Resolving Entrainment–Mixing in Marine Stratocumulus: The Role of LES Grid Resolution and Super-Droplet Number

Marine stratocumulus clouds profoundly affect Earth’s energy budget by reflecting solar radiation over extensive oceanic areas. Yet, using large-eddy simulation (LES) and a Lagrangian microphysics scheme (Super-Droplet Method, SDM) for entrainment-mixing studies, uncertainty remains in grid resolution and super-droplets number concentration (SDNC) required for accurate homogeneity capture. This study analyzes the homogeneous mixing degree (ψ) and the Damköhler number (Da) in stratocumulus using LES with SDM, from microphysical and dynamical perspectives, respectively. Results show that ψ and Da both display a top-to-base gradient, with more intense inhomogeneity near the cloud top and relatively homogeneous conditions toward the base, although the upper region is more complex. Even at fine horizontal resolution of 12.5 m and vertical resolution of 2.5 m, ψ remains sensitive and does not converge, whereas Da converges at coarser grid spacing (up to 25 m horizontal and 10 m vertical spacing) in mid-cloud region. Similarly, ψ requires SDNC well above 128 per cell for near-complete convergence, while Da converges once SDNC exceeds about 16 per cell. This difference arises because ψ depends on microphysical detail, demanding high SDNC to capture local droplet inhomogeneities, whereas Da reflects turbulence–evaporation timescales that converge more readily once extreme droplet gradients are resolved. We further find that ψ and Da exhibit a significant negative correlation, with stronger anti-correlation emerging under finer spatial resolution, reinforcing their complementary roles in diagnosing mixing regimes. Overall, these findings provide guidelines for selecting numerical configurations in entrainment–mixing simulations, ensuring that both turbulence-driven and microphysical processes are adequately resolved.