  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
parameterizations of BC mass absorption cross-section (MACBC) and its
enhancement factor (EMACBC), resulting from internal mixing with non-refractory
and non-light 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 MACBC and
EMACBC evolve with increasing internal mixing ratios in simple power-law
exponents of 1/3. Remarkably, MACBC remains inversely proportional to
wavelength 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 under prediction of MACBC. We elucidate the responsible
mechanism based on shielding of photons by the skin depth of a sphere and
establish a correction factor that scales with a 3/4 power-law exponent.
