We use the emissions from the Global Fire Emission Database version 4.1s (GFED4.1s) to validate the simulated fire emissions. GFED4.1s provides monthly fire emission fluxes of various air pollutants based on satellite retrieval of area burned from the Moderate Resolution Imaging Spectroradiometer (MODIS) (van der Werf et al., 2017). Area burned in GFED4.1s is mainly derived from the MODIS burned-area product (Giglio et al., 2013), taking into account “small” fires outside the burned-area maps based on active fire detections (Randerson et al., 2012). The gridded fire emission dataset has a spatial resolution of 0.25∘×0.25∘ and is available for every month from July 1997. To compute anthropogenic ignition and suppression effects (see Sect. 2.3), we use a downscaled population density dataset from Gao (2017, 2020). Monthly sea surface temperature (SST) and sea ice concentration (SIC) obtained from the Hadley Centre Sea Ice and Sea Surface Temperature (HadISST) dataset (Rayner et al., 2003) are used as the boundary conditions for the climate model.

The chemistry–climate–vegetation model ModelE2-YIBs is used to simulate the two-way coupling between fire aerosols and climate systems. The ModelE2-YIBs is composed of the NASA Goddard Institute for Space Studies (GISS) ModelE2 (Schmidt et al., 2014) model and the Yale Interactive terrestrial Biosphere Model (YIBs) (Yue and Unger, 2015). GISS ModelE2 is a global climate–chemistry model with a horizontal resolution of 2∘×2.5∘ latitude by longitude and 40 vertical layers extending to the stratosphere (0.1 hPa). The dynamics and physics codes are executed every 30 min, and the radiation code is calculated every 2.5 h.

The gas phase chemistry scheme considers 156 chemical reactions among 51 species, including NOx–HOx–Ox–CO–CH4 chemistry and different species of volatile organic compounds. Aerosol species in ModelE2 include sulfate, nitrate, ammonium, sea salt, dust, BC, and organic carbon (OC), which are interactively calculated and tracked for both mass and number concentrations. Heterogeneous chemistry on dust surfaces and NOx-dependent secondary organic aerosol production from isoprene and terpenes is included in the model (Bauer et al., 2007b; Tsigaridis and Kanakidou, 2007). The thermodynamic gas–aerosol equilibrium module is used to calculate the phase partitioning of the H2SO4/HSO4-/SO42-–HNO3/NO3-–NH3/NH4+ –HCl/Cl-–Na+–Ca2+–Mg2+–K+–H2O system (Metzger et al., 2006; Bauer et al., 2007a). The aerosol microphysical scheme is based on the quadrature method of moments, which incorporates nucleation, gas particle mass transfer, new particle formation, particle emissions, aerosol phase chemistry, condensational growth, and coagulation (Bauer et al., 2008). The residence time of aerosol species varies greatly in space and time due to different removal rates. Turbulent dry deposition is determined by a resistance-in-series scheme, which is closely coupled to the boundary layer scheme and implemented between the surface layer (10 m) and the ground (Koch et al., 2006). The wet deposition consists of several processes including scavenging within and below clouds, evaporation of falling rainout, transportation along convective plumes, and detrainment and evaporation from convective plumes (Koch et al., 2006; Shindell et al., 2006).

In ModelE2, gases can be converted to aerosols through chemical reactions, while aerosols affect photolysis and provide reaction surface for gases. For example, the formation of sulfate aerosols is driven by modeled oxidants (Bell et al., 2005), and the chemical production of nitrate aerosols is dependent on nitric acid and gaseous ammonia (Bauer et al., 2007b). Moreover, the disturbances of aerosols on climate systems via direct, indirect, and albedo effects are considered in ModelE2. Aerosol optical parameters are calculated by the Mie scattering theory using a complex refractive index depending on chemical speciation and particle size. The first AIE is estimated by the prognostic treatment of cloud droplet number concentration, which is a function of species-dependent contact nucleation, auto-conversion, and immersion freezing (Menon et al., 2008, 2010). The AAE of BC is considered by estimating the decline in surface albedo as a function of aerosol concentrations at the top layer of snow or ice (Koch and Hansen, 2005). We note that average BC deposition to snow estimated by measurement-based average scavenging ratios is used as a climatological proxy to the physical process of BC deposition (Hansen and Nazarenko, 2004). The latter involves size-resolved and meteorologically dependent BC deposition fluxes, as would be found in a chemical transport model but is not used here due to computational constraints. More detailed descriptions of ModelE2 can be found in Schmidt et al. (2014). It has been extensively evaluated for meteorological and chemical variables against observations, reanalysis products, and other models and widely used for studies of climate systems, atmospheric components, and their interactions (Schmidt et al., 2014).

YIBs is a process-based vegetation model that dynamically simulates tree growth and terrestrial carbon fluxes with prescribed fractions of nine plant functional types (PFTs), including deciduous broadleaf forest, evergreen needleleaf forest, evergreen broadleaf forest, tundra, shrubland, C3/C4 grassland, and C3/C4 cropland. Essential biological processes such as photosynthesis, phenology, and autotrophic and heterotrophic respiration are considered and parameterized using the state-of-the-art schemes (Yue and Unger, 2015). Dynamic daily leaf area index (LAI) is estimated based on carbon allocation which is updated every 10 d and prognostic phenology which is dependent instantaneously on temperature and drought conditions. Simulated tree height, phenology, gross primary productivity, and LAI agree well with site-level observations and/or satellite retrievals (Yue and Unger, 2015). The YIBs model joined the dynamic global vegetation model inter-comparison project TRENDY and showed reasonable performance of carbon fluxes against available observations (Friedlingstein et al., 2020). In the coupled model, ModelE2 provides meteorological drivers to YIBs, which feeds back to alter land surface water and energy fluxes through changes in stomatal conductance, surface albedo, and LAI. By incorporating YIBs into ModelE2, the new coupled model ModelE2-YIBs can simulate interactions between terrestrial ecosystems and climate systems through the exchange of water and energy fluxes and chemical components (Yue and Unger, 2015; Yue et al., 2017).

We implemented the active global fire parameterization from Pechony and Shindell (2009) into the ModelE2-YIBs model. The parameterization considers key fire-related processes including fuel flammability, lightning and human ignitions, and human suppressions. Flammability is a unitless metric indicating conditions favorable for fire occurrence and is calculated using the vapor pressure deficit (VPD, hPa), precipitation (R, mmd-1), and LAI (m2m-2) as follows: 1Flam=VPD×LAI×e-CR×R, where LAI represents vegetation density and is dynamically calculated by YIBs model. CR is a constant set to 2. VPD is a vital indicator of flammability conditions: 2VPD=es×1-RH100, where es is the saturation vapor pressure and RH is surface relative humidity. es can be calculated by the Goff–Gratch equation: 3es=est×10Z, where est is 1013.246 hPa and 4Z=a×TsT-1+b×log⁡TsT+c×(10d1-TsT-1)+f×(10hTsT-1-1), where a, b, c, d, f, and h are constants set to -7.90298, 5.02808, -1.3816×10-7, 11.344, 8.1328×10-3, and -3.49149, respectively. Ts is the boiling point of water and equal to 373.16 K. VPD and LAI in Eq. (1) are calculated in half-hourly and daily time steps, respectively, while 30 d running average precipitation is employed to avoid unrealistically huge flammability fluctuations. It should be noted that the response of flammability to abovementioned factors may not be instantaneous but may occur over time. For example, a reduction in precipitation in one season at a given location may reduce foliage growth and hence reduce the fuel available for combustion in another season.

The natural and anthropogenic ignition rates determine whether the fire can actually occur. If the ignition rate is zero, the resulting fire emissions will be zero, regardless of flammability. The natural ignition rate IN depends on the cloud-to-ground lightning (CoGL) strike rate, which is simulated by ModelE2 following the parameterization of Price and Rind (1994): 5IN=CoGL=3.44×10-5×H4.9over land6.4×10-4×H1.73over ocean, where H is the cloud depth (unit: km).

Humans influence fire activity by adding ignition sources and suppressing fire events, the rates of which increase with population and to some extent counteract each other. The anthropogenic ignition rate IA (numberkm-2permonth) is calculated as follows (Venevsky et al., 2002): 6IA=k(PD)×PD×α, where PD is population density (numberkm-2). k(PD)=6.8×PD-0.6 stands for ignition potentials of human activity, assuming that people in scarcely populated areas interact more with the natural ecosystems and therefore produce more ignition potential. α is the number of potential ignitions per person per month and set to 0.03.

In principle, the successful suppression of fires is dependent on early detection. It is reasonably assumed that fires are detected earlier and suppressed more effectively in highly populated areas. Therefore, the fraction of non-suppressed fires FNS can be expressed as 7FNS=c1+c2×exp⁡(-ω×PD), where c1, c2, and ω are constants and set to 0.05, 0.95, and 0.05, respectively. The selection of constant values in Eq. (7) is done in a heuristic way, due to lack of quantified data globally. It assumes that up to 95 % of fires are suppressed in the densely populated regions but that only 5 % are suppressed in unpopulated areas.

With the calculation of flammability (Flam), ignition (IN and IA), and non-suppression (FNS), the fire count density Nfire (unit: numberkm-2) at a specific time step can be derived as 8Nfire=Flam×(IN+IA)×FNS.

Finally, fire emissions of trace gases and particulate matters (FireEmis) are calculated as 9FireEmis=Nfire×EF, where EF is the PFT-specific emission factor of an air pollutant such as BC, OC, NOx, NH3, SO2, CO, alkenes, and paraffin. For each species, simulated gridded emissions are grouped by the dominant PFT and compared to annual total emissions from GFED4.1s over the same grids. The EF is then calibrated to minimize the root-mean-square error between the simulated and GFED data for all land grids. Such calibration adjusts only the global total amount of fire emissions without changing the spatiotemporal pattern predicted by the parameterization. The EF is the intrinsic attribution of wildfire emissions that should not vary greatly with climatic conditions. The fire-emitted minerals or dust-like materials are not implemented in the current model, given that these species are not included in the current version of GFED4.1s.

Compared to fire indexes, such as the Canadian Forest Fire Weather Index system (Wagner, 1987), this fire parameterization shows advantages in integrating the effects of meteorology, vegetation, natural ignition, and human activities (both ignition and suppression) on fires. Furthermore, it is physically straightforward and has been validated based on global observations (Pechony and Shindell, 2009; Hantson et al., 2020). In ModelE2-YIBs, fire emissions are affected by environmental factors following above parameterizations. In turn, the radiative effects of fire-emitted aerosols feed back to affect those climatic and ecological factors. Note that the changes in the environmental factors may result in changes to fire emissions later. We consider only the fire emissions at the surface due to the large uncertainties in depicting fire plume height (Sofiev et al., 2012; Ke et al., 2021). The fire emissions include both primary aerosols and trace gases, the latter of which react with other species to form the secondary aerosols. These particles could be transported across the globe by three-dimensional atmospheric circulation and eventually removed through either dry or wet deposition.

We perform four groups of sensitivity experiments (Table 1) with the ModelE2-YIBs model to quantify the fire–climate interactions through different radiative processes. The first group with the suffix “AD” considers only the ADE. The second (third) group with the suffix “AD_AI” (“AD_AA”) considers both ADE and AIE (ADE and AAE). The fourth group with the suffix “AD_AI_AA” includes all three aerosol radiative effects (ADE, AIE, and AAE). Within each group, two runs are performed with (YF) or without (NF) fire emissions. For YF simulations, fire-induced aerosols including primarily emitted and secondarily formed are dynamically calculated based on fire parameterization (see Sect. 2.3) and atmospheric transport. These fire emissions cause radiative perturbations and the consequent fast atmospheric adjustments, which feed back to influence fire emissions. For NF simulations, fire emissions are calculated offline at each step without perturbing the climate system, which can be considered to mean that there is no fire emission. By comparing the climatic variables from the YF and NF runs in the first group, we isolate the impacts of fire aerosols on climate through ADE. By comparing the climatic effects from the first and second (third) groups, we isolate the AIE (AAE) of fire aerosols. By comparing the climatic variables from YF and NF runs in the fourth group, the overall effect (ADE + AIE + AAE) is obtained. Besides, the differences in fire emissions between simulations of “YF_AD_AI_AA” and “NF_AD_AI_AA” represent the feedback of fire-aerosol-induced environmental perturbations. Note that fire-emitted gas phase species also perturb radiation via atmospheric absorption and/or feedback from rapid adjustment; these perturbations are far less than aerosol forcing and could be ignored.

For each simulation, climatological mean CO2 concentrations, SST and SIC, and population density during 1995–2005 are used as boundary conditions to drive the model. Such a configuration ignores the year-to-year variability in climate systems, which may cause significant changes in annual fire emissions (Burton et al., 2020). Each simulation is integrated for 25 years with the first 5 years spinning up and the last 20 years averaged. A two-tailed Student's t test is performed to assess 90 % confidence levels of the predicted radiative and climatic responses (p<0.1). The global mean or sum value is depicted in the form of the mean value ± standard deviation. In this study, downward (upward) radiative/heat fluxes are defined as positive (negative). Given that the model is driven by prescribed SST and SIC, only the rapid adjustments of atmospheric variables are taken into account, and we mainly focus on climate changes over the land grid. The radiative effect simulated with such a model configuration is termed the effective radiative forcing (ERF) (IPCC, 2014).

Simulated fire emissions of BC and OC show hotspots in the tropics, such as the Amazon, the Sahel, central Africa, and Southeast Asia (Fig. S1 in the Supplement). The large tropical fire emissions are related to abundant vegetation and/or distinct dry seasons. Compared to GFED4.1s data, ModelE2-YIBs slightly underestimates boreal fire emissions especially over northern Asia and North America. On the global scale, fire releases 1.85 ± 0.01 TgCyr-1 (1Tg=1012 g) of BC and 16.8 ± 0.92 TgCyr-1 of OC in ModelE2-YIBs, close to the 1.86 TgCyr-1 of BC and 16.4 TgCyr-1 of OC estimated by GFED4.1s. In general, ModelE2-YIBs reasonably captures the spatial distribution of fire emissions, with high spatial correlations of 0.67 (p<0.01) for BC and 0.58 (p<0.01) for OC and low normalized mean biases of 0.6 % for BC and 2.4 % for OC against satellite-based observations.

Figure S2 in the Supplement shows the fire-induced changes in aerosol optical depth (AOD) at 550 nm. Fire emissions largely enhance surface aerosols especially over tropical regions. Hotspots are located in southern Africa and South America with regional enhancement larger than 0.05. In addition, large enhancement is also found at boreal high latitudes (>0.01). At the global scale, fires enhance AOD by 0.006 ± 0.001 with 0.010 ± 0.001 over land.

Fire aerosols cause large perturbations in net radiation at the top of the atmosphere (TOA). Globally, the net radiation at TOA decreases by 0.565 ± 0.166 Wm-2 for fire aerosols (Fig. 1a). Regionally, negative changes are predicted over central Africa, western South America, western North America, and the boreal high latitudes. Diagnosis shows that fire-induced AIE dominates the reduction in TOA flux with a global value of -0.440 ± 0.264 Wm-2 (Fig. 1c), accounting for 78 % of the total TOA radiative effect by fire aerosols. The spatial correlation coefficient is 0.62 over land grids between the perturbations by all aerosol effects and that by AIE alone. Compared to AIE, the changes in TOA radiative fluxes are much smaller for fire ADE (-0.058 ± 0.213 Wm-2, Fig. 1b) and AAE (-0.016 ± 0.283 Wm-2, Fig. 1d) with limited perturbations on land.

Fire aerosols decrease net shortwave radiation reaching the surface up to 9 Wm-2 in central Africa and 7 Wm-2 in Amazon (Fig. 2a), where biomass-burning emissions are most intense (Fig. S1). Such a pattern is in general consistent with the changes in TOA fluxes (Fig. 1a), leading to an average reduction of -1.227 ± 0.216 Wm-2 in the shortwave radiation over global land. The fire-induced ADE alone reduces land surface shortwave radiation by 0.654 ± 0.353 Wm-2 with the maximum center in the Amazon (Fig. S3a in the Supplement). As a comparison, the fire-induced AIE causes a smaller reduction of -0.553 ± 0.518 Wm-2 with the hotspot in central Africa (Fig. S3c). The net effect of AAE (0.263 ± 0.551 Wm-2) by fire aerosols is positive mainly because fire AAE reduces surface albedo and increases shortwave radiation over the Tibetan Plateau and boreal high latitudes (Fig. S3e). However, the magnitude of AAE is much smaller compared to that of ADE and AIE.

Changes in surface longwave radiation (Fig. 2b) are much smaller than those in shortwave radiation (Fig. 2a). Regionally, positive changes are predicted in the western US, eastern Amazon, and South Africa, where fire-induced surface cooling (Fig. 3a) decreases the upward longwave radiation. On the global scale, fire aerosols cause a decrease of 0.281 ± 0.371 Wm-2 in surface upward longwave radiation. As a result, fire aerosols induce a net atmospheric absorption of 0.191 ± 0.227 Wm-2 over land grids (Fig. 2c). The reductions in surface shortwave radiation are largely balanced by changes in heat fluxes at the surface, which shows an average decrease of 0.826 ± 0.311 Wm-2 in the upward fluxes over land grids (Fig. 2d). Fire ADE and AIE lead to reductions of 0.503 ± 0.289 and 0.432 ± 0.411 Wm-2 in surface upward heat fluxes, respectively (Fig. S3b and d). Changes in sensible heat account for 82.2 % of the changes in total heat reduction, much higher than the contributions of 17.8 % by latent heat fluxes (Fig. S4 in the Supplement). Regionally, the upward sensible heat decreases in the western US and Amazon mainly due to fire ADE, while the upward latent heat decreases in central Africa mainly by fire AIE (Fig. S5 in the Supplement).

In response to the perturbations in radiative fluxes, land TAS decreases by 0.061 ± 0.165 ∘C globally for fire aerosols (Fig. 3a). Such cooling is mainly located in the western US, the Amazon, and boreal Asia, following the large reductions in shortwave radiation (Fig. 2a). Meanwhile, moderate warming is predicted at the high latitudes of both hemispheres especially over the areas covered with land ice such as Greenland and Antarctica. Sensitivity experiments show that both ADE (Fig. 4a) and AIE (Fig. 4c) of fire aerosols result in net cooling globally, with regional reductions in TAS over boreal Asia and North America. In contrast, the fire AAE causes increases in TAS over boreal Asia and North America (Fig. 4e), where the deposition of BC aerosols reduces surface albedo. Consequently, the fire AAE results in a global warming of 0.054 ± 0.163 ∘C, which in part offsets the cooling effects by the ADE and AIE of fire aerosols.

Meanwhile, global land precipitation decreases by 0.180 ± 0.966 mmpermonth (1.78 % ± 9.56 %) with great spatial heterogeneity (Fig. 3b). Decreased precipitation is predicted over central Africa, boreal North America, and eastern Siberia. In contrast, increased rainfall is predicted in the western US, the eastern Amazon, and northern Asia. The reduction in precipitation is mainly contributed by fire AIE, which reduces cloud droplet size and inhibits local rainfall in central Africa (Fig. 4d). Consequently, latent heat fluxes are reduced to compensate the rainfall deficit in central Africa (Fig. S4b).

The fire-aerosol-induced fast response in precipitation, VPD, lightning, and LAI can feed back to affect fire emissions. However, these changes may have contrasting impacts on fire activities. For example, the aerosol-induced reduction in precipitation in central Africa (Fig. 3b) increases local VPD (Fig. 5a) and consequently causes more fire emissions. Meanwhile, such an enhanced drought condition inhibits plant growth and decreases local LAI (Fig. 5c), which has negative impacts on fire emissions by reducing fuel density. Furthermore, the fire AIE inhibits the development of convective clouds, which limits cloud height and the number of cloud-to-ground lightning strikes in central Africa (Fig. 5b), leading to reduced ignition sources and fire emissions.

To illustrate the joint impacts of fire-aerosol-induced fast climate responses, we count the number out of the four factors contributing positive effects to fire emissions over land grids (Fig. 5d). The larger (smaller) number indicates a higher possibility of increasing (decreasing) fire emissions. Most areas show a neutral number of 2, indicating offsetting effects of the changes in fire-prone factors. Only 13.5 % of land grids show numbers higher than 2 with a sparse distribution. In contrast, 32.1 % of land grids show numbers smaller than 2, especially for the grids over Siberia and the western US where the increased rainfall (Fig. 3b) and decreased VPD (Fig. 5a) inhibit fire emissions. Furthermore, the regional reductions in lightning ignition or LAI promote the inhibition effects. As a result, fire emissions in YF_AD_AI_AA slightly decrease by 31.0 ± 35.9 Ggyr-1 (1.7 %) for BC and 493.6 ± 566.8 Ggyr-1 (2.9 %) for OC compared to NF_AD_AI_AA in which fire emissions do not perturb climate (Fig. 6).