The numerous factors and variables needed to adequately map high risk wildfire areas will be subsequently organized into a hierarchical framework in order to rank each vulnerability and susceptibility factor into low-to-high risk elements. The spatial analysis required, in combination with the hierarchal and weighted data structure, best suits a GIS-based MCE tool to effectively create a combined wildfire risk model (Galiana-Martín and Karlsson, 2011). Much of the data used in this particular model requires equal consideration for the weighted factors, in combination with more than one dependent variable of susceptibility and vulnerability. As such, an index model of discrete variables, or a regression model does not suit the particular needs of this analysis. The general MCE equation (Eq. 1) will be used to combine the vulnerbility factors in order to create the vulnerbility layer, then used again with the susceptibility factors to create the single susceptibility layer.  With these two layers created they can then be combined to create the final risk layer. 

Equation 1. General MCE equation for suitability with a constraint.  

SUIT = (Constraint) ∑(W_kX_K)

Factor Weighting:

     Weights for each factor are calculated using a pairwise comparison matrix. After the pairwise ranks has been established, the individual weights are calculated from the comparison matrix, averaged and summed into their total weights (Tables 1 and 2).

Vulnerability Factors

     All vulnerability weights are ranked using the findings in a 2010 study by Tutsch et al. This study surveyed wildfire managers in British Columbia in order to evaluate the most important factors for consideration and protection from forest fires. This study determined that the factors analysed should be put in the following order from most to least important: Potential for loss of human life, rare element loss (Ecological Vulnerability), economically valuable land loss, culturally important land loss (park land), and non-culturally important land loss. These factors were therefore weighted accordingly, with weights based on their rankings and the relative difference between these rankings (Table 1).

Table 1. Pairwise ranks and final weights of vulnerability factors.

Consistency ratio (CR) was calculated for this pairwise comparison matrix (Table 1). The CR value was found to be 0.005, which is much less than 0.10 (Zhou et al., 2016). This indicates that the ranks were consistent throughout.

Susceptibility Factors    

     All susceptibility factors were ranked based on relative importance to predict wildfire susceptibility (Table 2). Overall, climatic considerations were considered to be the most highly predictive category of the model, and fuel type was the least predictive category. Ignition potential, both natural and anthropogenic, will be weighted less heavily than fuel conditions and climatic considerations due to the relatively higher uncertainty associated with ignition potential variables (Kilinc and Beringer, 2007; Valdez et al., 2017). Drought is the most significant overall climatic indicator of wildfire risk and is often measured in terms of annual precipitation (Mori and Johnson, 2013). As a result, the annual precipitation is assigned a heavier weight than maximum temperature, which is another important climatic considerations. The factor of biomass was determined to be important, but not as important as the climatic conditions, resulting in a lower weighting (15.8% weighting) (Woolford et al., 2014; Reinhardt et al., 2008; Thompson et al., 2017). Also stand type, stand age and dead/alive ratio are based on the works of Duff (2017), Beverly et al. (2009), Renkin and Despain, (1991), and Thompson (2017), which listed these factors as important components of wildfire susceptibility. Fuel type, as a whole, was the category with the lowest predictive capabilities. It was found that the factor of stand type was the least important of these factors, with the most important fuel type considerations being both stand age and dead/alive ratio (Duff, 2017; Beverly et al. 2009; Renkin and Despain, 1991). The data for dead/alive ratio was incomplete and not suitable for use in this analysis, so it could not be considered even though is it an important factor in wildfire susceptibility. 

Table 2. Pairwise ranks and final weights of susceptability factors.

Consistency ratio (CR) was calculated for this pairwise comparison matrix (Table 2). The CR value was found to be 0.00130, which is much less than 0.10. This indicates that the ranks were consistent throughout.

Factor Standardization:

     The factors to be utilized will be standardized on a scale of 0-100 as cost factors or beneficial factors. This standardization allows for data that has variable units to be combined into a common scale of measurement. Standardization will be done using the reclassify tool in ArcGIS, and will use 10 unique classes of values that are specified using Jenk’s (natural breaks) classification method. These classes will then be reclassified as either cost or beneficial factors on a scale of 0 – 100, with the first class representing the lowest range of values and the tenth class representing the highest range of values (Tables 3 and 4). This method was used in order to control for extreme disparity between maximum and mean values, which made linear standardization methods produce results with little utility for the analysis. 

Table 3. Beneficial Factor Standardization input

Table 4. Cost Factor Standardization input

     The way in which each vulnerability and susceptibility factor is standardized will be determined based on whether a higher value produces a higher (Beneficial) or lower (Cost) risk value (Tables 5 and 6). Certain factors are standardized into unique index rankings based on findings of previous studies (Tables 7 and 8). These factors were all standardized on a scale of 0-100, with higher values representing higher susceptibility or vulnerability to wildfires overall.

Table 5. Quantitative factor Standardization Scheme used for each vulnerability factor.

Table 6. Quantitative factor Standardization Scheme used for each susceptibility factor.

     Tutsch et al. (2010) found that land use directly influenced economically productive land loss (agricultural and timber supply), park land loss, and non-park non-timber forest land (Tutsch et al., 2010) (Table 7).

Table 7. Index of relative land value for lands vulnerable to wildfire.

     Renkin and Despain (1991) state that Douglas-fir and lodgepole-pine are less likely to burn than the Engleman-spruce, all of which are coniferous species common to the study area. This results in an increasing chance of burning in forests consisting of Engleman-spruce compared to those mainly consisting of the other coniferous trees. The relative flammability of stand type from most to least flammable values were based on the findings of Beverly et al. (2009) Renkin and Despain (1991) (Table 8)

Table 8. Stand type index and relative land value (Scale of 0-100).