The Small-Alpha Method: Sublinear Sampling for Enhanced Superdroplet Resolution in Lagrangian Cloud Models

Particle-based methods have been shown to model the stochastic collision and coalescence of hydrometeors with high fidelity. The superdroplet method, where each computational particle or superdroplet represents a number of identical individual particles, converges to analytical and numerical solutions for the stochastic collection equation when using a sufficiently high number of superdroplets. Lower numbers of superdroplets result in a higher ensemble spread of modeled droplet size distributions, especially under some initial conditions. Often computational demands limit the number of superdroplets used, resulting in increased stochastic variability.

This study explores the small-alpha method, a sublinear sampling technique designed to address the resolution challenges confronted by the superdroplet approach, specifically in the context of the collision-coalescence process. Through a set of box model Monte Carlo simulations of superdroplet collision-coalescence with the All-Or-Nothing algorithm, we find that a sufficiently low occurrence of collisions enables the sampling of fewer pairs of superdroplets. We assess a key assumption from prior work that expectation value of collisions is well approximated by scaling up the probabilities of a complete non-overlapping set of pairs, and find that this assumption holds for even smaller sets of non-overlapping pairs. While the small-alpha technique has the potential for accelerating model performance at the expense of longer timestep convergence, its more fitting application may lie in the mitigation of ensemble spread while preserving computational efficiency.