A total of 15 wildland fires in the northwestern US were selected for this study (Fig. 1). Fires were chosen to represent coniferous forest stands ranging from those dominated by fire-resistant species to those dominated by fire-susceptible species. Forests dominated by fire-resistant species were typically composed of Pseudotsuga menziesii, Pinus ponderosa, Larix occidentalis, and lesser quantities of Abies grandis. Forests dominated by fire-susceptible species were typically composed of Picea engelmannii, Abies lasiocarpa, Pinus contorta, and lesser quantities of Pinus albicaulis. To assess the pre-fire dominant forest cover for each fire, we used the LANDFIRE Existing Vegetation Type (EVT) 30 m product (LANDFIRE, 2013). Fire selection was based on the following criteria: i.

Located in northwestern United States temperate forests to minimize latitudinal climatological gradients;

For each fire, we assessed post-fire NPP trajectories as a function of colocated FRP using MODIS NPP and FRP products. We used the MOD17A3 version 055 1 km NPP product (kg C m-2 yr-1) to characterize changes in productivity within and between our study fires. The NPP product is detailed in Running et al. (2004) and Hasenauer et al. (2012). MODIS land cover, FPAR (fraction of photosynthetically active radiation), and LAI (leaf area index) products are used in tandem with meteorological data (incoming photosynthetically active radiation, stress scalars for high vapor pressure deficit and temperature) and physiological parameters for different vegetation types to calculate daily GPP. NPP is calculated as the sum of GPP over a year minus maintenance and growth respiration. We acquired the NPP product from the Numerical Terradynamic Simulation Group (NTSG) at the University of Montana. NPP data for years 2000–2015 were downloaded from the NTSG FTP site and analyzed in the native sinusoidal equal area projection.

To calculate FRP metrics colocated with each NPP pixel we used the Collection 6 MODIS 1 km Level 2 active fire product that identifies and quantifies active fire detections from NASA Terra (MOD14) and Aqua (MYD14) satellites (Giglio et al., 2016). MODIS FRP is derived from the linear relationship between midinfrared (4 µm) spectral radiance and FRP (Wooster et al., 2003) and is affected by several factors, including fire background characterization and atmospheric water vapor (Wooster et al., 2005). The 1 km spatial resolution MOD14 and MYD14 products provide an active fire mask showing which pixels contain active fire as well as the date, time, FRP, and other ancillary data (Giglio, 2015). Following Boschetti and Roy (2009), MOD14 and MYD14 data were projected to the 1 km MODIS sinusoidal projection using nearest-neighbor resampling. Importantly, this methodology accounts for increasing MODIS pixel size at large scan angles (Wolfe et al., 1998) so that the location of fire detections and total FRP is preserved post-reprojection. The resulting range of FRP for all fires was comparable to FRP observed in other closed-canopy temperate forests (Giglio et al., 2006; Heward et al., 2013). We used MTBS fire perimeters and metadata to screen any fire detections that were not colocated with recorded fire events spatially and temporally. Fire detections outside the MTBS perimeter were included in the subsequent analysis if they were closer than 1000 m from the MTBS fire boundary (as fires can occur anywhere in the 1 km FRP product). On average, FRP observations were available for > 88 % of the area within the MTBS fire polygons (Table 1).

We calculated FRP distributional statistics (peak, 90th percentile, mean) and FRE for each fire-affected pixel. FRE was calculated following Boschetti and Roy (2009), where FRP values are integrated over time assuming that FRP varies linearly between observations. FRP and FRE metrics were chosen as they have been demonstrated to have a dose–response relationship with conifer growth and mortality (Smith et al., 2016, 2017; Sparks et al., 2017). Fire-affected pixels were grouped by FRP and FRE percentile classes (0–25, 25–50, 50–75, 75–100) for each forest type (fire-susceptible, fire-resistant, mixed). Unburned pixels were manually selected outside the MTBS fire perimeters to serve as “control” pixels. Control pixels were selected if they (1) were within a 5 km buffer of the MTBS perimeter, (2) were in the same forest type as the fire-affected pixels, and (3) had pre-fire mean NPP within ±50 g C m-2 yr-1 of pre-fire mean NPP of fire-affected pixels. Pre- and post-fire NPP were used to calculate the percent deviation from mean pre-fire NPP, or relative NPP, for each pixel (i,j) and year (t), which was calculated following Eq. (1): Relative NPPt(%)=NPPi,j,t-NPP‾prefire(i,j)NPP‾prefire(i,j). To account for interannual variability in NPP not caused by the fires we subtracted the unburned (control) pixel values from the burned pixel values (Bright et al., 2013; Goetz et al., 2006). After confirming normality and homogeneity of variances, differences between FRP percentile classes were assessed using ANOVA with a post hoc Tukey's honest significant difference test (α=0.05). Recovery time for the fire affected pixels was also assessed and was defined as the time necessary for post-fire mean NPP to equal or surpass mean pre-fire NPP at the same location.

Fires in forests dominated by fire-susceptible species were more intense, in terms of FRP metrics and FRE, than those dominated by a mix of species or fire-resistant species (Fig. 2). This finding is consistent with other observations in these, and similar, forest types where lower-biomass, open-canopy forests dominated by fire-resistant species tend to support lower intensity fires, and higher biomass, closed-canopy forests dominated by fire-susceptible species tend to support higher intensity fires (Shinneman and Baker, 1997; Morgan et al., 2001; Schoennagel et al., 2004; Rogers et al., 2015).

For fires that occurred in forests dominated by a mix of species or fire-resistant species, higher FRP or FRE magnitude resulted in lower post-fire NPP. This dose–response relationship was most apparent 1 year post-fire, where mean relative NPP decreased with increasing FRP and FRE (Fig. 3). For forests dominated by fire-resistant species and mixed forests, the dose–response pattern was very similar regardless of whether relative NPP was grouped by FRE or FRP percentile classes (Figs. 4, S1 in the Supplement). The observed dose–response relationship for these forest types persisted for > 8 years post-fire, especially in forests dominated by mixed species (Fig. 4a, b, column 2). In forests dominated by fire-susceptible species (Fig. 4a, b, column 3) there were few differences between percentile classes with only the highest FRE percentile class displaying lower NPP compared with the other percentile classes (Fig. 4b).

Maximum relative NPP loss occurred at 1 year post-fire for all fires and differed by species composition. Generally, mixed stands consisting of fire-susceptible and fire-resistant species had the largest relative post-fire NPP losses with an average loss of 40.7 % (-216.7 g C m-2 yr-1), followed by stands that were dominated by fire-susceptible species with an average loss of 33.9 % (-154.8 g C m-2 yr-1). Stands dominated by fire-resistant species had the smallest average loss of 23.3 % (-126.8 g C m-2 yr-1).

Post-fire observations ranged from 4 to 12 years post-fire (average 8.4 years) for the 15 fires, however, only the lowest FRP class of one fire (2006 South Fork Fire) had recovered to pre-fire NPP levels at the end of the observational period (∼ 9 years post-fire). While some fires displayed linear recovery trajectories, most exhibited nonlinear trajectories where NPP increased until ∼ 2011 and then began decreasing again or leveling off (Figs. S2–S4).

To date, research has largely analyzed post-fire forest productivity with fire as a binary predictor variable (presence-absence). In the current study, we applied a dose–response methodology that has been demonstrated on the tree scale (Smith et al., 2016, 2017; Sparks et al., 2016, 2017) to large fires using landscape remote sensing datasets. A dose–response relationship between FRP or FRE and NPP was shown in forests dominated by fire-resistant species and mixed species (Figs. 3 and 4, columns 1–2). Forests that were dominated by fire-susceptible species were not as sensitive to FRP or FRE, indicating that NPP in these forests may be reduced to similar levels regardless of fire intensity (Figs. 3 and 4, column 3). Additionally, forests dominated by fire-resistant species had lower post-fire relative NPP losses compared to those dominated by fire-susceptible species or a mix (Fig. 4). These data are congruent with evidence on the tree scale where trees that do not develop fire-resistant traits, such as thick bark, have a higher probability of fire-induced damage and mortality (Midgley et al., 2011; Ryan and Reinhardt, 1988; VanderWeide and Hartnett, 2011). NPP loss at 2 years post-fire (∼ 19–152 g C m-2 yr-1) in forests dominated by fire-resistant species is comparable to 2-year post-fire aboveground NPP differences between unburned and burned temperate Pinus ponderosa forest stands (∼ 83–148 g C m-2 yr-1), estimated using field measurements (Irvine et al., 2007).

There was considerable variability in the dose–response relationships within each fire resistance grouping, which could potentially be attributed to differences in stand structure and age as well as differing proportions of burned and unburned area within each NPP pixel (mixed pixels). Previous studies have indicated that smaller trees are more susceptible to fire-induced mortality than larger trees (Hood et al., 2007). Additionally, there is evidence that similar FRP doses can lead to widely different growth responses depending on tree age (Smith et al., 2017; Sparks et al., 2017). For example, 2.5-year-old Pinus contorta and Larix occidentalis saplings exposed to highly controlled laboratory surface fires (peak FRP ranged from 4.1 to 12.9 kW m-2) had radial growth at 1-year post-fire that was -2.5 to -20 % of unburned saplings (Smith et al., 2017). In contrast, a similar range of peak FRP (0.2–16.3 kW m-2) was observed in prescribed fires in 34-year-old Pinus ponderosa stands, but resulted in tree radial growth that was -10 to -45 % of unburned tree radial growth at 1.5 years post-fire (Sparks et al., 2017). The forests analyzed in this study likely had highly heterogeneous stand structures and ages within each 1 km MODIS pixel, which could lead to highly heterogenous fire behavior and vegetation response within a pixel. While previous studies mainly assessed surface fire impacts on trees, it is likely that areas within each of the fires in this study had complete overstory removal via crown fire. Variability in fire behavior can also lead to unburned islands within each fire perimeter. Previous studies have quantified unburned proportions within MTBS perimeters ranging from ∼ 10 to 25 % of the within-perimeter area (Kolden et al., 2015; Meddens et al., 2016), which could lead to more mixed pixels (pixels containing burned and unburned forest). These subpixel differences could lead to widely different patterns of mortality and recovery and mask any pixel-scale dose–response relationship.

The observed dose–response relationship was likely affected by the number of MODIS FRP observations per pixel. Spatiotemporal aggregations of observations have been shown to substantially reduce uncertainties in sums of FRP (Freeborn et al., 2014). Due to the pixel-level variability in ages and species composition in these forests, only temporal FRP aggregations were employed in this paper. There were many pixels with few (1–2) MODIS FRP observations and large NPP losses (Fig. 3). This pattern could be attributed to greater FRP uncertainty resulting from the long temporal intervals between consecutive satellite overpasses and, consequently, a poorer overall characterization of the fire behavior for a particular pixel (Giglio, 2007; Freeborn et al., 2014). This factor could also account for the slight differences observed between FRP metrics and FRE, as the long intervals between consecutive satellite overpasses have a high probability of missing increased fire activity associated with peak FRP (Giglio, 2007).

Despite an average post-fire observational period of 8.4 years across all fires, only the lowest FRP or FRE percentile class of one fire (2006 South Fork Fire) had recovered to pre-fire NPP levels ∼ 9 years post-fire. Other studies that have used remote sensing observations reported recovery time ranging from 5 years (Goetz et al., 2006) to 9 years (Hicke et al., 2003) in boreal forests. Likewise, chronosequence studies in boreal forest have estimated recovery to be ∼ 10 years (Amiro et al., 2010). The results from this study are consistent with observations showing large differences in productivity between burned and unburned forest stands at time periods greater than 10 years post-fire (Dore et al., 2008). The convergence of some of the NPP trajectories could be attributed to rapid recovery and colonization of fire-affected areas by understory species (Goetz et al., 2006). The forests in the current study occur in areas where rapid post-fire colonization by shrub and herbaceous species is common (Jorgensen and Jenkins, 2011), which could make NPP appear to recover more rapidly in areas where the forest overstory has been removed (Bright et al., 2013). Additionally, it is clear that variability in climate can significantly alter vegetation establishment and growth post-fire. Drier post-fire conditions can significantly reduce tree regeneration (Stevens-Rumann et al., 2017) and potentially lead to conversion to nonforest (Millar and Stephenson, 2015). Higher temperatures can also reduce tree growth and recovery, while increased precipitation can lead to greater growth (Bond-Lamberty et al., 2014). In this study, the incorporation of unburned pixels in the relative NPP calculation allowed for this methodology to control for climate variability and help isolate impacts resulting from the initial fire intensity.

A growing number of studies have observed mechanistic links between fire intensity (or proxies of fire intensity such as crown scorch) and post-fire mortality and productivity in saplings (Sparks et al., 2016; Smith et al., 2017) and mature trees (Ryan and Reinhardt, 1988; Hood et al., 2007; Sparks et al., 2017). The results presented in this work, building upon tree-scale studies, suggest that such linkages scale to the landscape scale. However, it is clear that more ground measurements will be needed to confirm this hypothetical framework (Fig. 5). In this conceptual system, several post-fire recovery pathways exist for trees or forests depending on the initial fire intensity. We hypothesize that higher intensity fires cause trees to incur more damage, which can lead to rapid mortality if trees have insufficient resources to repair physiological function in the weeks and months following a fire. The highest fire intensities lead to the greatest losses in physiological function and net primary productivity in surviving trees (Smith et al., 2017; Sparks et al., 2017) as well as the highest probability of delayed mortality in the years after a fire (Sparks et al., 2016). Several studies have observed heat-induced cavitation in xylem conduits of cut plant segments (Michaletz et al., 2012; West et al., 2016), leading to the hypothesis that reduced xylem conductivity is a dominant mechanism behind fire-caused mortality (Kavanagh et al., 2010; van Mantgem et al., 2013). Moderate levels of fire intensity cause enough damage to decrease growth and productivity and alter a tree's vulnerability to secondary mortality agents (e.g., insects, disease, and drought). Vulnerability may be lessened if permanent defensive structures, such as resin ducts in Pinus species used for expelling bark beetles, are induced by the fire (Hood et al., 2015; Sparks et al., 2017). On the contrary, fire may make trees more susceptible to secondary mortality agents if the photosynthetic machinery of trees is sufficiently impaired (Davis et al., 2012). Trees experiencing low-intensity fires will likely have reduced growth, but a higher probability of surviving than trees subjected to higher fire intensities. For any post-fire pathway, trees in better physiological condition or those exposed to fewer environmental stressors will likely experience a lower impact to post-fire growth and a lower probability of mortality.

The dose–response relationship we observed between FRP or FRE and post-fire NPP does not necessarily mean this methodology can now be directly applied to the characterization of landscape-scale C dynamics; several limitations need to be considered. First, this study analyzed fires that occurred in forests with little-to-no management disturbance. Applying this methodology to managed forests may produce significantly different results, as land management disturbances (e.g., timber harvest, urban development) may alter the dose–response relationship between FRP and NPP. Second, in forests with less than 100 % canopy cover, or where fire has completely removed the overstory, MODIS observes reflectance from overstory and understory forest vegetation. Understory vegetation that recovers rapidly could alter the magnitude of post-fire NPP reduction and make it appear that the overstory recovers more (or less) quickly. Finally, due to the fact that MODIS FRP observations per pixel were generally low (mean = 3.9 observations pixel-1), caution should be used when interpreting results and comparing to other ground- and remote-sensing-based measurements.