Fine-Scale Droplet Clustering in Atmospheric Clouds: 3D Radial Distribution Function from Airborne Digital Holography

The extent of droplet clustering in turbulent clouds has remained largely unquantified, and yet is of possible relevance to precipitation formation and radiative transfer. To that end, data gathered by an airborne holographic instrument are used to explore the three-dimensional spatial statistics of cloud droplet positions in homogeneous stratiform boundary-layer clouds. The three-dimensional radial distribution functions $g(r)$ reveal unambiguous evidence of droplet clustering. Three key theoretical predictions are observed: the existence of positive correlations, onset of correlation in the turbulence dissipation range, and monotonic increase of $g(r)$ with decreasing $r$. This implies that current theory captures the essential processes contributing to clustering, even at large Reynolds numbers typical of the atmosphere.

Figure 1

Quantifying the uncertainty due to counting statistics in the estimation of $g(r)$ as a function of scale for differently shaped volumes and realistic cloud droplet concentrations. Each panel shows a range where the measured $g(r)$ might lie when the intrinsic system $g(r)$ is known to be unity. These curves are derived from applying $\sqrt{N}$ uncertainty estimates to the counting statistics needed to compute $g(r)$. The 3D volumes match the aspect ratio of the HOLODEC sample volume, while the 1D volumes are designed to mimic a typical single-particle-counting instrument viewing the same total volume. Note that the scale of the 1D volume panels had to be magnified, since the uncertainty is many times larger for 1D data sets. Individual hologram $g(r)$ estimates for HOLODEC data drop below 10% uncertainty for spatial scales somewhere between 1 and 3 mm, depending on droplet number concentration.

Figure 2

The interval-averaged radial distribution functions for each of the four flight intervals examined in this study. The observed radial distribution functions exceed the maximum value expected based on sampling uncertainty throughout the range 1–5 mm in all flight intervals. Three key theoretical predictions are observed: positive correlation, onset of correlation in the dissipation range (less than approximately 10 mm), and monotonic increase of $g(r)$ with decreasing $r$. The two shaded regions quantify the sampling uncertainty via two independent methods explained in the text.