Cluster Analysis Tailored to Structure Change of Tropical Cyclones Using a Very Large Number of Trajectories

Abstract

Major airstreams in tropical cyclones (TCs) are rarely described from a Lagrangian perspective. Such a perspective, however, is required to account for asymmetries and time dependence of the TC circulation. We present a procedure that identifies main airstreams in TCs based on trajectory clustering. The procedure takes into account the TC’s large degree of inherent symmetry and is suitable for a very large number of trajectories [O⁡(106)]. A large number of trajectories may be needed to resolve both the TC’s inner-core convection as well as the larger-scale environment. We define similarity of trajectories based on their shape in a storm-relative reference frame, rather than on proximity in physical space, and use Fréchet distance, which emphasizes differences in trajectory shape, as a similarity metric. To make feasible the use of this elaborate metric, data compression is introduced that approximates the shape of trajectories in an optimal sense. To make clustering of large numbers of trajectories computationally feasible, we reduce dimensionality in distance space by so-called landmark multidimensional scaling. Finally, k-means clustering is performed in this low-dimensional space. We investigate the extratropical transition of Tropical Storm Karl (2016) to demonstrate the applicability of our clustering procedure. All identified clusters prove to be physically meaningful and describe distinct flavors of inflow, ascent, outflow, and quasi-horizontal motion in Karl’s vicinity. Importantly, the clusters exhibit gradual temporal evolution, which is most notable because the clustering procedure itself does not impose temporal consistency on the clusters. Finally, TC problems are discussed for which the application of the clustering procedures seems to be most fruitful.