Improved biomass burning emissions from 1750 to 2010 using ice core records and inverse modeling

Domain: earth_science
Published: 2024-04-30
Editorial outcome: major_revision

Abstract
Estimating fire emissions prior to the satellite era is challenging because observations are limited, leading to large uncertainties in the calculated aerosol climate forcing following the preindustrial era. This challenge further limits the ability of climate models to accurately project future climate change. Here, we reconstruct a gridded dataset of global biomass burning emissions from 1750 to 2010 using inverse analysis that leveraged a global array of 31 ice core records of black carbon deposition fluxes, two different historical emission inventories as a priori estimates, and emission-deposition sensitivities simulated by the atmospheric chemical transport model GEOS-Chem. The reconstructed emissions exhibit greater temporal variabilities which are more consistent with paleoclimate proxies. Our ice core constrained emissions reduced the uncertainties in simulated cloud condensation nuclei and aerosol radiative forcing associated with the discrepancy in preindustrial biomass burning emissions. The derived emissions can also be used in studies of ocean and terrestrial biogeochemistry.

Introduction
Wildfires have an important effect on climate and atmospheric chemistry by emitting large amounts of greenhouse gases, reactive gases, and aerosols into the atmosphere1. Large uncertainties in historical fire emissions hinder understanding of fire-climate interactions, aerosol radiative forcing, and the accuracy of future climate change projections. In the present day (PD), remote sensing detections of active fire and burned areas provide constraints on global biomass burning (BB) emissions2–5, although large regional discrepancies still exist among different inventories6–8. Historical BB emissions before the satellite era, which typically are constructed based on dynamic fire modeling and fire proxies, have even larger uncertainties in both magnitudes and temporal trends9–11. Some emission inventories, such as AeroCom12 and BB4CMIP13 show a relatively pristine atmospheric state in the preindustrial period (PI) compared to PD because they assume a positive correlation between fire activities and population density. More recent studies suggest that these inventories may underestimate PI BB emissions because human activities may have reduced burned area by active fire suppression or more passively through land cover change and landscape fragmentation14,15. Comparisons with ice core fire proxies indicate that wildfire emissions during the late Holocene PI may be higher than those in PD11,16.

Extensive efforts have been made to reconstruct historical BB emissions based on various types of proxy records, such as charcoal records17,18, fire-scarred tree rings19, and gases and aerosols preserved in ice cores20–22. Most of the studies, however, provide only qualitative temporal trends. Previous studies have demonstrated that both the trends and magnitude of global BB emissions can be constrained by ice core proxies of gases20,23,24 using chemical transport model or box model simulations, but the reconstructed emissions usually have relatively low temporal (>100 years) and spatial (hemispheric) resolutions, limited by the species lifetime and measurement resolution. Recent work by Eckhardt et al.22 estimated the historical refractory black carbon (rBC) emissions in the Northern Hemisphere (NH) from 1850 to 2000 using inverse modeling constrained by an array of ice core records. The results highlighted a large discrepancy between the reconstructed rBC emissions and the a priori bottom-up estimates used in CMIP6, although the different sources of rBC (i.e., biomass burning vs. anthropogenic fossil fuel/biofuel) were not distinguished.

Quantitative estimates of global historical BB emissions that can be used as a boundary condition for climate modeling are scarce, representing one of the largest uncertainties in the assessment of aerosol climate forcing11,16,25. Previous studies have highlighted that BB emissions can largely shape the terrestrial cloud condensation nuclei baseline during the PI, and the uncertainty in PI BB emissions can be a major contributor to the overall uncertainty in the estimates of aerosol radiative forcing16,25. Accurate knowledge of PI-to-PD aerosol forcing also is essential for understanding the climate sensitivity of global temperature to changing greenhouse gases, as historical warming has been partially masked by aerosol cooling.

In this study, we use existing bottom-up historical emission inventories (BB4CMIP13 or LPJ-LMfire11,26 for BB emissions and CEDS27 for fossil fuel/biofuel emissions) as the a priori emissions and combine these with a spatially extensive array of high-resolution, continuous measurements of ice-core rBC records developed from 31 sites in both hemispheres (Figure S1) as observational constraints. We reconstruct a posteriori BB emissions from 1750 to 2010 using an inverse model based on the chemical transport model GEOS-Chem. Our reconstructed BB emissions support previous findings that PI (represented by 1750–1780 in this study) BB emissions can be similar to or even exceed the PD level (represented by 1997–2010 in this study)9,11,16, a scenario that is not currently considered in climate model studies. The reconstructed a posteriori emissions for several major BB source regions capture temporal variability not evident in a priori emissions and are generally consistent with regional climate proxy records28,29, charcoal records17,18, and ice core records of other BB tracers30. We further demonstrate that the ice-core rBC records provide observational constraints that can reduce the uncertainty of aerosol-cloud albedo forcing (CAF) associated with the uncertainty in the PI aerosol baseline. We also show that our gridded, model-ready a posteriori BB emissions can be used in Earth System Models to study the carbon cycle, marine biogeochemistry, and other climate-relevant endpoints.

Results
The reconstructed historical rBC emissions from 1750 to 2010

We divided the global rBC emissions into 17 continental regions following the divisions used in BB4CMIP13 (Table 1, Figure S1). We derived the a posteriori BB emissions BB4CMIP (from a priori emissions of BB4CMIP13) and LPJ-LMfire (from the a priori emissions of LPJ-LMfire11,26) in each region for each year from 1750 to 2010, using inverse modeling based on ice core rBC records and deposition-emission sensitivities simulated by GEOS-Chem (Methods). Both inversions also use a priori anthropogenic fossil fuel and biofuel emissions from CEDS27. We set the a priori emission error by assuming that the emission uncertainties were larger in earlier years and gradually decreased towards the PD (Methods). Despite large discrepancies in the a priori emissions (Fig. 1a-b), the two a posteriori BB emissions show similar magnitudes and temporal trends, especially in earlier years when observational constraints were stronger (Fig. 1c-d). Both a posteriori BB emissions are relatively steady at ~2.1 Tg a−1 rBC from 1750 until the early 1800s, higher than that in BB4CMIP (~1.6 Tg a−1) and lower than that in LPJ-LMfire (~2.4 Tg a−1); both a posteriori emissions decline at around 1850, followed by an increase until around 1930. This temporal trend is predominantly governed by emission variations in South Hemisphere Africa (SHAF), which contributes ~30% of the global total BB emissions. From the late 1900s to the present, both a posteriori emissions tend to converge to the a priori emissions because we assumed that the a priori emissions in PD, which are constrained by satellite observations, have smaller errors than those in the early years (Methods). The two a posteriori emissions show similar PI-to-PD ratios, both of which are larger than 1. These results support previous findings that BB emissions in PI could be similar or even higher than in PD, based on ice core measurements9,21,31, charcoal measurements17, and fire modeling11,16.

The a posteriori emissions are constrained by rBC flux measurements from a global array of ice core records. These ice core sites have different sensitivities to rBC emissions from specific source regions, therefore providing constraints on emissions at regional to hemispherical scales. However, due to the relatively short lifetime of rBC (~5 days in our simulations, consistent with other observed32,33 and simulated results34,35), our records, which are mostly clustered in the polar regions, mainly reflect emission variations in high- and mid-latitude regions that are closer to the ice core sites and have a large contribution to the measured deposition fluxes. Specifically, rBC in Antarctic ice cores is mainly sourced from and sensitive to emissions in SHAF, South America (ARCD and SARC), and Australia (AUST), while rBC deposited in Greenland primarily originates in North America (BONAW, BONAE, TENAW, TENAE), Europe (EURO), and Boreal Asia (BOAS) (Figures S2-S3). Our analysis suggests that emissions in these regions (40%−60% of the global total) are relatively well constrained by ice core data as indicated by similarities of two a posteriori emissions in this region after the inverse modeling process (Figure S4), compared with emissions from low-latitude regions, including North Hemisphere Africa (NHAF), North Hemisphere South America (NHSA), Central America (CEAM), Equatorial Asia (EQAS), and Middle East (MIDE), which have relatively small contributions to the deposition fluxes observed at the ice core sites (Figures S2-S3). As a result, a posteriori emissions in these regions are essentially unchanged from their a priori emissions (Figure S5). Even so, comparisons between the two a priori BB emissions indicate that high- and mid-latitude regions account for most of the discrepancies in global total emissions in PI, and our inverse modeling can provide a tight constraint for these regions and reduce discrepancies, further improving the estimates of the global total BB rBC emissions in the PI (Figure S6).

Regarding Greenland and Antarctica, our simulations using different emissions emphasize the contrast in relative importance between anthropogenic fossil fuel/biofuel and BB emissions across different regions (Fig. 2). In Antarctica, using the a posteriori BB emissions BB4CMIP and LPJ-LMfire results in simulated rBC deposition that is in better agreement with the ice core data compared with simulations using the a priori BB emissions, while using a posteriori anthropogenic fossil fuel/biofuel emissions does not provide further improvement. In contrast, simulations using a posteriori BB emissions in NH barelly improve the consistency with ice core observations in Greenland, compared with those using the a priori BB emissions (Fig. 2b). In particular, the modeled results with the a priori fossil fuel/biofuel emissions fail to reproduce the rBC deposition peak between 1900 and 1950 that is evident in most Greenland ice cores and has been attributed to anthropogenic fossil fuel combustion from North America36 (Figure S1). The a posteriori fossil fuel/biofuel emissions (i.e., CEDS, Figure S7) could improve the agreement between simulations and observations and suggest that fossil fuel/biofuel emissions in TENAE need to be 200% higher compared with the a priori CEDS estimate (~1.5 Tg a−1 as suggested by the a posteriori CEDS emissions compared with ~0.5 Tg a−1 in the a priori CEDS emissions, Figure S7) to agree with the observational constraints. This finding is consistent with a recent study of NH ice core rBC records that argued emissions in North America should be a factor of two higher than the CMIP6 emissions (i.e., BB4CMIP+CEDS) for the period 1850-192022.

There are several ice core records sporadically located in other regions, including South America, North America, Boreal Asia, and Europe. Although these ice core records are not representative of the conditions in the whole region, using a posteriori BB emissions or anthropogenic fossil fuel/biofuel emissions could also result in a better agreement between the simulation results and ice core records (Figure S8).

Temporal variations and comparisons with previous studies

In the SH, both a posteriori emissions consistently show BB rBC emissions decreased by ~40% from 1820 to 1860 and increased later until early the 1900s, while the two a priori emissions are stable during the same period. The increased temporal variability is constrained robustly by multiple ice core records measured at different locations in Antarctica (Figure S1), which are sensitive to emission changes in SH regions (i.e., ARCD, AUST, SARC, and SHAF). However, the high a posteriori error correlation in these regions indicates it is challenging to quantify the emissions in these regions independently (i.e., the same modeled results that match the observations could be obtained by adjusting emissions in either of the regions or a combination of several regions). Similar error correlation issues were discussed in previous work by Maasakkers et al.37. To show the results in the most extreme case, we further conducted sensitivity tests to examine how emissions in one of the four regions would change to match the observational values if emissions in all other three regions remain unchanged (Figure S9). These results provide an upper-limit estimate of emission changes constrained by ice core records. The sensitivity analysis suggests that adjusting emissions in ARCD or SARC only marginally improves the agreement between the model and ice cores (Figure S9k, l). Thus, this temporal variation is more likely driven by the emission trends in SHAF and AUST. While Figure S9 shows the upper limit of the a posteriori emissions in SHAF and AUST, the similar trends for both regions in the BB4CMIP and LPJ-LMfire suggest that the simulated emissions are reasonable given that the ice core records at different locations of Antarctica consistently show similar trends as well. In addition, although emissions within different SH regions have uncertainties, total emissions in SH regions consistently show similar levels and trends (Figure S9).

We have identified a possible connection between the decrease in BB emissions in SHAF during the first half of the 19th century, as revealed in both a posteriori emissions and relatively sustained arid periods characterized by low precipitation. This hypothesis is supported by a comprehensive reconstructed “wetness” index in different middle and southern African regions based on documentary evidence and gauge data38 (Figure S10b-d). This trend also is moderately correlated with the reconstructed Palmer Drought Severity Index (PDSI) from Last Millennium Reanalysis (LMR, r = 0.33-0.36)39 (Figure S10e). In the savanna and woodland ecosystems that are prevalent in central and southern Africa, wildfire activity can be limited by herbaceous fuel availability in dry seasons40,41. Decreasing precipitation, suggested by the evidence above, would hinder the accumulation of herbaceous fuel, decreasing fuel availability and wildfire activity.

In NH regions close to the ice core sites, the a posteriori BB emissions generally exhibit higher levels compared with the a priori emissions (Figure S4). The largest discrepancy is observed in BOAS, which is one of the most important BB source regions in the NH. The two a posteriori emissions consistently show higher BB emissions in 1750-1780 and around 1850 and a decreasing trend in the late 1800s. This variability is not captured by the a priori emissions and is constrained mostly by the rBC records from Akademii Nauk and Flade Isblink, where the contribution of BB to rBC deposition from BOAS is larger than that from North America (Figure S2). The decrease after 1850 in boreal Asia also is reported by a previous emission reconstruction study with similar ice core records, and attributed to anthropogenic emission changes in Russia due to economic collapse during the October Revolution and World War I22. In contrast, we suggest that the decreasing trend, together with the two earlier periods of high rBC emissions, is likely related to BB emission changes because the trends are consistent with other BB tracers (i.e., para-hydroxybenzoic acid, p-HBA, and vanillic acid, VA) measured in the Akademii Nauk ice core (Figure S11)30.

Human influence on BB gradually increased relative to the climate influence as population expand rapidly following the 19th century42. The a posteriori BB emissions show a declining trend starting from the late 1800s to the early 1900s in multiple regions, including SHAF, South America (ARCD and SARC), North America (BONAE, BONAW, TENAE, TENAW), and BOAS (Figure S4), although population and anthropogenic emissions continue to rise during this period. The declining trend in BB emissions is consistent with the charcoal records from the same regions17 (Figure S10f, Figure S11d, Figures S12-13). The opposite trends in BB emissions and population change in this period suggest an overall negative effect of human activities on BB, likely caused by the rapid expansion of agricultural landscapes from natural landscapes that reduce biomass fuel load, landscape fragmentation resulting in reduced fire spread, and land management to control fires14,43,44.

Implications on cloud albedo forcing

Regional scale factors (i.e., a posteriori and a priori emission ratios) were derived for BB rBC from 1750 to 2010. These rBC scaling factors can be applied to other species co-emitted from BB, such as organic carbon (OC), under the assumption that emission factors used in a priori emissions remain applicable. These BB emissions (Figures S14-S15), together with CEDS emissions, were used in GEOS-Chem to simulate the PI-to-PD changes in aerosol concentration, cloud condensation nuclei (CCN) concentration, cloud droplet number concentration, and CAF (See Methods).

The results reveal that the two different a priori BB emissions lead to similar global mean CCN concentrations (Fig. 3) with large spatial discrepancies (Figure S16a-b). Here, the CCN concentrations were calculated, including aerosols from anthropogenic, biomass burning, and natural sources in both PI and PD. These spatial discrepancies mainly arise in SH regions due to large differences in BB emission levels and spatial distributions in these regions (Figure S14-S15). The a posteriori BB emissions constrained by ice core records indicate a reduction in the difference in PI BB rBC emissions between the two inventories from 0.86 Tg a-1 to 0.07 Tg a-1 globally (Fig. 3a) and from 0.80 Tg a-1 to 0.10 Tg a-1 in SH (Fig. 3c). As a result, the differences in simulated total PI CCN concentration also are reduced (Fig. 3d-f, Figure S15). We further calculated CAF between PI and PD due to anthropogenic aerosol emission changes using the different BB emissions (Fig. 3, Figure S17). The calculated CAF uncertainty related to PI BB emissions reduced from 0.08 Wm-2 (i.e., difference of simulations using the two a priori BB emissions) to 0.04 Wm-2 (using the two a posteriori emissions) globally (0.13 Wm-2 to 0.09 Wm-2 in SH and 0.02 Wm-2 to 0.00 Wm-2 in NH). These results highlight that observational constraints from ice core records can significantly reduce uncertainties in BB emissions by improving the estimates of PI CCN baseline and PI-to-PD CAF. Two a posteriori emissions scenarios consistently suggest higher BB aerosol emissions in PI compared with the CMIP6 emissions widely adopted in current climate models (i.e., BB4CMIP+CEDS). This conclusion remains robust even when considering the emission uncertainties (Figure S4). These findings suggest higher CCN concentrations during the PI which will result in less cooling effects of CAF when employed in climate models. The current climate model using CMIP6 emissions might need to be reevaluated, given the underestimation of BB emissions in PI. Studies have found that even small uncertainty in simulated aerosol radiative forcing could lead to significant differences in climate model results, such as global surface temperature and sea ice area45. The reduced uncertainties with observational constraints demonstrated in this study could possibly help with improving the climate model performance and climate sensitivity estimations, further improving future climate change projections.

Implications for nutrient deposition from biomass burning

One major finding of our study is that PI BB emissions in SH regions were probably higher than indicated by the widely used BB4CMIP emissions. This implies that BB in the PI was a more important source of nutrients to terrestrial and marine ecosystems than previously estimated. To illustrate this point, we estimated one important nutrient species, phosphorus (P) deposition from BB based on simulated rBC deposition and compared it with estimated P deposition from mineral dust. We assumed a P:rBC ratio of 0.0029 for BB aerosols46 with solubility of 15%47 and P:dust ratio to be 0.0018 with solubility of 5%47.

Although dust is the dominant source of P deposition globally, BB could be an important source regionally47,48, especially in South America, southern Africa, and the tropical Atlantic Ocean (Figure S18), contributing to more than 60% of the soluble P deposition from the atmosphere regionally. Our results suggest 0.18 Gg a-1 higher annual soluble P emissions from BB in SH compared with baseline simulation using BB4CMIP, resulting in 0.06 Gg a-1 higher soluble P deposition over land and 0.12 Gg a-1 higher deposition over the ocean. The relative increases in annual P deposition were more than 50% in some regions compared with the baseline (Figure S18c). These increases are more pronounced during the boreal fall (September-November) when P deposition from dust is relatively minor (Figure S18d). As a caveat, the above estimates only consider P emitted from BB and from mineral dust. Other sources also could be important. For example, biogenic sources are estimated to be as large as 10% to 100% of P emitted from mineral dust48–50. Our results, therefore, represent an upper-limit estimate.

Higher P deposition in the P-limited Amazon region could affect forest productivity and carbon uptake51–53, while increased P in the N-limited tropical Atlantic Ocean could enhance nitrogen fixation by phytoplankton and further affect marine productivity and the global carbon cycle54. Our BB emissions from inverse modeling can affect the PI baseline state of the carbon cycle, and the associated climate effects could be further studied using coupled Earth system models.

Methods
Ice core measurements

The inverse modeling in this study is constrained by a total of 31 rBC records, including 29 previously published and unpublished datasets developed at the Desert Research Institute (DRI), as well as two additional published rBC records from other studies (Figure S1)56. Detailed information on the ice core sites can be found in Table S1. The DRI records presented here all were developed using the well-established Single Particle Soot Photometer (SP2) method as part of the DRI Continuous Flow Analytical (CFA) system36,57, thus ensuring comparable uncertainties across the records. Annual deposition fluxes were determined using net water-equivalent snowfall rates derived from volcanically constrained, multi-parameter annual layer counting58. The rBC records were smoothed for the inversion process using a 30-yr running average to reduce large interannual variations due to climate variations, occasional fire events, and glaciological noise. As a caveat, data at some ice core sites are unavailable during the beginning of the study period. Any gaps in the rBC datasets were filled by assuming the same temporal trend of the nearest site with available data for the missing period. The error for such sections was assumed to be twice the error of the actual measurement.

A priori emission inventories

Two BB emissions (i.e., BB4CMIP and LPJ-LMfire) and one fossil fuel/biofuel emission (i.e., CEDS) were used in this study. BB4CMIP13 is a historical BB emissions dataset starting from 1750 that is based on different records, including a satellite-based dataset (Global Fire Emission Database version 4 with small fires, GFED4s) after 1997, fire model results from the Fire Model Intercomparison Project (FireMIP) before the satellite era, and limited existing observational proxies (such as charcoal records and visibility observations) if available. LPJ-LMfire is a dynamic global vegetation model coupled with a fire module, with consideration of human influences on fire by hunter-gatherers, pastoralists, and farmers26. The model output is burned area and is scaled to the GFED4s burned area for the overlapping 1997-to-2015 period for each region11. Emission factors for different vegetation types were taken from GFED4s to derive emissions of rBC and other species. CEDS emission is a historical emissions dataset of reactive gases and aerosols from anthropogenic fossil fuel and biofuel combustion27. BB4CMIP emissions are available at a spatial resolution of 0.25° × 0.25°, while LPJ-LMfire and CEDS emissions are available at a 0.5° × 0.5° resolution and are regridded in this study to 0.25° × 0.25°.

GEOS-Chem simulations

We used GEOS-Chem v13.4.0 to construct the sensitivity matrix of rBC deposition flux to emission perturbations (Jacobian matrix) for the inversion analysis. The model has a horizontal resolution of 4° × 5° and 72 vertical layers and was driven by meteorology from the latest atmospheric reanalysis of the modern satellite era, MERRA2, from NASA’s Global Modeling and Assimilation Office59. By default, the model assumed 80% of emitted rBC particles were hydrophobic (BCPO), with an e-folding time of 1.15 days before becoming hydrophilic (BCPI)60. We assumed fossil fuel/biofuel emissions were injected from the surface layer and BB emissions were injected partially below the planetary boundary layer (65%) and partially above the planetary boundary layer (35%)61. We ran the model simulations for five years, with emissions from 2000 to 2004 to represent the PD condition and with emissions from 1750 to 1754 to represent the PI condition. We used MERRA2 meteorology from 2000 to 2004 for both PI and PD scenarios, so the simulated differences between PI and PD were caused solely by the emission difference, but we further analyzed the potential uncertainty related to different meteorology conditions using the meteorology input simulated by version E2.1 of the NASA Goddard Institute for Space Studies (GISS) general circulation model coupled in GEOS-Chem62 (Text S1.1).

We assumed current emission inventories and meteorology conditions from MERRA2 in PD are accurate because they are all well-constrained by satellite data, energy use records, and direct measurements. We evaluated the model performance by comparing the simulated rBC deposition flux with the measured flux at the ice core sites between 2000 and 2004. The model shows relatively good performance, with a correlation coefficient (r) of 0.91. However, it overestimates the rBC flux by 11% to 12% (Figure S19a, c). Since the coarse resolution model cannot accurately represent the high-altitude mountain regions where some of the ice core sites were located, we made corrections to the simulated wet deposition and dry deposition flux. Specifically, we corrected the simulated wet deposition by summing only the modeled flux in layers above the site altitude, and we corrected the simulated dry deposition by scaling with the ratio of rBC concentration in the layers of the site altitude to that at the surface. After these corrections, the slope of the regression line decreased from 1.11-1.12 to 1.03-1.02, indicating an improvement in model performance (Figure S19 b, d). We also conducted sensitivity tests for parameters that could affect the model performance, including fire plume injection height and rBC aging e-folding time. These tests show that changes in these parameters had limited effects on the simulated rBC deposition flux at the measurement sites, most of which are located far from the sources, and the results are consistent between different years, indicated by the relatively low standard deviations (Figures S20-S23).

Since rBC has a very low chemical reactivity in the atmosphere, with the major sources being BB and fossil fuel/biofuel emissions and sinks being wet and dry deposition63, we assumed a linear relationship between rBC emission and deposition. To construct the Jacobian matrix, we tagged tracers of BCPI and BCPO from BB emissions as well as from anthropogenic fossil fuel/biofuel emissions in 17 regions. We calculated the sensitivity from each region and each source by dividing the total deposition fluxes at each grid cell by the total emissions of the corresponding tracers. Four Jacobian matrices with four sets of emissions are derived for the inverse modeling purpose (CEDS+BB4CMIP in 1750–1754, CEDS+BB4CMIP in 2000–2004, CEDS+LPJ-LMfire in 1750-1754, and CEDS+LPJ-LMfire in 2000-2004), and the average values in the 5-year periods were used as the final Jacobian matrices for each scenario. Although we treated emissions in each region as a whole, the different spatial patterns of emissions within each region between PI and PD could lead to large variations in the calculated sensitivities, most of which occur in the low-sensitivity conditions (Figure S24). To account for the effects of emission distribution transition from PI to PD in the inverse modeling process without consuming excessive computational resources to calculate the sensitivity matrices for the whole 261-year period, we simply used linear transition by assuming the sensitivity changed linearly from 1750 to 2000 and became constant after 2000. The details of the uncertainties are discussed in Text S1.1.

Bayesian inversion framework

We solved the a posteriori emissions of rBC from BB and fossil fuel/biofuel processes in each region (x) using Bayesian inverse analysis with measured rBC deposition flux from ice cores (y) as constraints. The cost function J of this problem can be described as:

J(x) = (x-xa)T Sa-1 (x-xa) + γ(y-Kx)T So-1 (y-Kx) (1)

Where x is a 34 by 1 vector that represents the optimized estimates of BB emissions in 17 regions and fossil fuel/biofuel emissions in 17 regions, xa is a 34 by 1 vector that represents the a priori BB emissions (from either BB4CMIP or LPJ-LMfire) and fossil fuel/biofuel emissions (from CEDS). Vector y with a size 31 by 1 is the observed rBC deposition flux from 31 ice core measurements. To overcome the model bias compared with the observations in PD (Figure S19), we scaled the observed values for the 2000–2004 period to the modeled values for the PD scenario to avoid unreasonable adjustments for the a posteriori emissions in the PD due to model bias instead of emission errors. We applied the same scale factors during the study period by assuming this model-observation bias does not change with time. Results without scaling show lower a posteriori emissions in the PD (Figure S25), contrary to our assumption that emissions in PD are accurate. The error covariance matrices for the a priori emissions (Sa, with a size 34 by 34) and observations (So, with a size 31 by 31) are represented by diagonal matrices, with the diagonal elements being the error variance of the emissions in each region (σ2a) and the error variance of the observations at each site (σ2o), respectively. All the off-diagonal elements are zero because we assumed the errors are uncorrelated with the neighboring values. Matrix K, with a size 31 by 34, is the Jacobian matrix. The constant γ is a regularization factor to balance the a priori emission error (the first term of Eq. 1) and the observational error (the second term of Eq. 1).

The BB4CMIP emissions were constructed based on the ensemble of six fire models when no observational data were available13. We estimated the a priori error (σa) for BB4CMIP to be half of the range of the six fire model results and no less than 50% in each region. The resulting a priori emission errors for BB4CMIP range from 50% to 400%, similar to previous studies using errors 30% to 300%6,22. In the absence of better information, we set the a priori emission errors of LPJ-LMfire based on an initial guess (50%) and adjusted the error to avoid overfitting (i.e., negative a posteriori emission values) while maintaining consistency with observations. This leads to the a priori error (σa) to be 5% for SH regions (including ARCD, AUST, SARC, and SHAF), where simulations with LPJ-LMfire already show good agreement with observations in Antarctica11; 10% for NH regions with high emission levels (i.e., NHAF and CEAS) and 50% in all other regions. We estimated the a priori error for CEDS to be 100% between 1750-1850, with a linear decrease to 30% between 1850 and 2000 and remaining at 30% thereafter22. With these assumptions, the uncertainties of fossil fuel/biofuel emissions were generally smaller than those of BB emissions under most conditions. In the PI period, the fossil fuel/biofuel emissions were relatively low and began to significantly increase only after 1850. Even when we assumed a large relative uncertainty of 100% for fossil fuel/biofuel emissions, the absolute values were still lower than those of BB emission uncertainties. After 1850, while fossil fuel/biofuel emissions increased, the assumed relative uncertainty began to drop, leading to lower absolute errors for fossil fuel/biofuel emissions compared to BB emissions. This reflected our assumption that fossil fuel/biofuel emissions were relatively more accurate than BB emissions because more records (such as energy production and consumption data and population) were available as constraints.

The observational errors (σo) include measurement errors (σo1) and atmospheric modeling errors (σo2)6. We assumed the measurement error to be 10% of the measured values or 20% of the hypothetical values used to fill missing data sections and the modeling errors to be (y-K×xa), ranging from 2% to 173% of the measured values at different sites. We aggregated these errors by assuming σ2o = (σ2o1 + σ2o2). We set the regularization factor γ to be 0.5 based on the L-curve plot of squared observational and model errors (Figure S26).

We used the analytical solution for ∂J/∂x = 0 to obtain the optimal estimates of the a posteriori emissions x^ by Eq. 2. The calculations were performed annually from 1750 to 2010 using observations, a priori emissions, and sensitivity matrix for each year. We obtained two sets of a posteriori emissions separately with different a priori emissions (i.e., BB4CMIP+CEDS and LPJ-LMfire+CEDS).

x^ = xa + (γKTSo-1K + Sa-1)-1 γKTSo-1(y-Kxa) (2)

We used Monte Carlo simulations to evaluate the uncertainty of a posteriori emissions associated with all the inverse modeling parameters, including observational error, a priori BB emission error, a priori anthropogenic fossil/fuel biofuel emission error, and simulated emission-deposition sensitivity error. Detailed discussion and description of error distributions can be found in Text S1. The overall uncertainties of the a posteriori emissions were aggregated by σ2 = ∑σi2 and represented by the 2.5% to 97.5% ranges shown by the shaded area in Figures S4-S5.

The annual a posteriori emission from the optimization process x^ is a 34 by 1 vector with the first 17 elements to be the a posteriori BB emissions in 17 regions and the last 17 elements to be the a posteriori fossil fuel/biofuel emissions in 17 regions, all for rBC. We assumed the spatial distribution of burned area and emission factors of all the species to be the same as the a priori emissions so we derived the gridded a posteriori emission of rBC as well as other species by scaling the gridded a priori emissions by the factor x^BC/xa,BC for each species in each region.

Cloud albedo forcing calculation

We performed simulations using GEOS-Chem with TwO Moment Aerosol Sectional (TOMAS) online microphysics to simulate aerosol number, mass, and size distribution64. The TOMAS module has 15 size sections ranging from 3 nm to 10 μm for aerosol components of sulfate, organic carbon, BC, sea salt, and dust. We performed simulations under fixed meteorological conditions in 2000 with average emissions from 1750 to 1780 for PI conditions and from 1997 to 2010 for PD conditions. We performed simulations in PI conditions and PD conditions with four sets of emissions, i.e., CEDS+BB4CMIP, CEDS+BB4CMIPpost, CEDS+LPJ-LMfire, CEDS+LPJ-LMfirepost.

We calculated the cloud albedo effect at the top of the atmosphere (TOA) based on monthly size-resolved aerosol output from GEOS-Chem-TOMAS following the steps in our previous study11. In short, we used the sectional representation of cloud activation65 to calculate aerosol droplet number concentrations (CDNC) for an updraft velocity of 0.3 ms-1. We assumed a uniform cloud droplet radius of 10 μm for the PD conditions, and we calculated the effective radii of low- and mid-level clouds (up to 600 hpa) by taking the ratio of CDNC between PI conditions and PD conditions to the one-third power. The change in radiative flux at the TOA due to the change in cloud effective radius was calculated by the offline version of the Rapid Radiative Transfer Model for Global climate models (RRTMG). The difference in aerosol radiative effect between PD and PI was the aerosol radiative forcing caused by BB emissions. As a caveat, the radiative forcing calculated here did not consider the rapid adjustments of atmosphere and surface to aerosol perturbations, cloud lifetime effect, and the climate feedback of the updated fire emissions. These effects could be further studied using fully-coupled Earth system models.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "General comments:\nThe authors estimated global biomass burning emissions data from 1750-2010 using ''top-down''\ninverse approach, using historical emissions inventory data and constraints on ice core records of\nrefractory black carbon deposition fluxes. The study analyzed biomass burning emission historical\ntrends based on the reconstructed inventory. The novelty of this study, especially the methodology\nshall be clarified compared to the previous study about inversion emission based on ice core record\nof BC. Moreover, the inversion results should be verified and be carefully analyzed. For example,\nhow to prove the inversion result is biomass burning emission rather than other fossil fuel\ncombustion sources, and how to prove the rationality of results based on the ice core records of\nrBC. The significance and the scientific impact of this study also need to be described in detail. The\nconcerns mentioned below should been addressed. Several main comment:\n(1) The same meteorological conditions were set throughout the simulations over the years\nespecially when building the Emission-deposition sensitivities matrix. Moreover, the study made\nassumptions that are not supported by data when setting the priori inventory errors. These\nprocesses all lead to large uncertainties in the inversion of emissions. The reliability of results\nbased on the ice core records of rBC need to be further verified. In addition, how to prove the\ninversion result is biomass burning emission rather than other fossil fuel combustion sources. BB is\nnot the only source of the rBC.\n(2) The study should provide scientific evidence for the findings by providing additional data or\nobtaining new data. For example, in the section \"Implications on cloud albedo forcing\", the\nconclusion \"the cooling effect of aerosol radiative forcing from PI to PD may be overestimated in\ncurrent climate models\" have yet to be proven fully. Further evidence is needed to demonstrate\nwhether this conclusion is valid considering the inventory error and simulation error.\n(3) This study have created the biomass burning emissions inventory for a period. The significance\nfor present/future climate assessments and pollution analysis, and the applicability of the\nmethodology for the inversion of the BB emissions need to clarify in this study.\nSpecific comments (P represent Page X which was shown in the lower right corner of reviewer\nproof):\nP2 line 58: What is the dividing line between preindustrial period(PI) and present period (PD), the\nbeginning of the Industrial Revolution ?\nP2 line 58: Did \" these inventories\" refer to the lists estimated using satellite monitoring data?\nP3 line 70-75: The literature cited in the article utilized BC precipitation data recorded in ice cores\nand the idea of inversion to obtain historical emission inventories. The methodology innovation of\nthis study need to be further explained.\nP4 line 102: In this paragraph, the article analyzed that the inverse emission inventories are\ncharacterized by different discrepancies from the a priori emission inventories in the PI and PD\nperiods. What is the reason for this different discrepancies? In addition, the boundary between the\nPI and PD periods in Figure 1 should be to clearly mark.\nP5 line 131-136: MS showed that the constraints on the ice core data work differently in different\nregions, what is the reason? Why the constraints are not effective in low latitude regions? Is it\nrelated to the location of the observation site or the sedimentation fraction of the region? This part\nneeds to be more clearly explained.\nP5 line 137-140: The BB emission in low latitudes region were seemingly not well constrained by\nice core data. It cannot be shown that the inverse model can provide a tight constraint on the total\nglobal BB emissions in the PI. Actually, The BB emission in low latitudes region and accurate\ninversion result should be pay more attention\nP6 line141-143: Were the in the modeling of the different emission inventories evident only\ndifferent in these two regions? Are the differences not reflected elsewhere? Why?\nP6 line161-175: What is the significance of the sensitivity analysis of emissions by region to the\nmodel? What is the role of sensitivity analysis?\nP7 line 196-200: What does the passage mean?\nP7 line 201-202: The MS mentioned that the downward trend in emissions from the late 19th to\nearly 20th centuries could be attributed to changes in the nature of human impacts on wildfires.\nThe author should expand on why this change led to the decline in emissions.\nP8 line 235-237: This result seems to be one of the important conclusions of this research and a\nnew finding in reconstructing emission inventories relative to the priori inventories. Is it possible to\nfurther explain what can be further analyzed by obtaining this result? What are the new\nimplications of this result for the climate environment?\nP8 line 246-249: The statement that \"biomass burning is also an important regional source of\nglobal P deposition\" needs to be supported by support data or other literature.\nP10 line 294-296: The study should state that how to determine the processed rBC data were all\nfrom biomass burning and verify the reliability of the inversion result.\nP11 line 342-344: All these tests mentioned in MS were conducted with the year 2000 as the\nscenario. Would the test situation vary in different years? The test scenarios for other years should\nbe added to further supplement the cases to enhance persuasiveness.\nP12 line 359-363: It is necessary to explain why the sensitivity is assumed to change linearly from\n1750 to 2000 and remain constant after 2000.\nP12 line 363-366: The study discussed the reasons for using the same meteorological conditions in\nthe multi-year simulations in a Supplementary Document. However, it is still not sufficient to\njustify it because the results of the simulations under different meteorological conditions differed\nsignificantly in some areas, as illustrated in Figure S25.\nP12 line 377-379: The reasons and justification for the adjustment of the measurements should be\nfurther clarified, and a detailed description of how the adjustments were made should be\npresented.\nP13 line 388-408: It is necessary to further prove the reasonableness of the assumption of the\nrange of the priori errors. The practical evidence of current assumption is not enough, and the\nuncertainty of the priori inventory can be determined by comparing the simulation using the priori\ninventory and the observation, or by conducting several experiments to set different error ranges\nto prove the reasonableness of the setting.\nP14 line 433-434: It can be found that the uncertainty of emissions seems to be different in each\nregion, and the uncertainty range of emissions in different regions should be marked in the form of\na map.\nP18 figure3: The sequence number of the subgraph should be indicated.", "reviewer_2": "Review of “Improved Estimates of Biomass Burning Emissions from 1750 to 2010 using Ice Core\nRecords and Inverse Modeling”\nThis work uses inverse modeling to reconstruct biomass burning (BB) emissions spanning the\npreindustrial-to-present day period (1750 to 2010), using records of refractory black carbon (rBC)\nfrom 31 ice cores, two emission inventories (BB4CMIP and CEDS) and emission-deposition\nsensitivities simulated by the atmospheric chemical transport model GEOS-Chem. The authors\nfound that preindustrial era BB emissions can match or exceed emissions from present day, a\nscenario not currently considered in climate model studies, and suggest that the cooling effect of\naerosol radiative forcing from preindustrial era to present day may be overestimated in current\nclimate models. The authors also found that preindutrial era BB emissions were higher than\nindicated by one of the emissions inventories used (BB4CMIP) for the southern hemisphere,\nsuggesting that BB was a more important source of nutrients for terrestrial and marine ecosystems\nthan previously estimated.\nConsidering the overall uncertainty related to BC in climate forcing estimates regionally and\nglobally, specially in the preindustrial era, the results and conclusions presented in this work are of\nsignificance. This work is original, the methodology presented was sound and thoroughly detailed\n(both in the manuscript and supplementary information); this work used a robust dataset obtained\nby well established methods, and results support the conclusions claimed. I recommend this\nmanuscript to be published with no additional comments or issues to resolve."}, "author_response": "ResponsetoReviewer#1\nComment1\nThe authors estimated global biomass burning emissions data from 1750-2010 using ''top-down''\ninverse approach, using historical emissions inventory data and constraints on ice core records of\nrefractory black carbon deposition fluxes. The study analyzed biomass burning emission historical\ntrendsbasedonthereconstructedinventory.Thenoveltyofthisstudy,especiallythemethodologyshall\nbe clarified compared to the previous study about inversion emission based on ice core record of BC.\nMoreover,theinversionresultsshouldbeverifiedandbecarefullyanalyzed.Forexample,howtoprove\nthe inversion result is biomass burning emission rather than other fossil fuel combustion sources, and\nhow to prove the rationality of results based on the ice core records of rBC. The significance and the\nscientificimpactofthisstudyalsoneedtobedescribedindetail.\nResponse\nWe thank the reviewer for their review and constructive comments. We conducted a more detailed\nanalysis of the uncertainties related to the parameters within the inverse modeling process and discussed\nhow these uncertainties may affect the results. We clarified the statements that could cause confusion\npointed by the reviewer, including the novelty of this study compared with the previous work, PI and\nPD period definition, conclusions related to aerosol radiative forcing. We update the results, figures,\ndiscussions related to the changes throughout the manuscript. We hope that this revised version of the\nmanuscript addresses all of cWTaTeXTfTaqbR^]RTa]b&\nComment2\nThesamemeteorologicalconditionsweresetthroughoutthesimulationsovertheyearsespeciallywhen\nbuilding the Emission-deposition sensitivities matrix. Moreover, the study made assumptions that are\nnot supported by data when setting the priori inventory errors. These processes all lead to large\nuncertainties in the inversion of emissions. The reliability of results based on the ice core records of\nrBC need to be further verified. In addition, how to prove the inversion result is biomass burning\nemissionratherthanotherfossilfuelcombustionsources.BBisnottheonlysourceoftherBC.\nResponse\nMeteorological conditions: We agree with the reviewer that the change in meteorological conditions\nfrom PI to PD can cause changes in emission deposition sensitivity. In the revised manuscript, we added\nnew sensitivity tests using PI and PD emission deposition sensitivity matrices, constructed based on\nGISS-GC simulations using the CMIP6 historical meteorology from the GISS model (see Methods).\nThe GISS meteorology shows large change from PI to PD1 but has limited effects on the inverse\nmodeling results (Fig. S30). The results indicate that our inversion remain robust under different\nmeteorological conditions.\nFigure S30 Timeseries of a posteriori BB rBC emissions with different emission deposition\nsensitivity matrices.\nA priori inventory errors: We estimated the a priori emission errors of BB4CMIP based on the\nmagnitude of the relative difference among the six fire models (Methods), assuming largest\ndiscrepancies among model results suggest larger uncertainties. The resulting a priori emission errors\nfor BB4CMIP range from 50% to 400%, consistent with previous studies using errors 30% to 300%2, 3.\nWe set the a priori emission error of LPJ-LMfire based on an initial guess (50%) and adjust the error\nto avoid overfitting (i.e., negative emission values) while maintaining a good consistency with\nobservations. We believe the a priori emission errors used in this study are reasonable and could lead\nto reasonable results (Figure 2).\nWe revised the Methods section to include more details in determining the a priori emission errors and\nthe references in Lines 399-410 as follows:\noWe estimated the a prioriTaa^a!z ) for BB4CMIP to be half of the range of the six fire model results\na\nand no less than 50% in each region. The resulting a priori emission errors for BB4CMIP range from\n50% to 400%, similar to previous studies using errors 30% to 300%2, 3. In the absence of better\ninformation, we set the a priori emission errors of LPJ-LMfire based on an initial guess (50%) and\nadjusted the error to avoid overfitting (i.e., negative a posteriori emission values) while maintaining\nmaintaining a good consistency with observations. This leads to the a priori Taa^a !z ) to be 5% for SH regions\na\n(including ARCD, AUST, SARC, and SHAF), where simulations with LPJ-LMfire already shows good\nagreement with observations in Antarctica; 10% for NH regions with high emission levels (i.e., NHAF\nand CEAS) and 50% in all other regions. We estimated the a priori error for CEDS to be 100% between\n1750-1850, with a linear decrease to 30% between 1850 and 2000 and remaining at 30% thereafter3.p\nTo study the uncertainty, we further perturbed the error within a range ('20%, Text S1) and shown the\nrelated uncertainties in Figure S27. We thus do not expect setting a priori emission errors in this range\ncould lead to large uncertainties and change our conclusions.\nReliability of the results: We used Monte Carlo simulations to estimate the uncertainty of the a\nposteriori emissions associated with different input parameters including Jacobian matrices, a priori\nemission errors, and observational errors. To do so, we perturbed each parameter separately and\naggregated cWTc^cP[Taa^aQhz2=!z2. The description of this process in the main text in Lines 432-438\ni\nare modified as follows:\noWe used Monte Carlo simulations to evaluate the uncertainty of a posteriori emissions associated with\nall the inverse modeling parameters, including observational error, a priori BB emission error, a priori\nanthropogenic fossil/fuel biofuel emission error, and simulated emission-deposition sensitivity error.\nDetailed description on error distributions and discussion can be found in Text S1. The overall\nuncertainties of the a posteriori emissions were aggregated by z2=!z2 and represented by the 2.5% to\ni\n97.5% range shown by the shaded area in Figures S4-S5.p\nIn the revised SI text, we made substantial edits and added detail descriptions of assumptions and\nconsiderations related to how uncertainty in each input parameter were set in our model, as follows:\noText S1. Uncertainties related to inverse modeling parameters.\nIn this study, we used Monte Carlo simulations to evaluate the uncertainty related to parameters in\ninverse modeling including simulated Jacobian matrices, a priori BB emission errors, a priori\nanthropogenic fossil/fuel biofuel emission errors, and observational errors. We quantified the\nuncertainty related to each parameter individually by conducting 1,000 simulations, wherein each\nparameter was perturbed according to assumed error distributions. The overall error was aggregate by\nPbbd\\]Vz2=!z2. Detailed assumptions and related uncertainties were discussed as follows.\ni\nText S1.1 Uncertainties related to Jacobian matrices.\nTo calculate deposition-emission sensitivity at each ice core site, we treated emissions in each region\nas a whole. However, sensitivities to these regional emissions can vary with spatial variations within a\nregion across different inventories, potentially resulting in discrepancies in the calculated Jacobian\nmatrices throughout the study period (Figure S24). Additionally, interannual fluctuations in\nmeteorological conditions can affect the calculated Jacobian matrices. To estimate the uncertainty of\nJacobian matrices due to spatial variations in emissions from PI to PD as well as interannual variations\nof meteorological conditions, we assumed that sensitivities follow a bimodal normal distribution. The\nmeans and standard deviations of the two normal distributions were assumed to be the average values\nand the standard deviations of the calculated sensitivities from 5-year GEOS-Chem simulations using\nthe PI (i.e., 1750-1754) and PD (i.e., 2000-2004) emissions, respectively. The resulting uncertainties of\nglobal BB emissions are shown in Figure S27(a).\nWe used the same meteorology data from 2000-2004 from MERRA2 to drive GEOS-Chem and\ncalculate Jacobian matrices for both PI and PD due to the lack of reliable observation-constrained\nmeteorology in PI. To account for the changes in meteorological conditions from PI to PD, we\nconducted additional sensitivity tests using GEOS-Chem driven by meteorological fields from the\nNASA Goddard Institute for Space Studies E2.1 (GISS-E2.1)1. We performed simulations from 1852\nto 1856 for the PI scenario and from 2002 to 2006 for the PD scenario. The estimated Jacobian matrices\nwith PI meteorology (K ) were derived by scaling the sensitivity matrices with PD meteorology from\nPImet\nMERRA2 (K ) with the PI-to-PD ratio simulated with GISS meteorology, i.e., K = K\nPDmet, MERRA2 PImet PDmet,\n× (K / K ).\nMERRA2 PImet, GISS PDmet, GISS\nOur results reveal that the relative difference in total rBC deposition fluxes between these two scenarios\ngenerally falls within ' 30%, indicating a relatively modest impact of meteorology on the annual\naverage deposition fluxes (Figure S28). Although the relative difference in some model grids can reach\nas high as 100%, these effects are less likely to be discernible in our observational data since these grid\ncells are located far from the ice core sites. Similarly, relative differences in the emission-deposition\nsensitivities for most polar ice core sites fall within the range of ' 30% (Figure S29), a range narrower\nthan the sensitivity error we assumed as discussed above (mostly range from -85% to 90%). Large\nrelative differences mainly occur in cases with low sensitivity values, which have limited effects on the\ninverse modeling results. This conclusion can be further supported by the inverse modeling results with\nthe default K and the scaled K (Figure S30). Overall, we concluded that our method of\nPDmet, MERRA2 PImet\nusing fixed PD meteorological conditions in all simulations is justified, and the resulting uncertainty\nshould be smaller than that shown in Figure S27(a).\nText S1.2 Uncertainties related to a priori BB emission errors.\nUncertainties related to a priori BB emission errors could affect the inverse modeling results. Too small\nerrors might undermine the constraint of the observational data, leading to a posteriori emissions nearly\nidentical to the a priori emissions. Too large errors might weaken the constraint of the a priori emissions,\nleading to overfitting to the observational records and unreasonable a posteriori emissions. In Monte\nCarlon simulations, the a priori error for both BB emissions are assumed to be uniformly varied within\n±20%. The resulting uncertainties of global BB emissions are shown in Figure S26(b).\nText S1.3 Uncertainties related to a priori anthropogenic fossil fuel/biofuel emission error.\nWe assumed the a priori anthropogenic fossil fuel/biofuel emission error to be uniformed distributed\nwithin a range of ±20% of the emissions. We do not expect the uncertainty of this parameter could\nintroduce large uncertainties into our inverse modeling results, as shown in Figure S26(c).\nText S1.4 Uncertainties related to observational error.\nWe assumed the observational error to be uniformly distributed within a range of ±20% of the\nmeasurement values and larger than 0%, while the default observational errors range from 10% to 174%\n(see Methods). We do not expect the uncertainty of this parameter could lead to large uncertainties to\nour inverse modeling results, as shown in Figure S26(d).p\nWe added Figure S27 in SI text as follows,\nFigure S27. Timeseries of estimated BB rBC emissions from 1750 to 2010 in BB4CMIP and\npost\nLPJ-LMfire inventories. The shaded areas represent the 2.5% and 97.5% uncertainty range of the\npost\na posteriori emissions related to the uncertainty of (a) Jacobian matrices (Text S1.1) (b) a priori BB\nemission errors (Text S1.2) (c) a priori anthropogenic fossil fuel/biofuel emission errors (Text S1.3) (d)\nobservational errors (Text S1.4).\nComment3\nThestudyshouldprovidescientificevidenceforthefindingsbyprovidingadditionaldataorobtaining\nnew data. For example, in the section \"Implications on cloud albedo forcing\", the conclusion \"the\ncooling effect of aerosol radiative forcing from PI to PD may be overestimated in current climate\nmodels\"haveyettobeprovenfully.Furtherevidenceisneededtodemonstratewhetherthisconclusion\nisvalidconsideringtheinventoryerrorandsimulationerror.\nResponse\nWe have revised the manuscript to highlight the major conclusion that using observational constraints\ncan reduce the uncertainty of CAF associated with the uncertainty in PI biomass burning emissions.\nThe discrepancies between the two a posteriori emissions decrease compared with the two a priori\nemissions, consequently reducing the uncertainties of CCN simulations and CAF calculations related\nto BB emissions. Our results show that using a posteriori BB emissions leads to a lower CAF compared\nwith that using BB4CMIP emissions, which is widely used in climate models. This result is broadly\nconsistent with previous studies4, 5. However, here we would like to emphasize the effect on the\nuncertainty of CAF.\nTo clarify this point, we revised the text in Lines 220-226 as follows:\noTwo a posteriori emissions scenarios consistently suggest higher BB aerosol emissions in PI compared\nwith the CMIP6 emissions widely adopted in current climate models (i.e., BB4CMIP +CEDS). This\nconclusion remains robust even when considering the emission uncertainties (Figure S4). These\nfindings suggest higher CCN concentrations during the PI which will result in less cooling effects of\nCAF when employed in climate models. Current climate model using CMIP6 emissions might need to\nbe reevaluated given the underestimate of BB emissions in PI.p\nComment4\nThis study have created the biomass burning emissions inventory for a period. The significance for\npresent/futureclimateassessmentsandpollutionanalysis,andtheapplicabilityofthemethodologyfor\ntheinversionoftheBBemissionsneedtoclarifyinthisstudy.\nResponse\nTo discuss the significance of the past BB emissions derived in this study, we added the following\nsentences in Lines 226-231:\noStudy have found that even small uncertainty in simulated aerosol radiative forcing could lead to\nsignificant differences in climate model results, such as global surface temperature and sea ice area6.\nAnd the reduced uncertainties with observational constraints demonstrated in this study could possibly\nhelp with improving the climate model performance and climate sensitivity estimations, further improve\nfuture climate change projections.p\nFor the applicability of the inversion to derive BB emissions, we think this method could derive\nreasonable a posteriori emissions with reliable past observational constraints and reasonable model\nsimulations results. We believe that we could easily extend the study to the earlier period with longer\nice core records, model-simulated a priori emissions, and emission deposition sensitivity simulated\nunder different climate conditions, as we discussed in Lines 284-288 in the main text.\nComment5\nP2 line 58: What is the dividing line between preindustrial period(PI) and present period (PD), the\nbeginningoftheIndustrialRevolution?\nResponse\nPreindustrial (PI) period denotes the era before the significant increase of human influence (i.e., fossil\nfuel/biofuel combustion) on the climate. Climate variabilities in PI are predominately governed by\nnatural factors, thus it is a baseline to estimate the extent of human impact on climate change. Present\nday (PD) refers to the more recent period with substantial human impact on the climate. Different\nstudies cited in this manuscript use different periods to represent PI and PD. Our work used the period\n1750-1780 to represent PI and 1997-2010 to represent PD, which is specified in the Method section\n(Lines 450-452). To avoid confusion, we emphasized these specific timeframes in the main text (Lines\n58-59) as follows,\noOur reconstructed BB emissions support previous findings that PI (represented by 1750-1780 in this\nstudy) BB emissions can be similar or even exceed the PD level (represented by 1997-2010 in this study)\n4, 5, 7, a scenario that is not currently considered in climate model studies.p\nComment6\nP2line58:Did\"theseinventories\"refertothelistsestimatedusingsatellitemonitoringdata?\nResponse\nThese emissions refer to the aforementioned emissions AeroCom and BB4CMIP. The emission used in\nAeroCom and most of the emissions used in BB4CMIP assumed a positive correlation between fire\nactivity and population density, leading to lower emissions in PI compared with PD. In contrast, some\nstudies (Refs 14, 15 mentioned in the following sentence) show a more complex relationship between\nfire activity and population, and a decrease in fire activity may occur as population increases. We thus\nsuggest emissions with a simple positive correlation between fire activity and population in AeroCom\nand BB4CMIP might underestimate emissions in PI.\nTo avoid confusion, we revised the sentence in Lines 23-26 as follows,\noSome emission inventories such as AeroCom8 and BB4CMIP9 show a relatively pristine atmospheric\nstate in the preindustrial period (PI) compared to PD because they assume positive correlation between\nfire activities and population density.p\nComment7\nP3line70-75:TheliteraturecitedinthearticleutilizedBCprecipitationdatarecordedinicecoresand\ntheideaofinversiontoobtainhistoricalemissioninventories.Themethodologyinnovationofthisstudy\nneedtobefurtherexplained.\nResponse\nOur study utilizes similar data and methods with the study by Eckhardt et al3. Both studies use a\nchemical transport model to calculate emission-deposition sensitivity, use existing emission inventory\nas a priori emissions, and use ice core rBC deposition flux as observational constraints. However, this\nstudy has major improvement over the previous work.\nFirst, the study by Eckhardt et al focuses on highlighting large discrepancies between current widely\nused emission inventories (i.e., CMIP 5 and CMIP 6) and ice core records. They provide an estimate of\ntotal emissions, but they did not differentiate between different sources (i.e., anthropogenic fuel\ncombustions or BB), as we mentioned in Lines 42-43 in the manuscript. We focus more on correcting\nthe current emission inventories based on the ice core records, and we aim to provide model-ready,\ngridded emission files that can be directly used in model simulations. We separated the emissions from\nanthropogenic combustion or BB, thus by comparing with other proxy records, we are able to identify\nthat some discrepancies between observations and simulations can be explained by BB emissions (such\nas the temporal variations in SHAF and AUST before 1900s) and some are more likely explained by\nanthropogenic fuel combustion emissions (such as the rBC deposition peak in Greenland mentioned in).\nThe study by Eckhardt et al provides an assumption that climate models might underestimate the BC\nradiative forcing in some regions and overestimate in other regions, while we are able to calculate\nradiative forcing with the gridded emissions derived in this study. We also provide another example of\nthe use of our gridded emissions (i.e., phosphorus deposition). Our gridded emissions can also be used\nin other studies.\nThe study by Eckhardt et al focuses on NH only, and the study period started from 1850. We do the\ninversion on a global scale and investigate the results in both NH and SH, and we extend the study\nperiod from 1750 to PD, as pre-1800 conditions are widely used as the PI baseline in atmospheric\nradiative forcing studies4, 5, 10, 11, and both of the a priori emissions (BB4CMIP and LPJ-LMfire) are\navailable from 1750. By extending the spatial and temporal scope, we are able to identify and analyze\nmore discrepancies between current emission inventories and observations. The a posteriori emissions\nderived in our studies bridge some of the gaps between observations and simulations (Figure 2a).\nThird, the previous study uses the average values of CMIP5 and CMIP6 emissions as the a priori\nemissions. We use two a priori emissions which are significantly different from each other (Figure 1,\na-b) and do the inversion separately. The similarity of two a posteriori emissions indicates the\nrobustness of our results.\nLast but not least, deposition flux at the ice core sites can be affected by both emissions and\ntransportation (related to meteorology). While the previous study uses the same sensitivities during the\nstudy period (1850-2000), we conduct additional sensitivity test to prove the limited effects of\nmeteorological condition change to the results (Figure S29).\nTo further clarify the differences between the previous study and our study, we add the following\ndiscussion in Lines 260-269,\noAlthough our study utilized many of the same Arctic ice core rBC fluxes records and similar methods\n(inverse modeling with chemical transport model simulated sensitivities) with the previous study by\nEckhardt et al3, here our aim is to provide a gridded, model-ready global-scale emission datasets that\ncan be used directly in modeling studies. This is in contrast to the study by Eckhardt et al (2023) that\nmainly highlighted the large discrepancies between current widely used emission inventories and ice\ncore data in the NH. Furthermore, we differentiated the a posteriori emissions between different sources\n(i.e., BB or anthropogenic fossil fuel/biofuel) and applied the gridded emissions in model simulations\nto estimate CAF and nutrient emissions and deposition. Consistency between results with two different\na priori emissions and different meteorological conditions indicate the robustness of our results.p\nComment8\nP4 line 102: In this paragraph, the article analyzed that the inverse emission inventories are\ncharacterizedbydifferentdiscrepanciesfromtheaprioriemissioninventoriesinthePIandPDperiods.\nWhat is the reason for this different discrepancies? In addition, the boundary between the PI and PD\nperiodsinFigure1shouldbetoclearlymark.\nResponse\nLarger a priori emission error (smaller S -1 in the cost function) in PI leads to smaller weights to the a\nA\npriori emission constraint and larger weights to the observational constraints. Thus the two a posteriori\nemissions tend to converge to a similar level to match the observational records. On the contrary,\nsmaller a priori emission error in PD leads to larger weights to the a priori emission constraints, thus\nthe a posteriori emissions tend to converge with their a priori emissions.\nWe further clarified this point in the revised manuscript (Lines 78-80) as follows:\noWe set the a priori emission error by assuming that the emission uncertainties are larger in earlier\nyears and gradually decreased towards the PD (Methods). Despite large discrepancies in the a priori\nemissions (Figure 1 a-b), the two a posteriori BB emissions show similar magnitudes and temporal\ntrends, especially in earlier years when observational constraints are stronger (Figure 1 c-d).p\nThere is no exact boundary for PI and PD periods and the definition varies with different studies. We\nadded the definition of PI and PD period used in this study in the main text based on comments 5 for\nclarification.\nComment9\nP5 line 131-136: MS showed that the constraints on the ice core data work differently in different\nregions, whatisthereason? Whythe constraints arenoteffectivein low latitude regions? Is it related\ntothelocationoftheobservationsiteorthesedimentationfractionoftheregion?Thispartneedstobe\nmoreclearlyexplained.\nResponse\nDifferent constraints in different regions are influenced by both the proximity of emission source\nregions to the observational sites and the relative contribution of emissions from these regions. When a\nregion is closer to the observational site, the sensitivity of deposition to emission change in this region\nis higher; When emission in one region contribute more to the deposition at the ice core sites, then it is\nmore likely that emission variations captured at this ice core site reflect emission change in this region.\nTo clarify this point, we revise the paragraph in Lines 95-109 as follows,\noHowever, due to the relatively short lifetime of rBC (~5 days in our simulations, consistent with other\nobserved12, 13 and simulated results14, 15), our records, which are mostly clustered in the polar regions,\nmainly reflect emission variations in high- and mid-latitude regions that are closer to the ice core sites\nand have a large contribution to the measured deposition fluxes. Specifically, rBC in Antarctic ice cores\nis mainly sourced from and sensitive to emissions in SHAF, South America (ARCD and SARC), and\nAustralia (AUST), while rBC deposited in Greenland primarily originates in North America (BONAW,\nBONAE, TENAW, TENAE), Europe (EURO), and Boreal Asia (BOAS) (Figures S2-S3). Our analysis\nsuggests that emissions in these regions (40% - 60% of the global total) are relatively well constrained\nby ice core data as indicated by similarities of two a posteriori emissions in this region after inverse\nmodeling process (Figure S4), compared with emissions from low-latitude regions, including North\nHemisphere Africa (NHAF), North Hemisphere South America (NHSA), Central America (CEAM),\nEquatorial Asia (EQAS), and Middle East (MIDE), which have relatively small contributions to the\ndeposition fluxes observed at the ice core sites (Figures S2-S3).p\nComment10\nP5 line 137-140: The BB emission in low latitudes region were seemingly not well constrained by\nice core data. Itcannotbeshown thatthe inversemodelcanprovidea tight constrainton thetotal global\nBBemissionsinthePI.Actually,TheBBemissioninlowlatitudesregionandaccurateinversionresult\nshouldbepaymoreattention.\nResponse\nThanks for pointing this out. We would like to highlight that the inverse model can constrain emissions\nin middle- and high-latitude regions that have larger discrepancies compared with low latitude regions.\nTherefore, tight constraints on middle- and high-latitude regions can largely improve the estimate of\ntotal emissions. We also noted the limitation that ice cores have relatively weak constraints on low\nlatitude emissions. This point has been discussed in the manuscript. To be more accurate, we revised\nthe sentence in Lines 110-114 as follows,\noEven so, comparisons between the two a priori BB emissions indicates that high- and mid-latitude\nregions account for most of the discrepancies in global total emissions in PI, and our inverse modeling\ncan provide a tight constraint for these regions and reduce discrepancies, further improve the estimates\nof the global total BB rBC emissions in the PI (Figure S6).p\nComment11\nP6line141-143:Weretheinthemodelingofthedifferentemissioninventoriesevidentonlydifferentin\nthesetworegions?Arethedifferencesnotreflectedelsewhere?Why?\nResponse\nWe discussed the difference in Greenland and Antarctica because our ice core sites are mostly clustered\nin these two regions, providing data to compare and validate the model performance. The Greenland\nice core records can represent the conditions in most of the NH regions, where anthropogenic emission\nis a more important rBC source especially after the industrial period, due to high population density and\nhigh anthropogenic fuel combustion. The Antarctic ice core records can represent the conditions in most\nof the SH, where anthropogenic emissions are relatively low due to lower population density and fuel\ncombustion. The differences are also reflected in areas with one ice core record available (i.e., South\nAmerica, Boreal Asia and Europe), and North America with three ice core records available. We added\nthe comparison results in other regions in Figure S8, and added descriptions in the main text in Lines\n133-137 as follows,\noThere are several ice core records sporadically located in other regions including South America, North\nAmerica, Boreal Asia, and Europe. Although these ice core records are not representative of the\nconditions in the whole region, using a posteriori BB emissions or anthropogenic fossil fuel/biofuel\nemissions could also result in a better agreement between the simulation results and ice core records\n(Figure S8).p\nComment12\nP6line161-175:Whatisthesignificanceofthesensitivityanalysisofemissionsbyregiontothemodel?\nWhatistheroleofsensitivityanalysis?\nResponse\nTo clarify this part, we revise the paragraph in Lines 144-160 as follows,\noHowever, the high a posteriori error correlation in these regions indicates it is challenging to quantify\nthe emissions in these regions independently (i.e., the same modeled results that match the observations\ncould be obtained by adjusting emissions in either of the regions or combination of several regions).\nSimilar error correlation issues were discussed in a previous work by Maasakkers et al16. To show the\nresults in the most extreme case, we further conducted sensitivity tests to examine how emissions in\none of the four regions would change to match the observational values if emissions in all other three\nregions remain unchanged (Figure S9). These results provide an upper limit estimate of emission\nchanges constrained by ice core records. The sensitivity analysis suggests that adjusting emissions in\nARCD or in SARC only can hardly improve the agreement between model and ice cores (Figure S9 k,\nl), thus this temporal variation is more likely driven by the emission trends in SHAF and AUST. While\nFigure S9 shows the upper limit of the a posteriori emissions in SHAF and AUST, the similar trends\nfor both regions in the BB4CMIP and LPJ-LMfire (Figure S4) suggest that the simulated emissions\npost post\nare reasonable given that the ice core records at different locations of Antarctica consistently show\nsimilar trends as well. In addition, although emissions within different SH regions have uncertainties,\ntotal emissions in SH regions consistently show similar levels and trends (Figure S9).p\nComment13\nP7line196-200:Whatdoesthepassagemean?\nResponse\nIn this paragraph, we found that the a posteriori emissions in BOAS show two periods of high BB\nemissions in 1750-1780 and in 1850, and a decreasing trend after 1850. The decreasing trend is also\nsuggested by the previous study using Greenland ice core rBC records to reconstruct NH emissions3\n(The consistency is mainly because we are using nearly the same ice core records in Greenland). But\nthe previous study only estimate total rBC emissions and did not distinguish between anthropogenic\nfossil fuel/biofuel emissions and BB emissions. They attribute this trend (decrease in 1850 and increase\nafterwards) to anthropogenic emission change in BOAS caused by economic reasons (such as October\nRevolution and World War I). We suggest that this change is mainly related to changes in BB emissions,\nbecause ice core records of p-HBA and VA (BB tracers) shows similar trend at the same period. To\nclarify, we revise the paragraph in Lines 172-185 as follows,\noIn NH regions close to the ice core sites, the a posteriori BB emissions generally exhibit higher levels\ncompared with the a priori emissions (Figure S4). The largest discrepancy is observed in BOAS, which\nis one of the most important BB source regions in the NH. The two a posteriori emissions consistently\nshow higher BB emissions in 1750-1780 and around 1850 and a decreasing trend in the late 1800s. This\nvariability is not captured by the a priori emissions and is constrained mostly by the rBC records from\nAkademii Nauk and Flade Isblink, where the contribution of BB to rBC deposition from BOAS is larger\nthan that from North America (Figure S2). The decrease after 1850 in boreal Asia also is reported by a\nprevious emission reconstruction study with similar ice core records, and attributed to anthropogenic\nemission changes in Russia due to economic collapse during the October Revolution and World War I3.\nIn contrast, we suggest that the decreasing trend, together with the two earlier periods of high rBC\nemissions, is likely related to BB emission changes because the trends are consistent with other BB\ntracers (i.e., para-hydroxybenzoic acid, p-HBA, and vanillic acid, VA) measured in the Akademii Nauk\nice core (Figure S11)17.p\nComment14\nP7 line 201-202: The MS mentioned that the downward trend in emissions from the late 19th to early\n20th centuries could be attributed to changes in thenature ofhuman impactson wildfires. The author\nshouldexpandonwhythischangeledtothedeclinein emissions.\nResponse\nAgricultural expansion could have suppressed wildfire activity in the following aspect: Converting from\nnatural landscapes (such as forest and grassland) to agricultural landscapes (land for cropping and\ngrazing) could reduce the biomass fuel load; landscape fragmentation through roads, fence lines,\npaddocks, farmsteads, and other structures could suppress fire spread; and landscape management\nmainly aim to reduce uncontrolled fires. To clarify this, we revised the paragraph from Lines 186-196\nas follows,\noHuman influence on BB gradually increased relative to the climate influence as population expand\nrapidly following the 19th century 18. The a posteriori BB emissions show a declining trend starting\nfrom the late 1800s to the early 1900s in multiple regions including SHAF, South America (ARCD and\nSARC), North America (BONAE, BONAW, TENAE, TENAW), and BOAS (Figure S4), although\npopulation and anthropogenic emissions continue to rise during this period. The declining trend in BB\nemissions is consistent with the charcoal records from the same regions19 (Figure S10f, Figure S11d,\nFigures S12-13). The opposite trends in BB emissions and population change in this period suggest an\noverall negative effect of human activities on BB, likely caused by rapid expansion of agricultural\nlandscapes from natural landscapes that reduce biomass fuel load, landscape fragmentation resulting in\nreduced the fire spread, and land management to controll fires20, 21, 22.p\nComment15\nP8 line 235-237: This result seems to be one of the important conclusions of this research and a new\nfindinginreconstructingemissioninventoriesrelativetotheprioriinventories.Isitpossibletofurther\nexplain what can be further analyzed by obtaining this result? What are the new implications of this\nresultfortheclimateenvironment?\nResponse\nIn this study we do not want to overly highlight this conclusion that we quantitively estimate the aerosol\ncooling effect should be lower after using the revised PI aerosol emissions, while this has been discussed\nby several previous studies4, 5. We revised this part in Lines 220-231 as shown in Comment 3 and\nComment 4.\nComment16\nP8line246-249:Thestatementthat\"biomassburningisalsoanimportantregionalsourceofglobalP\ndeposition\"needstobesupportedbysupportdataorotherliterature.\nResponse\nWe added two references in Line 241 from one observational study and one model study with a new\ncompiled emission dataset. Our study with the current widely used emissions (i.e., BB4CMIP + CEDS,\nwhich is lower than other BB emissions used in this study) also suggests the importance of BB source\nto P deposition regionally (Figure S18). It is important to know that all these studies are subject to large\nuncertainties and further comprehensive evaluation will be needed to enhance our understanding of the\nprocess. However, such in-depth assessments fall outside of the scope of this study. We primarily aim\nto provide an example of the potential utility of our new emission datasets.\nComment17\nP10 line294-296:Thestudyshould state thathow to determine the processedrBC data were allfrom\nbiomassburningandverifythereliabilityoftheinversionresult.\nResponse\nWe want to clarify that we did not assume all the measured rBC fluxes from the ice core records are\nfrom BB. Instead, we assumed that they are the sum of rBC emitted from BB and from anthropogenic\nfossil fuel/biofuel emissions. In the inverse modeling process, we used a priori emissions that include\nboth BB emissions (i.e., BB4CMIP or LPJ-LMfire) and anthropogenic fossil fuel/biofuel emissions (i.e.,\nCEDS), and we got the a posteriori emissions for both BB (Figure 1) and anthropogenic fossil\nfuel/biofuel combustion (Figure S7). We assumed the current CEDS emission inventory is relatively\naccurate compared with BB emissions since more records (such as energy use, fuel consumption, and\npopulation data) are available as constraint, thus we set smaller a priori emission error for CEDS (see\nMethods). Although we did not further discuss the a posteriori CEDS anthropogenic fossil fuel/biofuel\nemission because we mainly focus on BB, we do include this source in our inverse model.\nThe measured rBC fluxes have high interannual variability which might be affected by many factors\nother than emission change, such as climate variations, occasional fire events and glaciological noise.\nWe smooth the data to eliminate the other factors so that the changes in the smoothed records are most\nlikely reflect the change of emissions.\nComment18\nP11line342-344:AllthesetestsmentionedinMS wereconductedwiththeyear2000asthescenario.\nWould the test situation vary in different years? The test scenarios for other years should be added to\nfurthersupplementthecasestoenhancepersuasiveness.\nResponse\nTo show that this conclusion is consistent in different years, we extended the simulation period for 5\nyears from 2000 to 2004. Instead of showing the relative difference in 2000, we now show the relative\ndifference calculated based on the five-year averages (Figure S20 c and Figure S22 c), and we also\nshow the standard deviation of the relative difference for the five years (Figure S20 d and Figure S22\nd). There is no significant difference in the results when using the data for the year 2000 or the average\nvalues from 2000 to 2004. The standard deviation of the relative difference for the five-year period is\nmostly less than 5%. These further prove the consistency of the results in different years.\nWe revised the sentence in Lines 353-356 as follows,\noThese tests show that changes in these parameters had limited effects on the simulated rBC deposition\nflux at the measurement sites, most of which are located far from the sources. The results are consistent\nbetween different years indicated by the low standard deviations (Figures S20-S23).p\nWe update Figures S20-S23 and the corresponding caption as follows,\no\nFigure S23 Scatter plot showing BC deposition fluxes at ice core sitesfor the base case versus the\nperturbed case, with regard to hydrophobic-hydrophilic conversion. The settings in the base case\nand the perturbed case are as described in Figure S21. Each point represents the average values from\n2000 to 2004.p\nComment19\nP12line359-363:Itisnecessarytoexplainwhythesensitivityisassumedtochangelinearlyfrom1750\nto2000andremainconstantafter2000.\nResponse\nIn this study, to calculate deposition-emission sensitivity at each ice core site, we treat emissions in\neach region as a whole. However, sensitivity could change with different emission spatial variation\nwithin one region from PI to PD, potentially resulting in large discrepancies in the calculated Jacobian\nmatrices over the study period (Figure S24). To account for the effects of emission distribution\ntransition from PI to PD in the inverse modeling process without consuming too much computational\nresources on calculating the sensitivity matrices for the whole 261-year period, we simply assume the\nsensitivity changed linearly from 1750 to 2000 and became constant after 2000. We expect the resulting\nuncertainties to be within the range shown in Figure S27, which considers both the PI to PD emission\nspatial variation change and meteorological conditions change.\nWe revise the description in the Method Section in Lines 369-374 as follows,\noTo account for the effects of emission distribution transition from PI to PD in the inverse modeling\nprocess without consuming excessive computational resources to calculate the sensitivity matrices for\nthe whole 261-year period, we simply used linear transition by assuming the sensitivity changed linearly\nfrom 1750 to 2000 and became constant after 2000. The details of the uncertainties are discussed in\nText S1.1.p\nComment20\nP12line363-366:Thestudydiscussedthereasonsforusingthesamemeteorologicalconditionsinthe\nmulti-year simulations in a Supplementary Document. However, it is still not sufficient to justify it\nbecausetheresultsofthesimulationsunderdifferentmeteorologicalconditionsdifferedsignificantlyin\nsomeareas,asillustratedinFigureS25.\nResponse\nWe revised the uncertainty estimate caused by different meteorological conditions based on Comment\n2 and shown in Text S1.1. Additionally, we conducted sensitivity studies with K as well as K .\nThe\nPD PI\nresults suggest relatively small effects (Figure S30).\nComment21\nP12 line 377-379: The reasons and justification for the adjustment of the measurements should be\nfurtherclarified,andadetaileddescriptionofhowtheadjustmentsweremadeshouldbepresented.\nResponse\nIn the inverse modeling process, we assumed the PD emissions are accurate, and the simulated rBC\ndeposition fluxes are accurate. Thus there should be little adjustment on the PD emissions for model\nresults to match the observations. However, there is still bias between the simulated values and the\nobserved values (Figure S19). Simply ignoring this bias will cause unreasonable adjustments on PD\nemissions, further causing error when estimating a posteriori emissions during the whole study period.\nWe eliminated this error by scaling the observed fluxes to the modeled fluxes in PD. We assumed this\nbias between observations and simulations does not change during the study period. Thus for each year\nduring the study period, we corrected modeled values with the same ratio in PD.\nWe revise the text in Lines 384-390 as follows,\noTo overcome the model bias compared with the observations in PD (Figure S19), we scaled the\nobserved values for the 2000-2004 period to the modeled values for the PD scenario to avoid\nunreasonable adjustments for the a posteriori emissions in the PD due to model bias instead of emission\nerrors. We applied the same scale factors during the study period by assuming this model-observation\nbias does not change with time. Results without scaling show lower a posteriori emissions in the PD\n(Figure S25), contrary to our assumption that emissions in PD are accurate.p\nComment22\nP13line388-408:Itisnecessarytofurtherprovethereasonablenessoftheassumptionoftherangeof\nthepriorierrors.Thepracticalevidenceofcurrentassumptionisnotenough,andtheuncertaintyofthe\npriori inventory can be determined by comparing the simulation using the priori inventory and the\nobservation, or by conducting several experiments to set different error ranges to prove the\nreasonablenessofthesetting.\nResponse\nWe revised the uncertainty estimate part related to a priori emissions error based on Comment 2 and\nshown in Text S1.2 (a priori BB emission error) and Text S1.3 (a priori CEDS emission error). We\nused Monte Carlo simulations by perturbing the a priori emission error in the range of ±20%. The results\nin Figure S27 b-c show the related uncertainties.\nComment23\nP14line433-434:Itcanbefoundthattheuncertaintyofemissionsseemstobedifferentineachregion,\nandtheuncertaintyrangeofemissionsindifferentregionsshouldbemarkedintheformofamap.\nResponse\nThe uncertainty of a posteriori emissions varied in different regions and in different years, and we\nmarked the 2.5% to 97.5% uncertainty range in shaded areas in each panel in Figures S4-S5. The\nuncertainties shown here only represent uncertainties caused by our assumptions in different parameters\n(observational error, a priori BB emission error, a priori anthropogenic fossil/fuel biofuel emission\nerror, and simulated emission-deposition sensitivity error). The small variations in the low latitude\nregions in Figure S5 does not mean emissions in these regions are accurate. Instead, this means our\nassumptions have little effects on emissions in these regions.\nComment24\nP18figure3:Thesequencenumberofthesubgraphshouldbeindicated.\nResponse\nDone.\nReference\n1. Murray LT, Leibensperger EM, Orbe C, Mickley LJ, Sulprizio M. GCAP 2.0: a global 3-D\nchemical-transport model framework for past, present, and future climate scenarios. Geosci\nModel Dev14, 5789-5823 (2021).\n2. van der Velde IR, et al. Vast CO2 release from Australian fires in 2019n2020 constrained by\nsatellite. Nature597, 366-369 (2021).\n3. Eckhardt S, et al. Revised historical Northern Hemisphere black carbon emissions based on\ninverse modeling of ice core records. Nature Communications14, 271 (2023).\n4. Liu P, et al. Improved estimates of preindustrial biomass burning reduce the magnitude of\naerosol climate forcing in the Southern Hemisphere. Science Advances7, eabc1379 (2021).\n5. Hamilton DS, et al. Reassessment of pre-industrial fire emissions strongly affects\nanthropogenic aerosol forcing. Nature Communications9, 3182 (2018).\n6. Fyfe JC, Kharin VV, Santer BD, Cole JNS, Gillett NP. Significant impact of forcing\nuncertainty in a large ensemble of climate model simulations. Proceedings of the National\nAcademy of Sciences118, e2016549118 (2021).\n7. van der Werf GR, Peters W, van Leeuwen TT, Giglio L. What could have caused pre-\nindustrial biomass burning emissions to exceed current rates? Clim Past9, 289-306 (2013).\n8. Dentener F, et al. Emissions of primary aerosol and precursor gases in the years 2000 and\n1750 prescribed data-sets for AeroCom. Atmos Chem Phys6, 4321-4344 (2006).\n9. van Marle MJE, et al. Historic global biomass burning emissions for CMIP6 (BB4CMIP)\nbased on merging satellite observations with proxies and fire models (1750n2015). Geosci\nModel Dev10, 3329-3357 (2017).\n10. Gordon H, et al. Reduced anthropogenic aerosol radiative forcing caused by biogenic new\nparticle formation. Proceedings of the National Academy of Sciences113, 12053-12058\n(2016).\n11. Lee LA, Reddington CL, Carslaw KS. On the relationship between aerosol model uncertainty\nand radiative forcing uncertainty. Proceedings of the National Academy of Sciences113,\n5820-5827 (2016).\n12. Cape JN, Coyle M, Dumitrean P. The atmospheric lifetime of black carbon. Atmospheric\nEnvironment59, 256-263 (2012).\n13. Lund MT, et al. Short Black Carbon lifetime inferred from a global set of aircraft\nobservations. npj Climate and Atmospheric Science1, 31 (2018).\n14. Hodnebrog Ø, Myhre G, Samset BH. How shorter black carbon lifetime alters its climate\neffect. Nature Communications5, 5065 (2014).\n15. Samset BH, et al. Modelled black carbon radiative forcing and atmospheric lifetime in\nAeroCom Phase II constrained by aircraft observations. Atmos Chem Phys14, 12465-12477\n(2014).\n16. Maasakkers JD, et al. Global distribution of methane emissions, emission trends, and OH\nconcentrations and trends inferred from an inversion of GOSAT satellite data for 2010n2015.\nAtmos Chem Phys19, 7859-7881 (2019).\n17. Grieman MM, et al. Aromatic acids in a Eurasian Arctic ice core: a 2600-year proxy record of\nbiomass burning. Clim Past13, 395-410 (2017).\n18. Pechony O, Shindell DT. Driving forces of global wildfires over the past millennium and the\nforthcoming century. Proceedings of the National Academy of Sciences107, 19167-19170\n(2010).\n19. Marlon JR, et al. Climate and human influences on global biomass burning over the past\ntwo millennia. Nature Geoscience1, 697-702 (2008).\n20. Andela N, et al. A human-driven decline in global burned area. Science356, 1356-1362\n(2017).\n21. Archibald S, Roy DP, Van Wilgen BW, Scholes RJ. What limits fire? An examination of\ndrivers of burnt area in Southern Africa. Global Change Biology15, 613-630 (2009).\n22. Andela N, van der Werf GR. Recent trends in African fires driven by cropland expansion and\nEl Niño to La Niña transition. Nature Climate Change4, 791-795 (2014).\n23. Val Martin M, Logan JA, Kahn RA, Leung FY, Nelson DL, Diner DJ. Smoke injection\nheights from fires in North America: analysis of 5 years of satellite observations. Atmos Chem\nPhys10, 1491-1510 (2010).\n24. He C, Li Q, Liou KN, Qi L, Tao S, Schwarz JP. Microphysics-based black carbon aging in a\nglobal CTM: constraints from HIPPO observations and implications for global black carbon\nbudget. Atmos Chem Phys16, 3077-3098 (2016)."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The review of the manuscript “Improved Biomass Burning Emissions from 1750 to 2010 using\nIce Core Records and Inverse Modeling”\nThe revised manuscript demonstrates the significance of the study more clearly and several\nanalysis of the results has been supplemented. However, there are still some issues in the\nmanuscript that require further explanation. The MS can be considered for publication if these\nissues could been solved.\n1. The study mainly utilized inversion techniques to provide the BC emissions. It is recommended\nto modify the title “…emission” to “…emission of BC”.\n2. According to the response and the associated revision, the study could not provide the improved\nemissions at low latitudes. The study needs to provide further quantitative data to demonstrate\nthat the emissions at mid- and high-latitudes account for the majority of global emissions.\nOtherwise, it does not show that the results of this study improve global emissions. The title\nshould be revised to be consistent with the research results (e.g., Improved… emissions at mid-\nand high-latitudes from…).\n3. A priori inventories from different sources (e.g., biomass burning, fossil fuel/biofuel) were\ncombined in the treatment of a priori inventories for inversion. However, the methodology\ndescribed in the study could only obtain total rBC emissions and could not be able to distinguish\nthe different emission sources of rBC, if the relationship between the different emission sources\nand the ice-core rBC records were not established separately. How did the study determine the\nemissions from Biomass Burning of rBC? Otherwise, it is recommended to modify the title to\n“Improved Emissions of BC at mid- and high-latitudes from…”."}, "author_response": "Response to Reviewer #1\nComment 1\nThe study mainly utilized inversion techniques to provide the BC emissions. It is recommended\nto modify the title “…emission” to “…emission of BC”.\nResponse\nAlthough we performed the inversion for BC, we aim to use it as a tracer to infer biomass burning\nemission changes, because the budget is simple. We finally derived biomass burning emissions for other\ngaseous and aerosol species by applying scale factors. Besides, our analysis is not limited to BC. We\nused the whole biomass burning dataset to estimate the change of cloud condensation nuclei from\npreindustrial period to the present day and calculate cloud albedo forcing. We also provided another\nexample of the potential application of our dataset, which is estimating phosphorus emissions and\ndepositions from biomass burning.\nComment 2\nAccording to the response and the associated revision, the study could not provide the improved\nemissions at low latitudes. The study needs to provide further quantitative data to demonstrate that the\nemissions at mid- and high-latitudes account for the majority of global emissions. Otherwise, it does\nnot show that the results of this study improve global emissions. The title should be revised to be\nconsistent with the research results (e.g., Improved… emissions at mid- and high-latitudes from…).\nResponse\nWe think that the Illimani ice core record (in South America) shows constraint on the emissions in Arc\nof deforestation (ARCD), which is a low-latitude region. The emission difference in this region is\nsmaller in the a posteiori emissions compared with a priori emissions (Figure S4). As mentioned in\nlines 91-103, we think emissions in regions in Figure S4 are relatively well constrained by the ice core\nrecord. The total biomass burning emission in these regions contributes to 40% - 60% of the global total\nand more than 90% of the emission differences between BB4CMIP and LPJ-LMfire (Figure S6). Our\ninverse modeling can provide a tight constraint for emissions in these regions and reduce the\ndiscrepancies, thus improving the estimates of global total.\nComment 3\nA priori inventories from different sources (e.g., biomass burning, fossil fuel/biofuel) were combined in\nthe treatment of a priori inventories for inversion. However, the methodology described in the study\ncould only obtain total rBC emissions and could not be able to distinguish the different emission sources\nof rBC, if the relationship between the different emission sources and the ice-core rBC records were not\nestablished separately. How did the study determine the emissions from Biomass Burning of rBC?\nOtherwise, it is recommended to modify the title to “Improved Emissions of BC at mid- and high-\nlatitudes from…”.\nResponse\nAs we described in Lines 390-410, we treated emissions from biomass burning and fossil fuel/biofuel\nburning separately by setting different a priori emission errors. In short, we assumed errors for fossil\nfuel/biofuel emissions are much smaller than that for biomass burning emissions, as more records (such\nas energy production and consumption data, population record) are available for better estimation\nemissions from anthropogenic activities. The inverse modeling process made different adjustment on\nthe a priori emissions from different sources based on the errors we set. The input of the inverse\nmodeling (i.e., a priori emissions x ) is a 34 by 1 vector that represents the a priori BB emissions in 17\nA\nregions and fossil fuel/biofuel emissions in 17 regions, and the output (i.e., a posteriori emissions x) is\na 34 by 1 vector that represents the optimized estimates of BB emissions and fossil fuel/biofuel\nemissions."}]

Decision letter