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There is a long-standing challenge in cloud and climate models to simulate the process of ice particle riming realistically, partly due to the unrealistic parameterization of the growth of ice particle mass (m) and projected area (A) during riming. This study addresses this problem, utilizing ground-based measurements of m and ice particle maximum dimension (D) as well as theory to formulate simple expressions describing the dependence of m and A on riming. It was observed that beta in the m - D power law m = alpha D-beta appears independent of riming during the phase 1 (before the formation of graupel), with alpha accounting for the ice particle mass increase due to riming. This semi-empirical approach accounts for the degree of riming and renders a gradual and smooth ice particle growth process from unrimed ice particles to graupel, and thus avoids discontinuities in m and A during accretional growth. Once the graupel with quasi-spherical shape forms, D increases with an increase in m and A (phase 2 of riming). The treatment for riming is explicit, and includes the parameterization of the ice crystal-cloud droplet collision efficiency (E-c) for hexagonal columns and plates using hydrodynamic theory. In particular, E-c for cloud droplet diameters less than 10 mu m are estimated, and under some conditions observed in mixed-phase clouds, these droplets can account for roughly half of the mass growth rate from riming. These physically meaningful yet simple methods can be used in models to improve the riming process.