Integrated depth for trajectories of airborne microorganisms to Antarctica

Abstract

Sets of trajectories that begin or end at the same point, in the form of a bouquet, appear in several real-world problems, such as the dispersion of volcanic ash or forecasts of hurricane paths, among others. Our interest in this type of trajectory focuses on studying the biogeography of airborne microorganisms and their ability to colonise soils recently exposed due to climate change. For these functional data, we introduce a new integrated depth measure ($mathcal{D}$) that allows finding central and outlier curves in a dataset. First, circular local depths ($LD$) are calculated in concentric circles around the common point and, in a second step, these values are integrated along the curves, yielding the trajectory depth. Under mild conditions, both $LD$ and $mathcal{D}$ have good properties and are strongly consistent. In addition, we propose an efficient algorithm for working with large datasets. Finally, we apply this new technique to find the main routes followed by air masses carrying microorganisms to Byers Peninsula (Livingston Island, Antarctica).