0571-B1

Fire Behavior Prediction in Canadian Slash Fuels, Based on Fuel Characteristics

Ertugrul Bilgili^[1]

Abstract

Although the effect of fuel characteristics on fire behavior has well been established, fire behavior prediction systems currently in use depend on qualitatively described fuel types. This paper attempts to predict fire behavior in slash fuels using quantitatively described fuel properties. Results showed that rate of spread was related to the quantity of fuel available and the effect of weather expressed through the Initial Spread Index of the Canadian Fire Behavior Prediction System. Fuel consumption was related to the quantity of fuel available along with the moisture content (expressed through the Buildup Index) associated with it. Differences in fire behavior were clearly shown to be a function of fuel characteristics rather than fuel types in slash fuels.

Introduction

With the importance of slash fuels to constitute a high degree of fire hazard (McRae 1979) and a barrier to successful regeneration (Adams 1966; Heeney 1977; Foster et al. 1967), a great deal of research effort has gone into the prediction of fire behavior in these fuels. The results of many individual fire behavior study in slash fuels have contributed to generating fire behavior prediction models in the currently used fire behavior prediction systems (i.e., Australian, American and Canadian systems).

Although the models currently in use, allow for the prediction of fire behavior for a range of fuel, weather and topographic conditions they are not without problems. In the Australian and American systems, for example, fuels are parameterized in detail based on a number of standard fuel measurements. Based on the fuel measurements detailed, site specific fuel models can be generated for use in fire prediction models (Burgan 1987). The resulting system, however, is limited by the scale and multidimensional complexity of forest fuels.

In the Canadian system, however, fuels are described qualitatively rather than quantitatively (Forestry Canada 1989). The basic assumption in the Canadian Forest Fire Behavior Prediction (FBP^[2]) System is that fire behavior is a function of species type rather than common and measurable fuel characteristics (Bilgili 1995). The only quantitative measure available for slash fuels is the fuel type parameter values for Woody Fuel Load (WFL). However, all of these measures are unique (constant) for each fuel type (Forestry Canada 1993).

More importantly, the currently used systems are not responsive to changes in the characteristics of fuel. Each action taken has an effect on fuel properties (Bilgili 2002) and fuel characteristics and subsequent fire behavior are strongly linked with each other. Thus, the integration of fuel characteristics into fire behavior analyses is part of the general requirement for successful fire behavior prediction. This is particularly important in the FBP System in which fuel characteristics are not a part.

The objective of this paper is, therefore, to relate slash fuel characteristics to fire spread, fuel consumption and fire intensity through determining the a, b and c coefficients for the rate of spread (ROS)/Initial Spread Index (ISI), the Forest Floor Consumption (FFC)/Buildup Index (BUI) and Woody Fuel Consumption (WFC)/Buildup Index (BUI) relationships of the FBP System.

Material and methods

The data were compiled from the literature on the most appropriate fuel types of the FBP System. Much of the work relied upon existing data collected from stands which were experimentally burned by researchers from the Canadian Forest Service (Table 1). The data sets included: (i) fuel moisture codes: (the Fine Fuel Moisture Code (FFMC), the Duff Moisture Code (DMC), and the Drought Code (DC)), and fire behavior indices (the Initial Spread Index (ISI), the Buildup Index (BUI) and the Fire weather Index (FWI)) of the Fire Weather Index ((FWI) System of the Canadian Forest Fire Danger Rating System (CFFDRS) (Van Wagner 1974; Turner and Lawson 1978). (ii) fuel structure information: forest floor loading (FFL) and woody fuel loading (WFL). (iii) fire behavior properties: ROS, fuel consumption, fire intensity. Having completed the data set, the state of the foliage retained was determined through the foliage retention index (FRI). The data were then available for statistical analyses.

Results and discussion

Rate of spread prediction

Predicted rate of spread for each fuel type in the FBP System is largely a function of the Initial Spread Index (ISI). In all slash fuel types, rate of spread is defined by a single equation representing an S-shaped asymptotic curve (Alexander et al. 1984). The general equation for fire spread (ROS) is:

Where,

ROS = rate of spread;

ISI = the Initial Spread Index based on FFMC and wind, and adjusted for slope; the a, b and c coefficients are unique for each fuel type.

The only difference in the equations is in the values of the a, b and c coefficients for different slash fuel types. Thus, to predict ROS for any new fuel type the a, b and c coefficients need to be defined.

The a coefficient for the ROS equation for slash fuel types, which reflects the maximum rate of spread attainable for a fire ranges from 40 to 75 (Forestry Canada 1993).

These values are for the fuels in newly cutover areas. In this regard, it can be assumed that the range of ROS will vary from a maximum to a minimum determined by fuel characteristics along with the ISI. ROS values were determined based on this assumption. The analysis yielded the following equation which predicted the ROS values based on the WFL and ISI.

R² = 0.615 SE=0.669

Table 1. Summary of data on slash fuel types of the FBP System

The above analysis does not, however, provide the necessary coefficients for use in the ROS equations, but provide a means of calculating them. Since the original data used for the analyses did not allow for determining the maximum ROS due to insufficient range, an index approach was adopted to solve the problem. The concept behind the index approach is to predict ROS values at a specific ISI value (say 10). Then, relating the calculated values to the maximum and minimum ROS values (i.e., 40 to 70), the equation coefficients can be derived. So, in deriving the a and c coefficients, the relationship (Equation 2) was recalculated using the value of 10 for the ISI. This predicted the index ROS. The resultant relationship was of the form:

The ROS values generated from this index ROS relationship were used to calculate the a coefficient for open slash fuels, assuming a linear relationship across the range of the a coefficient (i.e., 40 to 75). The resultant relationship was of the form:

Since this relationship does not account for the effect of time on foliage retained, the a coefficient was corrected for the foliage retained to simulate its effect on ROS.

Where,

a_c = corrected a; and
f(F) = Foliage retention effect;

The effect of foliage retained on the ROS was assumed to decrease with a decrease in foliage retained (Van Wagner 1966), but to reach an equilibrium after 50% percent of the foliage has fallen. The equilibrium is sustained by the contribution of forest floor and fine fuels (i.e., fine branches and twigs) still attached to the slash. The following relationship was used for this purpose (after Bilgili 1995).

Where, FR is foliage retention (%).

The c coefficient was related to the corrected a coefficient, assuming a linear relationship between the two (Equation 7). The range of the c coefficient is from 1 to 5, which corresponds to that of the FBP system.

The b coefficient was generated partly in relation to the c coefficients in the FBP System. The relationship between the two coefficients was determined to be linear based on the simple linear regression considering c as the independent and b as dependent variable (r² =0.99 and P< 0.001). This analysis yielded the following relationship:

Resultant coefficients were used in the ROS equations for each fire. A regression of observed. and predicted ROS produced an R² value of 0.60 (P<0.05).

Fig. 1. Relationship between the predicted and the observed ROS for all fires.

Fuel consumption

Surface Fuel Consumption (SFC) may be calculated as the sum of Forest Floor Consumption (FFC) and Woody Fuel Consumption (WFC) or simply calculated as a single entity based on a regression using the BUI or FFMC. The former approach is taken with slash fuel types and Ponderosa Pine/Douglas-fir in the FBP System with the only difference in the equations being in the values of the a, b and c coefficients for different fuel types. The inputs required here, therefore, are the a, b and c coefficients to determine the relationships between the FFC, WFC, and the BUI.

To relate fuel characteristics to fuel consumption, the relationship between FFC and slash fuel characteristics was determined by multiple linear regression. Of the fuel characteristics, forest floor loading (FFL) and the BUI were used as the independent variables and FFC as the dependent variable. The examination of the residuals vs. predicted FFC indicated a non-homogeneity across the range of the data. Thus, a log-transformation of the data was performed. Then, a multiple linear regression analysis was carried out on the log-transformed data. Dominant factors influencing fuel consumption were the forest floor loading (FFL) and the BUI, accounting for 79% of the observed variation (P<0.01) (Fig. 2).

Fig. 2. Relationship between the predicted and the observed (ln) FFC for slash fuels (A), and residuals for the regression of A (B).

The relationship obtained is expressed in the form of an equation as:

R² = 0.792 SE= 0.358

As for the relationship between WFC and fuel characteristics, the same analysis technique was applied. WFL and the BUI were used as independent variables, and WFC as dependent variable. The relationship was found to be significant with the variables included, contributing significantly and explaining 69% of the variation (P<0.001) (Eq. 10) (Fig. 3).

R² = 0.693 SE=1.4

Fig. 3. Relationship between the predicted and the observed WFC for slash fuels (A), and residuals for the regression of A (B).

To see if the SFC could be better predicted by a single relationship, a stepwise regression analysis was carried out using the data in Table 1. The analysis resulted in the following relationship.

R² = 0.858 SE= 0.238

The relationship explained 86% of the observed variation. The result, in terms of percent variability explained, was far better than that for the separate relationships (i.e., FFC and WFC). Thus, only one relationship employing WFL and the BUI can be used to predict total SFC (Fig. 4).

Given the above analyses, the equation coefficients for the prediction of fuel consumption were calculated as follows.

These analyses formed the basis for calculating the a, b and the c coefficients in the models. The a coefficient for both the FFC and WFC is dependent on fuel quantity and BUI. The total fuel consumption cannot exceed the total amount of fuel present for consumption, the maximum fuel consumption, i.e., the a coefficient, can, therefore, be considered the total amount of fuel present.

Fig. 4. Relationship between the predicted and the observed SFC for slash fuels (A), and residuals for the regression of A (B).

The BUI then determines how much of this fuel will be consumed. The effect of the BUI and fuel characteristics will be reflected in the b and the c coefficients.

The b coefficient accommodates the effect of the BUI on fuel consumption with respect to fuel loading and was determined empirically based on the data available. The data indicated that 50% of the fuel present for consumption was consumed at about a BUI value of 50.

Having determined the a and the b coefficients, the c coefficient was determined by taking the best fit to the data. This yielded a value of 2.2 for the c coefficient for slash fuels.

As for the equation coefficients with respect to the WFC, theoretically, the maximum WFC should be equal to the total WFL. In practice however, it is known that most of the larger pieces (i.e., >7 cm) remain on the site unburned. The proportion of larger pieces to the total WFL increases as the WFL increases. Thus, the total WFL should be corrected in relation to the proportion of larger pieces of fuel to determine the a coefficient, i.e., the maximum WFC.

The a coefficient was accordingly calculated based on the relationship shown below.

The c and the b coefficients were determined by taking the best fit to the data. The values for the c and the b coefficients were 1.0 and 40, respectively, which are similar to those of the FBP System.

To examine the results of the analyses, equation coefficients were derived for each fire in the data set as explained above. Resultant coefficients were used in the FFC and WFC equations to generate fuel consumption for each fire. Fig. 5 is the graph of predicted FFC vs. observed FFC (A), and predicted WFC vs. observed WFC (B) for slash fuels.

A regression of observed FFC vs. predicted FFC and observed WFC vs. predicted WFC produced R² values of 0.73 and 0.71, respectively and were significant at the 95% significance level. Given the range of factors that influence fire behavior, these results are quite favorable.

Fig. 5. Relationship between observed and predicted FFC (A) and WFC (B) for all slash fires in the data set.

Fire intensity

The final step is to calculate the total frontal fire intensity (FFI) which requires the estimate of SFC, ROS and heat of combustion. It is calculated as:

Where, H = Heat of Combustion (18,000 kJ/kg)

The calculation of fire intensity requires the estimate of total surface fuel consumption, ROS and heat of combustion (Equation 15). Fig. 6 shows the predicted and observed values of FFI for all fires. A regression analysis of observed FFI vs. predicted FFI yielded an R² value of 0.48 at 95% of confidence level.

Fig. 6. Relationship between observed and predicted FFI for all fires listed in Table 1.

Summary and conclusions

The purpose of this study was to predict fire behavior in slash fuels based on species-independent, quantitative measures of fuel structure rather than qualitative descriptions of fuel types in order to facilitate and expand the application of fire behavior prediction. To achieve this objective, such readily measurable fuel properties that standardize fuels as SFL, WFL, fuel bulk density (BD) and FRI were related to the observed fire behavior parameters to establish the dependency of fire behavior on fuel properties. Then, fuel/fire behavior models based on these quantitative fuel characteristics were generated. The methodology used was based on a comparative analysis of existing fuels (Bilgili 1995), using quantitative fuel properties. The data for these analyses were compiled from the literature on the most appropriate fuel types of the FBP System. Results showed that rate of spread was related to the quantity of fuel available and the effect of weather expressed through the ISI. Fuel consumption was related to the quantity of fuel available along with the moisture content (expressed through the BUI) associated with it. Differences in fire behavior were clearly shown to be a function of fuel characteristics rather than fuel types in slash fuels. Therefore, the results of this study will allow fire behavior prediction in slash fuels based solely on fuel characteristics derived from fuel model outputs (e.g., Bilgili and Methven 1994) or relatively simple inventory data. With this ability to predict fire behavior in slash fuels, it will be possible to incorporate fire management considerations into overall fire management planning.

Acknowledgements

The author is indebted to the Canadian Forest Service for support under the Green Plan, and to the members of the Fire Danger Group of the Canadian Forest Service for access to their raw data, and for the foundation provided by the Canadian Forest Fire Behaviour Prediction System.

Literature cited

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Table. A1. List of abbreviations