Ocean Drifters (Madagascar Ocean Drifters)

From Schaub, Michael T., et al. "Random walks on simplicial complexes and the normalized hodge 1-laplacian." SIAM Review 62.2 (2020): 353-391.

This datataset comes from the Global Ocean Drifter Program available at the AOML/NOAA Drifter Data Assembly. While the entire dataset spans several decades of measurements, Schaub et al. focused on data from Jan 2011–June 2018 and limit ourselves to buoys that have been active for at least 3 months within that time period. They built trajectories by considering the location information of every buoy every 12 hours. As buoys may fail to record a position, there are trajectories with missing data. In these cases, they split the trajectories into multiple contiguous trajectories. For the analysis, they've examined trajectories around Madagascar with a latitude y_{lat} \in [−30, −10], and longitude x_{long} \in [39, 55]. This results in 400 total trajectories. To construct the Simplicial Complex, they first have transformed the data into Euclidean coordinates via an area-preserving (Lambert) projection. We discretize Euclidean space using a hexagonal grid, with the width of the hexagon equal to 1.66◦ (latitude). Each hexagon corresponds to a node, and we add an edge between two such nodes if there is a nonzero net flow from one hexagon to its adjacent neighbors. They considered all triangles (3-cliques) in this graph to be faces of the simplcial complex. The Laplacian Ls 1 of the resulting complex has a two-dimensional harmonic space. Each dimension of this space corresponds to an “obstacle” of the flow. Finally, the discretization of each trajectory was performed by rounding its positional coordinates to the nearest hexagon and consider the resulting sequence of edges that the trajectory traverses in the complex.