## 3 Results and Discussion
### Formatting of Mathematical Components
#### 3.4.2 Research Trend and Future Directions  
We employed Bibliometrix to analyze the topic trends in the BCL dataset. Figure 6b illustrates the topic trend graph, which is presented as a scatter plot with the \(x\)-axis representing time and the \(y\)-axis denoting the topics. To ensure clarity and conciseness in the visualization, we only included author keywords appearing in more than ten articles. Additionally, only the top two keywords for each year are displayed.  
As illustrated in Figure 6b, no keywords are present before 2008, mainly because the scarcity of the literature published from 2000 to 2008 did not meet the filtering criterion of keywords appearing more than 10 times. The keywords appearing before 2010 include \"atmospheric chemistry\", \"aerosols and particles\", \"global warming potentials\", and \"atmospheric composition and structure\". During this period, the themes exhibit characteristics strongly associated with climate-related topics [74; 75]. \"Atmospheric chemistry\" and \"global warming potentials\" are relatively macroscopic themes.  
Subsequently, specific substances serve as keywords, including \"brown carbon\", \"PM\({}_{2}\)5\", \"black carbon\", \"particulate matter\", \"aerosols\", \"biochar\", \"organic carbon\", \"charcoal\", \"soil organic matter\", and \"ozone\", with the majority of them representing substances in the atmosphere that impact the climate and air quality [50; 76]. A few terms, such as \"biochar\", \"charcoal\", and \"soil organic matter\", contribute to climate and soil dynamics by facilitating carbon sequestration [12]. Geographically significant keywords, such as \"Chinese Loess Plateau\" and \"Arctic\", highlight these regions as focal areas of research [41; 77]. Keywords also encompass both natural and anthropogenic phenomena of interest in this field, including \"drought\", \"wildfire\", \"biomass burning\", and \"climate change\" [16; 71; 78].  
Themes that appear frequently and persist over time serve as the foundation of the entire research field, including \"black carbon\", \"biomass burning\", \"climate change\", \"aerosols\", \"radiative forcing\", and \"atmospheric chemistry\". Meanwhile, keywords in the upper right corner of the graph represent emerging research fronts, such as \"MERRA-2\", \"machine learning\", \"drought\", \"brown carbon\", and \"wildfire\". These nascent research areas hold promise for deeper investigation in future directions. Further investigations were carried out on the keywords \"MERRA-2\" and \"machine learning\", which emerged as focal points in 2022 and 2023. By incorporating keywords like \"MERRA-2\" or \"machine learning\" into the original search criteria, researchers can investigate subsets of related topics, thereby facilitating the identification of characteristic research within these topics. For example, [PERSON] et al. [79] applied deep learning methodologies to develop a neural network model based on simulation data. Their model precisely predicts the extinction efficiency and single-scattering albedo of black carbon aerosols, providing a more convenient parameterization method for aerosol optical properties in remote sensing studies and atmospheric models. Likewise, [PERSON] et al. [80] conducted a quantitative evaluation of dust and black carbon concentrations in the vertical dimension using the MERRA-2 reanalysis dataset. Leveraging independent satellite-based measurements of aerosol component concentrations, the research highlights the regional applicability of MERRA-2 component datasets and demonstrates the practical value of satellite detection techniques.