The study area encompasses eastern Canada's boreal forest (Brandt, 2009) from Manitoba to Newfoundland, which ranges from 102.86 to 52.64∘ W and from 46.61 to 64.71∘ N (Fig. 1). The most common needleleaf tree species present in this region are black spruce (Picea mariana (Mill.) B.S.P.), white spruce (Picea glauca (Moench) Voss), balsam fir (Abies balsamea (L.) Mill.), jack pine (Pinus banksiana Lamb.), white pine (Pinus strobus L.), red pine (Pinus resinosa Ait.), eastern larch (Larix laricina (Du Roi) K. Koch), and eastern white cedar (Thuja occidentalis L.). The main broadleaf tree species are trembling aspen (Populus tremuloides Michx.) and white or paper birch (Betula papyrifera Marsh.) (Ecological Stratification Working Group, 1996; Brandt, 2009; Shorohova et al., 2011). The study area is divided from south to north into four ecozones (Fig. 1; Ecological Stratification Working Group, 1996). (1) The Boreal Shield (BS) ecozone is characterized by rocky and rugged landscapes influenced by a continental climate (long and cold winters; short and warm summers) and by the cold air masses flowing out from Hudson Bay. Landscapes are dominated by needleleaf tree species in the westernmost areas, and co-dominated by needleleaf and deciduous tree species in temperate eastern areas. (2) The Boreal Plain (BP) ecozone corresponds to drier areas that are characterized by glacial deposits of variable thickness on flat or slightly rolling terrain. Forests are dominated by mixed boreal species, mainly represented by black spruce, trembling aspen, and jack pine. (3) The Hudson Plain (HP) ecozone is characterized by a sparser vegetation, which is dominated by Sphagnum and shrubs. Poor drainage conditions constrain southern trees to establish at drier, higher elevations. (4) The Taiga Shield (TS) ecozone, which is split into Eastern (TSE) and Western (TSW) parts, is characterized by colder climate conditions. The landscape becomes more open along a latitudinal gradient from south to north. In all regions, the dominant tree species are black spruce and jack pine. Within the study area, high-intensity crown fires are the most common type of fire events (Flannigan et al., 2016). Fire regimes are heterogeneous, but generally follow a declining trend along a southwest–northeast gradient (Boulanger et al., 2012). During the period of 1961–1990, the highest burn rates occurred in the western part of the BS ecozone (> 1 % yr-1), while they were the lowest in the TSE ecozone (< 0.2 % yr-1) (Boulanger et al., 2014). Annual burn rates in the BP ecozone and in the eastern part of the BS ecozone varied from 0.2 to 0.5 % yr-1, whereas they varied from 0.5 to 1.0 % yr-1in the HP ecozone (Boulanger et al., 2014).

Simulations of the terrestrial ecosystem were carried out using the dynamic global vegetation model LPJ-LMfire, which includes updates of both LPJ and the SPread and InTensity of FIRE (SPITFIRE) wildfire module (Thonicke et al., 2010). The model has been extensively evaluated for boreal forests (Pfeiffer et al., 2013). LPJ-LMfire is designed to simulate regional ecosystem dynamics, structure, and composition, with vegetation and fire events as responses to changes in climate and carbon dioxide (CO2) concentration (Sitch et al., 2003). LPJ-LMfire describes the state of an ecosystem in terms of annual carbon stocks (living biomass, litter, and soil), NPP, net biome productivity, evapotranspiration, heterotrophic respiration, soil moisture fraction, and forest structure and vertical profile (cover fraction, individual density, crown area, leaf area index). In the present study, changes in the vegetation state are described in terms of NPP and total carbon stocks in living aboveground biomass. In LPJ-LMfire, vegetation is defined by up to nine plant functional types (PFTs). Each PFT represents one or several species sharing the same physiology and dynamics, governed by a short list of vital attributes, and constrained by bioclimatic limits (Sitch et al., 2003). Vegetation dynamics are updated annually based on the simulation of daily and annual processes. Daily processes are defined in terms of photosynthesis, stomatal regulation, soil hydrology, autotrophic respiration, leaf and root phenology, and decomposition. Annual processes are defined in terms of several sources of mortality, seedling establishment, reproduction, allocation, and tissue turnover (Smith et al., 2001; Sitch et al., 2003). The computational core of SPITFIRE is based upon Rothermel-type surface fire behaviour models (Rothermel, 1972; Andrews et al., 2008) and is designed to simulate processes of natural fires and their impacts on vegetation mortality and fire emissions (Thonicke et al., 2010). The LMfire module simulates lightning ignitions based upon a daily time step and uses fuel bulk density and fuel moisture to calculate the fire's rate of spread, intensity, and fire-related mortality. It allows fires to burn over multiple days and simulates fire extinction from changes in weather and fuel (Pfeiffer et al., 2013). As in the original version of SPITFIRE and nearly all other large-scale fire models, LMfire does not simulate the cell-to-cell spread of fire (Hantson et al., 2016; Pfeiffer et al., 2013; Rabin et al., 2017).

LPJ-LMfire was run monthly from 1901 to 2012 on 10 × 10 km equal-area grids covering eastern boreal Canada from Manitoba to Newfoundland. Driver data sets were prepared in netCDF format and are described in Table 1. Climate data were compiled at a monthly time step, while atmospheric CO2 concentrations were compiled at an annual time step (see Sect. 2.4). A 1120-year spin-up period was prescribed to equilibrate vegetation and carbon pools with climate at the beginning of the study period (Smith et al., 2001) and to ensure that forest biomass and fire disturbances were in stable condition (Tang et al., 2010). This spin-up run was made using linearly detrended 1901–2012 climate data and repeated 10 times.

LPJ-LMfire was calibrated for four PFTs that corresponded to the predominant tree genera currently present in the boreal forest of Canada: Picea, Abies, Pinus, and Populus. PFT-related parameters, e.g., fraction of roots in the upper soil layer or minimum and maximum temperatures of the coldest month for establishment, were assigned values from the published literature or global databases (see Table S1 in Supplement S2 for further details).

We assessed the performance of our customized LPJ-LMfire by comparing simulation results with previously published data sets on fire and maps of genus-specific aboveground biomass for Canada's forests.

The outputs of LPJ-LMfire for the eastern boreal forest of Canada were analyzed in terms of annual burn rates, NPP, and total aboveground biomass. Significant changes in each temporal series were highlighted by a regime shift calculation developed by Rodionov (2004, 2006). A sequential application of Student's t test on 1000 randomly chosen grid cells was used (Rodionov, 2004, 2006). To be statistically significant at P=0.10, the difference (diff) between mean values of two subsequent periods that was determined according to Student's t test should satisfy the condition diff=t2σi2/l, where t is the value from the t distribution with 2l-2 degrees of freedom at the given probability level P, l is the cut-off length of the growth phase to be determined (hereafter set to periods of 20 years), and σi2 is the average variance for running l-year intervals. The sample proportion, representing the fraction of k cells (integer ≥0) of a given population N (integer > 0), which was identified positively as recording a growth decline (or release), a biomass reduction (or biomass increase), and an increase in fire activity (or decrease), was computed for each sampled year from 1920 to 2007.

In terrestrial ecosystem models, changes in atmospheric CO2 concentration in the recent past and future often have a more important influence on vegetation than does climate change (Girardin et al., 2011). Therefore, their inclusion has a very important effect on simulated changes in productivity. Here, the effect of CO2 fertilization was explored using two experiments. In the first experiment, “Climate + CO2”, we ran the model with increases in CO2 concentration as presented in Sect. 2.4.4. This experiment was used throughout our evaluation of LPJ-LMfire simulations. In the second experiment, “Climate-only”, we ran the model with a constant CO2 concentration from 1901 to 2012, which was fixed at 296.23 ppm (year 1901 value). In this case, there was no response of vegetation gross primary production (GPP) or fire to changes in CO2 concentration. The effect of CO2 fertilization on vegetation was determined by the difference between simulations “Climate + CO2” and “Climate-only”. Due to the post-fire recruitment rules established in LPJ-LMfire (see Sect. 2.5.2), the effect of CO2 fertilization on fire was only determined by comparing the spatial pattern of annual burn rates simulated with the “Climate + CO2” and “Climate-only” experiments.

We used LPJ-LMfire, which was driven by gridded climatology, atmospheric CO2 concentration, and an estimate of lightning strike density to study the pyrogeography of eastern Canada's boreal forest. Compared with the previous modelling efforts that had been conducted by Pfeiffer et al. (2013) using the original LPJ-LMfire model, the results that are reported here show substantial improvement in the capacity of the DGVM to simulate fire ignition in the Canadian boreal forest. The use of a high-quality lightning strike data set instead of the low-resolution LIS/OTD global data set that was used by Pfeiffer et al. (2013) allowed us to capture the spatial gradient of fire activity in a substantially better manner (Baker et al., 2016). The results confirmed that fire in the study area is strongly ignition limited, while most fire models have simply assumed that fire would always occur under appropriate weather and fuel conditions, e.g., SIMFIRE (Hantson et al., 2016). LPJ-LMfire simulations confirmed the necessity of simulating fire in a model as the product of the probabilities that are associated with fuel, moisture and ignition.

Interannual variation in lightning strike density was more faithfully reproduced when weighting the mean flash climatology with the CAPE variable to predict lightning-induced fire ignitions and their variability (Peterson et al., 2010). However, this variation is still constrained by the short temporal depth of the years of record in the CLDN lightning strike data set (Orville et al., 2002; Kochtubajda and Burrows, 2010). Synchronicity in major fire activity years across provinces (e.g., 1961, 2005, 2007) was consistent with several studies on fire history, suggesting that changes in forest fire activity have been observed jointly over vast areas since the 1900s (e.g., Bergeron et al., 2004b; Macias Fauria and Johnson, 2008).

Annual burn rates (recent and historical) were underestimated in many areas of northern Québec. It appears that the simulation could not capture the expression of a climate type that is encountered in the Clay Belt of northwestern Québec, where periodic drought is known to occur. This may likely reflect some limitation that is imposed by the low density of weather stations north of 49∘ N. The lack of station replication can create excessively smoothed climate records, thereby reducing the possibility of correctly emulating the relationship between climate and forest fire activity during extreme drought and fire years (Girardin et al., 2006b, 2009; Xiao and Zhuang, 2007). For example, 1989 is known as a drought year, which was induced by changes in atmospheric circulation that were at the origin of numerous large fires (> 50 000 ha) in Manitoba and Québec (Fig. S4; Goetz et al., 2006; Xiao and Zhuang, 2007). Other large fires exceeding 50 000 ha were observed in northern Québec in 1983 and 2002 (Fig. S4). However, these extreme weather conditions were not reproduced in our input data set and, consequently, the model could not simulate these very large fires. These underestimates may also result, in part, from the lack of lightning strike records in these northernmost regions, which prevents fire ignition from being simulated there. Polarity or energy of lightning was not taken into account in our simulations. Positive lightning strikes (transfers of positive charges to the ground) mainly occur in the north and correspond to 10 % of all lightning strikes (Morissette and Gauthier, 2008), with the remaining lightning strikes being negative. Positive lightning strikes correspond to an exchange of energy between the highest part of the clouds and the soil, while negative lightning strikes are triggered in a lower part of the clouds. For this reason, positive lightning strikes are more likely to start fires because they carry higher energy owing to the greater travelling distance between the clouds and the soil (Flannigan and Wotton, 1991). As previously mentioned, the number of lightning sensors in northern regions (hatched areas in Fig. 4) is also limited (Orville et al., 2011), leading to a decrease in detection efficiency at these latitudes (Morissette and Gauthier, 2008). Thus, 10 % of positive lightning strikes are not appropriately captured and, consequently, the probability of fire ignition is also likely to be underestimated in these areas. Underestimation of fire activity in northern areas had consequences for the simulation results. Amongst other things, simulated tree mortality was underestimated and, hence, biomass proliferated (as can be noted in Fig. 4 with the Picea PFT).

Based upon the above preliminary agreement and despite some disagreements, the temporal patterns of annual burn rates that were simulated by LPJ-LMfire were strongly consistent with the forest fire histories that have been reconstructed in many studies (e.g., Stocks et al., 2003; Bergeron et al., 2004a; Girardin et al., 2006a). Multidecadal temporal changes in annual burn rates reflect the underlying influence of climate variability and extreme fire weather (Macias Fauria and Johnson, 2008; Girardin et al., 2009); these multidecadal temporal changes were well represented in the input climate data sets. An increase in temperatures and stability in precipitation between 1916 and 1924 (Fig. S9) could be at the origin of a high frequency of fire occurrence during those years, marking a pause in the decline of fire activity that had been observed since the 1850s (Bergeron et al., 2004a). Advection of humid air masses over eastern Canada between 1940 and 1970 contributed to the creation of moister conditions, which can lessen the capacity of a fire to spread after a lightning-induced fire ignition (Macias Fauria and Johnson, 2008). Both interannual variation and unsynchronized trends in climatic variables may have brought about changes in fire activity and could have affected the fire season, as it is proposed to have occurred over millennial timescales during the Holocene (Ali et al., 2012). For example, during the years 1977 and 1980, an increase in spring temperatures was observed, whereas spring precipitation decreased, which resulted in the total areas that were burned in spring being 50 % greater than in summer (Fig. S9).

Correlations between simulated and observed provincial annual burn rates were slightly higher than what has typically been encountered in past studies of fire–climate relationships over the region (e.g., Girardin et al., 2004, 2006a, 2009). For example, Girardin et al. (2009) reported that about 35 % of the variance in the annual areas that were burned in the provinces of Ontario and Québec was explained by summer moisture availability. In our modelling experiment, we obtained values between 41 and 50 % for these same provinces, without empirical adjustments (e.g., through regression analysis). The improvements that were made here reinforce the idea that aside from “top-down” climate control on fire activity, other factors such as lightning, fuel availability, and composition can influence fire statistics (Podur et al., 2002). This highlights the necessity of reconstructing fire history in a complex system that is related to climate and vegetation by taking into account several feedbacks (Hantson et al., 2016).

LPJ-LMfire simulations provide evidence for the combined influence of fuel conditions and ignition sources on fire within our study area. Indeed, an increase in precipitation around the 1930s constrained fire activity, despite a very high lightning strike density (Fig. S9). Conversely, at the end of the century, an increase in lightning strike density and a drier climate (Fig. S9) resulted in an increase in annual burn rates. The seasons during which precipitation events and lightning ignitions occur were also found to be important. Notably, LPJ-LMfire did not simulate the core of the fire season between June and August when the highest density of lightning strikes takes place (Morissette and Gauthier, 2008). This phenomenon finds an explanation in that heavy and intense rain events occurring later during the summer decrease the probability of starting fires; weather becomes less conducive to fire due to higher amounts of precipitation between July and September in comparison with April and June. That being said, our simulation was biased with regard to the onset of fire seasonality. LPJ-LMfire simulated the core of the fire season earlier than what is actually observed. LMfire excludes fire ignition when snow cover is present (Pfeiffer et al., 2013). However, detailed investigations at the grid-cell level in our study area revealed that the fire danger index, which was calculated by the LMfire module, was high as soon as all snow had melted in May and June. This index estimates the probability that an ignition event will start a fire, depending upon both fuel moisture and fire weather conditions (Thonicke et al., 2010). As suggested by Pfeiffer et al. (2013), LPJ-LMfire simulates a very quick drying-out of soils in spring when the snow cover has disappeared or snowmelt has occurred prematurely. This phenomenon may be the reason why it simulated fire season onset earlier than what is observed in Canada's eastern boreal forest.

CO2-induced enhancement of NPP (Norby et al., 2005; Huang et al., 2007) was clearly emulated in LPJ-LMfire. Our simulated 18 % growth enhancement, with a 32.5 % increase in CO2 concentration between 1901 and 2012, was higher than the 15 and 14 % growth increases that have been proposed by Hickler et al. (2008) and Girardin et al. (2011), respectively. LPJ-LMfire is highly sensitive to atmospheric CO2 concentration and interpreting its impacts must be carried out with caution (Girardin et al., 2011). That being said, our results suggest that CO2-induced enhancement of forest productivity can be offset by fires and climate, which is consistent with the results of Hayes et al. (2011) and Kelly et al. (2016). Despite strong CO2-induced enhancement of forest productivity in LPJ-LMfire, the total amount of aboveground biomass and forest composition did not change significantly during the course of the simulation period. The CO2-induced enhancement of NPP had a positive influence on annual burn rates by increasing the availability of fuel. Under very dry conditions, such as in 1971–1990 and 1991–2012, an increase in fire activity led to a decrease in growth and biomass. Drier conditions during the past few decades provided indications for an increase in growth decline events and in biomass reduction related to an increase in fire activity. A similar trend in such conditions was observed around the 1920s, but the range of these negative events during the past decades exceeds the historical range of variability recorded by the simulated forest. Fires had a non-negligible influence on the state of the boreal forest in eastern Canada, especially during the last few decades, but our results also confirm the relative influence of climate alone on the forest in northern regions. Indeed, in northern areas in Québec and Manitoba, biomass has not significantly increased, despite a very strong effect of CO2-induced enhancement (Fig. S6). We hypothesize that with ongoing global warming, growth decline events could increase substantially, given that the positive effect of CO2 concentration on the growth of forests may not be strong enough to compensate for the loss of biomass to fires and climate change (Kurz et al., 2008), which could lead to the opening up of landscapes.

The present study demonstrated that LPJ-LMfire is generally able to capture fire history and forest growth trends in the eastern boreal forest of Canada. However, several uncertainties persist. First, forest establishment and the start of growth during the spin-up phase was simulated using a detrended version of modern climate, as is usually performed in DGVM runs (Prentice et al., 2011; Pfeiffer et al., 2013; Yue et al., 2016; Knorr et al., 2016). This initial condition assumes that past relationships between climate, fire, and vegetation have been stationary through time and that variability in modern climate is representative of all variability that has been recorded over the past 1200 years (time of spin-up phase + 112 years of simulation). However, it has been increasingly recognized that such an assumption is invalid and that modern observations are not a good analogue for prehistoric variability (Kelly et al., 2016; Hudiburg et al., 2017). For example, fire activity over much of the Holocene was higher in terms of frequency and fire size than the current levels across broad areas of eastern Canada (Girardin et al., 2013a; Remy et al., 2017). It is likely that not accounting for such variability may introduce biases in forest productivity dynamics and levels, more specifically on soil carbon dynamics (Hudiburg et al., 2017). This may be less problematic when studying fire and forest dynamics over the last century because the mean age of the major part of eastern boreal forest is less than 100 years (Bergeron et al., 2002).

The non-negligible influence of forest composition on fire regimes (Hély et al., 2001) is limited in the model to the representation of three needleleaf PFTs and one broadleaf PFT. Improving LPJ-LMfire's representation of biodiversity with further broadleaf PFT genera could counterbalance or offset overestimates of fire activity in southern areas since these species are less flammable than needleleaf species. Similarly, improving LPJ-LMfire parametrization to account for mosses could reduce overestimation of the quantity of fuel available in northern areas. In the Clay Belt, the poor drainage conditions induced by the presence of an impermeable clay substrate, flat topography, and a cold climate facilitate the accumulation of thick layers of organic soil, an edaphic process that is referred to as paludification (Fenton et al., 2006). Once Sphagnum species increase on the forest floor, the depth of burn varies only slightly in response to changes in weather conditions, owing to very low fluctuations in the degree of water saturation of the organic layer (Fenton et al., 2006).

In the present study, simulations are limited by the relatively low accuracy of soil attributes in databases for Canada's boreal forest (Hengl et al., 2014). The input data set of soil attributes that was used in our simulations tended to underestimate clay and sand percentages in our study area when compared to point observations (Fig. S10). These effects add up to other weaknesses in physiological constraints, such as cold climate not being sufficiently restrictive and allowing Picea to become overly abundant in the simulation runs. While a previous study showed that the abundance of Picea decreases with latitude in the tundra region and is coupled with the occurrence of dwarf shrubs in the Ericaceae and herbs (Gajewski et al., 1993), such species were not parametrized in the current version of LPJ-LMfire due to a lack of information on their physiological and biogeographical preferences. Future research could incorporate recently developed parameterizations for boreal shrubs and non-vascular plants into LPJ-LMfire (Druel, 2017; Druel et al., 2017).

Forest stand structure and successional dynamics (age classes), together with processes leading to the formation of peatlands, are not included in the present version of LPJ-LMfire. However, all of these aspects are important determinants of fire ignition and propagation under a given climate (Hély et al., 2001) and can also influence the distinction between crown and surface fires, which affect tree mortality differently (Hély et al., 2003; Yue et al., 2016). Moreover, LPJ-LMfire, like most DGVMs, does not consider constraints on species migrations, phenotypic plasticity, and local adaptation of species (Morin and Thuiller, 2009). The simulation results may be overly optimistic in terms of the capacity of southern species to colonize newly available areas in northern regions as the climate warms. As previously mentioned by Morin and Thuiller (2009), species colonization in northern regions could be limited by forest attributes, such as fragmented landscapes or high competition levels from existing species, or through migrational lag (Epstein et al., 2007).

Wildland fires are the most important natural disturbances in Canada's eastern boreal forest, but non-fire and human disturbances also have considerable effects (Price et al., 2013) and may influence fire activity trajectories indirectly. Integrating a range of forest disturbances into a DGVM could improve the accuracy of forecasting and modelling climate change effects on Canada's eastern boreal forest. For instance, insect damage (MacLean, 2016) and outbreaks of eastern spruce budworm (Choristoneura fumiferana) in particular (Zhang et al., 2014; James et al., 2017) represent significant forest disturbances by the way they temporarily alter forest structure by affecting specific tree growth, tree survival, regeneration, and succession. These disturbances can also have an important impact on fire activity by modifying fuel distribution and connectivity (James et al., 2017). Additionally, successive fires that take place over a short period before the trees have attained maturity can lead to complete regeneration failure (Girard et al., 2008). Such events in young, unproductive stands can also lead to modified forest composition (Girard et al., 2008) and could exert a strong feedback on ecosystem structure by generating changes in temporal fire patterns over long timescales. Finally, the effects of human activities, such as forest management and active fire suppression efforts, on the composition and distribution of forest fuels were not implemented in the present LPJ-LMfire simulations. Nonetheless, the strong correlation between our simulated annual burn rates and observed data suggests that active fire suppression efforts and forest management since about the 1950s (Le Goff et al., 2008; Lefort et al., 2003) have not contributed much to shifting fire behaviour trajectories in our study region, which admittedly has very low densities of both population and infrastructure in comparison with other populated areas such as in the United States (e.g., Syphard et al., 2017).