Between Broadening and Narrowing: How Mixing Affects the Width of the Droplet Size Distribution

Abstract

Entrainment and mixing play an essential role in shaping the droplet size distribution (DSD), with commensurate effects on cloud radiative properties or precipitation formation. In this paper, we use a model that considers all relevant scales related to entrainment and mixing by employing the linear eddy model (LEM) as a subgrid‐scale (SGS) mixing model, coupled with a large‐eddy simulation model and a Lagrangian cloud model (LCM) for a single cumulus congestus cloud. We confirm that the DSD is broadened toward small‐size droplets during homogeneous mixing. During inhomogeneous mixing, the DSD width remains almost unchanged. The DSD width can also be narrowed after mixing. We show that this happens when DSD is broadened toward small‐size droplets, which evaporate rapidly, while larger droplets are almost unaffected. In addition, when droplets ascend during mixing, DSD narrowing is caused when the adiabatic increase in supersaturation is slower than the average droplet evaporation, allowing only the largest droplets to benefit from the newly produced supersaturation. The narrowing mixing scenario prevents clouds from having too broad DSDs and causes the DSD relative dispersion to converge around 0.2 to 0.4. As this scenario is more frequent when the LEM SGS model is used, our results indicate that adequately modeling turbulent mixing is necessary to represent a realistic DSD shape.

Life Cycle Evolution of Mixing in Shallow Cumulus Clouds

“…In extreme cases, IHMD can exceed 5, but approximately 98% of the IHMDs are smaller than this threshold and not included in the estimation. All in all, the DSD shape before and after mixing categorized by the IHMD (Figure A1) shows a good agreement with Lim and Hoffmann (2023), where the DSD width is broadened, unchanged, or narrowed after mixing for homogeneous, inhomogeneous, or narrowing mixing respectively.…”

“…Interestingly, the DSD shape-related parameters, such as d r and r m show higher positive (0.38) and negative ( 0.42) correlation than σ S (0.33), suggesting a distinct underlying process for narrowing mixing, in contrast to other two scenarios. Note that the increase in narrowing mixing with d r is balanced by the decreasing W (Figure 5a), which prevents further narrowing by lifting (Lim & Hoffmann, 2023). This correlation analysis shows that homogeneous and inhomogeneous mixing evolution is highly affected by the S and σ S changes over the cloud life cycle, apart from the strong correlation with cloud clock variables that also decreases gradually over the cloud life cycle, as expected from their strong life stage dependency (Figure 4).…”

“…In the mixing region, d r generally increases over the cloud life cycle (Figure 6c). Lim and Hoffmann (2023) showed that in the homogeneous mixing scenarios, d r increases after mixing, whereas d r barely changes or even decreases in the inhomogeneous and narrowing mixing scenarios, respectively. While homogeneous mixing is the predominant scenario, leading to a general increase in d r after mixing, this increase becomes weaker as the cloud matures due to the increased inhomogeneous and narrowing mixing fraction that prevents a substantial increase in d r during mixing (Figure 6c).…”

“…Nevertheless, the overall change in IHMD is negligible (Figure S1a in Supporting Information S1), as secondary activation is rare (Figure S1b in Supporting Information S1), potentially due to the aforementioned supersaturation restriction to under 0.05 before mixing. More detailed explanations on IHMD estimation can be found in Section 3 of Lim and Hoffmann (2023). To determine the predominant mixing type of a cloud, IHMDs are classified as one of three major mixing types.…”

Paths From Aerosol Particles to Activation and Cloud Droplets in Shallow Cumulus Clouds: The Roles of Entrainment and Supersaturation Fluctuations

“…Note that all super-droplets within the same LES grid box experience the same S. The inhomogeneous mixing by the subgrid-scale variation in S, as considered by Hoffmann et al (2019) and Chandrakar et al (2021), is not considered in the present work. It is known, however, that mixing tends to be more homogeneous in shallow-cumulus clouds, in contrast to stratocumulus clouds, and the parameterization of subgrid-scale mixing does not significantly alter the results when the grid size is sufficiently fine (Hoffmann et al, 2019;Lim & Hoffmann, 2023). Moreover, short-lived supersaturations caused by sub-grid scale turbulence are also less likely to contribute to activation, which requires supersaturations to be sustained for a longer time.…”