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Dust size distributions from the two-mode scheme and the continuous scheme are compared with AERONET observations. The two-mode dust scheme contains fine and coarse modes with fixed effective radius and effective variance for each mode. The continuous scheme takes into account the size distribution with a prognostic variation of effective radius and effective variance. The size distribution of the two-mode scheme changes with the fine/coarse mode mass ratio. However, it is impossible to make both effective radius and effective variance to match with the observed result by adjusting the fine/coarse mode mass ratio. The size distribution from the continuous scheme can be much closer to the observations.

A new parameterization for dust optical properties is proposed based on the continuous scheme. The shape of non-spherical dust particles is approximated using a rotational symmetric spheroid in optical property calculations.

This parameterization can also be used for the two-mode scheme. The parameterization is applied to a set of idealized one-dimensional radiative transfer calculations to investigate the sensitivity of dust radiative forcing to various attributes, including dust loading, dust solar heating rate, surface albedo, effective radius and variance. The parameterization is also evaluated in a climate model. Though at each selected region the two-mode scheme can always be tuned to approximate the results of the continuous scheme, on global scales, however, the two-mode dust scheme cannot produce similar radiative forcing as the continuous scheme and the relative error can be over 30% in several desert regions. The accurate results in radiative forcing can not be achieved by tuning the mass ratio. (C) 2018 Published by Elsevier Ltd.