SIParCS 2025 - Esther Gallmeier

Scalable Vector Calculus Operators for Geoscientific Analysis on Unstructured Grids in UXarray

Recorded Talk

Mathematical operators such as gradient, curl, and divergence are essential for analyzing scalar and vector fields in climate model outputs. As modern climate models increasingly adopt unstructured grid discretizations and operate at storm-resolving spatial resolutions, there is a critical need for scalable, high-performance implementations of these operators. UXarray is an open-source Python package for analyzing and visualizing geoscientific datasets defined on unstructured grids over the sphere, without requiring regridding to structured grids. During this internship, vector calculus operators were developed to enable analysis workflows on UXarray's wide-range of supported grid formats, including UGRID, MPAS, ICON, HEALPix, and others. High-performance Python libraries such as Numba were leveraged for just-in-time compilation and parallelization. Benchmarking was conducted using high-resolution unstructured datasets, including a variety of grid structures, to assess the robustness and performance of the implementations. To demonstrate the implementation and its scientific utility, Jupyter Notebook examples with detailed explanations and visualizations were created for the user community. Although formal analysis of numerical accuracy has not been carried out, the operators produce results that are visually consistent with expected field behavior and are well-suited for data analysis and visualization across a range of mesh configurations.

Mentors: Philip Chmielowiec, Orhan Eroglu, Katelyn FitzGerald, Rajeev Jain

Slides and poster