NMC Research Highlights New Approaches to Forest Structure Analysis at SIAM Conference
NMC Research Highlights New Approaches to Forest Structure Analysis at SIAM Conference
New Mexico Consortium (NMC) scientist Alex Masarie recently presented research at the Society for Industrial and Applied Mathematics (SIAM) Conference on the Mathematics of Planet Earth, showcasing new computational approaches for analyzing forest structure using terrestrial LiDAR data.
Masarie’s presentation, focused on applying Topological Data Analysis (TDA) to aerial/terrestrial laser scanning (A/TLS) point clouds [1], [2]. The research explores how topological methods can provide new ways to characterize the complex three-dimensional structure of forests and improve the analysis of ecological point cloud data, with potential applications in forestry, wildfire science, and computational ecology.
The work combines statistical measurements, dimensionality reduction, and topological data analysis to compare TLS point clouds. By combining these approaches, the NMC team is working toward a more consistent and reproducible way to evaluate forest structure across datasets collected with different sensors, processing methods, and sampling strategies. Such methods could improve the validation of forest-fuels datasets and support future wildfire modeling research.
The current research builds on a technical report on TDA [3] by Olivia Chandrasekhar that identified key computational tools – specifically, the Python GUDHI library [4] – and demonstrated visualizations about applying TDA methods to forest structure data, helping establish the foundation for the persistent geometric methods.
Scott Pokswinski, NMC Research Scientist, and Louise Loudermilk, USDA Forest Service, Southern Research Station, have contributed to the development and analysis directions of the current research. This has included facilitating advanced NMC access to Interagency Ecosystem Lidar Monitoring (IntEliMon) TLS point-cloud databases across the U.S. [5]
NMC’s role as a research incubator helps create opportunities for collaboration both within the organization and across institutions and disciplines. Internal technical expertise, research discussions, and support from colleagues provide a foundation for developing new ideas, while NMC’s organizational infrastructure helps researchers pursue external collaborations and turn promising conversations into new research directions. Administrative and organizational support from colleagues including Nora Arbuckle and John Engen helps make these collaborations possible.
The SIAM conference provided an opportunity to extend these discussions with researchers working across wildfire science, computational mathematics, and topology. Olivia Chandrasekhar presented a novel set of visual literature-review diagrams connecting historical and contemporary fire-modeling paradigms to their underlying mathematical foundations [6], Jonathon Hirschi of the University of Colorado Denver presented on time-warping methods for dead-fuel moisture prediction [7], and Mark Finney of the U.S. Forest Service Fire Sciences Laboratory presented on ongoing investigations of fundamental fire morphology using controlled flame-wind turntables [8].
The conference discussions are helping shape a TDA-inspired research effort, with a publication in preparation for submission to Multiscale Modeling & Simulation, a SIAM-edited journal. Better methods for comparing three-dimensional forest datasets could ultimately provide researchers with more rigorous tools for evaluating vegetation structure, wildfire fuels, and ecological change over time.
References
[1] Masarie, A. TLS Point Cloud Intercomparison: Toward Reproducible Evaluation of Forest Structure Datasets. SIAM Conference on the Mathematics of Planet Earth, 2026.
[2] Masarie, A. Analyzing Betti numbers in forest LiDAR data: Spatial correlation with voxelized fuel loading. 4th Southwest Fire Ecology Conference, Modeling and Mapping Poster Session, 2024.
[3] Chandrasekhar, O. (2023). Topological Data Analysis for Lidar Forestry Data. New Mexico Consortium. With technical guidance from E. Louise Loudermilk, USDA Forest Service, Southern Research Station. GitHub repository: https://github.com/o-chandra/lidar-tda
[4] GUDHI, “Geometry understanding in higher dimensions.” [https://gudhi.inria.fr/]
[5] U.S. Geological Survey. (2026). IntELiMon (Interagency Ecosystem Lidar Monitoring). U.S. Geological Survey database. https://doi.org/10.5066/P13T3UG3.
[6] Chandrasekhar, O. Visualizing 55 Years of Collaboration in Mathematics and Wildland Fire. 2026/7. SIAM Conference on the Mathematics of Planet Earth, 2026.
[7] Hirschi, J., Mandel, J., & Kochanski, A. (2026). Transfer Learning for Dead Fuel Moisture Prediction Using Time-Warping Recurrent Neural Networks.
[8] Ren, X., Sluder, E. T., Heck, M. V., Grumstrup, T. P., Finney, M. A., Mäkiharju, S. A., & Gollner, M. J. (2025). Surface flow characterization of fires under the combined effect of slope and wind. Fire Technology, 61, 5445–5460. https://doi.org/10.1007/s10694-025-01789-9.
Top image caption: Following the SIAM Mathematics of Planet Earth 2026 session on Mathematics in Wildfire: Leveraging Mathematical Expertise in a Changing Field; session speakers [left to right] Dr. Mark Finney, USDA Forest Service Rocky Mountain Research Station, Missoula Fire Sciences Laboratory; Dr. Alex Masarie, New Mexico Consortium; Dr. Olivia Chandrasekhar, KBR supporting the U.S. Geological Survey; Dr. Jonathon Hirschi, University of Colorado Denver. (Photo credit: Olivia Chandrasekhar)
Image caption: Topological representation of a terrestrial LiDAR scan. The TLS point cloud (left) is transformed into an error-robust simplicial representation (right) using a fast Delaunay-based construction. Geometry: simplex counts—175,031 vertices, 319,825 edges, 111,988 triangles, and no higher-dimensional simplices—characterize the geometric construction. The topology is then summarized by the three Betti numbers, β₀ = 45, β₁ = 98, and β₂ = 13. The resulting simplex counts characterize the geometry; the Betti numbers summarize the topology.