TriCCo -- a cubulation-based method for computing connected components on triangular grids

TL;DR

The paper introduces TriCCo, a cubulation-based method that efficiently identifies connected components on unstructured triangular grids by mapping them onto structured cubic grids, facilitating climate model analyses.

Contribution

It presents a novel cubulation approach for connected component detection on triangular grids, enabling the use of existing cubic grid software and demonstrating its implementation in a Python package.

Findings

TriCCo can handle grids with up to 500,000 cells.

The method's performance is comparable to graph-based BFS for medium-sized grids.

Computational efficiency can be improved for larger grids.

Abstract

We present a new method to identify connected components on triangular grids used in atmosphere and climate models to discretize the horizontal dimension. In contrast to structured latitude-longitude grids, triangular grids are unstructured and the neighbors of a grid cell do not simply follow from the grid cell index. This complicates the identification of connected components compared to structured grids. Here, we show that this complication can be addressed by involving the mathematical tool of cubulation, which allows one to map the 2-d cells of the triangular grid onto the vertices of the 3-d cells of a cubic grid. Because the latter is structured, connected components can be readily identified by previously developed software packages for cubic grids. Computing the cubulation can be expensive, but importantly needs to be done only once for a given grid. We implement our method in a Python package that we name TriCCo and make available via pypi, gitlab and zenodo. We document the package and demonstrate its application using simulation output from the ICON atmosphere model. Finally, we characterize its computational performance and compare it to graph-based identifications of connected components using breadth-first search. The latter shows that TriCCo is ready for triangular grids with up to 500,000 cells, but that its speed and memory requirement should be improved for the application to larger grids.