water Article A Lagrangian Backward Air Parcel Trajectories Clustering Framework Iulia-Maria R ˘ adulescu * , Alexandru Boicea , Florin R ˘ adulescu and Daniel-C ˘ alin Popeang ˘ a   Citation: R˘ adulescu, I.-M.; Boicea, A.; R ˘ adulescu, F.; Popeang˘ a, D.-C. A Lagrangian Backward Air Parcel Trajectories Clustering Framework. Water 2021, 13, 3638. https:// doi.org/10.3390/w13243638 Academic Editor: Kai Yan Received: 25 November 2021 Accepted: 12 December 2021 Published: 17 December 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Computer Science and Engineering Department, University Politehnica of Bucharest, 060042 Bucharest, Romania; alexandru.boicea@upb.ro (A.B.); florin.radulescu@upb.ro (F.R.); daniel.popeanga@upb.ro (D.-C.P.) * Correspondence: iulia.m.radulescu@upb.ro Abstract: Many studies concerning atmosphere moisture paths use Lagrangian backward air parcel trajectories to determine the humidity sources for specific locations. Automatically grouping trajecto- ries according to their geographical position simplifies and speeds up their analysis. In this paper, we propose a framework for clustering Lagrangian backward air parcel trajectories, from trajectory generation to cluster accuracy evaluation. We employ a novel clustering algorithm, called DenLAC, to cluster troposphere air currents trajectories. Our main contribution is representing trajectories as a one-dimensional array consisting of each trajectory’s points position vector directions. We empirically test our pipeline by employing it on several Lagrangian backward trajectories initiated from Bˇ reclav District, Czech Republic. Keywords: Lagrangian backward trajectories; clustering; HYSPLIT; position vectors 1. Introduction Many researchers rely on Lagrangian backward trajectories clustering to extract im- portant insights regarding water-related extreme weather phenomena, such as heavy rainfalls, violent storms, floods, or diffuse water pollution (Hao et al. [1], Juhlke et al. [2] Karaca et al. [3], and Borge et al. [4]). To support their studies, we propose a complete, efficient, and accurate framework for Lagrangian backward trajectories visualization and cluster analysis. Our method is especially suitable for investigating the causes of particular meteo- rological events: one can employ it directly on a trajectory file instead of combining the results of several complicated tools, thus simplifying and standardizing the process. We improve the performance and correctness of the clustering operation by combining lightweight trajectory representation with a flexible and accurate clustering algorithm. To validate our method, we use a real-world example with applications in flood risk management. However, we do not explain the results from the meteorological point of view since this is out of this paper’s scope. In the following paragraphs, we briefly describe the proposed pipeline. First, we use a free online tool to compute several air parcel trajectories starting from a specific location, relying on archived gridded meteorological information, such as the wind vector at different time intervals. We choose the recent extreme meteorological events in the Czech Republic (June 2021) to exemplify our method, thus initiating the trajectories in the Bˇ reclav District. Before employing the actual clustering operation, we apply several transformations on the trajectories: (i) we convert the geographical coordinates into Cartesian coordinates, (ii) we normalize the resulting values, (iii) we translate the trajectories’ points relative to the Bˇ reclav District’s location, and (iv) we represent trajectories as one-dimensional arrays, consisting of each point’s position vector’s direction. To cluster the preprocessed data, we choose a recent clustering algorithm called DenLAC [5] due to its flexibility. The DenLAC algorithm accurately clusters various cluster types: spherical, elongated, and with different sizes and densities. Finally, we validate Water 2021, 13, 3638. https://doi.org/10.3390/w13243638 https://www.mdpi.com/journal/water