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<strong class="journal-contentHeaderColor">Abstract.</strong> Meteorological simulations produce large amounts of data, which can represent a challenge when trying to store, share, and analyze it. As weather and climate models increasingly simulate the atmosphere at higher spatio-temporal resolution, it becomes imperative to compress the data effectively. While compression algorithms exist for weather data stored in a gridded Eulerian frame, there are, to date, no specialized alternatives for data stored in the Lagrangian frame. In this study, we present psit, a system to compress weather data stored in the Lagrangian frame. The system works by mapping the trajectories to a grid structure, performing additional encodings on these, and passing them to either the <em>JPEG 2000</em> image compression algorithm or <em>SZ3</em>. The specialty of the algorithm is the mapping phase and the following encodings, which generate the grids in a way that allows the aforementioned compression algorithms to perform well. To gauge the performance of psit, we test a variety of metrics. We demonstrate that in the majority of cases, equivalent or superior compression performance is attained through the utilization of psit as opposed to naive compression with <em>ZFP</em>. We also compare compression with measurement inaccuracies. Here, we show that the density of 168 hour long trajectories compressed with a ratio in the range of 30 to 40 behaves similarly to trajectories calculated from uncompressed wind fields with additional random perturbations with magnitude of 0.1 ms<sup>-1</sup> in the horizontal and around 6⋅10<sup>-3 </sup>Pa s<sup>-1</sup> in the vertical component. Additionally, we conduct two case studies in which we discuss the impact of compression on the study of warm conveyor belts associated with extratropical cyclones and the impact of compression on the radioactive plume prediction of the Fukushima incident in 2011.