The amount of aerosol is a key parameter modulating cloud microphysical and macrophysical properties and their subsequent long-term impact on climate. Broadly speaking, aerosol has two primary effects on cloud microphysics of warm-phase clouds. The first is the cloud albedo effect (Twomey, 1974(Twomey, , 1977: given a fixed amount of liquid water content, an increase in aerosol concentration ( a E N ) leads to smaller droplets but higher total surface area, which reflects more sunlight. The second is the lifetime effect (Albrecht, 1989): as smaller droplets are slower to precipitate, more liquid water remains as part of the cloud and spend more time reflecting sunlight. These two mechanisms can change the average albedo of the Earth and thus affect the climate.A lesser-discussed effect is the proposed "dispersion effect" (Liu & Daum, 2002). Dispersion, or more specifically, relative dispersion ( E  is defined as the ratio of standard deviation and mean droplet size, and it is one way to quantify the width of the distribution, i.e., smaller E  for a narrower distribution, and vice versa. The dispersion effect refers to the idea that cloud droplet distributions formed in higher aerosol concentration environments will have different values of relative dispersion from those formed in low aerosol concentration, which in turn impacts the albedo of the clouds.

Modeling clouds is hard. As noted in great detail in Morrison, van Lier-Walqui, Fridlind, et al. (2020), the two biggest obstacles are (a) the sheer number of cloud and precipitation particles to predict and (b) the lack of the fundamental understanding of microphysical processes involved. With quintillions of droplets in a typical cloud, it is infeasible to predict the evolution of each droplet and its environment. In addition, there does not exist a fundamental governing equation or benchmark model that can help inform the modeling of microphysics in larger scale, unlike other subgrid physical processes such as radiation, turbulence, and convection. Clouds are thus only modeled from a macroscopic perspective with its parameterizations determined empirically. Aside from the more recently developed Lagrangian superdroplet method (e.g., Shima et al., 2009), the two most well-established microphysics scheme types are the bulk microphysics scheme and the bin microphysics scheme. Bin schemes keep track of the number of droplets of within discrete size or mass ranges (i.e., size-resolved or mass-resolved), allowing the particle size distribution (PSD) to evolve freely but is therefore computationally expensive (A. P. Khain et al., 2015). On the other hand, bulk schemes predict quantities proportional to moments of the PSD (i.e., moment-resolved), typically mass and number concentration (e.g.,