitized and stored in the GIS.
All prescribed bum perimeters were stored in a single polygon shapefile as a data
layer in the GIS. Each burn perimeter was associated with an ID number in an attribute
table. Data for each bum were stored in the attribute table and included date of burn and
acres, as calculated by the GIS.
Each detected wildfire on SWFWMD lands was recorded and archived by use of a
wildfire report. All wildfire reports of wildfires on GSWP were pulled from archives and
examined for this study. Dating back to 1979, these reports included wildfires caused by
arson (19%, n = 11), escaped from prescribed burns (12. 1%, n = 7), unknown (10.3, n =
6), miscellaneous (5.2%, n = 3), and lightning (53.4%, n = 31). Only lightning-ignited
wildfires (hereafter referred to as lightning-fires) were analyzed in this study.
Each wildfire report contained; 1) date of fire, 2) location, 3) cause, if determined
4) origin of fire, if determined, 5) time fire was first reported, 6) time suppression was
initiated, 7) weather parameters, 8) names of personnel involved, 9) acres burned, 10)
damage assessment, 11) landscape type(s) burned. As with the prescribed burn plans,
data quality improved over time. Reports from the 1970s through the early 1990s
contained maps consisting of blue-line aerial photos with hand-drawn wildfire boundaries
while those from the mid-1990s through 2002 utilized maps created in a GIS with
relatively current DOQQ images. Overall map accuracy of wildfire boundaries was
judged as "high" due to the heterogeneity of the landscape providing recognizable
landmarks, visible in the field as well as on the maps, and to a high degree of familiarity
of the land management personnel with the property. All lightning-fire records (n=3 1)
were judged as adequate in terms of data quality and were included in the study. The
boundary of each lightning-fire was digitized over a digital ortho quarter-quadrangle
developed from aerial images taken in 1999. ArcGIS software was utilized for all
digitizing work and spatial data analysis.
All lightning-fire perimeters were stored in a single polygon shapefile as a data
layer in the GIS. Each fire perimeter was associated with an ID number in an attribute
table. Data for each lightning-fire were stored in the attribute table and included date of
burn and acres, as calculated by the GIS.
Fire Return Interval
Once all the prescribed burn perimeters and lightning-fire perimeters were digitized
and their respective attribute tables were populated, the fire return interval for each
lightning fire location could be determined. Overlaying the lightning-fire shapefile on
top of the prescribed burn shapefile graphically depicted their spatial relationships. A
query of the database or a simple point and click of the computer mouse was used to
illustrate the date of the last burn on any chosen point across the landscape. The fire
return interval for each lightning-fire was then calculated to the nearest whole number in
months. The date of last burn as recorded on the wildfire report was used where those
data could not be ascertained through a GIS query (n= 4). Lightning-fires which
occurred in areas with no previous burn history (n=1 1) for example, swamps or flood-
plain forests, were excluded from fire interval calculations.
Landscape type in this study refers to relatively discrete vegetation assemblages
existing on the landscape as defined by the Florida Land Use and land Cover
Classification System (FLUCCS) data (FDOT 1999). Table 2-1 describes each landscape
type used in the analyses. The data were imported into a GIS as a layer. Covering the
entire state of Florida, this layer was clipped to the perimeter of the GSWP to reduce the
size of the data file and to increase processing speed. The total acres of each landscape
type were then calculated in the GIS for the entire GSWP. The prescribed burn layer and
the lightning-fire layer were in turn overlayed onto the FLUCCS layer and total acres of
each landscape type were subsequently calculated for both fire shapefiles. Landscape
types were then grouped into eight distinct categories based on similar characteristics and
based on ground-truthed verifications (Table 2-1).
Table 2-1. Description of landscape types
Landscape Type Description and other FLUCCS categories included in the variable
Flatwoods Longleaf and/or slash pine with palmetto, includes Shrub and
Wet Prairie Same as Flatwoods but with canopy cover < 10%
Pasture Non-native grassland, "improved pasture"
Freshwater Marsh Herbaceous wetland, includes Emergent Aquatic and Herbaceous
Cypress Forested wetland systems, includes Bottomland, Wetland
Coniferous Forest, Wetland Forested Mixed, and Bay Swamp
Planted Pine Commercial plantation of slash pine or longleaf pine
Upland Forest Dense upland forest, includes Upland Coniferous, and Hardwood
Other Disturbed lands, includes Utilities, Reservoir, Disturbed, Extractive
Rainfall data from one sensor, located at 28021'39.7" N, 82ol'20.4" W, near the
center of the GSWP, were obtained from the SWFWMD. No other rainfall sensors were
located on the property during the study period. Though rainfall may have been
significantly different from location to location, it was assumed that the data from the
centrally located sensor accurately represented the general trend of rainfall. Those records
dated back to April of 1981 and consisted of daily totals organized by month and year.
Thirty-day rainfall totals (1-MO RAIN) were calculated for each lightning-fire
occurrence by summing the rainfall for the 30 days previous to the burn date. Three-
month (3-MO RAIN), 6-month (6-MO RAIN), and 12-month (12-MO RAIN) rainfall
totals preceding each lightning-fire occurrence were also calculated. Rainfall
accumulations on the day of a lightning-fire occurrence (0-D RAIN), on the day
preceding an occurrence (1-D RAIN), and seven days preceding an occurrence (7-D
RAIN) were also obtained. In addition, total rainfall for each calendar year from 1981
through 2002 was calculated (ANN RAIN). Table 2-2 provides a description of the
weather related variables used in the study.
Lightning strike data were collected through the use of the Lightning Location and
Detection Network (Vaisala Inc.), covering all of central Florida from 1989 through 2002
(Hildebrand pers. comm.). Lightning strike data for a circular area with a radius of five
miles, centered on the GSWP and covering its entire boundary were obtained for the
study. The total number of flashes (NUM STRIKES) was determined for each date a
lightning-fire occurred during that time period. Total number of flashes were also
calculated for the two days previous to each lightning-fire (STRIKES 2d) and for the
seven-day period preceding each lightning-fire occurrence (STRIKES 7d).
Table 2-2. Description of weather variables used in the study
Variable Description of Variable
0-D Rain Rainfall total on the day of a lightning-fire
1-D Rain Rainfall total one day preceding a lightning-fire
7-D Rain Rainfall total for seven days preceding a lightning-fire
1-MO RAINT Rainfall total for the 30 days preceding a lightning-fire
3-MO RAINT Rainfall total for the 90 days preceding a lightning-fire
6-MO RAINT Rainfall total for the 180 days preceding a lightning-fire
12-MO RAINT Rainfall total for the 360 days preceding a lightning-fire
ANN RAINT Rainfall total for a calendar year
NUM STRIKES Total number of strikes the day of a lightning-fire
STRIKES 2d Total number of strikes 2 days preceding a lightning-fire
STRIKES 7d Total number of strikes 7 days preceding a lightning-fire
General descriptive statistics were developed from the prescribed burn records and
the lightning-fire reports. Mean and standard deviation values were calculated for annual
acres prescribed burned, for all individual prescribed burns, annual lightning-fire acres,
and individual lightning-fires. As a descriptor of seasonality, prescribed bums were
separated by date into lightning-season and non-lightning-season. All of the lightning-
fires which occurred on the GSWP during the study period were within the time-period of
May through August. Therefore, prescribed burns which were conducted between May 1
and August 31 were categorized as lightning-season burns and all others were non-
lightning-season burns. Total acres of burns from both seasons were calculated for each
Landscape Type Proportion
Acreage data used in ratio calculations were transformed with the Freeman-Tukey
method to avoid problems of unequal variance (Cressie and Read 1989):
Zi = (1000(B,)/a,)1/2 + (1000(B, + 1)/a,)1/2
where B, is the acres burned in the ,th observation, and a, is the total area of the ,th burn
unit or landscape type. The yield from this transformation was a proportion of a given
landscape type in a specific polygon layer (e.g. GSWP) to the total acreage of that layer.
It is similar to a percentage, but which does not sum to 100.
Zi values were calculated for the GSWP as a whole, for aggregated prescribed
burns, and for aggregated lightning-fires. Differences between each set of landscape type
proportions was tested with the Chi-square goodness-of-fit test (Ott and Longnecker,
2001) set to a 1:1 ratio. The test result indicates whether a statistical difference exists
between the contrasted layers (e.g. prescribed bum vs. lightning-fire) for at least one
landscape type proportion. Pair-wise comparisons to test which landscape type
proportions were different were not conducted since the proportions were sums of the
entire population (study area) rather than samples used to construct means and other
Fire Return Interval
The time since last burn (FI), in months, was calculated for each lightning-fire with
a known fire history. Frequency distribution analyses (Minitab 2000) were performed on
those data to test the fit with: 1) Weibull, 2) normal, 3) exponential, 4) logistic, and
5) lognormal base e, frequency distributions. The Anderson-Darling goodness-of-fit
statistic and Pearson's correlation coefficient were used to evaluate the fit, and shape and
scale parameters were calculated for each distribution where applicable.
Multiple Linear Regression
Regression analysis is used to investigate the relationship between a response
variable (Y), and one or more predictor variables (X) as illustrated by the formula:
Y = Bo + B1X1 + B2X2 -- ..
where Bo is the y-intercept, B1 is a coefficient, and e is an error term.
The coefficient for each predictor variable, as calculated by the regression model,
represents the change in the response for each unit change in the predictor variable. The
regression equation represents the best "fit" of a line through a plot of X versus Y which
results in the smallest total sum of the squared differences of all of the plot points from
the regression line.
Two key assumptions of regression analysis are that the regression related errors
for each variable are normally distributed with constant variance. Plots of the residuals
for each variable were examined for indications of departures from this. In addition,
normality tests were conducted on all variables and those variables with non-normal
distributions were transformed to achieve normality. Of those variables which required
transformation, a natural log of the data accomplished that goal. As a dependent variable,
FI did not require transformation.
Initially, all the data for each variable were entered into a spreadsheet for
preliminary analysis. A Pearson's Correlation matrix was computed for the set of
variables to detect significant relationships (Table 3-3). The matrix facilitated an
examination of collinearity between variables and the strength and statistical significance
of the correlation between the predictor and the response variable. Correlations with p-
values < 0. 10 were considered candidates for inclusion in the regression analysis.
Regression equations were computed for all possible sets of predictor variables
(Tables 2-2 and 2-3) on the response variable, lightning-fire acres (ACRES). The same
process was applied to the response variable, fire interval (FI). Preliminary model
selection was based on several statistics generated with the regression including R2 p
value, and mean square error. In addition, normal probability plots of the residuals, plots
of the residuals versus the fitted values, and the residuals versus the variables were
plotted to assess assumptions of normality of the residuals and to look for indications of
non-linearities in the relationships between the variables. Finally, a set of candidate
models was ranked by use of Akaike's Information Criterion, corrected for small sample
size, (AICc) which balances the number of predictors in the model with its error variance
(Burnham and Anderson 1998). The formula for AICc is written:
AICc = n[1n(RSS)] + 2k + [2k(k + 1)/(n k)],
where RSS = residual sum of squares (from the regression), and k = # variables.
Table 2-3. Description of variables, excluding weather-related, used in the regression
ACRES Total acres burned in an individual lightning-fire
FI Time in months since an area last burned
JULIAN Julian date of a lightning-fire
PB ACRES Total acres burned by prescribed fire in a calendar year
L-F ACRES Total acres burned by lightning-fires in a calendar year
Burn plans prior to 1990 were incomplete, and specific dates and exact burn
boundaries were unclear, therefore data for burns were included only for years 1990
through 2002. During that time period 195 burns were conducted for a total of 94,3 59 ac,
with an average of 7258 ac/yr (SE = 1415). Annual acreage ranged from a low of 1 11 ac
in 1993 to a high of 15,630 ac in 1997 (Figure 3-1). Individually, prescribed burns
ranged from 15 acres to 2767 ac with a mean size of 43 5.7 ac (SE = 3 8.3). Combined
area of all individual burn units was 50, 158 ac (Figure 3-2). The fire interval, (FI), for
prescribed burns ranged from 31 mo to 96 mo with the average 45.5 mo. Burn unit
landscape types (Table 3-1) consisted primarily of pine flatwoods (Z = 42.8),
cypress/forested wetland systems (Z = 37.4), and pine plantation (Z = 17.4). Those
landscapes comprised 70.0% of the total Z-score of transformed acres. The composition
of landscape types of prescribed burns was different from the GSWP as a whole ( X2
22.56, df = 6, p-value = 0.001). Burn units were composed more of pine flatwoods than
the GSWP and none in the upland hardwood or disturbed categories, which comprised Z-
values of 13.0 and 7.9 respectively for the property as a whole (Figure 3-1).
Table 3-1. Composite transformed landscape type proportions of burn units
Landscape Typ FW WP P FM Cy PP UJF O Cateor
Z-value 43 12 14 8 37 17 0 8 Prescribed
50 19 3 4 29 26 0 0 Lightning
41 10 13 7 42 11 10 5 GSWP
1990 1995 2000
Figure 3-1. Total acres prescribed burned by year
Lightning-season bums (n = 36), defined as those bums occurring within the period
May August (based on lightning-fire occurrence dates in this study), averaged 1024
ac/yr ( SE = 372) and ranged from 0.0 in five different years to 4858 ac in 1999.
Individual lightning-season burns were smaller than non-lightning-season burns though
the difference was not statistically significant (t = 1.10, p-value = 0.277) and averaged
367.0 ac ( SE = 52.3). As a percentage of the total annual acres burned, lightning-season
prescribed burns ranged from 0% in five different years to 38.8% in 1999.
I O0 1.5 3 L Miles
Figure 3-2. Prescribed burn units and lightning-fire locations in the GSWP
A total of 31 lightning-Hires were recorded during the period from 1981 through
2002 for an average of 1.48 fires/yr (Figure 3-3). Those fires burned 1040 ac combined
and averaged 80.0 ac/yr ( SE = 27.5) for the 13 years in which lightning-Hires occurred.
Green Swamp Wilderness Preserve
Burn Units and Lightning-fires
The year 2000 had the greatest number of fires ( n = 11 ) and the largest total acres
burned in a year ( 317 ac ). Individual fires were an average of 34. 1 ac ( SE = 9.85)
though the median lightning-fire was 7.0 ac, and they ranged in size from 1 ac to 267 ac.
Landscape proportions were different from the GSWP (X2 = 33.28, df = 6, p-
value<0.000) and from the burn units containing those lightning-fires (X2 = 14. 16, df = 5,
p-value = 0.015). Lightning-fires were predominately pine flatwoods (Z = 50.4), cypress
systems (Z = 29.1), and pine plantation (Z = 25.7). They included no upland hardwood
forest or disturbed areas (Table 3-1).
O ug ..1. 1 .. g
1980 1990 2000
Figure 3-3. Total annual lightning-fire acres by year
Fire Interval (FI) for the set of 31 lightning-fires ranged from as little as 7 mo to
114 mo (Figure 3-4). However, 11 of the fires occurred in locations with unknown
history or no record of any previous burns, such as river floodplain and swamps, which
historically remained wet year-round (Vanlerberghe pers comm). The remaining 20
lightning-fires with known previous burn histories were used in the analysis of FI. Mean
fire interval was 37.1 mo (SE = 5.61), median FI was 30 mo, and the mode was 24 mo,
indicating that those data were not normally distributed. It can be seen from Figure 3-4
that the distribution of FI was skewed to the right. The Anderson-Darling normality test
confirmed that the data were non-normal (p-value = 0.036). The hypothesis that the
distribution of FI values would be appropriately modeled by the Weibull frequency
distribution was tested.
0 12 24 36 48 60 72 84 96 108
Figure 3-4. Fire interval frequency distribution of lightning-fires
Distribution function analyses were conducted to determine which frequency
distribution fit the data best. The Anderson-Darling statistic and Pearson's Correlation
Coefficient were the two statistical tests used. The Anderson-Darling statistic is a
measure of how far the plot points fall from the fitted line in a probability plot
(MINITAB Inc.2000). Smaller values indicate that the data Sits the distribution better
than those with larger values. Pearson's correlation measures the strength of the linear
relationship between the X and Y variables on a probability plot. A correlation of 1.0
represents a perfect relationship between those variables and the plot points lie in a
straight line on a probability plot. Therefore, a larger Pearson's correlation represents a
better fit to the data than a smaller correlation.
The FI data fit well the Weibull distribution (Shape = 1.77, Scale = 41.13) with an
Anderson-Darling statistic of 0.888 and a Pearson's correlation of 0.983 (Table 3-2) as
compared to a Normal distribution with Anderson-Darling = 1.296 and Pearson's
correlation = 0.926. However, the Lognormal distribution (base e and base 10) fit the
data best with an Anderson-Darling = 0.759 and Pearson's correlation = 0.984. The
Lognormal(e) distribution returned a 50th percentile value of 30. 15 mo.
Table 3-2. Fire interval distribution Goodness-of-fit statistics
Distribution Pearson's correlation Anderson-Darling statistic
Exponential N/A 2.716
Lognormal(e) 0.984 0.759
Normal 0.926 1.296
Weibull 0.983 0.888
Multiple Linear Regression
Multiple regression was used to develop a mathematical model which represents
the linear relationship between two or more independent, or explanatory, variables and a
dependent, or response, variable (Ott and Longnecker 2001). This general linear model
is expressed as:
Y = Bo + B1X1 + B2X2 + ... BkXk + ,
where y is the dependent variable, Bo is the y-intercept, B1 is the coefficient of X,
an independent variable, and e is the error term. Regression calculates a "best fit" line
through the plot of Y vs. the Xs as described by the resulting equation. The equation
indicates the scale and direction of influence of each explanatory variable on the
response. Values for Y may also be predicted by the equation in relation to changes in
the X values.
Correlation among variables
One of the first steps in regression analysis is determining which variables to
include. Relationships between each of the variables were investigated by examining the
correlation between each variable and all other variables in the dataset. A Pearson's
correlation coefficient matrix was generated that contains all the variables and which
displays the coefficients and their associated p-values for assessing statistical significance
(Table 3-3). Coefficients, which may be negative or positive and range from -1 to 1,
measure the strength of the correlation between two variables and are useful in
determining if potential problems of collinearity may occur. A coefficient of 0.90 or
above is considered a level where collinearity, or severe correlation between independent
variables, is likely. In this case, one of the two variables should be removed from the
analysis (Ott and Longnecker 2001). The correlation coefficient matrix generated with
the study variables revealed no potential problems of collinearity.
Table 3-3. Correlation matrix of variables used in the regression analyses
ACRES OD RAIN 1D RAIN 7D RAIN STR-PRV STRIKES 1-MO RAIN 3-MO RAIN
OD RAIN -0.193a
1D RAIN -0.118 0.021
7D RAIN 0.104 0.102 0.385
0.599 0.606 0.043
STR PRV -0.115 0.557 0.226 0.323
0.585 0.004 0.277 0.115
STRIKES -0.153 0.143 -0.137 -0.143 0.193
0.464 0.497 0.514 0.494 0.354
1MO RAIN 0.482 -0.033 0.097 0.509 -0.057 -0.213
0.008 0.869 0.622 0.006 0.786 0.307
3MO RAIN 0.307 -0.012 -0.126 0.423 -0.291 0.062 0.758
0.112 0.952 0.532 0.028 0.158 0.769 0.000
6MO RAIN 0.264 -0.010 -0.135 0.456 -0.270 0.055 0.698 0.938
0.175 0.960 0.500 0.017 0.192 0.794 0.000 0.000
12M RAIN 0.161 -0.130 -0.036 0.396 0.072 0.233 0.383 0.472
0.412 0.518 0.860 0.041 0.731 0.262 0.044 0.011
ANN RAIN 0.503 -0.075 -0.166 0.280 -0.198 0.154 0.436 0.402
0.006 0.710 0.409 0.157 0.343 0.464 0.020 0.034
FI 0.429 -0.308 -0.202 -0.071 -0.114 0.061 0.361 0.224
0.059 0.186 0.394 0.767 0.632 0.798 0.117 0.342
PRV BRNS -0.103 0.005 0.199 0.066 0.165 -0.269 -0.212 -0.361
0.580 0.982 0.310 0.739 0.429 0.193 0.270 0.059
KBDI 0.114 0.401 0.117 0.211 0.615 -0.291 0.525 -0.641
0.699 0.155 0.692 0.469 0.019 0.313 0.054 0.013
JULIAN 0.153 -0.134 -0.272 0.009 -0.585 -0.049 0.431 0.748
0.410 0.495 0.161 0.964 0.002 0.815 0.020 0.000
a denotes correlation coefficient, r
The p-value associated with each correlation is also important since it indicates the
statistical significance for the test of the hypothesis that the coefficient is different from
0. An alpha level of 0.10 was used as a standard for selecting potential variables for the
regression analysis. ACRES, was correlated with FI (r = 0.429, p-value = 0.059) and 1-
MO RAIN (r =0.482, p-value = 0.008). JUTLIAN was significantly correlated with
several variables but not with the response variables of interest, ACRES or FI, and was
not included in the regression analysis. Similarly, 3-MO RAIN, 6-MO RAIN, and 12-
MO RAIN were all significantly correlated with each other and 1-MO RAIN but were not
correlated with the response variables ACRES or FI. Correlations were also assessed on
a dataset which contained variables associated with aggregated annual sums (Table 3-4).
PB ACRES, the total acres prescribed burned in a year, was significantly correlated with
NUM WILDFIRES (r = -0.507, p-value = 0.077) and ANN RAIN, or total annual rainfall
(r = 0.506, p-value = 0.078).
Table 3-4. Variables used in the regression analysis of NUMFIRES
NUMFIRES Total annual number of lightning-fires
AC L-F Total annual acres burned in lightning-fires
AC PB-LS Total annual acres prescribed burned May 1-August 31
AC PB Total annual acres prescribed burned
ANN RAIN Total annual rainfall
Each selected variable was examined with a plot of the residuals versus the
predicted values and normality plots of the residuals derived from an initial regression
calculation. Residuals for ACRES, FI, and 1-MO RAIN were not normally distributed
and the data were transformed by calculating the natural log of each value. The resulting
residuals were normally distributed, thereby satisfying one of the assumptions of
The selection of the "best" model was a step-wise process beginning with variable
selection. Candidate variables identified in the correlation matrix were added to the
regression model with FI as the response variable and the equation was calculated.
Variables were removed one at a time from the model and the analysis was run again
with each new set of variables. Models for which the regression was significant at p <
0. 10 were retained for further assessment. Ultimately, Akaike's Information Criterion
(AICc), corrected for small sample size (Burnham and Anderson 1998), was used as the
final determination of the "best" model. The model with the lowest AICc is judged as
"best". AIC is a model selection technique which serves to choose models with a balance
of error variance and number of independent variables. Models with high error variance
and/or more variables result in a higher AIC score.
Table 3-5 includes the resulting models with their associated p-values, R2 ValUe,
and ranked by AICc. The "best" model (FI--1) describes FI of lightning-fires as a
function of the size of those fires. The model estimated that FI increased as acreage of
lightning-fires increased. The competing models include variables 12-MO Rain or 1-MO
RAIN in the regression equation and approached statistical significance based on their p-
values. These models indicate that with lightning-fire acreage held constant, FI increased
as rainfall amounts increased. Statistically insignificant t-tests for the individual weather
variables (12-MO p= 0.503, 1-MO p = 0.689) provided evidence that the size of the
lightning-fire was a more important predictor ofFI than weather parameters. Model FI-1
had a lower R2 than the other two models, yet it exhibited the highest R2(adjusted) value,
indicating it possessed the greatest predictive strength of the three models. In addition,
FI-1 had the most significant regression P-value (0.034). The R2 Of 22.6% for model FI-1
means the model explained 22.6% of the variation in FI.
Table 3-5. Regression models for FI ranked by AICc
Model P~model) COefficient SE p-value R2% AICc
FI-1 Constant (Bo) 0.034 24.33 7.53 0.005 22.6 184.84
InACRES 6.21 2.71 0.034
FI-2 Constant 0.090 2.30 33.09 0.946 24.7 186.76
InACRES 6.09 2.76 0.041
12-MO RAIN 0.60 0.88 0.503
FI-3 Constant 0.104 22.10 9.46 0.032 23.4 187.10
InACRES 5.74 3.01 0.073
Inl-MO RAIN 3.51 8.61 0.689
Model Selection--Lightning-fire Acres
The same model selection process described above was used to determine the
"best" model to describe size of lightning-fires. Plots of the residuals versus the variables
and the residuals versus the predicted values indicated that transformation of the response
variable, ACRES, was required. ACRES was natural log transformed (In ACRES) and
the plots of the residuals were deemed appropriate. Based on the lowest AICc score, the
"best" model was AC-1 (Table 3-6) which included 1-MO RAIN and FI as predictors of
lightning-fire size. The model revealed that ACRES increased as either 1-MO RAIN or
FI increased. FI (p = 0.056) was a more significant predictor of lightning-fire size than 1-
MO RAIN (p = 0.101). The competing models were significant at the alpha = 0.05 level,
although model AC-1 had the highest R2 value (31.7%).
Table 3-6. Regression models for ACRES ranked by AICc.
Model P~model) COefficient SE p-value R2% AICc
AC-1 Constant (Bo) 0.039 -2.78 1.98 0.178 31.7 82.01
InFI 1.15 0.56 0.056
In 1-MO RAIN 1.00 0.58 0.101
AC-2 Constant 0.050 -2.16 2.05 0.306 19.6 82.81
LnFI 1.24 0.59 0.050
Model Selection--Number of Lightning-fires
A single model of regression statistical significance (p < 0. 10) was developed
which explained the relationship between the response variable NUM FIRES and
independent variables derived from annual sums. The model was estimated as:
NUM FIRES = 4.09 0.000278 AC PB R2 = 23.8% p = 0.091
The model indicates that the annual number of lightning-fires decreased as the total
annual acreage of prescribed burns increased. Addition of either variable annual rainfall
or lightning-season prescribed burn acres to the model resulted in a statistically
insignificant regression and substantially increased error variance. Logically, the annual
total acres burned in lightning-fires was strongly correlated with NUMFIRES, but the
variable was omitted from the regression analysis because no new knowledge would be
gained by including it. The model's low R2 Of 23.8% is indicative of the wide variation in
the occurrence rate of lightning-fires on an annual basis. Figure 3-4 illustrates that
variability, expressed in annual lightning-fire acres, though the trend toward decreasing
lightning-fire acres with increasing annual prescribed burn acres is evident.
O 5000 10000 15000
Acres Prescrib~ed Burned
Figure 3-5. Annual acres prescribed burned by annual acres of lightning-fires.
Over 78% of the GSWP was included in a burn unit and burned at least once during
the study period. The GIS provided a means to visualize the distribution of bums and to
observe that essentially all of the property, except river floodplains and large swamps,
was treated with prescribed fire. Pine flatwoods represented the greatest proportion of
the landscape types in bum units which is not surprising given that pine flatwoods is the
predominate upland habitat in the GSWP and is a fire-dependent ecosystem (Myers and
Ewel, 1990). Though burn units also contained a large proportion of cypress and forested
wetland systems, it is important to note that it was impossible to determine if those
landscapes actually burned or whether water levels or moisture gradients prevented fire
from entering those wetlands. Notes contained within many burn plan evaluations
indicated that, in most cases, those wetlands were inundated or "damp" and therefore did
As established by this study, Prescribed burns tended to have occurred more
outside of the lightning-season than within. Roughly 18.5% of the total number of burns,
or 14.0% of average annual acreage, were conducted during the lightning-season.
Certain landscapes were specifically burned outside the lightning-season to achieve
planned obj ectives. For example, pine plantations were burned in winter to avoid
mortality and the resulting economic loss in timber revenue (Elliot, pers. comm.). The
smallest burn units (e.g. 15 ac) were pine plantation "pockets" which were separated out
from surrounding landscapes and burned in winter. In most cases those small burns were
conducted on the same date with several other burns.
Over one-third (n = 1 1) of the 3 1 lightning-fires which occurred during the study
period were located outside of bum units. Four lightning-fires were located on sites
which had reportedly either experienced a previous wildfire or prescribed fire (Elliott,
pers. comm.), however those data were not available for verification. An average of 0.91
fires/yr were detected in areas known to have previously burned by prescription. Those
47.3 ac/yr were equivalent to 0.14 fires/10,000 ac/yr. Compared to north-Florida (Busby
and Haines 1963), the GSWP experienced a lower rate of lightning-fire ignitions. They
found a rate of 0.51 fires/10,000ac/yr (421.5ac/1 0,000ac/yr) for lightning-fires during
their 4-year study period. Though the north-Florida study area was managed with
prescribed fire, greater numbers and larger sizes of wildfires occurred on areas with a FI
in excess of five years. The shorter average FI for prescribed bums on GSWP may
explain the reduced lightning-fire occurrence rate experienced there. Davis and Cooper
(1963) also reported that the probability of a wildfire occurrence and the acreage of the
fire increased dramatically after five years since a previous burn. The results of this
study indicated that lightning-fire size tended to increase over time but the probability of
an occurrence appeared to peak at around 30 mo and declined thereafter. Rather than an
inherent decrease in the flammability of the landscape >30 mo post-burn, however,
prescribed burn frequency may have reduced the likelihood of a lightning strike
contacting areas which had not burned in more than three years.
Hypothesis #2 (H(2)) WAS that the FI distribution of lightning-fires would be best
described by the Weibull frequency distribution. Though the data did fit the Weibull
distribution well, the lognormal (base e) distribution fit the data best. This finding lends
credence to the premise posed by McCarthy et al (2001) that the Weibull distribution
should not be assumed a priori as the most accurate description of fire frequency for a
given area. They argue that, biologically, it may make no sense to assume that FI would
follow a distribution based on the probability of a wildfire as a power function of time
since last burn (he,= ht/`b). In this study, FI appeared to have been strongly influenced by
the frequency and the extent of prescribed burns. Were it possible to allow lightning-
fires to burn unimpeded, over a significant time-period and in the absence of prescribed
burns, a completely different FI distribution may emerge.
It is important to note that the wildfire reports pertaining to nearly all of the
lightning-fires included some reference to fire suppression. This means that the size of
those fires was influenced by human activity designed to stop fire spread. Correlations
between fire size and FI or weather parameters were probably impacted as a result.
Additional variation was induced by factors such as a) time from fire detection to
suppression response and b) time required to suppress the fire. Those factors may help to
explain the relatively low R-sq values (22.6%-31.7%) obtained in the regression analyses.
Lightning-fires occurred more frequently in pine flatwoods, wet prairie, and planted
pine landscapes than those types existed across the GSWP. Planted pine areas were more
than twice as likely, proportionately, to be associated with a lightning-fire than their
availability would suggest. Pasture, mixed conifer and hardwood forest, and disturbed
areas were under-represented as components of lightning-fires in relation to the GSWP as
a whole. A lack of trees to act as lightning rods in pastures probably explains the reduced
involvement of that landscape type.
Fire interval was only significantly correlated with ACRES, and while the
relationship was statistically important (p =0.059), the strength of the correlation was not
strong (0.492). The regression equation with the lowest AICc score reflected that
correlation in that ACRES was the only predictor variable included in the model. The
regression was significant at the alpha = 0.05 level indicating that the model has
predictive value and, therefore, the size of a lightning-fire was a function of FI. The
model predicts that FI increases as the size oflightning-fires increase. This implies that
the longer a given area goes without being burned the larger a wildfire will be when it
Model FI-2, the second "best" model as determined by AICc, included 12-MO
RAINT as the second predictor. The coefficient was positive (0.603) indicating that FI
increased by 0.6 mo as 12-MO RAINT increased by one inch of rainfall. Stati sti cal
significance was approached (p = 0.090) but the R2(adj) value of 15.8% meant that the
model had low predictive value.
Only 22.6% of the variation in FI was explained by the FI -1 model. Fire
suppression efforts, undertaken by the Florida Division of Forestry, which controlled the
size of lightning-fires and were a function of time to begin and to complete fire control,
probably accounted for much of the variation in FI not explained by the model. The
actual effect of lengthened FI on the size of a lightning-fire was therefore distorted by fire
suppression efforts and the effect could not be definitively ascertained from the available
Size of Lightning-fires
Hypothesis #3 (H(3)) postulated that landscape type has greater influence on
ACRES than time since last burn, which has greater influence than climate variables.
The variable FWPROP, the proportion of Flatwoods in an individual lightning-fire, was
used as an indicator of landscape type influence because it was the most prevalent
category This hypothesis was tested indirectly through the regression analyses. The
regression coefficient and individual t-test for FWPROP were an indication of the
influence and predictive significance, respectively, of FWPROP on ACRES. Those
results indicate that H(3) WaS false and that FI and 1-MO RAINT had greater influence than
ACRES was significantly correlated with FI and 1-MO RAINT. Both correlations
were positive but were not strong and neither relationship exceeded a Pearson's
correlation coefficient of 0.500. Model AC-1 included both of those variables and was
statistically significant as a prediction equation (p = 0.039). This model explained 31.7%
of the variation in ACRES and predicts that the size of a lightning-fire increases as FI
increases a conclusion already indicated in model FI-1. It is likely that the low R-sq.
value was partly a result of the variability introduced due to fire suppression activities.
Much of the variation in ACRES may have been a result of reduced distance to access
roads, suppression tactics and other variables not accounted for in this study.
Surprisingly, this model also implies that the size of a lightning-fire increases with
increasing 1-MO RAINT (indicated by the positive Pearson's correlation and regression
equation coefficient). This finding would appear contrary to established fire behavior
models and fire danger indices. Rainfall increases soil and vegetative fuel moisture
levels which in turn reduce fire danger indices such as KBDI (Keetch and Byram 1968)
and decreases predicted fire spread rates (Finney 1998). Together, both models predict
that increased rainfall tends to decrease a fire's potential in terms of initial ignition and in
This anomaly of increased near-term rainfall correlating with increased ACRES
may be related to the cause of the fires lightning. Increased rainfall may have simply
been an indicator of increased lightning, without which no lightning-fires would have
occurred. Though lightning-fires are often thought to be a result of "dry" lightning
strikes (strikes not associated with rainfall), the data show that rainfall was recorded in
the month prior to all but one occurrence date (6/21/00). It is important also to note that
lightning-fires tended to occur on days with little lightning activity as compared to the
days preceding the occurrence. It is likely that during rain events lightning strikes may
have resulted in an ignition of fuel which only smoldered as a result of high relative
humidity and fuel moisture due to the rain. Smoldering may have continued for several
days before conditions allowed the smolder to advance to flaming ignition and ultimately
a lightning-fire occurrence.
Suggestions for Future Research
The use in this study of a GIS to develop a database of prescribed burns and
lightning-fires on GSWP creates opportunities for further research. The database can be
easily updated as prescribed burns are conducted and additional lightning-fires occur.
Wildfires from other causes can be included and the database can be updated regarding
additional management activities. Empirical fuel load descriptors could be incorporated
as those data are collected. Spatial and temporal aspects of wildfires may then be
investigated relative to a wider range of parameters than were examined in this study.
Future research should focus on the effects of human-related factors on lightning-
fire size. Aspects such as response time to initiation of suppression and completion of
suppression actions should be incorporated in the analysis. The suppression tactics used
to control the fire could be captured as factors. Distance from the fire to main roads and
secondary roads should be included as variables, an action easily accomplished with the
Incorporation of more spatially explicit weather and lightning strike data should be
pursued. Whereas this study relied upon one rainfall-recording sensor, radar and other
remote sensing technologies can produce rainfall estimates with much greater spatial
resolution. Lightning strike data bearing polarity and amperage tied to geographic
coordinates could be applied in the analysis of lightning-fire occurrences.
Alternative approaches to the study of lightning-fires may include the design and
establishment of applied experiments. Various and replicated applications of specified
prescribed fire return intervals and/or silvicultural treatments could be evaluated over
time relative to lightning-fire occurrence. These experiments and the other suggested
investigations could be accomplished with an expanded research association between the
SWFWMD and the University system.
Prescribed fire was used on the GSWP as the main management tool by the
SWFWMD Land Management staff for the stated purposes of ecosystem enhancement
and wildfire hazard reduction (Love pers comm). In comparison to the north Florida
study done by Davis and Cooper (1963) on a national forest managed with prescribed
fire, results indicate that the rate of lightning-fire ignitions and the acreage burned in
lightning-fires was further reduced by the extent of the prescribed burn program on
GSWP. Those results are notewothy given that the scope of this analysis was 20+ yr,
including prolonged periods of drought, and the north Florida study was 4 yr. It appeared
that one maj or difference in the two study sites was that 48.7% of the north Florida
property consisted of landscapes unburned for over 5 yr. In contrast, the majority of the
GSWP was maintained at less than 4 yr as indicated by the mean FI for prescribed burns
of 3.8 yr. Continuation of the current prescribed burn program, in terms of the FI and
extent across the landscape, will likely maintain lightning-fire ignitions and acreages at
The benefits of properly executed prescribed fire to Florida's ecosystems are well
documented, particularly for endangered plants (Breininger and Schmalzer 1990) and
animals (Machr et al 2001). Burns which occur during the lightning season, primarily
May-August, are concurrent with the growing season for plants and have been shown to
be especially beneficial in stimulating the flowering and fruiting of native species
(Robbins and Myers 1992). Priority should be given to conducting more lightning-
season burns on the GSWP. As a percent of the total acres burned annually, lightning-
season burns comprised from 0% to a maximum of 38.8% in 1999. In addition,
lightning-fires should be allowed to burn to their natural conclusions when possible.
Those fires which occur under acceptable prescription parameters for prescribed fires, for
example, could be monitored by trained fire managers to assure that obj ectives are met
and suppression is applied only where necessary to prevent smoke problems or other
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Darrell Lee Freeman was born in Texarkana, Texas, on 26 May 1959. In 1981 he
received a B.S. in wildlife and fisheries sciences from Texas A&M University. After
graduation Darrell owned and operated a landscaping business in Florida until 1992 when
he started a naturalist guiding and consulting operation in Arizona. In 1996 he began
work as a land manager for the Southwest Florida Water Management District in Florida.
In May 2004 he completed requirements for the Master of Science degree, at the
University of Florida. Darrell is married to his wife, Trish, with no children.