How different calculations of the refractive index affect estimates of the radiative forcing efficiency of ammonium sulfate aerosols

Calculations of the radiative properties of hydrated ammonium sulfate (AS) aerosols often employ the conventional volume mixing rule, in which the refractive indices of AS and water are linearly averaged, weighted by their respective volume fractions in solution, and the real part of the refractive index of pure AS is taken to be 1.52-1.55, based on measurements of dry crystalline AS. However, there are significant differences between the refractive indices of AS-water solutions calculated using the conventional volume mixing rule and empirically derived refractive indices. The authors use a simple model for calculating the direct solar radiative forcing efficiency (RFE; radiative forcing divided by optical depth) of an optically thin layer of aerosols to investigate the magnitude of these differences. The difference between the conventional volume mixing rule and empirically derived refractive indices amounts to a modest difference in the direct solar RFE of AS aerosols at the top of the atmosphere at 0.550-μm wavelength and at relative humidities of 37%-99.9%. Without black carbon, the difference in RFE is up to -0.42 W m^-2 for relative humidities less than around 66% and up to 0.25W m^-2 for relative humidities greater than 66%, whereas with 2% black carbon by volume, the range of difference in RFE is up to 20.59 W m^-2 for relative humidities less than 66% and up to 0.30 W m^-2 for relative humidities greater than 66%. Although modest, this difference in RFE may become important when investigating regional aerosol forcing in areas with a high concentration of urban and industrial pollution.