Scaling Laws for Light Absorption Enhancement Due to Nonrefractory Coating of Atmospheric Black Carbon Aerosol

Black carbon (BC) aerosol, the strongest absorber of visible solar radiation in the atmosphere, contributes to a large uncertainty in direct radiative forcing estimates. A primary reason for this uncertainty is inaccurate parametrizations of the BC mass absorption cross section (MAC(Bc)) and its enhancement factor (E-MAC(BC))-resulting from internal mixing with nonrefractory and nonlight absorbing materials-in climate models. Here, applying scaling theory to numerically exact electromagnetic calculations of simulated BC particles and observational data on BC light absorption, we show that MAC(BC) and E-MAC(BC) evolve with increasing internal mixing ratios in simple power-law exponents of 1/3. Remarkably, MAC(BC) remains inversely proportional to the wavelength of light at any mixing ratio. When mixing states are represented using mass-equivalent core-shell spheres, as is done in current climate models, it results in significant underprediction of MAC(BC). We elucidate the responsible mechanism based on shielding of photons by a sphere's skin depth and establish a correction factor that scales with a 3/4 power-law exponent.