In CARMA, particles are moved downward in each model layer by gravitational sedimentation. As described in Fan and Toon [2011], the sedimentation velocity (or fall velocity Vg) for spheres in CARMA is calculated as:
Where 
(unit: kg m-1 s-1) denotes air dynamic viscosity following Sutherland [1893]; 
denotes air density; 
denotes wet particle density; 
denotes wet particle radius; g denotes gravitational acceleration; Re denotes Reynolds number; 
denotes slip correction factor; and 
denotes air mean free path, where 
is thermal velocity of air molecule with mass ma and denotes air density. Reynolds number is calculated using fall velocity of stoke flow: 
. CARMA also has equations for particle fall velocities for a variety of shapes including oblate and prolate spheroids, and fractals.
It is rare for aerosols to be in the high Reynolds number regime in the Vg equation. However, as one moves up in altitude the mean free path increases and the ratio of mean free path to particle radius (the Knudsen number) becomes larger than one. Then the slip correction factor deviates significantly from one. In the limit of large Knudsen number the fall velocity equation is 
.
The Figure below illustrates the calculated fall velocity from CESM1/CARMA as a function of altitude for 20 aerosol size bins (dry radius from 0.05 to 8.7 um) denoted by each line. Sedimentation velocities for each bin are global averages and calculated using their wet radius. For particles larger than several lm, the velocity decreases only slightly with altitude as the air viscosity changes in response to temperature. For small particles the fall velocity increases with altitude as the air density declines. Each line represents a size bin: the leftmost line denotes a bin of 0.05 um in dry radius and the rightmost line denotes the biggest bin of 8.7 um. The only particle properties involved in the fall velocity are the particle density and the radius. The mixed particle densities are calculated assuming 1.35 g/cm3 and 1.923 g/cm3 for Sea Spray Organics and Sulfate, 2.65 g/cm3 for sea salt and dust, 1 g/cm3 for Primary biological aerosol particles, and 1.35 g/cm3 for POA and BC.
Reference: Yu et al., 2015. Appendix A7.