Estimating the multi-decadal carbon deficit of burned Amazonian forests

Wildfires in humid tropical forests have become more common in recent years, increasing the rates of tree mortality in forests that have not co-evolved with fire. Estimating carbon emissions from these wildfires is complex. Current approaches rely on estimates of committed emissions based on static emission factors through time and space, yet these emissions cannot be assigned to specific years, and thus are not comparable with other temporally-explicit emission sources. Moreover, committed emissions are gross estimates, whereas the long-term consequences of wildfires require an understanding of net emissions that accounts for post-fire uptake of CO2. Here, using a 30 year wildfire chronosequence from across the Brazilian Amazon, we calculate net CO2 emissions from Amazon wildfires by developing statistical models comparing post-fire changes in stem mortality, necromass decomposition and vegetation growth with unburned forest plots sampled at the same time. Over the 30 yr time period, gross emissions from combustion during the fire and subsequent tree mortality and decomposition were equivalent to 126.1 Mg CO2 ha−1 of which 73% (92.4 Mg CO2 ha−1) resulted from mortality and decomposition. These emissions were only partially offset by forest growth, with an estimated CO2 uptake of 45.0 Mg ha−1over the same time period. Our analysis allowed us to assign emissions and growth across years, revealing that net annual emissions peak 4 yr after forest fires. At present, Brazil’s National Determined Contribution (NDC) for emissions fails to consider forest fires as a significant source, even though these are likely to make a substantial and long-term impact on the net carbon balance of Amazonia. Considering long-term post-fire necromass decomposition and vegetation regrowth is crucial for improving global carbon budget estimates and national greenhouse gases (GHG) inventories for tropical forest countries.


Introduction
Wildfires, defined here as uncontrolled understory fires affecting forested areas (Barlow et al 2020), were once absent or incredibly rare in humid tropical forests (Cochrane 2003, Mcmichael et al 2012. However, since the 1980s they have been growing in prevalence due to increases in deforestation, forest fragmentation, and widespread use of fire in land management (Goldammer and Seibert 1990, Cochrane et al 1999, Mouillot and Field 2005. These factors combined with changes in climate, including increased temperatures and drought frequency, heighten fire probability (Fernandes et al 2017, Silva Junior et al 2019. It is predicted that by 2050, the southern Brazilian Amazon will have 16% of its extent affected by wildfires (Brando et al 2020). Wildfires can lead to large changes in species composition and forest structure (Van Nieuwstadt and Sheil 2005, Barlow and Peres 2008, Balch et al 2011, Oliveras et al 2018, with up to 50% of all trees dying when a forest burns for the first time (Barlow et al 2003). This is particularly worrying, as in years of extreme drought, emissions resulting from wildfires can be greater than those from deforestation (Alencar et al 2006, Anderson et al 2015, Aragão et al 2018. Given the recent magnitude of tropical wildfires, refined temporal estimates of their associated emissions are crucial for improving national and global carbon budgets.
Although it is recognized that tropical wildfires can significantly contribute to global climate change (Page et al 2002, Nepstad et al 2008, Brando et al 2020, their carbon emissions remain absent from most national and global-level accounting systems. For example, the official Brazilian System for Registering National greenhouse gases (GHG) Emissions (SIRENE, in Portuguese) and the Brazilian System for Estimating Emissions of GHG (SEEG, in Portuguese) do not account for wildfire-related emissions (MCTIC 2017, Azevedo et al 2018. There are two key knowledge gaps. The first is spatial; despite recent advances in remote sensing techniques (e.g. Anderson et al 2015, Hawbaker et al 2017, Chuvieco et al 2018, Reiche et al 2018 fire-emission datasets such as the Global Fire Emission Database (GFED) (van der Werf et al 2010), still rely on burned area products that can underestimate low-intensity understorey wildfires in closed-canopy forests by up to 11 times (e.g. see Withey et al 2018). The second is temporal; most estimates of emissions focus on immediate emissions from combustion (e.g. Withey et al 2018) or estimates of committed emissions from mortality (Barlow et al 2003, Alencar et al 2006, Anderson et al 2015, but no studies have yet attempted to quantify the dynamics of post-fire forest carbon fluxes in humid tropical forests. This study addresses this second knowledge gap. In Amazonia, during wildfire events, the immediate emissions from combustion of leaf litter and woody debris are likely to be dwarfed by the committed emissions resulting from tree mortality and subsequent decomposition. Tree mortality remains above-baseline levels for at least 7 yr after the fires . The subsequent decomposition of these dead trees will lead to CO 2 being emitted over decades later (Chambers et al 2000). These longerterm emissions could be partially or completely offset throughout a largely unquantified phase of post-fire regeneration, which is initially dominated by pioneers (Barlow andPeres 2008, Berenguer et al 2018), but later by slow growth higher wood density tree species . Without quantifying these processes, it is not possible to assign CO 2 emissions from wildfires to specific years, limiting our ability to compare emissions resulting from wildfires to those resulting from other sources, such as deforestation. This lack of temporal detail also hinders effective tracking of country-level emissions targets under the Paris commitments. Furthermore, a better understanding of the temporal progression of wildfire-related emissions would allow us to estimate their influence on the airborne fraction of CO 2 in the atmosphere, elucidating previously unknown sources and sinks.
Here, we provide the first evidence-based assessment of the temporal basis of gross and net CO 2 emissions resulting from Amazonian wildfires. We use a unique field-based dataset of trees, palms and lianas in four different regions in the Brazilian Amazon, where stem mortality, growth and recruitment have been assessed since 2009. We focused on CO 2 fluxes resulting from growth and decomposition of woody components, which store the largest Carbon content with the longest residence time in the forest. We develop a novel statistical approach to estimate yearto-year net CO 2 emissions from burned forests. For all four regions, nearby undisturbed forests were considered as our baseline for forest dynamics, allowing us to separate the marginal influence of fires from confounding drought effects, and other variation across sites. We address the following questions: (i) What is the temporal pattern of gross CO 2 emissions resulting from fire-induced stem mortality and decomposition? (ii) What is the contribution of postfire stem recruitment and growth to long-term CO 2 uptake? (iii) What is the multi-decadal net CO 2 fluxes of burned forests given the relative contribution of combustion and decomposition-related CO 2 emissions and post-fire CO 2 uptake? To answer question (i), we have used empirical models  to describe post-fire stem mortality rates, incorporating a decomposition constant rate previously estimated for the central Amazon (Chambers et al 2000). For question (ii), we have used the Chapman-Richard function to model post-fire tree growth and estimate how much CO 2 is taken up by vegetation over time. For question (iii), we have used data from questions (i) and (ii) to model the net CO 2

Study region and field measurements
Our dataset was collected in four different regions across the Brazilian Amazonia (figure 1), with permanent plots (0.25 ha) located in both burned (BF, n = 27) and unburned (UF, n = 24) terra firme primary forests (table S.M. 1). Burned forests were only affected by fire once, between 1 and 30 yr prior to sampling. Plots in unburned forests were located near burned ones (1.3-34.6 km) and sampled at the same time. In all plots, we measured all live stems (trees, palms and lianas; 7527) ≥10 cm of diameter at 1.3 m height. Aboveground biomass (AGB) were estimated according to Silva et al (2018), using specific allometric equations for trees (Chave et al 2014), palms (Goodman et al 2013) and lianas (Gerwing and Farias 2000). The AGB was estimated for all live stems in the plots, with the use of specific wood density and diameter for trees and only diameter for palms and lianas. We quantified plots AGB growth by adding the AGB of stems recruited with the AGB gain of live stems within censuses. The plot-level AGB losses due to stem mortality were quantified by adding the AGB of all dead stems (downed and standing) within censuses. The number of times each plot was revisited varied (2-6 times), as well as the time interval between censuses (1-4 yr). Corrections at the plot level were applied in order to account for stems recruitment and mortality not measured between censuses, as well as for stemlevel growth prior to mortality, following Talbot et al (2014).

Estimating gross CO 2 emissions 2.2.1. Fire-induced aboveground necromass production.
Aboveground necromass production (AGNp, Mg ha −1 y −1 ) is defined as being the same as the annual AGB loss due to stem mortality, from all causes, including downed and standing dead stems. The fire-induced AGNp (fAGNp) is determined by subtracting the AGNp of the control, unburned plots from AGNp of each burned plot after the fires, where AGNp BF(i) refers to annual AGNp of the ith plot of burned forest and AGNp UF refers to the average annual AGNp of all unburned forest plots measured in the same region at the same time of BF plots.
This allows us to exclude the influence from spatial (e.g. soil fertility) and temporal (e.g. droughts) drivers on fAGNp. We used a non-linear least squares regression and a standard exponential decay function to model fAGNp, where t is years since fire, and k is the rate at which fAGNp reduces over time. The regression analysis was done using the nls function from the stats R package ( where b is a constant decomposition rate estimated for unburned forests in central Amazonia (Chambers et al 2000), cAGN is combusted necromass stock that would have been emitted by decomposition, and t years since fire. The removal of cAGNd from total decomposition emissions is demonstrated in next section equation (4).

Decomposition of annual necromass inputs.
Over a decadal-time scale, changes in stem mortality mean there is a decreasing amount of aboveground necromass being produced in burned forests (fAGNp). After the first year, the fraction of AGN that decomposed at each year is added with the fractions decomposed in the previous years. Therefore, relative to unburned forests, the total losses by decomposition fAGNd (Mg CO 2 ha −1 y −1 ), occurring in burned forests at a given time t is the sum of all decomposed fractions (present and previous) minus the cAGNd at a given time t (see equation (3)), with all symbols defined as above. fAGNd was then converted into gross CO 2 emissions, using 0.5 as the biomass to carbon conversion factor (Penman et al 2003) and then by multiplying the value obtained by 3.67 (the ratio between C and CO 2 molecular weights) as the CO 2 conversion factor.

Estimating CO 2 uptake by stem growth and recruitment
Aboveground biomass growth (AGBg) is defined as the annual increment in AGB due to stem growth plus the AGB of recruited stems. Here, to estimate the fireinduced changes to growth rates (fAGBg) we used a similar relationship as equation (1), where AGBg BF(i) is the annual AGBg of every ith plot of burned forest and AGBg UF is the average annual AGBg of all unburned forest plots measured in the same region at the same time of BF plots. To model the process of post-fire forest growth according to the pattern observed in fAGBg over the years since fire, we fitted a Chapman-Richard growth function (Richards 1959), which is widely used in forestry to model tree population growth (Pommerening and Muszta 2016). We used a non-linear least squares regression to estimate the function parameters (S.M.2) as per fAGNp. We used the first derivative of this function to model the annual AGB growth rates of forests after the fire, ) (6) where gmax is the maximum growth the forest could reach corresponding to the inflection point of the cumulative function, g is the mean growth rate, c is a nondimensional parameter controlling the curve shape and the location of the inflection point, and other symbols defined as above. fAGBg is converted to CO 2 uptake as per fAGNd. We used CO 2 uptake instead of sequestration as the longevity of this sink remains uncertain.

Net CO 2 emissions and the relative contribution of combustion
Net CO 2 emissions were calculated by subtracting the modelled CO 2 uptake from the modelled CO 2 gross emissions. We compared the relative contributions of our estimates of net and gross CO 2 emissions (derived just from necromass decomposition) with published estimates of immediate CO 2 emissions deriving from the combustion of CWD, FWD and leaf litter in central Amazonia (Withey et al 2018). We used the cumulative values of each emission component to estimate their relative contribution over the 30 yr.
For all analysis, we quantified and propagated uncertainties throughout the model outputs (see supplementary material S.M.4).

Temporal pattern of gross CO 2 emissions from fire-induced stem mortality and decomposition
Immediately after fires, necromass production rates increased by 22.4 ± 4.5 Mg ha −1 y −1 above the levels of unburned forests (>4-fold the UF plots' necromass), and then declined over time at a constant rate of 0.32 ± 0.08 yr −1 (figure 2(a); tables S.M.6 and 7). Overall, the nonlinear regressions fit the fAGNp field data well (RSE = 6.63 Mg ha −1 y −1 ; df = 61). The initial necromass stock was the most important parameter for short-term changes in fAGNp, while the contribution from reduction rates ('k' in equation (2)) increased over time and was the most important parameter for the long-term changes (figure S.M.8).
One year after fires, the CO 2 emissions from necromass decomposition occurred at the rate of 0.27 ± 1.95 Mg ha −1 y −1 , as a result of low necromass stocks. New necromass stocks are produced in subsequent years as a result of delayed stem mortality, triggering new decomposition processes that will emit CO 2 (figure S.M.5). Gross CO 2 emissions reached their peak 5 yr after fire (8.13 ± 1.1 Mg CO 2 ha −1 y −1 ), and then decreased over time, approaching the baseline levels 30 yr after the fire event ( figure 2(b)).

3.2.
Temporal pattern of gross CO 2 uptake due to post-fire recruitment and growth AGB growth in burned forests increased above baseline levels accumulating the maximum of 22.5 ± 7.41 Mg ha −1 in 30 yr. AGBg slowly declined and reached baseline levels between 20 and 25 yr after the fire (figure 3). When burned forests AGBg peaked, CO 2 was taken up at the maximum rate of 5.59 ± 1.33 Mg ha −1 y −1 (figure 4(a)).
The nonlinear model fit the fAGBg data well (RSE = 2.21 Mg ha −1 y −1 ; df = 50). However, the nondimensional parameter related to the time and size of the growth peak ('c' in equation (6)) had the greatest variation (17.9 ± 18.4; tables S.M.6 and 7). All the three parameters in the Chapman-Richard function (gmax, k, c in equation (6)) controlling the forest growth had similar contributions (S.M.9) at the maximum growth (inflection point).

Multi-decadal net CO 2 flux from burned forests: comparing the contribution of combustion and decomposition-related CO 2 emissions with post-fire CO 2 uptake
The balance between gross emissions and uptake results in net CO 2 emissions that peaked 4 yr after the fire, with the release of 7.51 ± 1.39 Mg CO 2 ha −1 y −1 to the atmosphere ( figure 4(a)). After that, the net CO 2 emissions decline sharply due to increases in CO 2 removals. Net CO 2 emissions converged with baseline levels towards the end of the 30 yr period. However, when we combined our estimates of CO 2 emissions resulting from dead-wood decomposition with those from the combustion of woody debris and leaf litter (33.64 Mg CO 2 ha −1 , see Withey et al 2018), both cumulative gross and net CO 2 emissions remained above baseline levels ( figure 4(b)). We, therefore, estimate a cumulative gross emission of c. 126.1 Mg CO 2 ha −1 for 30 yr after a fire event. Cumulative CO 2 uptake only offsets 35% of these emissions (45.0 Mg CO 2 ha −1 ) within the same timeframe. Decomposition-related emissions account for approximately 58% (47.4 Mg CO 2 ha −1 ) of total net emissions. The inclusion of net decompositionrelated emissions doubles the emission estimates from combustion 7 yr after the fire.

Improving emission estimates from Amazonian wildfires
Our approach provides a calibrated method for integrating Amazonian wildfires into national and global emission databases. At present, in humid tropical forests, GFED focuses on emissions from deforestation fires and assumes that wildfires are carbon neutral in the long term, with regrowth offsetting respiration of woody debris and leaf litter (Landry and Matthews 2016). Also, the currently omitted CO 2 emissions and removals, from post-fire stem Figure 3. Fitted model (Chapman-Richard) for predicting fire-induced biomass growth (fAGBg). The grey dots are estimated fAGBg from field observations (n = 50), derived from the comparison between burned forest plots and locally measured unburned forest plots (equation (5)), black dots and bars are the mean ± standard error, and blue shaded area represent the 95% CI of the model. The dashed black line represents the baseline growth in undisturbed primary forests. mortality, growth and recruitment, in SIRENE and SEEG could be resolved by employing the approach proposed here. The omission of wildfire-related emissions is important: for example, while the emissions from the 2.6 million hectares of Amazonian forests affected by the 1998 wildfires (Alencar et al 2006) would have been ignored by GFED, SEEG and SIRENE, our analysis suggests that this single event would have emitted 0.17-0.25 Pg of CO 2 to the atmosphere by 2030, even without considering subsequent recurrent wildfires or deforestation. These are equivalent to 18%-27% of Brazil's intended contribution in 2030 (i.e. 0.9 Pg of CO 2 , see UNFCCC 2016) under the Paris agreement. Following these estimates, the CO 2 emissions resulting from 2010 and 2015-2016 wildfires, if properly accounted for, would have direct implications for Brazil's ability to meet its National Determined Contribution (NDC). Furthermore, as these emissions databases can be used for fire representation in dynamic global vegetation models, the omissions shown here may significantly impact the carbon budget of tropical countries, if complemented by accurate wildfire mapping.

The importance of avoiding further degradation in burned forests
Across the 30 yr period, burned forests acted as net CO 2 source, and cumulative net emissions were far higher than uptake. The average net annual emissions of burned forests over a 30 yr period were 1.52 Mg CO 2 ha −1 y −1 , which is approximately 36% of the estimated annual sink of old-growth secondary forests across tropical American rainforests (Suarez et al 2019). These long-term positive emissions are supported by the non-recovery of biomass stocks to pre-disturbance levels shown in Silva et al (2018). However, despite these emissions, burned forests also remain an important part of any strategy to mitigate carbon losses from degradation. Allowing burned forests to regrow offsets 35% of all decompositionand combustion-related emissions over the 30 year period, and, unlike secondary forest, does not require expensive tree planting or incur opportunity costs from the abandonment of agricultural land. The protection of burned forests from further disturbances and/or clearance may also offer other important ecosystem services, such as maintenance of hydrological cycling (Brando et al 2019), as well as providing habitat for biodiversity-albeit at a lower level than in undisturbed primary forests (Berenguer et al 2014, Barlow et al 2016, Ferreira & Lennox et al 2018, França et al 2020. Yet, protecting these forests from clearance has recently become more challenging-since 2012, deforestation rates have risen 16% on average (PRODES 2020) and burned forests are often located at the agricultural frontier where they may be more susceptible to clearance. Likewise, protecting burned forests from further disturbances is far from straightforward, since burned forests are more vulnerable to windstorms (Silvério et al 2019) and are increasingly susceptible to repeated fires (Cochrane et al 1999, Alencar et al 2011, Morton et al 2013, Da Silva et al 2018, which is likely to be exacerbated by climate change (Fonseca et al 2019). If burned forests burn again, the consequences for CO 2 emissions are likely to be far worse. These recurrent fires are often much more intense, leading to much higher levels of tree mortality (Cochrane et al 1999, Barlow andPeres 2004), a high turnover of species composition towards pioneer species (Barlow and Peres 2008), and slower rates of post-fire carbon uptake through regrowth (Balch et al 2013).

Quantifiable uncertainties
While we present the first temporal estimate of emissions from Amazonian wildfires, we also recognise that many uncertainties remain. These include particularly the uncertainties associated with the growth parameters, especially relating to the phase when burned forests reach their peak of CO 2 uptake relative to unburned forests, where the confidence intervals were especially high ('c' in equation (6); table S.M.7). There are many reasons for such high uncertainty: post-disturbance growth is a complex process, and post-disturbance growth rates are known to vary significantly by species (Berenguer et al 2018), across regions (e.g. Poorter et al 2016), and can be affected by environmental factors including fire intensity and canopy openness (Balch et al 2013, Brando et al 2019, or even climate change or climate anomalies , Elias et al 2020. Although we tracked mortality over time in our burned plots, additional variability could have stemmed from the lack of samples in forests before they burned (e.g. França et al 2016). However, these pre-fire samples are only achievable by chance or through experimental fires, and the data-spread (figures 2 and 3) suggests our field observations are representative of some of the main environmental gradients within Amazonian forests (Johnson et al 2016). Finally, temporal limitations in the dataset represent a further source of uncertainty and our estimates of emission and regrowth are highly uncertain beyond 15 yr since fire. Narrowing this uncertainty remains challenging, as many of the sites impacted by 1980s and 1998 El Nino events have either been deforested, selectively logged, and/or burned again (e.g. see Bullock et al 2020).
Decomposition rates are also a source of uncertainty. We propagated the decomposition rate uncertainty measured in undisturbed forests, as decomposition rates in burned forests are unknown. Yet, the decomposition rates in burned forests may differ due to (1) drier microclimate brought on by changes in forest structure and canopy openness (Uhl andKauffman 1990, Barlow andPeres 2008); (2) changes in decomposer community structure, including invertebrates (Ashton et al 2019) and microbes, relating to changes in pH and microclimate (Carvalho et al 2016); (3) changes in the litter quality, especially as wood density negatively affects decomposition rates in undisturbed forests (Chambers et al 2000, Chao et al 2009, and at least part of the mortality is related to short-lived lower wood density species that colonise rapidly after fires ; and (4) stem mode of death, which impacts wood decomposition rates because dead stems standing and suspended from the ground have much slower decomposition rates than downed stems (Gora et al 2019). None of these potential drivers of change in decomposition rates has been previously investigated or quantified in burned humid tropical forests.
Although vegetation is the most disturbance sensitive carbon pool in the forest (Berenguer et al 2014), uncertainties could also be reduced by evaluating other components of forest carbon cycle. For example, FWD and leaf litter, which corresponds to 34% of total NPP in undisturbed forests (Malhi et al 2009), is assumed to decompose at the rate of CWD. This makes the decay time of FWD and litter in our model longer (5 yr) than that expected (6 months-2 yr; Malhi et al 2011), causing a delay in the emissions. Moreover, not all carbon from woody debris and leaf litter is released as CO 2 to the atmosphere; part of it is biologically transformed and locked up in the soil or leached to groundwater. The net dissolved organic carbon (DOC) export from forest soil is, however, a very small component of the forest carbon cycle (0.003%-1.9% of total NPP; Malhi et al 2009). While burned forests soil carbon pool does not differ from unburned forests (Berenguer et al 2014), increases in DOC may be expected for burned forests. Further carbon release can be also expected through CH 4 emissions from termite's activity and anaerobic decay of wood and litter. However, anaerobic activity increase is unlikely in free-draining terra-firme forests where oxygen is not limited, and the production of CH 4 in terra-firme forests represents a small component of carbon cycle (0.005%-0.06%; Malhi et al 2009), and the sources have not been identified (Do Carmo et al 2006). While changes in CH 4 emission due to termites is a possibility, this has not been investigated in burned humid tropical forests.
Another important set of uncertainties go beyond our approach and relate to the spatiotemporal scaling of our results. For example, wildfires are mostly missed by active fire counts and estimates of burned area derived from satellite measures (Anderson et al 2015), meaning that we lack a reliable large-scale and historical mapping of fire scar coverage across Amazonia. Furthermore, even if fires are mapped with the use of improved techniques (Morton et al 2011, Anderson et al 2015, Withey et al 2018, prefire forest conditions will play an important role in determining fire intensity and mortality (Barlow et al 2012, Brando et al 2016. Forests that have experienced disturbances from logging or fires prior to the satellite era may harbour large fuel loads, resulting in more intense fires, albeit with lower initial carbon stocks. However, this source of uncertainty may remain unresolved due to the lack of both, on-theground and remote sensing data. Mortality is also likely to be higher near forest edges (Brando et al 2019), where necromass accumulation is higher.

Conclusion
Most estimates of wildfire-related CO 2 emissions account for committed emissions without considering the temporal evolution of stem mortality, the time taken for the subsequent decomposition of dead biomass, and the amount taken up by regrowth. By incorporating long-term field-data on biomass gains and losses, we developed an approach that addresses these knowledge gaps, showing that decompositionrelated emissions make a significant contribution to the total CO 2 emitted and are only partially offset (~35%) by post-fire forest regrowth in 30 yr. Our approach allows the scaling-up of the net CO 2 emissions resulting from wildfires across the Amazon basin, providing a way of incorporating them into both national and global carbon budgets and databases. This, however, depends on the enhancement of forest fire detection and mapping.