A novel way to calculate shortwave black carbon direct radiative effect

Black carbon (BC) aerosol has a strong radiative forcing effect and significantly affects human beings and the environment. Therefore, it is important to quantitatively calculate its direct radiative effect (BC DRE) at the surface (SFC) and the top of the atmosphere (TOA). Current studies mainly use empirical formula methods or broadband methods to calculate BC DRE. However, these two methods do not consider the differences of sky diffuse light ratios in different wavelength bands. To overcome this problem, a new scheme named the multiband synthetic method is proposed to calculate blue sky albedo at MODIS narrow bands, and then, the blue sky albedo at the whole shortwave band is synthesized with these separate narrowband blue sky albedos. Based on BC concentration measured in Xuzhou over two years (from May 2014 to July 2016), aerosol optical depth (AOD) and microphysical parameters provided by AERONET, and the black sky albedo (BSA) and white sky albedo (WSA) provided by Google Earth Engine (GEE) products, shortwave BC DRE was calculated numerically with the use of the 6S radiative transfer model. The range of BC DRE computed by the multiband synthetic method at the TOA and SFC are 0.84 ± 0.08 to 3.27 ± 1.01W/m² and -14.57 ± 4.53 to -4.31 ± 0.36W/m². The shortwave BC DRE calculated by the multiband synthetic method was higher than that calculated with the broadband method and empirical formula method by 0.11% to 0.36% (at the SFC), 0.14% to 1.4% (at the SFC) and 3.4% to 10.1% (at the TOA), 5.5% to 15.8% (at the TOA), respectively. The BC DREs calculated by these three methods have small differences at the SFC. However, the difference was large at the TOA. The results of this study suggest that it is important to consider the differences between different narrow bands when calculating the broadband shortwave blue sky albedo.