Estimates of 3D Radial Distribution Function from in situ Cloud Particle Tracking Experiments

The collision-coalescence process in cloud droplets, driven by particle dynamics in turbulent environments, plays a critical role in cloud formation and precipitation. However, this process remains poorly understood due to the complex interactions influenced by turbulence. Given the vast range of scales involved, accurately studying these interactions requires both in situ measurements and nuanced analytical tools.

The Radial Distribution Function (RDF) is a central tool for evaluating particle clustering and thus furthering our understanding of collision-coalescence. Calculating the RDF from experimental data is often challenging due to the confounding effects of finite measurement volume and non-uniform detection likelihood. Existing methods, which either lose data or are computationally expensive, only partially address these challenges. In response, we present a robust methodology that circumvents these obstacles effectively. We derive a general formula and compare it with numerical simulations for standard geometris such as spheres, cylinders, cubes, prisms, toroid and cones. We aim to demonstrate how the theoretical insights gained can be effectively applied to normlize RDF obtained from experimental settings.

To demonstrate the suitability of our analytical approach, we leverage in situ data collected through 3D Lagrangian Particle Tracking (LPT) experimental setup situated at an altitude of 2650 m on Mt. Zugspitze (Germany) near the Schneefernerhaus environmental research station. Due to its favorable positioning, this location experiences natural cloud cover about a quarter of the time, offering an excellent opportunity for field studies. The LPT experimental setup probes a volume of ~40x20x12 mm ³ using three Vision Research v2511 cameras with maximum frame rate of 10 kHz, and the spatial resolution of ~1 µm. This enables simultaneous and accurate measurements of particle size and position, providing a rich dataset.

In this talk, we also showcase early-phase results of the calculated RDF, derived from the astute application of our analytical methodology to the data procured from our LPT experimental setup to deepen our understanding of cloud formation and precipitation.