For this study a simplified version of the GFED model was used. GFED is rooted in the Carnegie–Ames–Stanford approach (CASA) biosphere model, which was developed to simulate the terrestrial carbon cycle, using satellite data to constrain carbon uptake and other fluxes (Field et al., 1995; Potter et al., 1993). Van der Werf et al. (2003) extended this model to include fire processes and provided spatially resolved estimates of fire emissions for the (sub)tropics. Over time, further modifications were made to GFED, including improved burned area identification (Giglio et al., 2006, 2013) and a distinction between different sources of fire emissions on a global scale (van der Werf et al., 2006, 2010). The most recent version, GFED4s, also aims to account for relatively small fires that remain undetected by most burned area algorithms (Randerson et al., 2012; van der Werf et al., 2017). These small fires add about 15 % burned area to our study area in Africa. Recent research suggests this increase in burned area may be conservative (Roteta et al., 2019). For this study we have simplified the GFED model so it can be run at 500 m resolution on a continental scale; as compared to the 0.25∘ resolution of GFED4s running on a global scale. Only the main GFED functionality relevant for aboveground dynamics in biomass, litter, and fire emissions was maintained. More refined mechanisms represented in GFED, such as belowground dynamics, herbivory, grazing, and fuelwood collection, were not implemented. Furthermore, no specific deforestation mechanisms were modelled. These simplifications not only made required computational resources manageable, but also made it easier to disentangle mechanisms that cause differences between the model runs at different resolutions, which was our key objective.

The model has a pool-based structure wherein net primary productivity (NPP) is partitioned over various biomass pools that are affected by losses due to turnover and fire processes. Aboveground biomass (AGB) and belowground biomass (BGB) are considered as the live part of the total available carbon above and below the ground, and the total aboveground live and dead carbon is referred to as aboveground biomass and litter (AGBL), all expressed in mass of carbon per unit area (g C m-2). NPP was calculated as the product of incoming solar radiation (SSR), the fraction of photosynthetically active radiation (fPAR) and a biome-specific light-use efficiency (LUE; εbiome): 1NPP(x,t)=SSR(x,t)⋅fPAR(x,t)⋅εbiome, where x is the grid location coordinate and t is the time in months. NPP was distributed over tree and non-tree vegetation classes by multiplication with fractions of tree and non-tree vegetation cover and further distributed in equal parts over the corresponding biomass pools. Trees were represented as leaf, stem, and root pools, all receiving one-third of tree-allocated NPP. Non-tree vegetation was represented as grass and root pools, both receiving half of non-tree-allocated NPP. In this simplified categorization other non-tree vegetation types, such as shrubs, are part of the grass pool. For trees the root pool was subdivided into separate fine- and coarse-root pools, with 20 % of the stem NPP allocated to the coarse roots, whereas for non-tree vegetation all root biomass consisted of fine roots. We used biome-specific LUE values based on those reported by Field et al. (1995). Since LUE was not reported for the savanna biome, we used the open-shrubland value of 0.208 g C MJ-1 for open savannas and an empirically determined value of 0.280 g C MJ-1 for woody savannas (see also Table 1). The LUE value for woody savannas was chosen to be between values reported for forest and grassland biomes.

When the model reaches its equilibrium state after the spin-up phase, the carbon input from NPP is balanced by the carbon output via fires and respiration because of decomposition. Depending on pool-specific turnover rates and fire processes, biomass decays into three litter pools: fine litter, coarse woody debris (cwd), and soil organic matter. The pool-specific turnover rates, loosely based on those used in GFED4 (van der Werf et al., 2017), were optimized to biome-specific values in a series of model validation steps (see Sect. 2.3, Model optimization). The vegetation exposed to fire is either combusted and emitted as carbon directly, killed and converted to litter, or unaffected by the fire. The amount of biomass and litter exposed to fire was calculated by multiplication of the available flammable carbon and the burned fraction for each pixel: 2C(x,t)=∑No. of poolsAGBLpoolx,t⋅Mtree(FTC)⋅CCpoolεSM(x,t)⋅BAx,t⋅fc, where C is the amount of carbon combusted and released to the atmosphere, Mtree is a fire-induced tree mortality scalar, CC is the combustion completeness, BA is the burned area, i.e. the fraction of pixel burned, and fc is the fraction of carbon in fuel, for which we used 50 %. The part of fire-exposed carbon that is combusted was determined by pool-specific combustion completeness values that were scaled linearly between a predefined minimum and maximum value (see Table 1 in van der Werf et al., 2010) dependent on an empirically defined soil moisture scalar. This scalar was defined as 3εSM(x,t)=SMx,t0.37-0.40.6with0.1<εSM<1.0, where SM is the volumetric soil water content in units of volume fraction. The scalar was obtained by first standardizing the SM values to a range between 0 and 1 and then dividing by 0.6 and capping at 1 to remove anomalously high values related to wetlands. Additionally, the scalar values were capped to not be lower than 0.1, simulating a minimum soil moisture level below which moisture-dependent processes are not further affected. Dry conditions result in CC values closer to the maximum and vice versa for wet conditions. A mortality scalar for woody vegetation simulated whether trees exposed to fire are killed, and consequently directly combusted, or left as litter (van der Werf et al., 2003). This scalar was expressed as the squared fraction of tree cover to total vegetation to resemble the range from low fire-induced mortality in open landscapes (where trees are adapted to fire) to high mortality in dense tropical forests where trees are not adapted. When a tree is killed, all of the unburned aboveground and belowground biomass is transferred to the litter pools. More specifically, leaves and grass become fine litter, dead stems are added to the cwd pool, and dead roots are added to the soil pool.

The decomposition of litter is dependent on temperature and moisture conditions. The rate of decomposition was based on pool-specific turnover rates (Table 1) and scaled by an abiotic scalar. The abiotic scalar (εA) was defined as 4εA=εT⋅εSM0.9with0.1<εA<1.0, where εT is the temperature scalar: 5εT=Q10T-3010withεT>1.0=1.0, where T is the temperature in ∘C and Q10 is the temperature coefficient, for which we used a value of 1.5 and a capped maximum of 1.0 at 30 ∘C, similar to van der Werf et al. (2013). A Q10 value of 1.5 implies a 50 % increase for every 10 ∘C rise in temperature. Just like the moisture scalar, the abiotic scalar was standardized to a range from 0 to 1 and capped at a minimum of 0.1. Part of the turnover-exposed carbon is respired directly, based on a respiration fraction of 0.5. The remaining part degrades consecutively through the cwd (only originating from trees), fine litter, and soil pools and finally enters the slow decomposition stage. Every degradation step is again subject to direct respiration. The belowground organic matter algorithm was simplified compared to GFED because the belowground dynamics are not relevant for fire dynamics in our study area; fires generally do not occur in wetlands and peatlands in Africa. The LUE values and turnover rates used for the biomass and litter pools for each biome are summarized in Table 1. This table also gives the average effective turnover rates for the litter and cwd pools after application of the abiotic scalar.

The model used MODIS (MODerate resolution Imaging Spectroradiometer) Collection 6 satellite observation products with a 500 m spatial resolution as input where available and previous MODIS collections or coarser non-MODIS datasets otherwise (see Table 2). The meteorological input parameters were based on 0.25∘ resolution ERA-Interim reanalysis data (Dee et al., 2011) from the European Centre for Medium Range Weather Forecasts (ECMWF). The datasets used cover the time period from 2002 to 2017, unless noted otherwise. The MODIS MCD15A2H product of fraction photosynthetically active radiation (fPAR; Myneni et al., 2015) was used in combination with reanalysis SSR (Dee et al., 2011) to calculate NPP (see Eq. 1). The distribution of biomass over tree and non-tree vegetation classes was based on the MODIS MOD44B vegetation continuous fields (VCF; Dimiceli et al., 2015) product for the fractions of tree cover (FTC) and non-tree vegetation cover (NTV). Fire extent was based on BA from the MODIS MCD64A1 dataset (Giglio et al., 2018). The decomposition of litter was based on temperature and soil moisture scalars derived from ERA-Interim reanalysis air temperature (2 m temperature) and soil moisture (volumetric soil water layer 1) data. We delineated biomes in terms of land cover types based on the MODIS MCD12Q1 land cover type product, collection 5.1 (Friedl et al., 2010). The last available year of data for this product, 2013, was also used for subsequent years. For this study, the Land Cover Type 2 classification scheme produced by the University of Maryland (UMD) was used.

The 500 m resolution MODIS input datasets were spatially aggregated to 0.050∘, 0.125∘, and 0.250∘ resolution using average-based aggregation. As an exception, the qualitative land cover type data were aggregated using majority-based aggregation by assigning the most frequently occurring land cover class to the aggregate grid cell. The 0.25∘ resolution reanalysis data were resampled to 500 m resolution by nearest-neighbour interpolation, i.e. by using the reanalysis 0.25∘ grid cell value nearest to each MODIS pixel. All MODIS data with sub-monthly temporal resolution were averaged to monthly resolution, using the number of days in the month as weights.

We tuned our model to match satellite-based data on aboveground woody biomass (AGBw) (Avitabile et al., 2016) and field measurements of fuel load and consumption (van Leeuwen et al., 2014). Since NPP is the driver for biomass growth, we first ensured that biome-level NPP corresponded to GFED4 (van der Werf et al., 2017). Then, the AGBw was optimized to agree with observation-based gridded estimates by Avitabile et al. (2016) by tuning the turnover rates per biome. As a first-order approximation we tuned AGBw with the stem turnover rate, since the stems of trees hold at least 95 % of the total AGB for all forest biomes (Poorter et al., 2012). Herbaceous (i.e. non-tree) biomass is typically below 250 g C m-2 and therefore within the uncertainty range of the dataset by Avitabile et al. (2016). After optimization of the stem biomass, the turnover rates of the leaf, grass, and root pools were adjusted to attain root : stem : leaf biomass ratios (i.e. root : shoot ratios) in line with the biome-specific ratios as reported by Poorter et al. (2012). The previously described subdivision of root biomass into separate coarse- and fine-root pools was used to improve root : shoot ratios. The chosen turnover rates also influence the amount of litter produced. Even though the amount of tree biomass is not always relevant for fires, since most African fires are ground fires and deforestation mechanisms are not specifically part of the model, it does determine the amount of cwd and part of the fine litter produced.

In the final validation step, modelled FL and FC were compared to the compilation of field measured values by van Leeuwen et al. (2014). For the African continent the database contained 16 measurement records that reported FL and FC, of which 9 are grouped into different fuel classes (e.g. grass, leaves, litter, cwd). Additional field studies compiled by Scholes et al. (2011) on FL in African savannas were included in the comparison, giving 73 measurements on total FL. For all field records used, measured FL consists of grass, litter, cwd, and occasionally leaves. As a consequence, the total FL estimates reported in our comparison to the measurements involved a variable number of model pools, dependent on what fuel classes were measured in the corresponding field study. Our definition of FL does not include the stem fuel class (and thus is not the same as AGBL) as this class was not reported in any field record used, which all consider ground fires in grass-dominated biomes where trees are generally not affected. The field measurements were collocated with model results based on the field plot coordinates. The modelled FL was optimized for each biome separately by tuning turnover rates of the grass and litter pools to match measured average FL and spread in measurements. The root : shoot ratios were not significantly affected by this parameter tuning. Due to the lack of sufficient field data on FC (16 records, at only 6 unique locations), we validated FC only using the average of all records over all biomes.

All field measurements in the database were taken in savanna-type biomes, and all except one (in Burkina Faso) were taken in southeast Africa (south of 12∘ S and east of 23∘ E), resulting in the sample set being less representative of other biomes and regions in Africa. Furthermore, the majority of records did not report separate measurements of specific fuel classes and thus only provided an overall fuel load value for the combined fuel classes. As a result, the model validation was restricted to a comparison of total reported FL and FC. The validation of individual fuel classes was also complicated by the large spatial variability in biomass allocation to fuel classes for field plots with similar properties and because field conditions that determine the allocation ratios were unknown for most records (such as last fire occurrence, slash-and-burn or not, early or late season fires).

For most field records, the field plot coordinates were given with a precision of 2 decimal degrees. This yields an uncertainty of about 1 km, which is larger than the model pixel size of 500 m. Therefore, more accurate coordinates with 4 decimal degrees precision were hand-picked based on the field site descriptions using Google Earth. Where possible, homogeneously vegetated areas were picked to remove the influence of other land cover types at a sub-500 m scale. For some field records the coordinates of a settlement or city nearby the field plot were reported instead of the actual plot, in which case again a neighbouring pixel was chosen or the actual field plot was retraced in the vicinity of the reported coordinates. Many of the reported measurements were conducted before our study period, in which case the first model year, 2002, was used. For studies where only the year of measurement was known, the month in the middle of the regional fire season of the pixel was used. Finally, if there were recent burned area and related drops in biomass in a pixel, indicative of the influence of recent fires, a neighbouring unburned pixel was chosen.

We ran our model at 500 m native MCD64A1 resolution for the 2002–2017 period, with a monthly temporal resolution.

A 200-year spin-up was done based on the 2002–2006 climatology in order to stabilize the model pools and match total carbon in- and outflow. Additional simulations were performed for the three aggregated resolutions (0.050, 0.125, 0.250∘) to study the effect of spatial resolution on modelled biomass, litter, and emissions. We restricted our analysis to the African continent, in particular to the Northern Hemisphere Africa (NHAF) and Southern Hemisphere Africa (SHAF) regions as defined in GFED (van der Werf et al., 2006). These two regions contain the African continent south of 23∘ N latitude and will be referred to as sub-Saharan Africa.

We calculated the differences that occur in modelled AGBL and fire emissions due to running the model at different spatial resolutions. We considered two categories of differences: those that occur as part of the model calibration and those that occur as part of the model simulation. The model calibration is dependent on resolution because it includes parameter tuning to match model pixels with field measurements, which is subject to a representation error. This error exists due to the scale mismatch in comparing field measurements to model grid cell averages (Janjić et al., 2018). At coarser resolution, the error is larger and as a consequence the model calibration is more biased. This leads to different model results at different resolutions, due to resolution-dependent model settings. We will refer to the differences between aggregated and 500 m resolution model results due to different model calibration as calibration differences. Besides calibration-related differences, differences in the model simulation result from the spatial aggregation of input datasets and the subsequent coarse computation of the model algorithm. We will refer to the related differences in model results between aggregated and 500 m resolution as simulation differences. We define simulation difference as the difference that occurs when running identical models with the exact same calibration but at different spatial resolutions.

The modelled total AGBw for Africa was 40.2 Pg C, compared to 40.6 Pg C for the Avitabile et al. (2016) reference dataset. Area-averaged values corresponded well, and the model was able to capture most of the spread in values (Fig. 1). This was as expected, since the model was calibrated to match the reference dataset. On a biome level, AGBw for tropical forest was 31.2 Pg C, which was 1.4 Pg C lower than the reference dataset. For woody and open savannas AGBw was 6.9 and 1.1 Pg C, respectively. Open savannas were slightly overestimated by 0.1 Pg C. The tropical forest, woody savanna, and open-savanna biomes contained the vast majority of tree biomass in Africa. Even though area-averaged AGBw for other forest types was significant, these biomes together constituted only 0.6 % of African land surface and did not contribute significantly to total AGBw.

The comparison between modelled FL and field measurements based on the 500 m model calibration is shown in Fig. 2a. A robust agreement was found, with an r value of 0.78 (r2=0.60). The model tended to overestimate low FL and underestimate high FL. Overall, the average, median, and spread over all field sites agreed well between modelled and measured values (Fig. 2b). On average, FL for woody savanna and grassland was overestimated by approximately 15 % (46 and 28 g C m-2, respectively), whereas for shrubland values were underestimated by 11 % (20 g C m-2). Model estimates for open savannas agreed well with measurements, even though the range of values was underestimated for this biome. The shrubland and grassland statistics were both based on only four or five field measurements, which explains the large differences in quantiles and restricted the analysis to a comparison of averages and ranges.

Figure 2c and d shows the same comparison to field measurements, but simulated at 0.25∘ resolution. As in Fig. 2a and b, this comparison was based on the 500 m resolution calibration and thus only differed in simulation resolution. Compared to the 500 m resolution simulation, FL modelled at 0.25∘ resolution had a much lower range and was substantially underestimated in most biomes except grasslands. The flat regression slope indicates that the spread in measured FL was not captured at coarse resolution. This was partly because several FL measurements were within one 0.25∘ grid cell and thus yielded the same model value. The 0.25∘ simulation showed large estimation errors, especially for high FL measurements. One woody savanna measurement was incorrectly classified as tropical forest, leading to a large overestimation of FL (Fig. 2d, black arrows).

The 2002–2017 annually averaged total fire emissions for sub-Saharan Africa were 0.68 Pg C yr-1 based on the 500 m model, with an average FC of 249 g C m-2 burned (Fig. 3, solid blue). The spatial distribution of emissions was dictated by burned area (Fig. 4). The majority of emissions occurred in the subtropical savanna regions. About 90 % of the fire emissions (0.61 Pg C yr-1) originated from the woody and open-savanna regions, where the majority (87 %) of the annually averaged burned area was found. The highest FC was found in the tropical forest, where the average was 998 g C m-2 burned. However, the burned area was relatively low in this biome, resulting in low emissions.

These 500 m emission estimates for sub-Saharan Africa were 24 % lower than GFED4 (without small fires), which estimated 0.90 Pg C yr-1 and an average FC of 331 g C m-2 burned (Fig. 3). All biomes with substantial emissions contributed to this difference, but woody savannas were the biggest contributor. The lower emissions in our model were the direct result of differences in FC compared to GFED4 because the amount of BA of the two estimates was identical. The spatial distribution of FC was less variable for most biomes in our model, except for the forest-dominated biomes. The variability of FC across biomes in the model was represented in a similar way as GFED4.

The parameters used for the 0.25∘ resolution model calibration differed from the 500 m calibration in terms of slower turnover rates for the stem, grass, and litter pools for some biomes (Table 1). This resulted in roughly a 2.5 Pg C increase in AGBw and a 3.0 Pg C increase in AGBL. The majority of this increase was accounted for by the savanna biomes (both open and woody). Comparatively, non-woody AGB and litter increased more than woody AGB. Figure 5 shows the resulting modelled FL compared to field measurements – equivalent to Fig. 2, but for the 0.25∘ instead of the 500 m resolution model calibration. For this coarse calibration, again simulations for both 500 m (panel a and b) and 0.25∘ resolution (panel c and d) are shown.

By calibrating the model at 0.25∘ resolution, the FL simulated at 0.25∘ resolution agreed better with measurements for all biomes (compare Figs. 2c, d and 5c, d). On the other hand, with this coarse calibration, the 500 m resolution simulation significantly overestimated FL and performed more poorly than the 0.25∘ resolution simulation in terms of biome average and distribution (Fig. 5a and b). An exception was the shrubland biome, for which all 0.25∘ model pixels respective to the field sites were strongly influenced by low-biomass areas in that pixel. This resulted in a consistent underestimation of FL for both calibration resolutions. For the 0.25∘ calibration, the 500 m resolution simulation still showed much better correlation with measurements (r2=0.57), compared to the coarser simulation (r2=0.07). The 0.25∘ calibration led to a regression slope that was steeper and closer to 1 for both resolutions, as high FL was amplified relative to low FL.

The increase in biomass and litter when using the 0.25∘ calibration led to higher emissions; 0.82 Pg C for both resolutions (Fig. 3, transparent bars). As expected, this was much closer to the estimate of 0.90 Pg C from GFED4 (without small fires) than for the 500 m calibrated model. The largest change in emissions was in the open and woody savanna biomes. The resemblance to GFED4 emissions suggests that our simplified model is able to roughly reproduce GFED4 when calibrated at the same resolution of 0.25∘, while additionally enabling 500 m resolution modelling.

Besides calibration differences, model results varied because of resolution differences during the simulations. We calculated simulation differences between 500 m and 0.25∘ resolution runs, using the model calibrated for 500 m resolution (Fig. 6). For the 0.25∘ resolution simulation, AGBw and AGBL estimates were 4.0 and 4.6 Pg C lower than the 500 m simulation, respectively, with contributions from all biomes (Fig. 7a). The main positive differences were found at the transitions from barren to vegetated landscapes (e.g. at the fringes of the Sahara and Kalahari) and from land to water (Fig. 6). Notably, smaller positive differences were also found in the southern part of West Africa. The average AGBL was lower at coarser resolution for all biomes, with a larger difference for biomes with more biomass (Fig. 7b).

Total fire emissions for the 0.25∘ run were 0.66 Pg C yr-1, which was 3 % lower than the 500 m resolution simulation (Fig. 3, solid orange versus blue bars). Even though the total emission estimates at different resolutions were relatively similar, significant regional differences in emissions occurred, with deviations of up to a factor of 1.5 and higher deviations (of up to a factor of 4) at the border of water bodies and deserts (Fig. 6b). The lower emissions at 0.25∘ resolution were mostly the result of lower emissions in savannas and other grass-dominated biomes, whereas for tropical forests (i.e. the Congo Basin) and other forests, emissions were higher (see also Fig. 7a and b). Note that the relative differences shown for emissions are the same as for FC because the burned area is equal for both resolutions.

The results in Sect. 3.4 indicated that simulation differences were modest at a continental scale but substantial at regional scales. The various mechanisms that explain part of these differences were identified and quantified by doing additional simulations with altered model configurations and comparing them to the base model (see Sect. 2.5.2).

Overall, most of the simulation difference stemmed from the use of biome-specific parameters, especially where they varied considerably between biomes. In our model, the turnover rates were particularly variable, and they varied among biomes for all biomass pools. In contrast, in GFED4 only the stem pool turnover rates are set to biome-specific values, which we expect to result in relatively small errors. The biome-specific parameter error was largest in aggregate grid cells with a large sub-grid heterogeneity in land cover types and a large gradient in parameter values between neighbouring pixels. Isolation of this error mechanism showed the largest AGBL differences in biome transition regions, where the variation in biomes is highest (Fig. 8a). Lower AGBL at 0.25∘ resolution for grass-dominated regions is explained by the misclassification of grid cell minority forest patches as grassland. At coarse resolution, average biomass is underestimated because the whole grid cell is simulated as a grassland (the majority biome), whereas at finer resolution the presence of a forest is revealed, with accompanying different turnover rates and LUE. Conversely, higher AGBL at a 0.25∘ resolution for tree-dominated regions is explained by the misclassification of grid cell minority grassland as forest. This is comparable to previous studies that found an underestimation of small fragmented burned or forest area and an overestimation of large homogeneous burned or forest area, as a result of majority-based aggregation of binary classified pixels to coarser resolution (Eva and Lambin, 1998; Miettinen and Liew, 2009; Nelson et al., 2009; Silva et al., 2005).

The biome-specific parameter error in AGBL was mostly related to stem biomass because AGBL mostly consisted of stem biomass and because the stem pool had the largest range of turnover rates. The stem turnover rates for the open and woody savanna biomes differed by a factor of 7, which explains the notably large biome-specific parameter errors at transitions between those biomes, such as around the 10∘ N and 15∘ S latitudes (Fig. 8a). The large negative differences on the eastern flank of the continent are also likely explained by a combination of the heterogenic mosaic of agriculture, savannas, and forest biomes and thus a large variability in tree cover and related turnover rates in this region. However, the error can similarly be significant for biomass pools other than the stem pool, since other turnover rates varied with up to a factor of 4 (see Table 1). This is especially important in biomes with little tree cover.

The biome-specific parameter error in AGBL directly affected emissions by determining the amount of fuel and consequently again AGBL via the removal of fuel. However, for most pixels the relative difference in emissions was smaller than in AGBL (Fig. 9). Compared to 500 m resolution, running the model at 0.25∘ resolution generally increased emissions in tropical forests and decreased emissions in savannas. A small area of grassland burning in an area predominately covered with forest results in an overestimation of emissions at aggregated resolutions, since the grid cell average fuel load is mostly determined by forest biomass. The resulting emissions resemble a misclassified forest fire, instead of the actual grass fire. By contrast, the burning of a small patch with high fuel load surrounded by a majority of low fuel load leads to an underestimation of emissions at coarse resolution. For these reasons, Fig. 9a shows positive–negative dipole patterns around the biome transitions. Emissions were overestimated on the more forested side of each biome transition and underestimated on the grassier side of each transition. These patterns were the direct result of the biome-specific parameter error in AGBL (Fig. 8a). There were no biome-specific parameters for fire, so no additional error was introduced in the calculation of emissions from AGBL. Notably, the relative error for emissions was much smaller than for AGBL. This can be explained by the fact that AGBL was mostly determined by stem biomass, whereas emissions were mostly determined by grass and litter (and leaf) biomass.

We expect that the AGBL after a fire is only minorly influenced by the biome-specific parameter error in emissions. Since most emissions originate from grass fires, there is a minor impact on stem biomass and thus AGBL. This is also indicated by the absence of an emission-like pattern in Fig. 9a, suggesting that this error in emissions is small where emissions are significant. By performing a simulation without fire-induced tree mortality, we established that virtually all fire-related resolution difference in AGBL (Fig. 8c) is caused by mortality, instead of by direct emissions. Fire mostly affects AGBL by killing trees, but this does not directly translate to emissions because there is a time lag in the combustion of dead stems (i.e. cwd) and the CC is relatively low.

The non-linear behaviour of the model algorithm led to an additional input aggregation error because of Jensen's inequality. This error was largest for input data with high spatial variability and thus most apparent in grid cells with large heterogeneity in land cover types, where the bias due to averaging is strongest. Previously, we identified fire-induced tree mortality to be the main reason for the fire-isolated resolution difference in AGBL (Fig. 8c). This pattern is clearly resembled in Fig. 8b, which suggests that mortality is strongly affected by the input aggregation error. This can be explained by the quadratic factor in calculating mortality, which amplifies Jensen's inequality because of increased non-linearity.

By aggregating the input data for each biome separately, the input aggregation error was reduced by decreasing the variability related to the heterogeneity in land cover types. Using this method, the spatial resolution was effectively increased by a factor roughly equal to the number of biomes. However, variability inside individual biomes remains and is not accounted for using this approach and likely accounts for the remaining unexplained simulation difference (Yuan et al., 2007). Besides biomes, more or other aggregation classes can be chosen that ideally reduce the variability within those classes as much as possible with as few classes as possible. This could for example be a division based on tree cover intervals. However, the input aggregation error is unavoidable when modelling at aggregated resolutions, unless an appropriate estimator for Jensen's inequality can be derived to account for this error. Since the reanalysis climate datasets we used had a 0.25∘ resolution for both our coarse- and fine-resolution simulations, no additional input aggregation error was introduced by these input datasets. However, in the case of finer-resolution climate data being aggregated, Jensen's inequality will exist for these datasets as well. We aim to substitute all remaining coarse-resolution input data with finer-resolution data when available, e.g. by using data from ERA5 (Hersbach and Dee, 2016). The error will probably be less substantial, as climate data are generally smoother and more homogeneous spatially.

The aggregation of BA fractions to coarser resolution in particular led to additional errors, owing to temporal mechanisms. Firstly, the aggregation of BA altered fire return intervals, resulting in an underestimation of emissions at aggregated resolutions, especially in frequently burning areas. In GFED4, van der Werf et al. (2017) accounted for this effect by introducing the MBF. With our 500 m resolution model, we were able to demonstrate the effectiveness of the MBF. Indeed, the MBF (Fig. 9c) accounted for the majority of underestimation in emissions at aggregated resolution, especially in frequently burning areas (mostly savannas).

We introduce a second mechanism related to this, which occurs due to the temporal non-linearity of the modelled biomass build-up. This is a case of Jensen's inequality in the temporal dimension. The effect is illustrated in Fig. 12 for a hypothetical case of stem biomass build-up. For this example, we assumed 100 % CC and a uniform fuel load. At 500 m resolution, the burned fraction is binary; a pixel is either completely burned or unaffected. In the case of a pixel burning, all stem biomass is removed by this hypothetical fire. In the next month, the biomass regrows from the start of the regrowth curve, where the slope is relatively steep, which leads to fast regrowth. By contrast, in the case of aggregated burned fractions the same net amount of biomass is removed from the grid cell, but only a fraction of the total biomass. This results in slower regrowth from a later point on the regrowth curve. This leads to an underestimation of fuel load at coarse resolution, due to slower biomass regrowth on average after a fire. Even though in normal model scenarios with partial CC the effect would be less extreme, it could still be of importance, especially in the case of canopy fires. In general, the effect is stronger for slow turnover rates and short fire return intervals. In the case of a grass fire, most biomass has already recovered in the first months after the fire. Only in the case of a short fire return interval could an effect on emissions be noticeable. However, additional analysis is required to quantify the contribution of this error mechanism.

We found that emissions were in total lowered by 0.14–0.02 = 0.12 Pg C yr-1 (calibration minus simulation difference) when increasing model resolution from 0.25∘ to 500 m resolution. For these results, we have relied solely on MCD64A1 burned area dataset which did not account for small-fire burned area. Therefore, this difference may be offset by an increase in emissions due to the inclusion of small fires. In GFED4s, emissions increased by 0.36 Pg C yr-1 in our study region due to small fires, as compared to GFED4. An equivalent increase in emissions due to small fires in our model would offset the effects of spatial resolution 3-fold. However, our findings suggest that in a 500 m resolution model the inclusion of small fires may affect emissions differently. In GFED4s, small-fire burned area is added to the MCD64A1 product burned area (Collection 5.1), followed by the calculation of emissions at a 0.25∘ resolution as in GFED4. However, small fires mostly occur in croplands and at the border of tropical forests (i.e. deforestation), where the land cover is particularly heterogeneous (Randerson et al., 2012; van der Werf et al., 2017). Consequently, the GFED4s approach for calculating small fire emissions is prone to the error mechanisms that occur at coarse resolution as described in this work. Our results suggest that small fire emission estimates, in particular, should be modelled at a finer resolution or at least on a per-biome basis.

This is especially relevant considering the ongoing development towards finer-resolution burned area products. For example, Hawbaker et al. (2017) published a 30 m resolution burned area dataset for North America based on Landsat imagery. Furthermore, Roteta et al. (2019) developed a dataset of 20 m resolution burned area for Africa derived from the Sentinel-2 MultiSpectral Instrument (MSI) sensor. Their preliminary product assessment indicated that a very substantial amount of burned area is still missed, even in GFED4s which includes small fires using a statistical approach. Our work illustrates how the development of finer-resolution burned area datasets should be accompanied by the development of finer-resolution emission models or better parameterizations in order to reduce errors. Even in our 500 m resolution emission model, sub-500 m heterogeneity in burned area and fuel load is not accounted for and could introduce additional errors.

We have shown that for relatively fine spatial resolution, the model was roughly equally sensitive to resolution changes and coarser resolution (Fig. 11). The natural log relation implied that a 2-fold increase in resolution leads to a linear reduction in error. However, sub-500 m modelling of fire emission could reveal new sources of error related to small-scale heterogeneity. At these scales the log relation might no longer be applicable. Dependent on the model precision demands, an optimal spatial resolution can be chosen for which the simulation difference becomes insignificant. However, the calibration difference can still be substantial, dependent on the representation error. A study by Nelson et al. (2009), who looked at the effect of spatial resolution on forest inventories, concluded that there is an optimal resolution of around 300 m at which the pixel size is slightly smaller than the forest patch size and the essential heterogenic characteristics of the landscape are captured. In line with our findings, this suggests there is a similar optimal resolution for burned area, and other spatial data used in fire emission modelling, at which finer resolution no longer significantly improves captured variability in the data used and computational resources are optimized.