Carbon cycle and climate effects of forcing from fire-emitted aerosols

Aerosols emitted by landscape fires affect many climatic processes. Here, we combined an aerosol–climate model and a coupled climate–carbon model to study the carbon cycle and climate effects caused by fire-emitted aerosols (FEA) forcing at the top of the atmosphere and at the surface. This forcing (‘best guess’ present-day values of −0.10 and −1.3 W m−2 at the top of the atmosphere and surface, respectively) had a predominant cooling influence that altered regional land carbon stocks on decadal timescales by modifying vegetation productivity and soil–litter decomposition. Changes in regional land and ocean carbon stocks became much stronger for FEA forcing acting on multi-century timescales; this occurred because carbon stocks responded to the forcing itself on such timescales and also due to gradual effects on the climate (e.g. through increased sea ice cover) that further affected the carbon cycle. Carbon increases and decreases in different regions partly offset each other, so that absolute changes in global land, atmosphere, and ocean stocks were all <2 Pg C after 30 years of FEA forcing and <6 Pg C after more than 1000 years of FEA forcing. FEA-caused changes in land carbon storage did not substantially modify the magnitude of FEA emissions, suggesting there is no consequential regional-scale positive feedback loop between these two elements. However, we found indications that the FEA-caused cooling from frequently-burning regions in Africa and Australia increased land carbon stocks in eastern South America and equatorial Asia, respectively. This suggests the potential for remote carbon cycle effects from regions emitting large amounts of fire aerosols.


Introduction
Aerosols emitted during landscape fire events lead to a suite of impacts in the Earth system. By decreasing air quality, fire-emitted aerosols (FEA) could result in ∼300000 deaths annually (Johnston et al 2012). FEA also directly affect radiation exchanges throughout the atmosphere and modify cloud properties, generally decreasing precipitation and reducing surface radiation (Jones et al 2007, Jacobson 2014, Veira et al 2015, Jiang et al 2016. The net radiative forcing caused by FEA is highly uncertain, but might determine whether fires have a net warming or cooling influence on global climate (Jacobson 2004, Unger et al 2010, Ward et al 2012, Jacobson 2014, Landry et al 2015. FEA also modify carbon cycling through changes in nutrient distribution and physical climate . Nutrient-mediated effects happen as fires redistribute nitrogen and phosphorus (Mahowald et al 2005, Chen et al 2010 and fertilize oceans through iron deposition, although this last mechanism is likely consequential at the regional scale only (Guieu et al 2005). Effects mediated through changes in physical climate include the FEA-caused increase in diffuse radiation that enhances vegetation productivity (Rap et al 2015) and net ecosystem carbon uptake (Doughty et al 2010); this last study also found that FEA-caused cooling can enhance net ecosystem carbon uptake. In a previous study using a simplified approach to account for the FEA-caused radiative forcing at the top of the atmosphere and resulting temperature changes (but that neglected surface radiation changes), we reported that a very strong FEA-caused cooling could substantially increase land carbon storage by slowing down soil-litter decomposition, to the point where more frequent fires actually increased global land carbon stocks for many decades (Landry et al 2015). This outcome suggests the possibility of a strong regional-scale positive feedback between FEA forcing and carbon stocks, such that FEA-induced cooling from a given fire regime would increase land carbon storage, thereby increasing fuel stocks, leading to higher FEA amounts, and resulting in more cooling and land carbon storage.
Here, we combined an aerosol-climate model and a coupled climate-carbon model to study the impacts on carbon cycling due to FEA-caused changes in the physical climate, more precisely the modification of shortwave and longwave radiation fluxes at the top of the atmosphere (i.e. the effective radiative forcing (ERF); Myhre et al 2013) as well as shortwave radiation at the surface. To our knowledge, this is the first study assessing FEA effects on the carbon cycle in a global climate model. The main objective was to quantify FEA-caused changes in land, atmosphere, and ocean carbon stocks. We also considered various sources of uncertainty to provide insights about modelling FEA effects on the carbon cycle.

Coupled climate-carbon model
The University of Victoria Earth System Climate Model (UVic ESCM) version 2.9 is a coupled climate-carbon model of intermediate complexity simulating the exchanges of carbon, energy, and water among land, atmosphere, and ocean (Weaver et al 2001, Eby et al 2009. Atmospheric processes are represented through simplified energy and moisture balance equations with dynamical feedbacks (Weaver et al 2001). The ocean module simulates threedimensional circulation, sea ice dynamics and thermodynamics, inorganic carbon cycling, and ecosystem/biogeochemical carbon-nutrient dynamics (Weaver et al 2001, Ewen et al 2004, Schmittner et al 2008, Eby et al 2009. Terrestrial processes are represented with a simplified land surface scheme (Meissner et al 2003) coupled to a dynamic global vegetation model (Cox 2001) that accounts for competition among five plant functional types (PFTs) as well as carbon stocks in vegetation and soil-litter.
Each month, fire-caused emissions were computed as the product of prescribed burned area, PFT-specific fuel density simulated by the UVic ESCM, and PFTspecific combustion fractions; vegetation killed by fire but not fully combusted joined soil-litter, where it decomposed as a function of the local soil temperature and moisture that were influenced by fire-caused changes in atmospheric CO 2 and surface albedo (Landry et al 2015, Landry andMatthews 2016). We used the same prescribed burned area as Landry et al (2015), i.e. monthly-varying mean values for 2001--2012 from version 4 of the Global Fire Emissions Database (GFED4) (Giglio et al 2013). PFTs could colonize the burned area after each fire event, leading to a CO 2 regrowth flux that depended upon local competition among PFTs and was also influenced by fire-caused changes in the climate-carbon system. This approach captured the impacts of fire from local (e.g. altered vegetation composition) to global (e.g. fire-caused CO 2 fertilization) scales as well as the carbon trade-offs between fire and land-cover changes (i.e. fire-caused decreases in biomass density led to smaller carbon emissions from land-cover changes; Ward et al 2012). However, the UVic ESCM did not account for the increase in diffuse radiation that has been studied elsewhere (Doughty et al 2010, Rap et al 2015 or for the impacts of nutrient redistribution (Guieu et al 2005, Mahowald et al 2005, Chen et al 2010. We also neglected year-to-year variability in fire regime because we focussed on mean effects over decadal to multi-century timescales. Since we wanted to isolate FEA effects, we activated the fire module in all simulations but neglected FEA-caused forcing in the control simulations.

Amounts of fire-emitted aerosols
Here, we added to the UVic ESCM the computation of black carbon (BC), organic carbon (OC), and sulphur dioxide (SO 2 , a precursor of sulphate aerosols) emissions. We derived the required emission factors by combining GFED4 values (GFED4 2014), themselves based on Andreae and Merlet (2001) and Akagi et al (2011), with a conversion factor of 0.48 kg C per kg of dry matter (van der  Second, we adjusted all these regional emission factors so that the global emissions were three (for BC and OC) and two (for SO 2 ) times higher than the MIN estimates (

Forcing from fire-emitted aerosols
The simplified atmospheric module of the UVic ESCM makes long simulations computationally affordable, but prevents the process-based representation of FEA effects. To calculate the ERF and modified surface radiation caused by FEA, we used the ECHAM-HAMMOZ (ECHAM6.1-HAM2) aerosol-climate model (Zhang et al 2012, Stevens et al 2013. The model core is the atmospheric general circulation model ECHAM, which solves atmospheric flow and physics at a horizontal resolution of T63 (roughly 1.9 Â 1.9 ). The aerosol model HAM explicitly simulates emissions, microphysics, and removal of aerosol particles. Aerosol-cloud interactions are calculated online (Lohmann et al 2007) with the Lin and Leaitch (1997) semi-empirical cloud activation scheme (Lohmann et al 1999). The model accounts for aerosol direct, semi-direct, and indirect effects. BC, OC, and SO 2 from fire were distributed vertically based on predefined rules (Dentener et al 2006). We nudged ECHAM-HAMMOZ meteorology towards ERA-Interim reanalysis data (Dee et al 2011) and prescribed sea surface temperature. The runs lasted six years, in addition to the one-year spin-up period; similarly to FEA, emissions of anthropogenic aerosols did not vary between years. We performed all ECHAM-HAMMOZ simulations with and without monthly-varying FEA to diagnose the FEA-caused forcing. The resulting monthly-varying forcing fields then served as input data to modify radiation exchanges in the UVic ESCM at the top of the atmosphere and at the surface.

Simulation design
We performed transient (TR) and equilibrium (EQ) control simulations (CONT) in the UVic ESCM with the fire module, but without FEA forcing (table 1). These simulations started from previous results (Landry et al 2015) for year 1850 that included prescribed natural and anthropogenic forcings as well as the effect of fire. TR-CONT was driven by prescribed transient forcings during the 1851-2020 period simulated here, whereas EQ-CONT lasted 1000 years with prescribed forcings kept at their year-1850 values. Prescribed forcings in the UVic ESCM consisted of anthropogenic CO 2 emissions, other greenhouse gases, sulphate and volcanic aerosols, land-cover changes, and land ice (Weaver et  TR-30-X was similar to TR-CONT but included the effect of FEA forcing in the UVic ESCM during the 30-year period from 1991 to 2020; here X stands for the amount of FEA (MIN, BG, or MAX) calculated from the last 30 years of TR-CONT. FEA forcing was computed by ECHAM-HAMMOZ based on this UVic ESCM-estimated FEA amount, year-2005 emissions for aerosols other than FEA, and 2002-2008 meteorology. In all simulations, the nonaerosol forcings required by ECHAM-HAMMOZ (e.g. ozone concentration) were for year 2005. EQ-1000-X was similar to EQ-CONT but included the effect of FEA forcing for 1000 years, computed by ECHAM-HAMMOZ based on UVic ESCM-estimated FEA amount over the last 50 years of EQ-CONT, year-1850 emissions for aerosols other than FEA, and 2002-2008 meteorology. We used EQ-1000-X results as the starting point for TR-1170-X. This transient simulation included the same FEA forcing as TR-30-X, but applied from 1851 until 2020. Including the 1000-year EQ-1000-X equilibrium, TR-1170-X therefore felt FEA forcing over a total of 1170 years, with a switch from preindustrial to present-day FEA forcing on year 1851. We also performed sensitivity simulations. TR-30-X-M was similar to TR-30-X, except that ECHAM-HAMMOZ was nudged towards the 1992-1998 meteorology instead of 2002-2008. TR-1170-X-F was similar to TR-1170-X, except that the UVic ESCM-estimated FEA magnitude used by ECHAM-HAMMOZ came from TR-1170-X instead of TR-CONT. The purpose here was to assess potential feedbacks between FEA and the carbon cycle by comparing results for FEA magnitudes that themselves felt (TR-1170-X-F) or not (TR-1170-X) the long-term influence of FEA forcing. Unless otherwise mentioned, results correspond to the difference between a simulation with FEA forcing and the corresponding control (TR-CONT or EQ-CONT), thereby isolating FEA effects. We also note that even if MIN, BG, and MAX results actually came from different FEA amounts in ECHAM-HAMMOZ, the range of values presented below assesses the results sensitivity to varying FEA forcing strengths as estimated by other aerosol-climate models. Figure 1 shows FEA-caused ERF and surface radiation changes for TR-30-BG. The strongest negative ERF values occurred west of central Africa, whereas extensive regions of predominantly positive ERF were centered over the northern Pacific and around Australia. FEA usually decreased surface radiation, above all in the vicinity of Africa and Australia, i.e. the regions with the highest fire frequency. Spatial patterns were similar for MIN and MAX (figure S1), with weaker forcing for MIN and stronger forcing for MAX. Global mean ERF was À0:10, À0:03, and À0:25 W m À2 for BG, MIN, and MAX, respectively. The different meteorology had a small impact on simulated forcing. Spatial patterns were very similar although some differences were visible, especially for ERF (e.g. figures 1 vs. S2 for BG). The impact of meteorology on global mean ERF (a difference of 0:05 W m À2 between TR-30-BG-M and TR-30-BG) was also much smaller than the uncertainty associated with different FEA amounts (a difference of 0:22 W m À2 between TR-30-MIN and TR-30-MAX). Consequently, we henceforth present results for the 2002-2008 meteorology only.

Effects for 30-year forcing
When applied over 30 years  in the UVic ESCM, the BG forcing from ECHAM-HAMMOZ generally decreased atmospheric surface temperature except around the Bering Strait and close to Australia (figure 2(a)). Changes in atmospheric surface temperature came not only from FEA-caused modifications to atmospheric radiation absorption, but also from FEA impacts on land and ocean surface conditions as well as from energy redistribution. The strongest cooling was located west of the strongest negative ERF (figure 1 (a)) due to prevailing westward winds at these latitudes. Similar results were obtained for MIN albeit with less cooling or more warming, whereas Environ. Res. Lett. 12 (2017) 025002 more negative ERF for MAX led to cooling almost everywhere (figures S3(a) and S3(c)). Changes in both temperature and surface radiation modified carbon stocks ( figure 2(b)). The slight decrease in column-integrated ocean carbon west of central Africa involved lateral exchanges of carbon, because the colder surface temperature in this region actually increased the solubility of atmospheric CO 2 . FEA usually increased land carbon, especially for most of Latin America, westernmost Africa, and equatorial Asia, but extensive decreases occurred in central Africa and northern Australia. FEA-induced cooling invariably slowed down soil-litter decomposition, yet soil-litter carbon decreased despite cooling in central Africa because the much lower surface radiation substantially reduced vegetation productivity, strongly decreasing the vegetation carbon input to the soil-litter pool. Conversely, vegetation productivity increased in some regions (e.g. westernmost Africa) despite lower surface radiation, due to the beneficial impact of FEA-caused cooling in warm climates (Steiner andChameides 2005, Matthews et al 2007). Results for MIN and MAX were broadly similar to BG, with generally weaker and stronger effects, respectively (figures S3(b) and S3(d)).
At the local scale, changes in land carbon caused by 30-year FEA forcing often reached 1-3 % of total stocks, particularly in tropical regions. Yet changes in global carbon stocks were small (table 2). The firstorder impact of FEA forcing was to increase global land carbon, which decreased atmospheric carbon. Ocean carbon stocks were also reduced, because the global decrease in atmospheric carbon had a larger effect than the overall cooling-related increase of CO 2 solubility. The effects on global carbon stocks were stronger for MIN than for BG, which resulted from opposite impacts of FEA on vegetation productivity vs. soil-litter decomposition at the global scale. For BG, reduced productivity due to lower surface radiation initially had more impact than reduced decomposition due to lower temperature, so that five years elapsed before FEA actually increased land carbon. For MIN, on the contrary, the change in global productivity was marginal and FEA immediately started augmenting land carbon.
3.2. Effects for forcing over a multi-century timescale For simulations over many centuries, we first computed year-1850 FEA forcing. Results (figure S4) were broadly similar to the previous ones (figures 1 and S1), except that ERF and surface values were often slightly more negative in 1850 because lower anthropogenic aerosol levels led to stronger FEA-caused cloud-mediated effects (Spracklen and Rap 2013). We then performed a 1000-year equilibrium simulation in the UVic ESCM, with FEA forcing, for year 1850. When acting over such a long period, FEA-caused negative ERF triggered gradual changes in the physical state of the climate system, such as increased sea ice cover. As a result, for BG the global mean atmospheric surface temperature decreased by 0.11 K over the first 50 years, followed by an additional decrease of 0.07 K over the remaining 950 years ( figure 3(a)). Responses were qualitatively similar for MIN and MAX, but noticeably less and more pronounced, respectively (figures S5(a) and S6(a)).
Starting from these year-1850 results, we performed a 1851-2020 transient simulation with the present-day FEA forcing used in section 3.1 applied throughout. The sudden decrease in the magnitude of negative ERF caused the warming impact visible around year 1850 in figure 3(a). At the end of the transient simulation, the change in atmospheric surface temperature for BG ( figure 3(b)) was more negative than after applying FEA forcing over 30 years only (figure 2(a)), above all for the northern hemisphere due to increased Arctic sea ice cover. Effects were qualitatively similar for MIN (figures S5 (b) vs. S3(a)) and MAX (figures S6(b) vs. S3(c)).
Changes in 1991-2020 carbon stocks were clearly stronger for 1170-year (figure 3(c)) than for 30-year (figure 2(b)) FEA forcing. The stark contrast in ocean carbon changes between the Atlantic and Pacific broadly reflected the spatial differences in FEA-caused temperature changes, with ocean circulation contributing to finer-scale spatial patterns. Changes in land carbon often represented 1%-5% of local stocks. Land carbon changes for 1170-year vs. 30-year FEA forcing differed noticeably in boreal forests due to a legacy effect from the year-1850 equilibrium. At that time, FEA caused more negative ERF and much lower surface radiation over boreal forests than for present-day atmospheric conditions (figures S4(a)-(b) vs. 1(a)--(b)). Moreover, the gradual increase of Arctic sea ice cover further decreased temperature in boreal forests. FEA therefore markedly reduced preindustrial boreal forests productivity, which decreased soil-litter stocks. A similar legacy effect was visible in the MIN results (figures S5(c) vs. S3(b)). For MAX, FEA forcing over both 1170-year and 30-year timescales generally reduced carbon stocks in boreal forests, but the decrease was larger in the former case (figures S6(c) vs. S3(d)).
Despite much stronger FEA impacts on local carbon stocks for 1170-year vs. 30-year forcing, the effects on global carbon stocks remained small . This reflected the differences in enhanced CO 2 solubility due to FEAcaused cooling; for example, the large cooling for MAX led to net oceanic carbon uptake even though atmospheric CO 2 decreased. Finally, we performed the TR-1170-X-F simulations to assess the potential for FEA-induced cooling to result in a positive feedback by enhancing land carbon storage and the magnitude of FEA produced. Local-scale land carbon changes were often affected by FEA-carbon cycle interactions (figure S7; results are for TR-1170-X-F minus TR-1170-X). For MAX, the effect led to higher global land carbon stocks (by 0.7 Pg C for TR-1170-MAX-F vs. TR-1170-MAX) and caused noticeable increases in regions where FEA already substantially augmented land carbon (e.g. eastern South America and westernmost Africa; figures S7(c) and S6(c)), suggestive of a possible positive feedback loop. Nonetheless, the overall potential for strong regional-scale positive FEA-carbon cycle feedbacks appeared small because: (1) the effect was spatially heterogeneous; (2) there was no large region where the effect showed a noticeable and invariable increase from MIN through BG to MAX, contrary to what one would expect for a positive feedback; and (3) for MIN and BG, total land carbon was lower (by ∼ 0.4 Pg C) for the TR-1170-X-F simulations.
4. Discussion 4.1. Effects of fire-emitted aerosols on the carbon cycle We found that FEA-caused changes in both temperature and surface radiation affected carbon cycling. Over land, FEA decreased surface radiation almost everywhere and generally caused cooling. Lower surface radiation reduced vegetation productivity, but cooling had more variable impacts, for example increasing productivity in some tropical regions but decreasing it in cold climates. Changes in productivity altered input to soil-litter, which decomposed more slowly due to FEA-caused cooling. Local changes in land carbon therefore came from the complex interplay among several FEA-induced effects. In oceans, changes in local carbon depended upon modified temperature and atmospheric CO 2 level as well as three-dimensional circulation. Although more comparisons with empirical data are warranted, a previous study also concluded that FEA-caused cooling can increase carbon storage in tropical forests (Doughty et al 2010).
Some previous studies on the impact of anthropogenic ( Environ. Res. Lett. 12 (2017) 025002 aerosols on land carbon neglected aerosol-induced temperature changes, so they could not capture all the effects reported above. Conversely, we neglected the aerosol-induced increase in diffuse radiation that these previous studies addressed. Had we also included this diffuse radiation effect, our spatial patterns of land carbon changes would likely have remained similar but with results shifted towards more positive values. For most of Latin America, westernmost Africa, and equatorial Asia, FEA-caused increases in land carbon storage would therefore have been higher. We hypothesize that FEA would still have reduced land carbon in central Africa, albeit less than simulated here, because the large decrease in surface radiation (e.g. figure 1(b)) would have had a stronger impact than the corresponding increase in diffuse radiation, as suggested by the curvilinear relationship between productivity and diffuse fraction (Knohl and Baldocchi 2008) or FEA amount (Rap et al 2015) reported for other regions.
Effects on local carbon stocks became much stronger when FEA forcing acted over many centuries vs. 30 years (figure 3(c) vs. 2(b)), yet the global changes remained small (table 2) due to offsetting increases and decreases. Even if limited, FEA impacts on global carbon stocks should not be considered negligible: the mean FEA-caused decrease of atmospheric CO 2 over 1991-2020 was almost 12 ppmv under TR-1170-MAX, for which our ERF results (preindustrial and presentday global mean values of À0:38 and À0:25 W m À2 , respectively) were realistic. FEA forcing and its impacts might also increase in the future if fires become more frequent, but we stress that: (1) a larger FEA forcing did not always led to larger changes in global carbon stocks (table 2); and (2) for a given amount of FEA, the exact forcing also depends upon anthropogenic aerosol emissions.
We can also compare our results with the effect of fire itself on carbon stocks. We took the year-1750 'CO 2 only' equilibrium from Landry et al (2015), which did not account for FEA forcing, and continued the equilibrium simulation for 10000 years after suddenly switching off the fire module and letting all carbon pools evolve freely. The net effect of fire was to decrease land carbon stocks by 161 Pg C, which increased ocean and atmosphere carbon stocks by 129 and 33 Pg C, respectively. This corresponds to mean changes of about À1050 g C m À2 over land and þ360 g C m À2 over ocean. By comparison, FEA-caused local changes in carbon stocks for the year-1850 equilibrium had an absolute value ≥ 200 g C m À2 over 2%, 13%, and 32% of all grid cells for MIN, BG, and MAX, respectively (present-day values for multi-century FEA forcing (figures S5(c), 3(c), and S6(c)) were very similar).

Remote effects and feedbacks
We found consequential FEA remote effects acting on the carbon cycle over decadal timescales for at least two regions. Due to prevailing westward winds, the strong negative ERF west of central Africa (figure 1 (a)) contributed to the FEA-induced cooling over eastern South America (figures 2(a) and 3(b)). Vegetation productivity in the region benefited from this African-originating cooling, especially as the reduction in surface radiation was much less severe than for central Africa ( figure 1(b)). Slower decomposition of soil-litter, to which the African-originating cooling also contributed, then compounded the effect of enhanced vegetation productivity, resulting in relatively high carbon increases in the region (figures 2(b) and 3(c)). Due to prevailing northwestward winds over northern Australia, a similar remote effect generally increased land carbon in equatorial Asia. These remote effects are possibly strengthened by fire-caused exports of nitrogen (Chen et al 2010) and other nutrients transported by the same prevailing winds; these exports were not considered in our study.
Our results indicate another potential FEA remote effect on the carbon cycle on much longer timescales. Negative ERF due to FEA predominantly occurred in tropical regions ( figure 1(a)), yet on centennial timescales the resulting global cooling increased sea ice cover, especially in the Arctic, which further cooled the global climate (temperature trend in figure 3(a)) and substantially decreased high-latitude temperatures (figures 3(b) vs. 2(a)). As a result, carbon stocks decreased in boreal forests due to cooling-induced productivity reduction and probably increased in oceans due to cooling-induced effect on CO 2 solubility.
Although we did not address this question with fully prognostic and transient simulations, our simplified assessment seemed to go against the existence of strong regional-scale positive FEA--carbon cycle feedbacks, except possibly for the highest FEA amount considered. Even if potential positive feedbacks between FEA and the carbon cycle appeared small based on the effects studied here (i.e. FEA-caused changes in temperature and surface radiation), meaningful positive feedbacks could arise through other processes like FEA-induced decreases in precipitation over tropical regions (Tosca et al 2013(Tosca et al , 2015.

Modelling insights
Previous studies including aerosol-cloud interactions obtained present-day FEA-caused global mean ERF between À1:5 W m À2 (Ward et al 2012) and þ0:9 W m À2 (Jacobson 2014). Even if excluding these two extreme results, recent studies differ by ∼ 1 W m À2 . These discrepancies stem from the still relatively low level of scientific understanding for aerosol-cloud interactions (Myhre et al 2013), which represent the main uncertainty when modelling long-term FEA forcing over large spatial scales. FEA amounts and episodicity appear as smaller uncertainty sources. For the TR-30-X simulations, we found a range of Environ. Res. Lett. 12 (2017) 025002 0.22 W m À2 for global mean ERF between MIN and MAX, which likely bounded the range of plausible FEA amounts. A study on the episodicity of FEA in a model giving much more negative ERF than ECHAM-HAMMOZ found a global mean ERF difference of 0.2 W m À2 between emissions interpolated from monthly mean values vs. emissions that accounted for the number of fire days and fire events each month (Clark et al 2015). Simple vs. parameterized FEA emission heights (Veira et al 2015) as well as the nudging meteorology and the potential FEA-carbon cycle feedback assessed here appear as even smaller effects, modifying global mean ERF by about 0.04, 0.05, and 0.01 W m À2 , respectively. However, nudging itself and the set of variables used for it might have an effect comparable to FEA amounts and episodicity (Zhang et al 2014).
Modelling FEA effects on the carbon cycle is challenging, because aerosol-climate models are computationally demanding whereas temperature--carbon feedbacks evolve over multi-century timescales. The limited impacts on our results of nudging meteorology as well as feedbacks between FEA forcing and magnitude of FEA suggest that fully online and transient simulations of FEA-carbon interactions might not be necessary to capture firstorder effects over long timescales. The major differences between figures 2 and 3, however, highlight the importance of accounting for the existence of FEA forcing over the past centuries and beyond. Due to non-linear interactions between FEA and anthropogenic aerosols (Spracklen and Rap 2013), modellers should ideally use FEA forcing representative of preindustrial atmospheric conditions for equilibrium; given the other uncertainties involved, updating FEA forcing each decade might then be sufficient for transient simulations. Due to seasonal variations in vegetation productivity and sign changes in FEA forcing at the same location during the year, using monthly-variable FEA forcing fields as we did here seems advisable.

Study limitations
ECHAM-HAMMOZ does not account for brown carbon, which is the fraction of OC that absorbs radiation and therefore warms the climate. Effects of brown carbon are only starting to be represented in aerosol-climate models and remain highly uncertain (Jacobson 2014, Saleh et al 2015, Jo et al 2016. Our results also excluded the warming caused by BC deposition on snow. Although very small globally, this warming is consequential for climate-related processes in snow-covered regions (Flanner et al 2007, Jiang et al 2016 and might have reversed the FEA-caused cooling we found around the Arctic ( figure 3(b)). In addition to FEA impacts on diffuse radiation and nutrient redistribution discussed above, we neglected nitrate FEA (Akagi et al 2011) and biogenic secondary organic aerosols (Scott et al 2014), and our modelling framework did not allow to fully capture the effects of FEAcaused precipitation changes (Tosca et al 2013(Tosca et al , 2015. By prescribing monthly burned area based on 2001-2012 data, we also missed the large fire years of 1997 and 1998, which might be consequential for equatorial Asia (van der Werf et al 2010); furthermore, this approach did not account for the regional-scale variations in fire frequency over the past centuries (Marlon et al 2013). Although each fire event in the UVic ESCM led to bare ground available for colonization by the different PFTs, these fire-created patches were not subsequently tracked on an individual basis, thereby neglecting the effects of the resulting 'subgrid cell dynamic heterogeneity' . Finally, future studies separating the carbon cycle effects due to FEA-caused forcing at the top of the atmosphere vs. at the surface could provide additional insights.

Conclusion
We combined an aerosol-climate model and a coupled climate-carbon model to assess FEA forcing effects on carbon cycling over decadal and multicentury timescales. FEA-caused changes in both temperature and surface radiation affected land and ocean carbon stocks, even under the minimum estimate of FEA amounts for which forcing values were much smaller than in previous studies. On decadal timescales, FEA forcing-which had presentday best guess (minimum to maximum) values of À0:10 (À0:03 to À0:25) and À1:3 (À0:4 to À2:3) W m À2 at the top of the atmosphere and surface, respectively-directly altered vegetation productivity and soil-litter decomposition, modifying global land, atmosphere, and ocean carbon stocks by <2 Pg C each under all FEA amounts. On a multi-century timescale, FEA-induced cooling increased sea ice cover, further affecting temperature and carbon exchanges. Regional carbon increases and decreases offset each other on land and in oceans, explaining why changes in global stocks remained small (<6 Pg C each under all FEA amounts) even for multi-century FEA forcing. We also found remote effects of FEA-caused cooling from fire in Africa and northern Australia on carbon stocks in eastern South America and equatorial Asia, respectively. The existence of strong regional-scale positive feedbacks between FEA and the carbon cycle was not supported by the simple assessment we performed. We finally emphasize that, contrary to anthropogenic aerosols, consequential amounts of FEA have been affecting the carbon cycle and climate for millions of years. Given that fire activity has been changing through time and that the carbon cycle can take many centuries to respond to a given level of FEA forcing, a long-term perspective on FEA-carbon interactions seems warranted. Environ. Res. Lett. 12 (2017)