A three-dimensional hail trajectory clustering technique

Abstract

Recent advances in hail trajectory modeling regularly produce data sets containing millions of hail trajectories. Because hail growth within a storm cannot be entirely separated from the structure of the trajectories producing it, a method to condense the multidimensionality of the trajectory information into a discrete number of features analyzable by humans is necessary. This article presents a three-dimensional trajectory clustering technique that is designed to group trajectories that have similar updraft-relative structures and orientations. The new technique is an application of a two-dimensional method common in the data mining field. Hail trajectories (or “parent” trajectories) are partitioned into segments before they are clustered using a modified version of DBSCAN. Parent trajectories with segments that are members of at least two common clusters are then grouped into parent trajectory clusters before output. This multi-step method has several advantages. Hail trajectories with structural similarities along only portions of their length, e.g., sourced from different locations around the updraft before converging to a common pathway, can still be grouped. However, the physical information inherent in the full length of the trajectory is retained, unlike methods that cluster trajectory segments alone. The conversion of trajectories to an updraft-relative space also allows trajectories separated in time to be clustered. Once the final output trajectory clusters are identified, a method for calculating a representative trajectory for each cluster is proposed. Cluster distributions of hailstone and environmental characteristics at each timestep in the representative trajectory can also be calculated.