International Journal of Wildland Fire, 2007, 16,

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1 CSIRO PUBLISHING International Journal of Wildland Fire, 2007, 16, Modelling the probability of sustained flaming: predictive value of fire weather index components compared with observations of site weather and fuel moisture conditions Jennifer L. Beverly A,C and B. Mike Wotton B A Canadian Forest Service, Northern Forestry Centre, Street, Edmonton, AB T6H 3S5, Canada. B Canadian Forest Service, Great Lakes Forestry Centre, 1219 Queen Street East, Sault Ste Marie, ON P6A 2E5, Canada. C Corresponding author. jbeverly@nrcan.gc.ca Abstract. We investigated the likelihood that short-duration sustained flaming would develop in forest ground fuels that had direct contact with a small and short-lived flame source. Data from 1027 small-scale experimental test fires conducted in field trials at six sites in British Columbia and the North-West Territories between 1958 and 1961 were used to develop logistic regression models for ten fuel categories that represent unique combinations of forest cover, ground fuel type, and in some cases, season. Separate models were developed using two subsets of independent variables: (1) weather variables and fuel moisture measurements taken at the site of the test fire; and (2) Canadian Fire Weather Index (FWI) system components calculated from weather observations recorded at a nearby station. Results indicated that models developed with FWI system components were as effective as models developed with site variables at predicting the probability of short-duration sustained flaming in most fuel categories. FWI system components were not useful for predicting sustained flaming in spring grass fuels and had limited usefulness for modelling the probability of sustained flaming in aspen leaf ground fuels during summer conditions. For all other fuel categories, FWI system components were highly effective substitutes for site variables for modelling the probability of sustained flaming. Additional keywords: Canada, fire behaviour, fire danger, fire hazard, logistic regression, probability of ignition. Introduction The conditions under which sustained flaming develops in forest ground fuels exposed to an ignition source are both varied and complex. Sustained flaming can be considered the outcome of a successful fire ignition and encompasses three factors identified by Anderson (1970) as determinants of flammability: ignitability, sustainability and combustibility. Ignitability refers to the ease of ignition. Combustibility is the post-ignition rate of burning, and sustainability refers to how well the fuel continues to burn, or combustion stability. Forest fuel receptivity to ignition will depend on the type of fuel exposed to the ignition source, the fuel moisture content, the characteristics of the ignition source, and the influence of micro-site variables such as air flow, wind (Brown and Davis 1973) and fuel shading (Lin 1999). Fuelspecific assessments of the likelihood of sustained flaming are important for understanding the mechanisms that lead to the initiation and spread of forest fires and for predicting forest susceptibility to fire in a given geographical location and time period, which is important for both research and operational fire management applications. Daily, hourly, and instantaneous fluctuations in fire susceptibility can result from changes in weather variables that influence fire behaviour and fuel moisture content. Seasonal variations are associated with long-term weather trends and phenological changes in vegetation. Fire danger rating systems, like the Canadian Fire Weather Index (FWI) system (Van Wagner 1987), were developed to provide daily and hourly ratings of fire susceptibility. Calculated for individual weather stations from a set of weather observations, the FWI system provides nationally consistent and readily available ratings of fire susceptibility. Although fuel moisture codes of the FWI system were developed to be representative of fuels in a mature, closed canopy jack pine (Pinus banksiana Lamb.) or lodgepole pine (Pinus contorta Dougl.) stand, in practice FWI system components are not regarded as fuel-specific indicators. FWI system components are considered generalisations of fuel moisture and fire susceptibility applicable to a wide variety of stands and are based on fundamental relationships between weather variables, fuel moisture conditions, and observed fire behaviour. Statistical models have been used to investigate these fundamental relationships using either historical data of observed wildfire events or experimental fires ignited in laboratory or field settings. Models based on historical data have been used to describe landscape level relationships among weather variables, fuel or vegetation characteristics, and patterns of observed fire events (e.g. Wotton and Martell 2005; Krawchuk et al. 2006). Socioeconomic variables and fire management activities have also been combined with ecological variables to model variability in fire events across large areas (e.g. Mercer and Prestemon 2005). Effectiveness of fire danger rating indices at predicting IAWF /WF /07/020161

2 162 Int. J. Wildland Fire J. L. Beverly and B. M. Wotton fire activity across large areas has also been explored through investigations of the weather associated with observed fire events (e.g. Andrews et al. 2003). Landscape-level models provide coarse-scale estimations that are limited by the accuracy of historical fire event data, which varies in completeness, and by the quality of weather data and spatial data used to represent landscape characteristics. Fine-scale modelling of ignition processes can be achieved with a small-scale experimental test fire approach, which has been applied in numerous studies in Canada and elsewhere using either laboratory apparatus or field ignition trials. Small-scale experimental fires are an appealing research method because they are inexpensive; can be conducted under controlled laboratory conditions or with minimal disruption of field site locations; and they can be conducted under extreme fire weather conditions that would often preclude the use of large-scale experimental fires. Laboratory test fires (e.g. Latham and Schlieter 1989; Frandsen 1997; Lawson et al. 1997; Pérez-Gorostiaga et al. 2002; Engstrom et al. 2004; Liodakis et al. 2005) have been used to isolate specific fuel properties relevant to ignition by controlling external influences (e.g. weather, climate, and location). Laboratory tests have also been used to explore interactions among a small number of factors that influence ignition (e.g. Lin 2005). Field ignition trials (e.g. Lawson and Dalrymple 1996; Lin 1999; Larjavaara et al. 2004; Ray et al. 2005; Tanskanen et al. 2005) differ in that they incorporate complex micro-site variablities among many variables that are known to be present at actual wildfire ignition points. In typical field ignition trials, the outcome of a fire ignition is categorised as either a success or a failure, and logistic regression methods are used to model the probability of a successful fire ignition as a function of one or more independent variables. Independent variables used to model the probability of ignition generally fall into two groups: site variables that describe weather and fuel moisture conditions at the time and location of the fire, and fire weather index values that represent approximations of these conditions. The practical application of models based on site variables is restricted to those situations where on-site sampling and weather measurement is feasible, such as experimental or prescribed burning operations. Models that predict the probability of sustained flaming in an area from readily available fire weather index values have widespread research and operational applications. Daily FWI system values for multiple weather stations across an area can be interpolated to provide continuous spatial ratings of fire susceptibility, which can be associated with a fuel map to identify FWI system component values that correspond to a particular fuel type in a given area on a given day. The spatial representation of actual site variables relevant to fire ignition (e.g. fuel moisture content) is currently impractical because of the time and resources that would be associated with a large-scale daily fuel moisture sampling program. Remote sensing technology may provide a future means of estimating spatial variation in fuel moisture conditions of live fuels, but it currently has limited use for assessing the condition of dead fuels (see review by Chuvieco et al. 2004). By modelling the probability of sustained flaming with FWI system values, fast and inexpensive assessments of fuel-specific fire susceptibility can be obtained for an area. Predictive models of the likelihood of sustained flaming can be used in research applications that require fuel-specific representations of fire processes and in daily operational planning by fire management agencies to distribute fire response resources in a manner that reflects spatial variations in relative fire susceptibility across their jurisdictions. While the practical advantages of modelling with FWI system components are clear, the degree to which predictions of fire susceptibility based on FWI system components approximate predictions based on site variables has been largely unexplored. We used data from field trials of small-scale test fires to investigate the likelihood that short-duration sustained flaming would develop in forest ground fuels that had direct contact with a small and short-lived flame source (wooden match). Models were developed for 10 fuel categories that represent unique combinations of forest cover, ground fuel type, and in some cases, season. For each fuel category, we compared the predictive ability of models composed of FWI system components to models that used site observations of weather variables and fuel moisture content to predict the probability of sustained flaming. Implications of results for fire research and fire management applications are discussed. Methods Study sites Four of the six study sites included in the analysis were located near Fort Smith, North-West Territories (60 00 N, W) and two were located near 100 Mile House, British Columbia (51 39 N, W). Study sites were within a 4.8 and 2.9-km radius of a weather station established at Fort Smith and 100 Mile House locations, respectively. Test fire sites were typically square or rectangular, ranging from 232 to 3716 m 2 in size, and surrounded by a 0.5-m trench cleared to mineral soil (Macleod 1948). Detailed descriptions of the six test fire sites are provided in Table 1. Test fire data Canadian federal government fire researchers initiated a smallscale test fire program in the 1930s. By 1940, program procedures had been standardised, and between 1940 and 1961, small-scale test fires were conducted at nine field stations across Canada. The test fire program involved daily weather documentation, systematic fuel moisture sampling, and detailed evaluations of the outcomes of small-scale experimental test fires conducted at field sites chosen to reflect representative fuel types across the country (Paul 1969). Results were used to develop early systems for rating fire susceptibility on a given day. These early systems were instrumental in the conceptual development of the FWI system, although test fire data collected between 1940 and 1961 were not used directly in FWI system models. Paul (1969) noted that the small-scale test fire program involved documentation of extensive supplementary information on fire weather, fuel moisture, and fire behaviour that was undertaken without a specific objective or research plan. This may explain why large portions of the database have never been subjected to a thorough and systematic analysis. Since the release of the FWI system in 1970, only a few studies have utilised data collected during the small-scale test fire program. Notably,

3 Modelling the probability of sustained flaming Int. J. Wildland Fire 163 Table 1. Site descriptions by fuel category Fuel category Site Location Cover type Ground fuel Site description A FC1. Grass (spring) Mile House, Grass Grass Open site with scattered Douglas fir (Pseudotsuga menziesii (Mirb.) Franco) on a south-west slope. FC2. Grass (summer) British Columbia Mile House, Grass Grass Open site with scattered lodgepole pine (Pinus contorta Dougl.) on an exposed south-west slope. British Columbia FC3. Pine, lichen Fort Smith, Jack pine Lichen, moss, Dense, even-aged, 85-year old jack pine (Pinus banksiana Lamb.) stand of fire origin, located FC4. Pine, moss North-west needles 80 m from the weather station with a basal area of 26 m 2 per hectare. Average diameter at FC5. Pine, needles Territories breast height (DBH) is 10 cm and maximum tree height is 20 m. There is a low density of minor vegetation. Predominant surface fuels are Hylocomium and Calliergon spp. mosses and Cladonia spp., with scattered needles and twigs, and clumps of Linnea, Vaccinium, Arctostaphylos spp. and grass present. Scattered Shepherdia and Salix spp. shrubs occur. Surface fuels overlie a thin, partly decomposed layer (fermentation layer [F]) and a 1.3 cm decomposed layer (humus [H]). The full organic layer is generally <5 cm deep over fine sand. FC6. Mixed wood, moss Fort Smith, Mixed wood Moss, needles, Mature, uneven-aged white spruce (Picea glauca (Moench) Voss)-trembling aspen (Populus FC7. Mixed wood, North-west leaf tremuloides spp.)-jack pine stand with a basal area of 34 m 2 per hectare. High bush cranberry needles leaf (summer) Territories (Viburnum opulus L. var. americanum (Mill.) Ait.) and Shepherdia spp. shrubs cover 20 30% of the understory. Dominant surface fuels include Hylocomium and Calliergon spp. mosses, leaves and needles. The full organic layer varies in depth from 1.3 to 3.8 cm. Researchers noted evidence of fire 45 to 50 years before the test fires. FC8. Spruce, moss Fort Smith, Spruce Moss Very dense, 85-year old, even-aged black spruce (Picea mariana (Mill.) BSP) stand with a basal area of North-west 37 m 2 per hectare. A large proportion of the trees are suppressed, giving the stand an uneven-aged Territories appearance. Hylocomium spp. moss, cm deep covers 100% of the ground surface. The organic layer reaches a depth of 18 cm in some locations, overlying very fine silty sand. FC9. Aspen, grass (summer) Fort Smith, Aspen Grass, leaf Pure, 60-year old even-aged trembling aspen stand with a basal area of 22 m 2 per hectare. During the FC10. Aspen, leaf (summer) North-west summer months there is dense minor vegetation cover consisting of clumps of Salix spp., Shepherdia Territories spp. and Rose (Rosa spp.) bushes. Underneath this shrub layer is a fairly complete cover of Epilobium, Lathyrus, Vicia spp. and grass. Leaf cover is cm in depth. A Unpublished progress reports on forest fire research, Fort Smith (1961) and 100 Mile House (1957).

4 164 Int. J. Wildland Fire J. L. Beverly and B. M. Wotton Lawson and Dalrymple (1996) presented models of the probability of sustained ignition that were based on a small number of test fires conducted in British Columbia. Data collected during the test fire program is contained in a Canadian Forest Service database (Paul 1969; Simard 1970). 1 Each test fire record in the database contains information on the location of the fire; weather conditions recorded on site and at a nearby weather station; a description of the fuels and a measure of fuel moisture content; observations of test fire behaviour; and FWI system components calculated from weather station data. Not all test fire records are complete, and while all records include weather observations from a nearby weather station, relatively few include observations of site weather conditions at the time of the fire. Only 1845 test fire records contain site observations of temperature and relative humidity, and 1662 (90%) of these test fires were conducted at seven sites located at two field stations: Fort Smith, North-West Territories (five sites), and 100 Mile House, British Columbia (two sites). We used data from these two field stations to investigate the predictive ability of FWI system components in comparison with site variables for modelling the probability of sustained flaming. Test fire records (345) from one site in Fort Smith were dropped from the analysis because of a lack of site descriptive data. Of the remaining records, only those that contained a fuel moisture measurement for the ground fuel type consumed by the fire (e.g. grass, lichen, moss, needles, and leaf) were included in the analysis. For each of the six sites, remaining data was divided into categories that reflected unique fuel conditions based on forest cover, ground fuel type, and in some cases, season. Some fuel categories were excluded from the analysis because they had insufficient numbers of test fires. In total, 10 fuel categories and 1027 test fires were included in the analysis. Following technological changes, the records contained in the test fire database have undergone several format transformations and data manipulations over the past 60 years. Test fire behaviour was originally documented with field notes written by researchers who observed the test fire. This information, along with weather and fuel moisture data, were transferred to punched cards (Joly and Fraser 1961, 1962; Fraser and Joly 1965) and eventually to magnetic tape (Simard 1970). More recently, FWI components were added to each test fire record and initial data cleaning was undertaken. 2 We merged test fire records that had been archived separately for each province into a single database, converted all fields into metric, and assembled detailed descriptions of each field in the database. To ensure that data accuracy and integrity of the test fire database had not been compromised by these transformations and data manipulations, we compared original test fire field notes from a random sample of 100 test fires with records of those fires currently contained in the test fire database. Variables particularly significant to the present analysis were selected for comparisons and included fire ignition type, three variables rating fire behaviour and three variables describing fuel type. An error was recorded if an entry for a variable in the digital database did not match the corresponding entry recorded in the field notes. Site fuel moisture and weather data Efforts were made to locate the test fire area in close proximity to the moisture sampling area, and moisture sampling sites were chosen to approximate tree and ground cover characteristics found at the test fire site (Macleod 1948). At the Fort Smith field sites, fuel moisture sampling was carried out twice daily to coincide with morning and afternoon test fire schedules. These fuel samples were collected during or immediately after each test fire observation (unpublished report on forest fire research, 1961, Fort Smith, NWT). Fuel moisture samples at 100 Mile House field sites were collected in the afternoons only, and field notes indicate that moisture samples at a site were conducted at the same time as test fires ignited at the site. Fuel moisture samples were collected for individual ground fuel types, including grass, moss and lichen, and for a ground fuel category called the top layer duff, which could contain needles, leaf or a mixture of the two, depending on the duff species code recorded at the site of the fire. Samples were collected on site in tins, weighed, and oven-dried at a temperature of 118 C overnight without their lids, before re-weighing (Paul 1969). Percent moisture content was calculated as the difference between the wet sample and dry sample weights divided by the difference between the dry sample weight and the container tare weight. Most moisture-content values associated with the test fire records are calculated from single samples. Although sampling locations were chosen to represent conditions at the location of the test fire, micro-site characteristics no doubt introduced variability in fuel moisture at a fine scale. Variability in fuel moisture samples can be expected to decrease as fuel conditions become progressively drier. The majority of test fires (91%) occurred on days when the diurnally adjusted Fine Fuel Moisture Code (FFMC) was 70. Test fires conducted on days with a FFMC <70 were excluded from the analysis to control for increasing variability in fuel moisture measurements taken during moister conditions. Existing documentation of the test fire data and field procedures associated with the test fire program (e.g. Paul 1969; Simard 1970) make little reference to the site weather measurements taken at the location and time of the test fires. Information on the timing of site weather measurements in relation to the timing of the test fires, as well as the instrumentation used to obtain these measurements, were verified from annual progress reports that documented activities at each field station and from the original test fire field notes completed by researchers at the site of each test fire. These records indicate that a sling psychrometer was used to record dry bulb temperature, wet bulb temperature and relative humidity each time a test fire was conducted. In cases where a series of consecutive test fires were conducted at a site within a short period of time (i.e min), a single set of 1 A more detailed report describing the test fire procedures and experimental sites is being prepared: J. L. Beverly and B. M. Wotton: The Canadian small-scale test fire database: historical overview and data documentation. Canadian Forest Service, Northern Forestry Centre, Information Report (in preparation). 2 Unpublished report. Lynham TJ, Martell DL (1989) Preliminary report on a national database of experimental fire in Canada. In Proc. National Workshop on Forest Fire Occurrence Prediction May 3 4, 1989, Forestry Canada.

5 Modelling the probability of sustained flaming Int. J. Wildland Fire 165 site weather measurements were used to represent conditions for the series (i.e. duplicated for each test fire record in the series). In some cases the weather measurements were taken at the time of the first fire in the series, while in other cases the measurement was taken mid-way through the series, which would have improved the representativeness of the measurement. For example, the field notes for 5 July 1961 at site (Fort Smith) indicate that test fires were conducted in moss and needle-leaf ground fuels at 1435, 1440 and 1445 LST and site weather measurements recorded at 1440 were used for all three of these fires. Ninety-three percent of test fires with duplicate site weather measurements occurred within 15 min of each other. At Fort Smith, where each site was visited twice daily and consecutive test fires conducted in the morning and afternoon were spaced with several hours between them, a new set of site weather measurements were recorded for afternoon test fires. Test fire procedures Test fires were conducted between May and September (Table 2). Once procedures at a site were initiated for a given year, the site was visited daily with the exception of Sundays. Test fires were attempted on all rain-free days provided that an informal on-site assessment indicated that fuel moisture was not overly saturated. Because researchers made subjective assessments about whether or not conditions were appropriate for test fire experiments, our restriction of the data to test fires conducted on days when the FFMC was 70, which was introduced to account for increasing variability in fuel moisture measurements at low FFMC values, also provides an objective criterion for determining whether or not a given day would be a test fire day. Fires were ignited in both spring and summer seasons, although the majority (88%) occurred during summer conditions. We used phenological records to categorise test fires in grass and leaf fuels according to season. Spring fires represent conditions before the onset of leaf flush, and summer fires represent conditions after leaf flush but before the onset of leaf fall. Test fire procedures are described by Macleod (1948) and Paul (1969). We acquired additional methodological details from unpublished historical documents, which included test fire field notebooks, original test fire field data cards and annual progress reports that summarised fire research activities at test fire field stations active in Canada between 1940 and The majority of test fires (98%) occurred between 0800 and 1700 LST. Test fires at 100 Mile House sites were restricted to the afternoon. Fort Smith test fires were conducted at each site twice daily, in the morning and afternoon. Test fires were ignited Site Table 2. Duration of sampling by site and year Year May 5 Sept 7 May 2 Sept Aug 5 Sept 7 May 2 Sept May 11 Sept May 12 Sept June 29 Aug May 31Aug by placing the flame of a large, household sized wooden match in contact with ground fuels considered to be representative of fuel moisture content on the site. The temperature of a match flame is 1260 C (Brown and Davis 1973).A match ignition can be described as contact with a flame mm in length for a duration of s. If the match extinguished before the ground fuel ignited, the procedure was repeated. Sixty percent of the 1027 test fires were ignited with a single attempt, and 73% were ignited with three attempts or less. In a small number of cases (3%), match ignition of ground fuels could not be achieved after repeated attempts. In these situations, we classified the outcome of the test fire as no sustained flaming. Once ground fuels were ignited, the fire was generally observed for 120 s. Some fires became extinct before 120 s, either as a result of poor burning conditions or through the action of investigators seeking to limit aggressive fire behaviour. Weakly burning fires were sometimes observed for more than 120 s to establish evidence of flame sustainability. The average observation period was 103 s with a range of 15 to 300 s. Researchers documented observed test fire behaviour by assigning each fire a qualitative rating called the vigour code (Table 3). We classified the outcome of a test fire ignition as achieving sustained flaming if the vigour code was 3 5. Statistical analysis We modelled the probability of sustained flaming with logistic regression by classifying the outcome of a test fire as either sustained flaming (1), or no sustained flaming (0): 1 P(sf ) 1 + e (β (1) 0+β 1 x 1 + +β n x n ) where P(sf) is the probability of sustained flaming, x 1 n are the independent variables, and β 0 n are regression coefficients. For each of the ten fuel categories, the probability of sustained flaming was modelled as a function of two separate groups of independent variables: (1) FWI system components, and (2) site measurements of weather and fuel moisture conditions. The FWI system contains three fuel moisture codes that account for daily and hourly changes in the fuel moisture content of ground fuels layered at increasing forest floor depths. Moisture code values are calculated for individual weather stations Code Table 3. Vigour code descriptions (Paul 1969) Description 1 At 2 min the fire is burning very weakly on one front only and goes out by itself 2 At 2 min the fire is burning slowly and poorly on two or more fronts and seems likely to go out on its own accord rather than continue indefinitely 3 At 2 min no sign of fire going out by itself, burning fairly briskly, but not on all fronts 4 Fire burning briskly at 2 min on all fronts with tendency to become progressively stronger, but no difficulty in putting it out with feet (stomping) 5 As for 4 but difficult or impossible to put out fire with feet after 2 min 9 Fire goes out before 2 min

6 166 Int. J. Wildland Fire J. L. Beverly and B. M. Wotton from consecutive, daily observations of weather conditions (dry bulb temperature, relative humidity, 10-m open wind speed, and precipitation) recorded throughout the fire season. Relative daily ratings of potential fire intensity, spread rate, and fuel consumption are provided by three fire behaviour indices generated from the moisture codes, for a total of six FWI system components (Van Wagner 1987): FFMC: represents the moisture content of litter and other cured fine fuels. Duff Moisture Code (DMC): represents the moisture content of loosely compacted, decomposing organic matter. Drought Code (DC): represents moisture conditions in a deep layer of compact organic matter. Initial Spread Index (ISI): a combination of wind and FFMC that represents the rate of fire spread independent of fuel quantities. Buildup Index (BUI): a combination of the DMC and DC that represents the total fuel available to the spreading fire. FireWeather Index (FWI): a combination of the ISI and BUI that represents the intensity of the spreading fire as energy output rate per unit length of fire front. The FFMC value represents litter moisture content at peak burning conditions, 1600 LST. We used documentation of the timing of fires during the day to produce a diurnally adjusted FFMC value for each test fire record (i.e. Van Wagner 1972; Lawson et al. 1996).This FFMC value was then used to calculate a diurnally adjusted Initial Spread Index (ISI) and a diurnally adjusted FWI. Fuel moisture content is commonly used to predict fire ignition potential and sustainability (e.g. Blackmarr 1973; Frandsen 1997; Lin 1999). We used records of fuel moisture content for the ground fuel type consumed by the test fire (e.g. grass, lichen, moss, needles, and leaf) as an independent site variable. We also included two site weather variables that are commonly used as predictors of fire ignition and sustainability: relative humidity and temperature (e.g. Lin 1999). Vapour pressure deficit, a measure of evaporative drying potential, was calculated from measurements of site relative humidity and temperature for each test fire record, and was included as a fourth site variable in the analysis. Wind is known to influence fire behaviour and has also been used as a predictor in models of fire ignition and sustainability (e.g. Lawson et al. 1994; Lin 1999). It was not included as a predictor of sustained flaming in this study because test fire records do not include site wind speed measurements at the time of the fire. Approximately 80% of the test fire records do contain a qualitative rating of site wind conditions, and 90% of these fires were conducted with wind speeds of 4.8 km h 1, likely a result of the impracticality of conducting match ignition tests under moderate or high wind conditions, which suggests that wind speed likely did not have a major influence on test fire outcomes. Maximum likelihood estimates of model parameters were computed with SAS LOGISTIC (SAS Institute 2004). Model selection between and within the two groups of independent variables, (A) FWI system components and (B) site variables, was based on Akaike s information criterion (AIC). Model predictive ability and goodness of fit was assessed by the likelihood ratio χ 2 test, the Wald χ 2 test for individual parameters, and the C statistic. For each model, validation was conducted with cross-validated predicted probabilities computed in SAS. The procedure involved withholding single observations from the dataset, building the model without it, and then testing the observation in the model. The process was repeated until all observations had been tested, and cross-validation accuracy was estimated from the frequency of times an observation was not re-classified during the cross-validation procedure. Results Correspondence between data entered in the original test fire field notes for a random sample of 100 test fires and data entered for those 100 fires in the current database was 99.3% for the seven variables that were assessed (i.e. ignition type, three fire behaviour variables and three fuel type variables). This suggests that data transformations and manipulation of the test fire data over the past 60 years have not compromised data integrity. Because of their insignificant numbers, it is most likely that the infrequent errors observed in the database occurred during the initial transfer of test fire field notes to punched cards in the 1960s. The average moisture content of ground fuels, and relative humidity at the time of the fire, were significantly lower for fires that achieved sustained flaming as compared with fires that did not achieve sustained flaming for all fuel categories (Appendix 1). Average temperature and vapour-pressure deficit at the time of the fire were significantly higher for fires that achieved sustained flaming as compared with fires that did not achieve sustained flaming, for all fuel categories, with the exception of average temperatures associated with test fires in FC9, aspen grass fuels during summer conditions, which did not differ between the two test fire outcomes. Fires that achieved sustained flaming were associated with a higher proportion of FWI system component values that exceeded median values (calculated from all test fires and all fuel categories), as compared with fires that did not achieve sustained flaming (Appendix 2). Exceptions were found in FC9, aspen grass fuels during summer conditions, where the proportion of both the FFMC values and BUI values that exceeded median values did not differ significantly between the two test fire outcomes. For FC1, spring grass fuels, there were no significant differences in the proportion of FWI components that exceeded median values between the two test fire outcomes, with the exception of BUI. The proportion of test fires associated with a DC that exceeded the median value was not significantly different between the two test fire outcomes for six of the ten fuel categories. For fuel categories 8 10, the proportion of fires with a DC that exceeded the median value was significantly greater for fires with no sustained flaming, which reflects a seasonal trend rather than the influence of fuel moisture conditions in the deep organic layer on ignition processes. These results are consistent with other studies that indicate ignition outcomes are related to all FWI system components except the DC (i.e. Tanskanen et al. 2005), and as a result, we limited further analysis to FFMC, DMC, ISI, BUI and FWI.

7 Modelling the probability of sustained flaming Int. J. Wildland Fire 167 Table 4. Correlations between independent variables: FWI system components and site weather variables Numbers refer to fuel categories (1 10) where two independent variables were not significantly correlated. BUI, Buildup Index; DMC, Duff Moisture Code, diurnally adjusted Initial Spread Index (ISI) calculated from FFMC and the 10-m open wind speed; FFMC, diurnally adjusted Fine Fuel Moisture Code; FWI, Fire Weather Index calculated from the BUI and diurnally adjusted ISI Correlation FFMC DMC ISI BUI Relative Temperature Vapour pressure humidity deficit DMC 2, 5 9 ISI 5,7,9 BUI 2,5 9 5,7,9 FWI Temperature 9 Vapour pressure deficit Moisture content 2, 6, 8 1, 2, 8, 9 2, 8 Table 5. Comparison of models composed of (A) FWI system components and (B) site variables, by fuel category Variables are significant independent variables used in the model (P-values given in parentheses); P ( ) is the P-value for the likelihood ratio χ 2 statistic; AIC B AIC A, the difference in Akaike s Information Criterion between models A and B; C, the C statistic that indicates concordance between predicted probabilities and observed outcomes; DMC, Duff Moisture Code; FFMC, diurnally adjusted Fine Fuel Moisture Code; FWI, Fire Weather Index calculated from the Buildup Index and diurnally adjusted ISI; ISI, diurnally adjusted Initial Spread Index calculated from FFMC and the 10-m open wind speed; MC, moisture content (%) of the ground fuels specified by the fuel category (grass, lichen, moss, needles and leaf); RH, relative humidity (%) Fuel category A n Sustained flaming (A) FWI system components (B) Site variables AIC B AIC A No Yes Variables P ( ) C Variables P ( ) C FC RH (22) 01 FC FFMC (<01) RH (<01) B FC FFMC (<01) MC (<01) C FC FWI (<01) MC (<01) B FC ISI (28) 01 MC (3) D DMC (0.0118) FC FFMC (33) MC (1) C DMC (<01) RH (07) FC FFMC (94) VPD (62) B FC FFMC (<01) MC (02) C DMC (<01) RH (<01) FC FWI (53) MC (0.0124) B FC DMC (<01) MC (<01) E A See Table 1 for definition of categories. B Substantial evidence for both models. C Model B is highly unlikely. D Considerably less support for model B. E Considerably less support for model A. Correlation analysis indicated significant correlations between many independent variables. Uncorrelated independent variables for FWI system components and site weather variables are shown in Table 4. Only combinations of uncorrelated independent variables were used in model building. FWI components were as good as or better than site variables at predicting the probability of sustained flaming for eight of the ten fuel categories. For each fuel category, the independent variables included in the best FWI system component model and site variables model are shown intable 5. All models were highly significant with concordance between predicted probabilities and observed outcomes that ranged from 82 to 96%. Correspondence between model accuracy and accuracy computed from cross-validated predicted probabilities indicated that all models are robust, with the exception of the site-variables model estimated for FC5, which exhibited slight differences between model accuracy and that estimated in the cross-validation processes. For one category (FC1, spring grass fuels) the FWI system components were not useful for predicting sustained flaming, and for another category (FC10, aspen leaf fuels during summer conditions), the model based on FWI system components had considerably less support than the model based on site variables. The probability of sustained flaming was predicted for each fuel category (Figs 1 6) from the models listed in Table 6. For fuel categories 2 9, only the models based on FWI system components are shown, as these out-performed models based on site-variables for these fuel categories. Discussion Results indicate that sustained flaming ignition is driven primarily by the moisture content of fine fuels. Duff moisture content and relative humidity represent secondary influences on sustained flaming ignition for some fuel categories. Models

8 168 Int. J. Wildland Fire J. L. Beverly and B. M. Wotton Fuel category 1: Grass (spring) Relative humidity (%) Fig. 1. Predicted probability of sustained flaming in grass fuels during spring conditions (FC1) as a function of relative humidity (%). Fuel category 4: Pine, moss Fuel category 9: Aspen, grass (summer) FWI Fuel category 10: Aspen, leaf (summer) Fig. 3. Predicted probability of sustained flaming in pine moss ground fuels (FC4) and aspen grass ground fuels during summer conditions (FC9) as a function of the diurnally adjusted FWI Moisture content (%) Fuel category 2: Grass (summer) Fuel category 3: Pine, lichen Fuel category 7: Mixed wood, needles leaf (summer) Fig. 2. Predicted probability of sustained flaming in aspen leaf ground fuels during summer conditions (FC10) as a function of leaf moisture content (%). developed from FWI system components were as effective as models developed from site variables at predicting the probability of sustained flaming for eight of the ten fuel categories. In five of these fuel categories, the probability of sustained flaming was driven by the diurnally adjusted FFMC. The diurnally adjusted ISI or FWI were key determinants of the probability of sustained flaming for three fuel categories. While a significant independent variable in four of the FWI system models, the DMC tended to represent a secondary influence on the probability of sustained flaming. These results are consistent with FFMC Fig. 4. Predicted probability of sustained flaming in grass fuels during summer conditions (FC2), pine lichen ground fuels (FC3), and mixed-wood needle-leaf ground fuels during summer conditions (FC7) as a function of the diurnally adjusted FFMC. the findings of Wotton and Beverly (in press) that DMC has an influence on surface fuel moisture that is not accounted for in the FFMC model. FWI system components were not useful to predict sustained flaming in spring grass fuels (FC1), where test fire outcomes were driven by site relative humidity at the time of the fire.

9 Modelling the probability of sustained flaming Int. J. Wildland Fire 169 Fuel category 5: Pine, needles (a) Fuel category 6: Mixedwood, moss ISI DMC Fig. 5. Predicted probability of sustained flaming in pine needle ground fuels (FC5) as a function of the diurnally adjusted ISI and the DMC. These results are not surprising. Drying processes in grass fuels in open areas, which are exposed to solar radiation and wind, differ markedly from those in closed canopy jack pine or lodgepole pine fuels on which the FWI fuel moisture codes are based. Grass fuels are highly responsive to changes in relative humidity because of its high surface area-to-volume ratio (de Groot et al. 2005). Test fire results indicate that with a relative humidity of 18%, there was a 99% chance or greater of sustained flaming in grass fuels during spring conditions (Fig. 1). FWI system components had limited usefulness for modelling the probability of sustained flaming in aspen leaf fuels during summer conditions (FC10). Although a model using the DMC was developed for this fuel category, it had considerably less support than one that used observations of moisture contents of leaf ground fuels. The probability of sustained flaming as a function of specific FWI system components varied by fuel category. While aspen grass fuels during summer conditions (FC9) and pine moss fuels (FC4) are both modelled as a function of FWI, aspen grass fuels require a much higher FWI value to achieve a 90% chance of ignition compared with moss fuels (Fig. 3). The probability of sustained flaming as a function of FFMC also varied by fuel category. For example, there is a 90% chance of sustained flaming in pine lichen fuels (FC3) with an FFMC of 86; in grass summer fuels (FC2) with an FFMC of 90; and in mixed-wood needles leaf fuels in summer conditions (FC9) with an FFMC of 94 (Fig. 4). The probability of sustained flaming in moss fuels differed between forest cover types (Fig. 6). With a DMC of 80 and an FFMC of 89, there is a 90% chance of sustained flaming in moss fuels in a mixed-wood stand (FC6) and a 96% of sustained flaming in moss fuels in a spruce stand (FC8). This study corroborates existing evidence that the probability of sustained flaming is determined by ground and canopy fuel characteristics, fuel moisture content of ground fuels, and site weather variables, and may be of practical importance for predicting forest susceptibility to fire in research and operational (b) FFMC Fuel category 8: Spruce, moss FFMC DMC DMC Fig. 6. Predicted probability of sustained flaming in (a) mixed-wood moss ground fuels (FC6) and (b) spruce moss ground fuels (FC8) as a function of the diurnally adjusted FFMC and the DMC. fire management applications. The short-duration flame ignition source used in this analysis is not representative of all potential ignition sources. Individual fire ignition points or events can occur under a range of circumstances. Multiple, simultaneous ignition points can occur as a result of firebrand transport from convective processes on large fires. If successful, these firebrand ignition points can collectively increase the rate of spread and intensity of the main fire (Brown and Davis 1973). Firebrands can occur in glowing and flaming states. Compared with the surface temperature of a glowing firebrand ( 650 C), the temperature of a match flame is much higher ( 1260 C) (Brown and Davis 1973). It has been suggested that firebrands fall at or near their terminal settling velocities and are most likely to be in a state of glowing combustion when impact with a fuel bed occurs, however, the presence of an air flow can sustain firebrands in a flaming state upon impact (Manzello et al. 2006). Pérez-Gorostiaga et al. (2002) conducted laboratory tests that compared the probability of ignition as a function of firebrand characteristics and found that ignition probability was consistently higher for firebrands in the flaming state with an absence of

10 170 Int. J. Wildland Fire J. L. Beverly and B. M. Wotton Table 6. Parameters of the logistic regression equation listed for each fuel category Fuel category A Model form: P(sf ) = 1 B 1 + e (β0+β1x1+ +βnxn) β 0 β 1 β 2 β 3 β 4 β 5 β 6 FC FC FC FC FC FC FC FC FC FC FC A See Table 1 for definition of categories. B Where P(sf) = predicted probability of sustained flaming, χ 1 = the diurnally adjusted FFMC, χ 2 = the DMC, χ 3 = the diurnally adjusted ISI, χ 4 = FWI, χ 5 = relative humidity (%), χ 6 = fuel moisture content (%). wind (no airflow) compared with firebrands in the glowing phase with wind ( km h 1 ). This suggests an apparent compensation between oxygen supply from the wind and associated decreases in heat transfer. Most test fires included in our analysis were conducted with site wind conditions of 4.8 km h 1,but all would have occurred with some degree of air flow. In addition to representing conditions associated with some firebrand ignitions from large fires, the short-duration flame ignition source used to ignite test fires in this analysis may also approximate ignitions associated with some lightning fires, if for example, a lightning strike ignites a tree crown resulting in the deposition of flaming embers on the fuel bed beneath the tree. Short-duration flame ignition sources may also be representative of conditions possible at the site of a smouldering ignition from a lightning strike or at a point along a formerly active fire perimeter where an isolated smouldering ignition remains. At these locations, the presence of glowing fire embers could conceivably transition to a flaming state with the addition of wind or other microclimatic changes to result in isolated points of small flaming ignition sources in contact with adjacent unburned fuel. Fuel-specific models of the probability of sustained flaming presented here can provide valuable insight into spatial variation in forest susceptibility to fire, but they have limitations for assessing the potential for flame propagation and surface fire spread following establishment of the sustained flaming state. While a positive test fire outcome indicated that the fire would continue to spread if fuel and weather conditions were unchanged, in reality the ability of the fire to continue to propagate will depend on its ability to overcome discontinuities in fuels or variability in fuel moisture. Experimental test fires have been used to explore the transition from a sustained flaming ignition to actively spreading surface fire. For example, Fernandes et al. (2002) conducted field trials using line ignitions of small experimental plots to investigate the determinants of sustained fire propagation. Similarly, Weise et al. (2005) modelled the probability of successful fire spread following line ignition of laboratory fuel beds. This study has shown that FWI system components are highly effective substitutes for site variables for modelling the likelihood that short-duration sustained flaming will develop in forest ground fuels that have direct contact with a small and short-lived flame source. Future analysis of test fire data contained in the Canadian small-scale test fire database will focus on developing a suite of fuel-specific models for modelling the probability of sustained flaming as a function of FWI components. Development of a new experimental test fire program to investigate the probability of sustained fire propagation would complement the current analysis by addressing the transition of a successful fire ignition from a sustained flaming state to that of an actively spreading surface fire. Acknowledgements We thank the many forest fire researchers with the Canadian federal government who participated in the design, development, and implementation of the small-scale test fire program and/or contributed to the maintenance of the test fire database over the past 70 years. Special thanks to B. Todd (Canadian Forest Service) for ensuring that key historical test fire documents were preserved to support future analysis of the test fire data. We thank T. Lynham (Canadian Forest Service), two anonymous reviewers and our assigning editor for providing helpful comments on the manuscript. References Anderson HE (1970) Forest fuel ignitability. Fire Technology 6, Andrews PL, Loftsgaarden DO, Bradshaw LS (2003) Evaluation of fire danger rating indexes using logistic regression and percentile analysis. International Journal of Wildland Fire 12, doi:171/wf02059 Blackmarr WH (1973) Moisture content influences ignitability of slash pine litter. USDA Forest Service, Southeastern Forest Experiment Station, Research Note SE-173. (Asheville, NC) BrownAA, Davis KP (1973) Forest fire control and use. 2nd edn. (McGraw- Hill Book Company: Toronto) Chuvieco E, Aguado I, Dimitrakopoulos AP (2004) Conversion of fuel moisture content to ignition potential for integrated fire danger assessment. Canadian Journal of Forest Research 34, doi: / X de Groot WJ, Wardati, Wang Y (2005) Calibrating the Fine Fuel Moisture Code for grass ignition potential in Sumatra, Indonesia. International Journal of Wildland Fire 14, doi:171/wf04054 Engstrom JD, Butler JK, Smith SG, Maxter LL, Fletcher TH (2004) Ignition behavior of live California chaparral leaves. Combustion Science and Technology 176, doi:180/