Comments from Reviewer #1 评论者#1

General comment: Using a machine learning technique and a “top-down” inversion approach, with remote sensing observations and meteorological reanalysis data as input, the authors analyzed the evolution of black carbon emissions in China from 2000 to 2020. Moreover, using an attributional model, the authors related premature mortality and black carbon exposure, and investigated the mortality due to black carbon exposure and its drivers. In addition, the authors discussed the uncertainties in the calculation of black carbon AAOD and health impact estimation. The manuscript is well structured and written, the methodology is well established, the results are well presented and discussed. Due to the issues listed below, I suggest a major revision before it is suitable for publication.

一般性意见：利用机器学习技术和“自上而下”的反演方法，以遥感观测数据和气象再分析数据为输入，分析了2000 - 2020年中国黑碳排放的演变。此外，使用归因模型，作者将过早死亡与黑碳暴露联系起来，并调查了黑碳暴露及其驱动因素导致的死亡率。此外，作者还讨论了黑碳AAOD计算和健康影响评估中的不确定性。手稿结构和书写良好，方法学建立良好，结果得到了很好的介绍和讨论。由于下面列出的问题，我建议在适合出版之前进行重大修改。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s positive comments on our paper, and have made point-by-point response and revisions as summarized below.

我们感谢审稿人对我们论文的积极评价，并作出了逐点回应和修改，总结如下。

Q1. Major issues: In the introduction, there is no review of studies on BC-associated premature mortality, especially over China. The motivation behind the authors' investigation into BC-associated premature motility and the research status of this premature motility is not clear. As the associated premature mortality is listed in the title and it is supposed to be one of the important parts of the paper.

Q1.主要问题：在引言中，没有对BC相关过早死亡的研究进行综述，特别是在中国。作者对BC相关的过早运动的研究背后的动机和这种过早运动的研究现状尚不清楚。由于相关的过早死亡率被列在标题中，这应该是本文的重要部分之一。

Response and main revisions:

答复和主要修订：

We appreciate and agree with the reviewer’s valuable comment. The review of studies on BC-associated premature mortality in China and the motivation of this study are summarized below.

我们感谢并同意评论者的宝贵意见。现将中国BC相关早死研究的综述和本研究的动机总结如下。

Based on the “bottom-up” emission estimates with great uncertainty and CTMs, previous studies have evaluated the BC-associated premature mortality in China for limited years (2000, 2013, and 2016, Cui et al., 2022; Qin et al., 2019; Saikawa et al., 2009; Wang et al., 2021). Large discrepancy exists in the magnitude (50,100-1,436,960 cases) and few analyses are available on the long-term spatiotemporal variations and driving forces of BC-associated health effects. The influence of human activities on quickly changing BC emissions and their associated health impact is inadequately or inaccurately understood, weakening science-based decision making for air pollution control.

基于具有很大不确定性的“自下而上”排放估计和CTM，先前的研究评估了中国有限年份的BC相关过早死亡率（2000年，2013年和2016年，Cui等人，2022; Qin等人，2019; Saikawa等人，2009; Wang等人，2021年）。在数量上存在很大差异（50，100 - 1，436，960例），并且很少有关于BC相关健康影响的长期时空变化和驱动力的分析。人类活动对快速变化的BC排放及其相关健康影响的影响没有得到充分或准确的理解，削弱了空气污染控制的科学决策。

We have added and reorganized the information in lines 95-100 in the revised manuscript.

我们在修订稿的第95-100行增加并重新组织了信息。

Q2. Major issues: In section 3.3, the results of premature mortality associated with BC exposure are only based on the estimation, without any validations, which makes the analysis less convincing. Is it possible to collect some data, either released in government reports or published in papers, to support your estimations? It does not need to be very precise, the magnitudes of the same order are sufficient.

Q2.主要问题：在第3.3节中，与BC暴露相关的过早死亡的结果仅基于估计，没有任何验证，这使得分析不太令人信服。有没有可能收集一些数据，无论是在政府报告中发布的还是在论文中发表的，来支持你的估计？它不需要非常精确，相同数量级的幅度就足够了。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. We have collected the all-cause premature deaths attributed to BC in China from limited published papers to validate our estimates. The all-cause premature deaths attributed to BC in China were reported as 50,100 cases in 2000 (Qin et al., 2019), 1,436,960 cases in 2013 (Wang et al., 2021) and 538, 400 cases in 2017 (Cui et al., 2022). All-cause premature deaths attributed to BC in China in this work were estimated as 733,910-937,990 in 2000-2020, within the wide range of 50,100-1,436,960 cases by previous studies.

我们感谢评论者的宝贵意见。我们从有限的已发表论文中收集了中国因BC导致的全因过早死亡，以验证我们的估计。2000年，中国因BC引起的全因过早死亡报告为50，100例（Qin等人，2019），2013年1，436，960例（Wang et al.，2021）和2017年的538，400例（Cui et al.，2022年）。2000-2020年，中国因BC导致的全因过早死亡估计为733，910 - 937，990例，在先前研究的50，100 - 1，436，960例病例范围内。

The health impact estimation could be biased by rare domestic β_BC values in China. Previous studies commonly adopted the same β_BC with PM_2.5 (Qin et al., 2019) or β_BC obtained from experiments conducted in Europe or the United States (Wang et al., 2021), resulting in large uncertainty. In this study, we relied on a unique cohort study in China and calculated the all-cause premature deaths attributed to BC at 733,910-937,980/yr. The β_BC values obtained from national-scale studies in the US and Europe indicate a 10-fold difference (220,980-2,386,060/yr, Supplementary Table S14), similar to the estimation conducted in the US (Li et al., 2016). More domestic epidemiological studies focusing on BC emissions are expected to further reduce the uncertainty.

中国国内罕见的β_BC值可能会导致健康影响估计出现偏差。先前的研究通常采用与PM_2.5相同的β_BC（Qin等人，2019）或从欧洲或美国进行的实验中获得的β_BC（Wang et al.，2021年，不确定性很大。在这项研究中，我们依赖于中国的一项独特的队列研究，计算出由BC引起的全因过早死亡为733，910 - 937，980/年。从美国和欧洲的国家规模研究中获得的β_BC值显示了10倍的差异（220，980 - 2，386，060/年，补充表S14），与美国进行的估计相似（Li等人，2016年）。预计更多的国内流行病学研究将侧重于BC排放，以进一步减少不确定性。

We have added the validations and uncertainty discussions in lines 533-536 and lines 610-618 in the revised manuscript.

我们在修订稿的第533-536行和第610-618行中添加了验证和不确定性讨论。

Q3. Specific points: L137: The Chinese Academy of Sciences is a huge organization. A detailed name where the data is obtained is needed. The website of the dataset rather than the website of the data center should be provided. If the dataset is associated with a published paper, then the paper should be cited.

Q3.具体要点：L137：中国科学院是一个庞大的机构。需要获得数据的详细名称。应提供数据集的网站，而不是数据中心的网站。如果数据集与已发表的论文相关，则应引用该论文。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. The land-use data were obtained from the Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences at a horizontal resolution of 1 × 1 km (https://www.resdc.cn/DOI/DOI.aspx?DOIID=129; last accessed on 25 June 2022). The elevation data were obtained from the Shuttle Radar Topography Mission at a horizontal resolution of 1 × 1 km (https://www.resdc.cn/data.aspx?DATAID=123; last accessed on 25 June 2022). We have corrected the data source information in lines 155-162 in the revised manuscript.

我们感谢评论者的宝贵意见。土地利用数据来自中国科学院地理科学与资源研究所，水平分辨率为1 × 1 km（https：www.resdc.cn/DOI/DOI.aspx? DOIID=129;最后一次访问于2022年6月25日）。高程数据来自航天飞机雷达地形使命，水平分辨率为1 × 1 km（https：www.resdc.cn/data.aspx? DATAID=123;最后一次访问于2022年6月25日）。我们已更正了修订稿第155-162行中的数据源信息。

Q4. Specific points: L148: References for CARSNET are needed.

Q4.具体要点：L148：需要CARSNET的参考资料。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. We have added the reference for CARSNET (Che et al., 2015) in line 172 in the revised manuscript.

我们感谢评论者的宝贵意见。我们已经添加了CARSNET的参考文献（Che等人，2015年12月17日，在修订稿中。

Q5. Specific points: L149: References for CARE-China and SONET are needed.

Q5.具体要点：L149：需要CARE-China和SONET的参考。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. We have added the reference for CARE-China (Xin et al., 2015) and SONET (Li et al., 2018) in lines 173-174 in the revised manuscript.

我们感谢评论者的宝贵意见。我们增加了CARE-China的参考文献（Xin等人，2015）和SONET（Li等人，2018年12月17日，在第173-174行修订稿中。

Q6. Specific points: L163: Have you tested uncertainties brought by using four months to represent four seasons?

Q6.具体要点：L163：你测试过用四个月代表四个季节带来的不确定性吗？

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. In this study, January, April, July, and October were selected as representative months of different seasons to avoid abundant calculations. This method has been widely applied in emission inversion researches (Zhang et al., 2015; Zhao et al., 2019). The relative difference between the average AAOD of four representative months and annual value were estimated within -4%~-1% during 2000-2020. We do not quantify this uncertainty due to computational costs in this work. We have added relative information in lines 193-194 in the revised manuscript.

我们感谢评论者的宝贵意见。在本研究中，选择1月，4月，7月和10月作为不同季节的代表月份，以避免大量的计算。该方法已广泛应用于发射反演研究（Zhang等人，2015; Zhao等人，2019年）。2000-2020年4个代表月平均AAOD与年平均值的相对偏差在-4%~-1%之间。我们不量化这种不确定性，由于在这项工作中的计算成本。我们在修订稿的第193-194行增加了相关信息。

Q7. Specific points: L166: Add references for CMAQ.

Q7.具体要点：L166：增加CMAQ参考。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. We have added the reference for CMAQ (USEPA, 2017) in lines 196-197 in the revised manuscript.

我们感谢评论者的宝贵意见。我们在修订稿的第196-197行中添加了CMAQ（USEPA，2017）的参考文献。

Q8. Specific points: L221: References are needed for the log-linear model.

Q8.具体要点：L221：对数线性模型需要参考。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. We have added the reference for the log-linear model (Wang et al., 2021) in line 256 in the revised manuscript.

我们感谢评论者的宝贵意见。我们增加了对数线性模型的参考文献（Wang et al.，2021年，在第256行修订稿中。

Q9. Specific points: L221: L231: References are needed for Equation 7.

Q9.具体要点：L221：L231：公式7需要参考。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. We have added the reference for the Equation 10 (Eq. 7 in the previous edition) (Wang et al., 2021) in lines 266-267 in the revised manuscript.

我们感谢评论者的宝贵意见。我们已经添加了公式10的参考（Eq. 7）（Wang et al.，2021年）在修订稿中的第266-267行。

Q10. Specific points: L257: Where are the RMSE and NMB values from? From which plots or tables?

Q10.具体要点：L257：RMSE和NMB值来自哪里？从哪些图或表？

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. We have added the data sources in line 295 in the revised manuscript and corresponding Supplementary Table S8 in the revised supplement.

我们感谢评论者的宝贵意见。我们已在修订稿第295行和修订补充件中相应的补充表S8中添加了数据来源。

Q11. Specific points: L284: Double brackets at the right side.

问题11.具体要点：L284：右侧双括号。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s reminder and the redundant bracket has been deleted in the revised manuscript.

我们感谢审稿人的提醒，在修订稿中删除了多余的括号。

Q12. Specific points: L314: I do not agree that the increase in AAOD from 2018 to 2020 is due to the increasing surface wind speed. In general, the near-surface wind speed has decreased significantly since 1980 and has become flat or increased slightly since about 2010~2013. Why did the AAOD still decrease from 2013 to 2020? Thus, near-surface wind speed only cannot explain the changing trend in AAOD. Moreover, from 2018 to 2020, only 3 years, the time period is too short for changing trend analysis.

Q12.具体观点：L314：我不同意2018年至2020年AAOD的增加是由于地面风速增加。总体而言，近地面风速自1980年以来显著下降，约自2010~2013年以来趋于平缓或略有上升。为什么2013年至2020年AAOD仍在下降？因此，仅用近地面风速不能解释AAOD的变化趋势。此外，从2018年到2020年，只有3年，时间段太短，无法进行变化趋势分析。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. Continuous air pollution controls during 2013-2020 have resulted in the reduction of light-absorption BC emissions, thereby the decline of AAOD of China. However, recent observations show that the frequency of sandstorms in northern China has increased after 2015 due to increasing surface wind speed (Yang et al., 2021). This resulted in greater emissions of light-absorption dust aerosols, thereby AAOD, partly offset the AAOD decline owing to black carbon emission mitigation in northern China. We agreed with the reviewer that the time period from 2018 to 2020 is too short for changing trend analysis, so we removed the trend analysis results for 2018-2020 from Figure 3 and the main text.

我们感谢评论者的宝贵意见。2013-2020年持续的空气污染控制导致了光吸收BC排放的减少，从而导致中国AOD的下降。然而，最近的观测表明，由于地面风速增加，2015年后中国北方沙尘暴的频率有所增加（杨等，2021年）。这导致更多的光吸收尘埃气溶胶的排放，从而AAOD，部分抵消了AAOD下降，由于在中国北方的黑碳排放的缓解。我们同意审稿人的意见，认为2018 - 2020年的时间段太短，无法进行变化趋势分析，因此我们从图3和正文中删除了2018-2020年的趋势分析结果。

We have included the discussion in lines 352-355 and modified Figure 3 in the revised manuscript.

我们在修订稿中纳入了第352-355行的讨论，并修改了图3。

Q13. Specific points: L327-329: Could you explain why a larger underestimation appears in 2000 and 2020?

问题13.具体要点：L327-329：你能解释为什么在2000年和2020年出现更大的低估吗？

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. The larger underestimation of simulated prior BC concentration in 2000 and 2020 may be caused by larger underestimation of BC emissions in these years.

我们感谢评论者的宝贵意见。2000年和2020年模拟的先前BC浓度的较大低估可能是由于这些年份的BC排放量的较大低估造成的。

For 2000, the under-reporting of activity levels and lack of local measurements for specific BC emission factors (EFs, emissions per unit of activity level) in very early year may lead to larger uncertainties in BC emission estimation (Fu et al., 2012; Guan et al., 2012). The increased uncertainty in prior BC emissions in 2020 may have resulted partly from an underestimation of increased fuel use owing to residential heating and cooking during the COVID-19 lockdown and quarantine (Zheng et al., 2020).

就2000年而言，由于活动水平报告不足，而且在最初一年缺乏对具体的BC排放系数（EFs，每单位活动水平的排放量）的当地测量，可能会导致BC排放量估算中的较大不确定性（Fu等人，2012; Guan等人，2012年）。2020年之前BC排放的不确定性增加，部分原因可能是低估了COVID-19封锁和隔离期间住宅供暖和烹饪导致的燃料使用量增加（Zheng等人，2020年）。

We have discussed the possible reasons in lines 366-367 and 407-418 in the revised manuscript.

我们在修订稿的第366-367行和第407-418行讨论了可能的原因。

Q14. Specific points: L345: Simulation -> simulation.

问题14.具体要点：L345：模拟-模拟。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s reminder. We are sorry for the mistake and have corrected it in line 384 in the revised manuscript.

我们感谢审查员的提醒。我们对这个错误感到抱歉，并在修订稿的第384行进行了更正。

Q15. Specific points: L361: What do you mean by the factor here?

Q15.具体要点：L361：这里的系数是什么意思？

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. The “factor” here represents the ratio of the difference between posterior and prior to the prior BC emissions, i.e., (a posterior – a prior) / a prior. We have modified the expression in lines 400-401 in the revised manuscript.

我们感谢评论者的宝贵意见。这里的“因子”表示先前BC发射的后和前之间的差的比率，即，（a posterior - a prior）/ a prior.我们修改了修订稿第400-401行的表述。

Q16. Specific points: L426: Why coal consumption or fossil fuel combustion are missing, which are also very important to BC emissions.

问题16.具体要点：L426：为什么煤炭消耗或化石燃料燃烧缺失，这对BC排放也很重要。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s important comment. There is a great correlation between provincial coal production and consumption. In Section 3.2.3, we used coal production as an indicator to distinguish the main coal production provinces and to further highlight the unique BC emission patterns for those provinces (Shanxi, Inner Mongolia, Henan and Shaanxi Province). Those patterns cannot be clearly revealed if coal consumption is used as the indicator.

我们感谢评论者的重要评论。各省煤炭产量与消费量之间存在很大的相关性。在第3.2.3节中，我们使用煤炭产量作为区分主要煤炭生产省份的指标，并进一步突出这些省份（山西、内蒙古、河南和陕西省）独特的碳排放模式。如果将煤炭消费量用作指标，则无法清楚地揭示这些模式。

Q17. Specific points: L490-493: How did you get those values? Calculated from equation 7?

问题17.具体要点：L490-493：你是如何得到这些值的？根据公式7计算？

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. The all-cause premature deaths attributed to BC here were calculated from equation 10 (equation 7 in the previous edition) in lines 266-278 in the revised manuscript.

我们感谢评论者的宝贵意见。此处归因于BC的全因过早死亡是根据修订稿第266-278行中的公式10（前一版中的公式7）计算的。

Q18. Specific points: L496-498: Can you calculate the relative premature deaths that divide the premature death cases by the total population? Then, one can get rid of the impacts of population density when comparing premature deaths in different regions of China.

问题18.具体要点：L496-498：你能计算出过早死亡病例除以总人口的相对过早死亡人数吗？这样，在比较中国不同地区的过早死亡时，就可以排除人口密度的影响。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. We calculated the premature death rate that divide the premature death cases by the total population and the results are shown in a new Supplementary Figure S9 in the revised supplement. Higher premature death rate in eastern China were attributed mainly to the relatively high BC exposure from developed industrial and commercial activities. We have added the corresponding statement in lines 536-539 in the revised manuscript.

我们感谢评论者的宝贵意见。我们计算了过早死亡率，即过早死亡病例除以总人口，结果显示在修订后的补充资料中的新补充图S9中。中国东部地区过早死亡率较高主要是由于发达的工业和商业活动导致的相对较高的BC暴露。我们在修订稿第536-539行增加了相应的声明。

Q19. Specific points: L499: What does cases/grid mean?

问题19.具体要点：L499：cases/grid是什么意思？

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. The “cases/grid” means the all-cause premature deaths attributed to BC in a model grid cell (27 × 27 km). Combined with the Q21 of reviewer #2, we have modified the unit “cases/grid” to “cases/1000 km²” and re-calculated the corresponding values in Table 3 in the revised manuscript to make the expression easier to understand. The corresponding sentences were modified to “The highest multiyear average of premature mortality was 1482 cases/1000 km² (the all-cause premature deaths attributed to BC per area of 1000 km²) in Shanghai, followed by 793, 761, 520, 450, and 442 cases/1000 km² in Beijing, Tianjin, Jiangsu, Henan, and Shandong, respectively (Table 3). These values were much higher than the national average of 86 cases/1000 km²” in lines 539-543 in the revised manuscript.

我们感谢评论者的宝贵意见。“病例/网格”是指在一个模型网格单元（27 × 27公里）中因细菌性感冒引起的全因过早死亡。结合2号审稿人的Q21，我们将单位“例/格”修改相应的句子被修改为这些数值远高于修订稿第539-543行中86例/1000 km²

Q20. Specific points: Table 1: Units are needed for the values of emission.

Q20.具体要点：表1：排放值需要单位。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. Table 1 shows the multiyear average relative differences between the posterior and various “bottom-up” estimates of BC emissions. We have added “unitless” for the relative difference in the caption of Table 1.

我们感谢评论者的宝贵意见。表1显示了后验和各种“自下而上”的BC排放量估计数之间的多年平均相对差异。我们在表1的标题中为相对差异添加了“无单位”。

Q21. Specific points: Figure 1: The quality of the figure needs to be improved. The words are too small and unreadable.

问题21.具体要点：图1：图的质量有待提高。这些字太小，难以辨认。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. We have improved the quality of Figure 1 in the revised manuscript.

我们感谢评论者的宝贵意见。我们在修订稿中改进了图1的质量。

Q22. Specific points: Figure 2: I highly recommend using five different colors for the data from five different years. The two dashed lines have to be introduced in the caption. The interval of bins is also needed to be introduced. The equations of NMB, NME, and RMSE should go to section 2.1.

问题22.具体要点：图2：我强烈建议使用五种不同的颜色来表示五个不同年份的数据。这两条虚线必须在标题中引入。还需要引入箱的间隔。NMB、NME和RMSE的公式应参见第2.1节。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment and modified the Figure 2. Firstly, we use 16 different colors to represent the data from 16 years (2005-2020) in Figure 2. Secondly, we added the introduction of the dashed lines and the interval of bins in the caption of Figure 2, i.e., “The red dashed line indicates the 1:1 line. The blue dashed line indicates the regression line. The interval of bins of the marginal histograms is 0.02”. Finally, the equations of NMB, NME and RMSE were moved to section 2.1 in lines 181-188 in the revised manuscript.

我们感谢审稿人的宝贵意见，并修改了图2。首先，我们使用16种不同的颜色来表示图2中16年（2005-2020）的数据。其次，我们在图2的标题中添加了虚线和区间的引入，即，“红色虚线表示1：1线。蓝色虚线表示回归线。边缘直方图的箱的间隔为0.02”。最后，将NMB、NME和RMSE的公式移至修订稿第2.1节第181-188行。

Q23. Specific points: Figure 3: The quality needs to be improved. Words and legends are not clear enough.

问题23.具体要点：图3：质量有待提高。文字和传说不够清楚。

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment and improve the quality of Figure 3 to make the words and legends clear enough.

我们感谢审稿人的宝贵意见，并改进了图3的质量，使文字和图例足够清晰。

Q24. Specific points: Figure 7: What do colors in Figures 7c and 7d stand for?

问题24.具体要点：图7：图7c和7d中的颜色代表什么？

Response and main revisions:

答复和主要修订：

We appreciate the reviewer’s valuable comment. The colors in Figures 7c and 7d stand for changes in provincial BC emission intensity (annual BC emissions per km²) in posterior BC estimates, which are the same as those in Figures 7a and 7b. We have added the information in the caption of Figure 7.

我们感谢评论者的宝贵意见。图7c和7d中的颜色代表后验BC估计中各省BC排放强度（每^平方公里的BC年排放量）的变化，与图7a和7b中的相同。我们在图7的标题中添加了信息。

Q25. Specific points: Figure 9: The quality of the figure needs to be improved. Words are not readable. Important information should be included in the caption, for example, what the gray bars are and why the numbers over the gray bars are missing.

问题25.具体要点：图9：图的质量有待提高。文字是不可读的。标题中应包含重要信息，例如，灰色条是什么以及为什么灰色条上的数字丢失。

Response and main revisions:答复和主要修订：

We appreciate the reviewer’s valuable comment and improve the quality of Figure 9 to make the words and legends clear enough. The grey bars stand for the total all-cause premature deaths attributed to BC exposure in China during 2000-2020 (with a 5-year interval), and the corresponding numbers are at the bottom of the Figure. The colored bars and numbers above the bars show the contributions of major factors to the national changing mortality. We have added the information in the caption of Figure 9 in the revised manuscript.

我们感谢审稿人的宝贵意见，并改进了图9的质量，使文字和图例足够清晰。灰条代表2000-2020年（间隔5年）中国因接触BC而导致的全因过早死亡总数，相应数字位于图底。彩色条和条上方的数字显示了主要因素对全国死亡率变化的贡献。我们在修订稿中的图9的标题中添加了信息。

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Comments from Reviewer #1

General comment: Using a machine learning technique and a “top-down” inversion approach, with remote sensing observations and meteorological reanalysis data as input, the authors analyzed the evolution of black carbon emissions in China from 2000 to 2020. Moreover, using an attributional model, the authors related premature mortality and black carbon exposure, and investigated the mortality due to black carbon exposure and its drivers. In addition, the authors discussed the uncertainties in the calculation of black carbon AAOD and health impact estimation. The manuscript is well structured and written, the methodology is well established, the results are well presented and discussed. Due to the issues listed below, I suggest a major revision before it is suitable for publication.

Response and main revisions:

We appreciate the reviewer’s positive comments on our paper, and have made point-by-point response and revisions as summarized below.

Q1. Major issues: In the introduction, there is no review of studies on BC-associated premature mortality, especially over China. The motivation behind the authors' investigation into BC-associated premature motility and the research status of this premature motility is not clear. As the associated premature mortality is listed in the title and it is supposed to be one of the important parts of the paper.

Response and main revisions:

We appreciate and agree with the reviewer’s valuable comment. The review of studies on BC-associated premature mortality in China and the motivation of this study are summarized below.

Based on the “bottom-up” emission estimates with great uncertainty and CTMs, previous studies have evaluated the BC-associated premature mortality in China for limited years (2000, 2013, and 2016, Cui et al., 2022; Qin et al., 2019; Saikawa et al., 2009; Wang et al., 2021). Large discrepancy exists in the magnitude (50,100-1,436,960 cases) and few analyses are available on the long-term spatiotemporal variations and driving forces of BC-associated health effects. The influence of human activities on quickly changing BC emissions and their associated health impact is inadequately or inaccurately understood, weakening science-based decision making for air pollution control.

We have added and reorganized the information in lines 95-100 in the revised manuscript.

Q2. Major issues: In section 3.3, the results of premature mortality associated with BC exposure are only based on the estimation, without any validations, which makes the analysis less convincing. Is it possible to collect some data, either released in government reports or published in papers, to support your estimations? It does not need to be very precise, the magnitudes of the same order are sufficient.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We have collected the all-cause premature deaths attributed to BC in China from limited published papers to validate our estimates. The all-cause premature deaths attributed to BC in China were reported as 50,100 cases in 2000 (Qin et al., 2019), 1,436,960 cases in 2013 (Wang et al., 2021) and 538, 400 cases in 2017 (Cui et al., 2022). All-cause premature deaths attributed to BC in China in this work were estimated as 733,910-937,990 in 2000-2020, within the wide range of 50,100-1,436,960 cases by previous studies.

The health impact estimation could be biased by rare domestic β_BC values in China. Previous studies commonly adopted the same β_BC  with PM_2.5 (Qin et al., 2019) or β_BC obtained from experiments conducted in Europe or the United States (Wang et al., 2021), resulting in large uncertainty. In this study, we relied on a unique cohort study in China and calculated the all-cause premature deaths attributed to BC at 733,910-937,980/yr. The β_BC values obtained from national-scale studies in the US and Europe indicate a 10-fold difference (220,980-2,386,060/yr, Supplementary Table S14), similar to the estimation conducted in the US (Li et al., 2016). More domestic epidemiological studies focusing on BC emissions are expected to further reduce the uncertainty.

We have added the validations and uncertainty discussions in lines 533-536 and lines 610-618 in the revised manuscript.

Q3. Specific points: L137: The Chinese Academy of Sciences is a huge organization. A detailed name where the data is obtained is needed. The website of the dataset rather than the website of the data center should be provided. If the dataset is associated with a published paper, then the paper should be cited.

Response and main revisions:

We appreciate the reviewer’s valuable comment. The land-use data were obtained from the Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences at a horizontal resolution of 1 × 1 km (https://www.resdc.cn/DOI/DOI.aspx?DOIID=129; last accessed on 25 June 2022). The elevation data were obtained from the Shuttle Radar Topography Mission at a horizontal resolution of 1 × 1 km (https://www.resdc.cn/data.aspx?DATAID=123; last accessed on 25 June 2022). We have corrected the data source information in lines 155-162 in the revised manuscript.

Q4. Specific points: L148: References for CARSNET are needed.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We have added the reference for CARSNET (Che et al., 2015) in line 172 in the revised manuscript.

Q5. Specific points: L149: References for CARE-China and SONET are needed.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We have added the reference for CARE-China (Xin et al., 2015) and SONET (Li et al., 2018) in lines 173-174 in the revised manuscript.

Q6. Specific points: L163: Have you tested uncertainties brought by using four months to represent four seasons?

Response and main revisions:

We appreciate the reviewer’s valuable comment. In this study, January, April, July, and October were selected as representative months of different seasons to avoid abundant calculations. This method has been widely applied in emission inversion researches (Zhang et al., 2015; Zhao et al., 2019). The relative difference between the average AAOD of four representative months and annual value were estimated within -4%~-1% during 2000-2020. We do not quantify this uncertainty due to computational costs in this work. We have added relative information in lines 193-194 in the revised manuscript.

Q7. Specific points: L166: Add references for CMAQ.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We have added the reference for CMAQ (USEPA, 2017) in lines 196-197 in the revised manuscript.

Q8. Specific points: L221: References are needed for the log-linear model.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We have added the reference for the log-linear model (Wang et al., 2021) in line 256 in the revised manuscript.

Q9. Specific points: L221: L231: References are needed for Equation 7.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We have added the reference for the Equation 10 (Eq. 7 in the previous edition) (Wang et al., 2021) in lines 266-267 in the revised manuscript.

Q10. Specific points: L257: Where are the RMSE and NMB values from? From which plots or tables?

Response and main revisions:

We appreciate the reviewer’s valuable comment. We have added the data sources in line 295 in the revised manuscript and corresponding Supplementary Table S8 in the revised supplement.

Q11. Specific points: L284: Double brackets at the right side.

Response and main revisions:

We appreciate the reviewer’s reminder and the redundant bracket has been deleted in the revised manuscript.

Q12. Specific points: L314: I do not agree that the increase in AAOD from 2018 to 2020 is due to the increasing surface wind speed. In general, the near-surface wind speed has decreased significantly since 1980 and has become flat or increased slightly since about 2010~2013. Why did the AAOD still decrease from 2013 to 2020? Thus, near-surface wind speed only cannot explain the changing trend in AAOD. Moreover, from 2018 to 2020, only 3 years, the time period is too short for changing trend analysis.

Response and main revisions:

We appreciate the reviewer’s valuable comment. Continuous air pollution controls during 2013-2020 have resulted in the reduction of light-absorption BC emissions, thereby the decline of AAOD of China. However, recent observations show that the frequency of sandstorms in northern China has increased after 2015 due to increasing surface wind speed (Yang et al., 2021). This resulted in greater emissions of light-absorption dust aerosols, thereby AAOD, partly offset the AAOD decline owing to black carbon emission mitigation in northern China. We agreed with the reviewer that the time period from 2018 to 2020 is too short for changing trend analysis, so we removed the trend analysis results for 2018-2020 from Figure 3 and the main text.

We have included the discussion in lines 352-355 and modified Figure 3 in the revised manuscript.

Q13. Specific points: L327-329: Could you explain why a larger underestimation appears in 2000 and 2020?

Response and main revisions:

We appreciate the reviewer’s valuable comment. The larger underestimation of simulated prior BC concentration in 2000 and 2020 may be caused by larger underestimation of BC emissions in these years.

For 2000, the under-reporting of activity levels and lack of local measurements for specific BC emission factors (EFs, emissions per unit of activity level) in very early year may lead to larger uncertainties in BC emission estimation (Fu et al., 2012; Guan et al., 2012). The increased uncertainty in prior BC emissions in 2020 may have resulted partly from an underestimation of increased fuel use owing to residential heating and cooking during the COVID-19 lockdown and quarantine (Zheng et al., 2020).

We have discussed the possible reasons in lines 366-367 and 407-418 in the revised manuscript.

Q14. Specific points: L345: Simulation -> simulation.

Response and main revisions:

We appreciate the reviewer’s reminder. We are sorry for the mistake and have corrected it in line 384 in the revised manuscript.

Q15. Specific points: L361: What do you mean by the factor here?

Response and main revisions:

We appreciate the reviewer’s valuable comment. The “factor” here represents the ratio of the difference between posterior and prior to the prior BC emissions, i.e., (a posterior – a prior) / a prior. We have modified the expression in lines 400-401 in the revised manuscript.

Q16. Specific points: L426: Why coal consumption or fossil fuel combustion are missing, which are also very important to BC emissions.

Response and main revisions:

We appreciate the reviewer’s important comment. There is a great correlation between provincial coal production and consumption. In Section 3.2.3, we used coal production as an indicator to distinguish the main coal production provinces and to further highlight the unique BC emission patterns for those provinces (Shanxi, Inner Mongolia, Henan and Shaanxi Province). Those patterns cannot be clearly revealed if coal consumption is used as the indicator.

Q17. Specific points: L490-493: How did you get those values? Calculated from equation 7?

Response and main revisions:

We appreciate the reviewer’s valuable comment. The all-cause premature deaths attributed to BC here were calculated from equation 10 (equation 7 in the previous edition) in lines 266-278 in the revised manuscript.

Q18. Specific points: L496-498: Can you calculate the relative premature deaths that divide the premature death cases by the total population? Then, one can get rid of the impacts of population density when comparing premature deaths in different regions of China.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We calculated the premature death rate that divide the premature death cases by the total population and the results are shown in a new Supplementary Figure S9 in the revised supplement. Higher premature death rate in eastern China were attributed mainly to the relatively high BC exposure from developed industrial and commercial activities. We have added the corresponding statement in lines 536-539 in the revised manuscript.

Q19. Specific points: L499: What does cases/grid mean?

Response and main revisions:

We appreciate the reviewer’s valuable comment. The “cases/grid” means the all-cause premature deaths attributed to BC in a model grid cell (27 × 27 km). Combined with the Q21 of reviewer #2, we have modified the unit “cases/grid” to “cases/1000 km²” and re-calculated the corresponding values in Table 3 in the revised manuscript to make the expression easier to understand. The corresponding sentences were modified to “The highest multiyear average of premature mortality was 1482 cases/1000 km² (the all-cause premature deaths attributed to BC per area of 1000 km²) in Shanghai, followed by 793, 761, 520, 450, and 442 cases/1000 km² in Beijing, Tianjin, Jiangsu, Henan, and Shandong, respectively (Table 3). These values were much higher than the national average of 86 cases/1000 km²” in lines 539-543 in the revised manuscript.

Q20. Specific points: Table 1: Units are needed for the values of emission.

Response and main revisions:

We appreciate the reviewer’s valuable comment. Table 1 shows the multiyear average relative differences between the posterior and various “bottom-up” estimates of BC emissions. We have added “unitless” for the relative difference in the caption of Table 1.

Q21. Specific points: Figure 1: The quality of the figure needs to be improved. The words are too small and unreadable.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We have improved the quality of Figure 1 in the revised manuscript.

Q22. Specific points: Figure 2: I highly recommend using five different colors for the data from five different years. The two dashed lines have to be introduced in the caption. The interval of bins is also needed to be introduced. The equations of NMB, NME, and RMSE should go to section 2.1.

Response and main revisions:

We appreciate the reviewer’s valuable comment and modified the Figure 2. Firstly, we use 16 different colors to represent the data from 16 years (2005-2020) in Figure 2. Secondly, we added the introduction of the dashed lines and the interval of bins in the caption of Figure 2, i.e., “The red dashed line indicates the 1:1 line. The blue dashed line indicates the regression line. The interval of bins of the marginal histograms is 0.02”. Finally, the equations of NMB, NME and RMSE were moved to section 2.1 in lines 181-188 in the revised manuscript.

Q23. Specific points: Figure 3: The quality needs to be improved. Words and legends are not clear enough.

Response and main revisions:

We appreciate the reviewer’s valuable comment and improve the quality of Figure 3 to make the words and legends clear enough.

Q24. Specific points: Figure 7: What do colors in Figures 7c and 7d stand for?

Response and main revisions:

We appreciate the reviewer’s valuable comment. The colors in Figures 7c and 7d stand for changes in provincial BC emission intensity (annual BC emissions per km²) in posterior BC estimates, which are the same as those in Figures 7a and 7b. We have added the information in the caption of Figure 7.

Q25. Specific points: Figure 9: The quality of the figure needs to be improved. Words are not readable. Important information should be included in the caption, for example, what the gray bars are and why the numbers over the gray bars are missing.

Response and main revisions:

We appreciate the reviewer’s valuable comment and improve the quality of Figure 9 to make the words and legends clear enough. The grey bars stand for the total all-cause premature deaths attributed to BC exposure in China during 2000-2020 (with a 5-year interval), and the corresponding numbers are at the bottom of the Figure. The colored bars and numbers above the bars show the contributions of major factors to the national changing mortality. We have added the information in the caption of Figure 9 in the revised manuscript.

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Fu, T. M., Cao, J. J., Zhang, X. Y., Lee, S. C., Zhang, Q., Han, Y. M., Qu, W. J., Han, Z., Zhang, R., Wang, Y. X., Chen, D., and Henze, D. K.: Carbonaceous aerosols in China: top-down constraints on primary sources and estimation of secondary contribution, Atmos. Chem. Phys., 12, 2725-2746, https://doi.org/10.5194/acp-12-2725-2012, 2012.

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Li, Y., Henze, D. K., Jack, D., Henderson, B. H., and Kinney, P. L.: Assessing public health burden associated with exposure to ambient black carbon in the United States, Sci. Total Environ., 539, 515-525, https://doi.org/10.1016/j.scitotenv.2015.08.129, 2016.

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Comments from Reviewer #2

General comment: The authors analyzed BC emission changes and the associated premature mortality in China during 2000-2020. Overall, the methodology is robust and the findings are valuable. The paper was well written and I enjoyed reading it. The following comments need to be addressed before publishing.

Response and main revisions:

We appreciate the reviewer’s positive comments on our paper, and have made point-by-point response and revisions as summarized below.

Q1. Line 31: Explicitly mention OMI and Extreme Gradient Boosting algorithm in the abstract.

Response and main revisions:

We appreciate the reviewer’s valuable comment and have added the specific information. The sentence has been modified as “Here, we present the spatiotemporal evolution of BC emissions and the associated premature mortality in China during 2000-2020, based on an integrated framework combining satellite observations from Ozone Monitoring Instrument (OMI), an Extreme Gradient Boosting (XGBoost) algorithm, a “top-down” inversion approach, and an exposure-response model” in lines 29-33 in the revised manuscript.

Q2. Line 47: “BC poses greater health risks than total PM2.5 due to its absorption”? Why would absorption be related to health?

Response and main revisions:

We appreciate the reviewer’s valuable comment. Here the “absorption” means the ability of BC to absorb the harmful matters. Epidemiological studies have indicated that BC absorbs polycyclic aromatic hydrocarbons (PAHs) and volatile organic compounds (VOCs) due to its fine particle size and porous structure, and readily penetrates human lung tissue (Pani et al., 2020). Thus BC exposure may cause cardiovascular diseases (CVDs) and respiratory diseases (RDs). We have modified the unclear expression and added the corresponding reference in lines 48-51 in the revised manuscript.

Q3. Line 64-65: “9%-22% (2005-2020) and 8%-12% (2006-2013)”. Reference?

Response and main revisions:

We appreciate the reviewer’s valuable comment. Here the data coverage ratio was calculated by the author based on the satellite AAOD datasets. We have added the data sources of OMI (https://disc.gsfc.nasa.gov/datasets/OMAEROe_003/summary; last accessed on 10 March 2022) and POLDER (https://www.grasp-open.com; last accessed on 4 May 2022) in lines 65-69 in the revised manuscript.

Q4. Line 72 “Existing bottom-up estimates”. Please explicitly list the name of these inventories mentioned here.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We have listed the name of the inventories mentioned here in lines 79-84 in the revised manuscript, i.e., the Multiresolution Emission Inventory for China (MEIC; Tsinghua University, 2023), the Emissions Database for Global Atmospheric Research (EDGAR; European Commission, 2022), Community Emissions Data System (CEDS; Mcduffie et al., 2020), the Peking University Fuel Inventory (PKU-Fuel; Wang et al., 2014), Regional Emission inventory in ASia (REAS; Kurokawa and Ohara, 2020), and others (Lu et al., 2011; Lei et al., 2011; Klimont et al., 2009; Qin and Xie, 2012).

Q5. Section 2.1: Move the description of XGBoost model from Supplement to the main text. And explicitly explain how it differs from a Random Forest Model.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We have moved the description of XGBoost model from Supplement to lines 120-127 in the revised manuscript. XGBoost has been widely used in predicting air pollution and shown to outperform various statistical and machine learning models (Liang et al., 2020; Liu et al., 2022; Wang et al., 2023; Xiao et al., 2018). The XGBoost algorithm is an additive model based on hundreds of decision tree models. It first builds multiple Classification and Regression Trees, and then integrates these trees as a new tree model using an additive function (Liu et al., 2021). The model continues to iteratively improve, and the new tree model generated in each iteration will fit the residual of the previous tree. The complexity of the ensemble model will gradually increase until the training achieves the best results. Different from the boosting approach of XGBoost, the Random Forest model fits a set of decision trees, and then a majority vote method is taken for final prediction (Lyu et al., 2019). Generally, XGBoost model requires less training and prediction time and presents better performance than the Random Forest model. We have added the comparison of two models in lines 128-131 in the revised manuscript.

Q6. Line 98: “extreme gradient boosting” ==> “Extreme Gradient Boosting”

Response and main revisions:

We appreciate the reviewer’s valuable comment. We have modified the “extreme gradient boosting” to “Extreme Gradient Boosting” in the main text (lines 31-32 and lines 108-109).

Q7. Line 110: “XGBoost has been widely used…” In this case, please provide more reference than Xiao et al., 2018.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We have added more relative references (Liang et al., 2020; Liu et al., 2022; Wang et al., 2023) in lines 121-122 in the revised manuscript.

Q8. In the Text S1 XGBoost model description, can you explain how you “integrates these trees as a new tree model”?

Response and main revisions:

We appreciate the reviewer’s valuable comment. The XGBoost algorithm is an additive model. For a given dataset, the XGBoost algorithm continuously perform feature splitting to grow a tree. Each time a tree is added, a new function is actually learned to fit the residuals of the last tree prediction. Eventually the model uses an additive function to “integrates these trees as a new tree model”, thus obtaining the final prediction. We have added the explanation in lines 123-125 in the revised manuscript.

Q9. Line 113: “random forest” ==> “Random Forest”.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We have modified the “random forest” to “Random Forest” in the main text (line 128 and line 131).

Q10. Line 139: To regrid from 1 km to 0.25 degree, you should use average rather than Bilinear interpolation.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We are sorry for the mistake and have modified it to “These parameters were resampled to the 0.25° × 0.25° grid system by averaging the 1-km resolution data.” in lines 162-163 in the revised manuscript.

Q11. OMI overpass time is ~13:30. Therefore OMI only measures AAOD at ~13:30 each day. Therefore when you use other MERRA-2 variables for model training, it’s better to use hourly values near 13:30 rather than daily average. You don’t need to redo the training. However please add a few sentences to discuss this.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We used the daily MERRA-2 data because the daily average MERRA-2 data was proved more reliable than the hourly data compared to the observation (Xu et al., 2020). However, as the reviewer said, application of the daily data may result in a mismatch with OMI-measured AAOD at ~13:30, thus leading to uncertainties in AAOD prediction. The complicated nonlinear response relationship of machine learning (i.e., XGBoost model) can partially compensate this mismatch, and our validation results also proved the robustness of the model. Evaluated by 10-fold CV and individual ground measurements, the predicted AAOD shows good agreements with observations, with RMSE of 0.013 and 0.017, respectively (Figure 2 and Supplementary Table S8). We have added the explanation in lines 153-155 in the revised manuscript.

Q12. Your developed monthly AAOD data represent the value at ~13:30 if you use OMI AAOD as the truth for training. Please discuss the impact of diurnal variation on your emission estimates. GEMS will provide more diurnal information in the future and can be used to further understand this issue.

Response and main revisions:

We appreciate the reviewer’s valuable comment and acknowledged the limitation in emission inversion of this work. As XGBoost predicted monthly BC AAOD at ~13:30, we could not capture the diurnal distribution of BC emissions. We simply applied the ratio of the posterior to prior emissions at 13:30 to correct emissions in other hours, causing uncertainties in the diurnal distribution of emissions. As mentioned by the reviewer, the Geostationary Environment Monitoring Spectrometer (GEMS) was launched on board the Geostationary KOrea Multi-Purpose SATellite 2B (GEO-KOMPSAT-2B) satellite in 2020 and provided hourly daytime observations of aerosols (Kim et al., 2020; Park et al., 2023). This can potentially be helpful for improving the temporal accuracy of BC emission inversion in the future. We have added the discussion of the uncertainty in lines 603-609 in the revised manuscript.

Q13. Line 163: While it makes sense to have five-year intervals, using 2015 and 2020 to interpolate the years in between will introduce biases due to COVID interruption (i.e., 2020 emission is an anomaly).

Response and main revisions:

We appreciate the reviewer’s valuable comment. We acknowledged that 2020 is an anomaly considering the influence of COVID-19. We compared the national monthly BC AAOD in 2015, 2020 and 2016-2019. Annual average BC AAOD in 2020 was 0.0235, slightly lower than that in 2015 (0.0239), while both of them were higher than the multi-year average BC AAOD in 2016-2019 (0.0227). The COVID-19 lockdown and quarantine may cause the increase of fuel use owing to residential heating and cooking (Zheng et al., 2020), thereby the increase of BC emissions. We have briefly discussed the influence of COVID-19 in lines 415-418 in the revised manuscript. To describe an emission trend of entire two decades, we kept using the five-year interval in the emission inversion analysis.

Q14. Line 181: To be more clear, I suggest to replace 𝐴𝐴𝑂𝐷_𝑠𝑖𝑚𝑖,, with 𝐴𝐴𝑂𝐷_BC_𝑠𝑖𝑚𝑖,𝑚,𝑛 here and after.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We have modified the “” to “” in the main text (line 211, 212, 231, 233, 238 and 239) and Table S2 in the revised supplement.

Q15. Section 2.2.2: I appreciate this part that the authors included four sensitivity tests to recalculate posterior BC emissions and explore the uncertainty in the inversion.

Response and main revisions:

We appreciate the reviewer’s positive comment on this work.

Q16. Line 227: “we applied the 1.25th percentile of BC concentrations as the threshold.” Why use 1.25? Is it from a previous study?

Response and main revisions:

We appreciate the reviewer’s valuable comment. The health impact threshold of BC (i.e., 1.25^th percentile of BC concentrations) was suggested by previous study (Pani et al., 2020; Wang et al., 2021). We have added the reference in lines 261-262 in the revised manuscript.

Q17. Figure 4: Have you described these BC concentration observations in the text? How were they measured?

Response and main revisions:

We appreciate the reviewer’s valuable comment. The BC concentration observations here were collected from 64 published researches as comprehensive as possible, covering various sampling regions in China and study period from 2000 to 2020, which are listed in Supplementary Table S3. Most studies analyzed BC using well-acknowledged reliable and widely used analyzers (Tao et al., 2017), for example, a DRI carbon analyzer or Sunset carbon analyzer. We have added the description of BC concentration observations in lines 244-248 in the revised manuscript.

Q18. Did you add anthro and fire BC emis together and updated them as a whole? Please be explicit.

If that’s the case, why would you compare your BC emission estimates (anthro+BB) with other anthropogenic emission inventories in Figure 5? If that’s not the case, did you separately update anthro and biomass burning BC emissions? Or you only updated anthro emissions? Biomass burning emissions are a large source for BC (sometimes larger than anthropogenic sources) and have to be considered.

Response and main revisions:

We appreciate the reviewer’s valuable comment and careful reminding. In this study, we added anthropogenic and fire BC emissions together and updated them as a whole. We acknowledged that comparing the posterior BC emissions (anthro+BB) with other “bottom-up” anthropogenic emission inventories (i.e., EDGAR, CEDS, REAS, et al.) was not rigorous enough. Here we added GFED open biomass burning BC emissions to various anthropogenic emission inventories and re-compared the posterior emissions with the new “bottom-up” emission estimates. It is worth noting that the PKU-Fuel, Lu et al. (2011) and Qin and Xie (2012) already includes emissions from wildfires. The posterior BC emissions presented an enhancement compared to various “bottom–up” estimates of China’s BC emissions (sum of anthropogenic and OBB emissions), with the lowest relative difference of 1.7 for the PKU-Fuel (http://inventory.pku.edu.cn/; last accessed on 1 May 2023) and highest value of 4.1 for EDGAR+GFED (https://edgar.jrc.ec.europa.eu/dataset_ap61; last accessed on 1 May 2023) (Figure 5d and Table 1). The posterior emissions presented a smaller interannual variability compared to the prior and other “bottom-up” estimates, with a net growth of 8% during 2000-2010 (the analogous numbers are 12%-55% for various “bottom-up” estimates including 24% for the prior used in this work, MEIC+GFED) and a decline of 26% during 2010-2020 (41% for MEIC+GFED, Figure 5e). Besides, the relative differences between posterior and other “bottom-up” BC emission estimates were smaller (1.1-2.1) in more economically developed regions (BTH, FWP, YRD, and PRD), but larger (3.5-5.6) in SCB, NE, and other regions (Table 1).

We have modified the Figure 5 and Table 1 and corresponding descriptions in lines 402-407, lines 419-423 and lines 429-432 in the revised manuscript.

Q19. Figure 5: The relative difference is larger in forest and grassland rather than rural or urban. Does that mean the uncertainties mainly come from biomass burning emissions rather than anthro?

Response and main revisions:

We appreciate the reviewer’s valuable comment. Yes, it means that the uncertainties of BC emissions in remote regions, including those from open biomass burning should be larger than those from more intensive human activities. The “bottom-up” approach could capture information about energy consumption and pollution controls more easily and accurately in regions with more intensive human activities. However the omission of small fires from satellite observations and application of global EFs led to an underestimation of biomass burning emissions. We have included the discussions in lines 411-413 and lines 442-446 in the revised manuscript.

Q20. Line 485: Just out of curiosity, is transportation a significant source sector for BC in China?

Response and main revisions:

We appreciate the reviewer’s valuable comment. The transportation sector is an important source of BC emissions in China. According to MEIC, the contributions of transportation sector to total anthropogenic BC emissions in China during 2000-2020 (i.e., our study period) varied between 17%-24%.

Q21. Line 501: It’s more intuitive to use unit cases/km² than cases/grid.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We have modified the unit “cases/grid” to “cases/1000 km²” and re-calculated the corresponding values in Table 3 in the revised manuscript. The corresponding sentences were modified to “The highest multiyear average of premature mortality was 1482 cases/1000 km² (the all-cause premature deaths attributed to BC per area of 1000 km²) in Shanghai, followed by 793, 761, 520, 450, and 442 cases/1000 km² in Beijing, Tianjin, Jiangsu, Henan, and Shandong, respectively (Table 3). These values were much higher than the national average of 86 cases/1000 km²” in lines 539-543 in the revised manuscript.

Q22. I like the Section 3.4 (detailed discussion on the uncertainties). It makes this manuscript more convincing.

Response and main revisions:

We appreciate the reviewer’s positive comment on this work.

Q23. It’s not convenient for the reviewers when you separate figure captions from figures. I had to go back and forth to understand a figure. I suggest in your future manuscript submissions, put figure and its corresponding caption in the same place.

Response and main revisions:

We appreciate the reviewer’s valuable comment. We have put figure and its corresponding caption in the same place.

Reference

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