Setting up the event attribution

A detection and attribution analysis (Bindoff et al. 2013) was used to assess whether anthropogenic influence has had a discernible effect on the base climate state in the larger western Canada region. Evidence that anthropogenic influence has altered the base state would increase confidence in the attribution of extreme events, which can be viewed as departures from this altered base state (NASEM 2016). Mean temperature was chosen due to its robust detection globally (Bindoff et al. 2013) and throughout many regions (Stott 2003; Zhang et al. 2006), its observational coverage, and its well understood relationship to increased greenhouse gases. As there can be smaller signal-to-noise ratios at the regional level and among other variables, it can be more difficult to provide a robust attribution (Stott et al. 2010). Performing a detection and attribution analysis for temperature over a larger region and longer time period helps to reduce the impact of noise on such analyses.

Observed monthly temperatures over land areas from the CRU-TS3 dataset (Harris et al. 2014) on a 0.5° grid were averaged over western Canada (Fig. 1). Similarly, monthly average temperatures from CanESM2 ALL and NAT realizations were averaged over the land grid boxes for this region. A detection and attribution analysis was performed for the longest period available (1960–2014); a thorough description of the methods applied here can be found in Kirchmeier-Young et al. (2016).

The ALL forcing signal was detected in the observations (Fig. S2) for the fire season (MJJAS), though CanESM2 overestimates the warming during this period. After scaling the model response to be consistent with the observations, the result is an attributed warming trend of about 1 °C over the period for which the FWI indices can be calculated (1980-2014). As anthropogenic forcing has had a demonstrable influence on the region, it is reasonable to pursue an event attribution analysis for a more localized region and for other variables that, while influenced by temperature change, likely present smaller signal-to-noise ratios.

Event definitions

A key first step for event attribution is framing the attribution question (NASEM 2016), which includes determining the spatial and temporal characteristics and climate variable to define the event of interest. Although the events chosen for attribution analyses are typically inspired by societally-relevant extreme events, selection bias becomes a concern when using an event definition that is too specific (e.g., observed extreme at a point location). Furthermore, using multiple event definitions can increase the robustness of event attribution results (NASEM 2016).

We use the class type of event definition (NASEM 2016) by defining an event as all possible outcomes for which a particular metric exceeds a chosen threshold (Table 2). First, we define a class of events for each FWI index by requiring the 90th percentile of daily index values for each fire season to exceed an NRCan (2016) defined “extreme” threshold. FWI index percentiles have been used in other studies (Wotton et al. 2010; Parisien et al. 2011; Wang et al. 2015) and are a better indicator of extreme fire days than a measure of central tendency. The NRCan thresholds are defined for all of Canada and may not completely characterize local extremes. For reference, the maximum value of each index during the first 4 days of the Fort McMurray fire, based on data from the Fort McMurray airport weather station, was FFMC-95, DMC-56, DC-370, ISI-21, BUI-81, FWI-40 (M. Flannigan, personal communication). Bearing in mind the inherent difference between station and gridded observations, these values correspond, respectively, to the > 99, 94, 89, > 99, 95, > 99th percentiles in the corresponding grid box of GFWED data.

Table 2 Event attribution results for many extreme fire risk metrics Full size table

We also considered events defined in terms of days with significant spread potential, by using the 90th percentile value of the ROS (Rate of Spread) and also the definition of Wang et al. (2014) that determines spread days in a rain-free period as those with FWI (Fire Weather Index) ≥19 and DMC (Drought Moisture Code) ≥20. Spread days are expressed as the number of days per season or the percentage of the fire season length, with thresholds for an extreme season being 38 days (25% of the climatological mean season length) or 25%, respectively. We also use the fire season 90th percentile of Head Fire Intensity (HFI) and metrics characterized by the number of days in fire intensity classes 5 and 6 (HFI > 4,000; NRCan 2016). Finally, we look at metrics describing the fire season, including start and end dates and the length of the season.

Methodology and metrics

For each of the metrics discussed above, the probabilities of an event occurring under ALL and under NAT forcing were calculated by pooling the values from all realizations for a chosen decade. Each metric was calculated by grid box and then averaged across HFR9. An example using the 90th percentile of the FWI is shown in Fig. 3. For each realization, each year and each grid box, the 90th percentile of daily FWI values is determined and averaged over HFR9; the result is a value for every year and every realization. Time series of the 90th percentile of FWI (Fig. 3a) show that as time progresses, the separation of the ALL (blue) and NAT (green) ensemble means increases, with a slight increasing trend under ALL forcing and no trend under NAT forcing.

Fig. 3 a Time series of fire season 90th percentile values of the Fire Weather Index (FWI) for the ALL forcing ensemble mean in blue and NAT forcing ensemble mean in green. Shading represents the 5th–95th percentile range across the ensemble. b Density plots for 2011–2020 for ALL in blue and NAT in green, pooling values from the ensemble members and using a Gaussian kernel density estimator. A non-parametric 90% uncertainty range is shaded, determined through bootstrapping. The vertical bar represents the threshold for an extreme value; for comparison, the Fort McMurray station saw an FWI value of 40 on the day of fire ignition. c Plots of p0, p1, PN, PS, and RR for a fire season 90th percentile value more extreme than the threshold on the horizontal axis. The probabilities (p0 and p1) are determined by empirically integrating the density curves and the shaded uncertainty ranges are a result of the uncertainty on the density curves Full size image

Choosing the current decade, 2011–2020, the values from each year and each realization are pooled together (500 years total) and density curves estimated (Fig. 3b). The density curve for ALL (blue) is shifted toward slightly larger values of FWI than the NAT curve. These densities are then used to calculate the probability of a particular event; p 0 is the probability under NAT forcing and p 1 the probability of the same event under ALL forcing (Fig. 3c). Numerous thresholds to define events (horizontal axis) are used. Both p 0 and p 1 decrease with increasing severity of FWI values, but p 1 decreases more slowly as the extreme events are more likely with ALL forcing.

The probabilities are used to calculate three event attribution metrics:

$$ PN = FAR = 1 - \frac{p_{0}}{p_{1}} $$ (1)

$$ PS = 1 - \frac{1 - p_{1}}{1 - p_{0}} $$ (2)

$$ RR = \frac{p_{1}}{p_{0}} $$ (3)

The probability of necessary causality (PN) and the probability of sufficient causality (PS) were introduced in Hannart et al. (2016). PN describes the probability that ALL forcing is a necessary cause of the particular event; that is, that ALL forcing is required for the event’s occurrence. PS describes the probability that ALL forcing is sufficient for the event, such that a scenario with ALL forcing will see the occurrence of this event every time. Any negative values of PN or PS are set to 0. PN is also the fraction of attributable risk (FAR; Stott et al. 2004), which describes the fraction of the risk of an event’s occurrence contributed by the anthropogenic (ANT) component. Finally, the risk ratio (RR) describes how many times as likely the event occurrence is with ALL than with NAT.

The resulting curves for the event attribution metrics are shown in Fig. 3c. PN increases with increasing severity of FWI values. A PN value of approximately 0.8 for a fire season 90th percentile value of the FWI exceeding 30 means that 80% of the risk of this event is due to anthropogenic (ANT) forcing, there is an 80% chance that ANT forcing is required for this event to occur, or eight out of ten occurrences of this event would not have happened with only NAT forcing. The PS values are small for the more extreme FWI thresholds, as such events are rare with both forcing scenarios (see Fig. 3b). Finally, the RR is greater than 1 (the event is more likely under ALL forcing) for all FWI thresholds. RR values increase rapidly for the more extreme values of FWI. An RR of 10 would imply the occurrence of that event is 10 times as likely under ALL forcing than under NAT forcing.

Results

All of the metrics show density curves for ALL forcing that favor more extreme values compared to NAT forcing for 2011–2020 (Fig. S3). For the FWI indices, this is likely due to the strong signal seen in temperature and to a lesser extent the difference in wind speed between the two forcing scenarios (Fig. S4, S5). The extreme thresholds (vertical bars) are rare events for many of the indices, resulting in small values of p 1 and even smaller values of p 0 for these events (Table 2). For the FWI indices, the RR values range from about 1.5 to 6 times as likely under ALL forcing and the confidence intervals on these values are generally small (Fig. 4).

Fig. 4 The risk ratio (RR) for many metrics based on a 2011–2020 climate. Values are for an event more extreme than that indicated on the horizontal axis and the vertical bar represents the threshold for an extreme value (see Table 2 and Table S1). The uncertainty range for each RR curve is shaded and was calculated using a bootstrapping method. The FBP metrics in panels (i)–(k) use the C2 fuel class Full size image

The significant spread days show similar results between the counts and percentage metrics, with approximately 70% of the event risk due to anthropogenic forcings (Table 2). Under ALL forcing, it is almost three times as likely for a fire season to have significant spread potential on more than a quarter of its days. Using the 90th percentile value of the ROS (Rate of Spread) sees smaller probabilities for events exceeding the extreme threshold and much stronger attribution results, with a PN value indicating ANT forcing is a necessary cause.

Events for the 90th percentile of the HFI (Head Fire Intensity) and the number of days in the top fire intensity classes are several times as likely under ALL forcing (Table 2). These results are sensitive to fuel type (Fig. S7) though it is expected that a spruce forest (C2) will have more burn potential than one with leafless aspen (D1).

An increased fire season length under ALL forcing (Fig. S3m) is consistent with other studies that demonstrated extended fire seasons under future scenarios including increased anthropogenic emissions (Flannigan et al. 2013; Liu et al. 2013). There is a 76% chance that ANT forcing is necessary for a fire season exceeding 165 days and such an event is 4 times as likely than with NAT forcing alone (Table 2). This is influenced by both a later end date and earlier start date to the fire season.

Generalizing to other thresholds, RR (Fig. 4) and PN (Fig. S8) curves are shown for an event more extreme than the given index value. Consistent with the densities (Fig. S3), all metrics see increasing PN values for more extreme thresholds, indicating an increased contribution of ANT forcing to the occurrence of such events. This is consistent with increasing RR values for more extreme thresholds. PN reaches 1.0 in the upper tail of the ALL distribution for most metrics with very large RR values, which would implicate ANT forcing as a necessary cause. Although the exact RR values can be sensitive to the estimation of very small probabilities, such events would be considerably more likely to occur with ALL forcing than with NAT forcing.