Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2505.10850

Tracking Low-Level Cloud Systems with Topology

Mingzhe Li·Dwaipayan Chatterjee·Franziska Glassmeier·Fabian Senf·Bei Wang
View original source ↗Read source document ↗Export metadata ↓

Abstract

Low-level clouds are ubiquitous in Earth's atmosphere, playing a crucial role in transporting heat, moisture, and momentum across the planet. Their evolution and interaction with other atmospheric components, such as aerosols, are essential to understanding the climate system and its sensitivity to anthropogenic influences. Advanced high-resolution geostationary satellites now resolve cloud systems with greater accuracy, establishing cloud tracking as a vital research area for studying their spatiotemporal dynamics. It enables disentangling advective and convective components driving cloud evolution. This, in turn, provides deeper insights into the structure and lifecycle of low-level cloud systems and the atmospheric processes they govern. In this paper, we propose a novel framework for tracking cloud systems using topology-driven techniques based on optimal transport. We first obtain a set of anchor points for the cloud systems based on the merge tree of the cloud optical depth field. We then apply topology-driven probabilistic feature tracking of these anchor points to guide the tracking of cloud systems. We demonstrate the utility of our framework by tracking clouds over the ocean and land to test for systematic differences in the two physically distinct settings. We further evaluate our framework through case studies and statistical analyses, comparing it against two leading cloud tracking tools and two topology-based general-purpose tracking tools. The results demonstrate that incorporating system-based tracking improves the ability to capture the evolution of low-level clouds. Our framework paves the way for detailed low-level cloud characterization studies using satellite data records.

Explore related subjects

cs.CG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Mingzhe Li, Dwaipayan Chatterjee, Franziska Glassmeier, Fabian Senf, Bei Wang. 2025-05-16. Tracking Low-Level Cloud Systems with Topology. https://arxiv.org/abs/2505.10850

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Almost Linear Universal Point Sets for Planar Graphs

A point set is universal for planar graphs on $n$ vertices if every such graph has a straight-line drawing without crossings whose vertices belong to the set. We construct universal point sets of size $n^{1+o(1)}$, improving the previous quadratic upper bound. Our construction uses the reduction of Bannister, Cheng, Devanny, and Eppstein from universal point sets to superpatterns for $213$-avoiding permutations. We represent these permutations by ordered rooted forests and construct a small family of intervals containing every such forest. The result follows from a straightforward bound on the size of the family of intervals. GPT-6 Astra assisted in developing the construction and proof.

cs.CG↗
arXiv2026

Some results on Archdeacon's conjecture for rotation systems

A rotation system on $n$ elements assigns to each element a cyclic order of the other $n-1$ elements. A four-element subset is non-planar if its induced rotation system cannot be realized by a crossing-free drawing of $K_4$. As a combinatorial strengthening of Hill's conjecture on the crossing number of the complete graph, Archdeacon conjectured that every rotation system on $n$ elements has at least $H(n)=\frac{1}{4} \lfloor\frac {n}{2}\rfloor \lfloor\frac{n-1}{2}\rfloor \lfloor\frac{n-2}{2}\rfloor \lfloor\frac{n-3}{2}\rfloor$ non-planar four-element subsets. We computationally verify Archdeacon's conjecture for $n\leq 10$ and show that every extremal rotation system in these orders is realizable by a simple drawing. With computer assistance, we prove that every rotation system on $n$ elements has at least $(8/9 - o(1)) H(n)$ non-planar four-element subsets. We also present a proof by hand for a weaker lower bound of $(2/3-o(1)) H(n)$. Finally, extending recent work of Felsner on antipodal pairs in drawings, we show that Archdeacon's conjecture holds for antipodally shellable rotation systems.

cs.CG↗
arXiv2026

The Hyperbolic Surface Distance, Diameter, and Dirichlet Problems

Despite the prominence of hyperbolic surfaces in mathematics, basic algorithmic questions about them, even computing the distance between two points, have remained open, leaving many features of these surfaces inaccessible. The classical machinery assumes a polyhedral structure absent on a smooth surface. We remove these obstacles. We begin with an efficient $O(g^2)$ algorithm for the distance between two points, where $g$ is the genus of the surface. Building on it, we obtain an $O(g^2 \log g)$ method for answering distance queries from a fixed source and, as a consequence, for recentering a Dirichlet domain around an arbitrary point. This understanding of distances on the surface then lets us approximate the diameter to within any $\eps$ in time $O(g^3 \log g / \eps^2)$. We further show that the diameter, a single real number encoding a great deal about the surface, is exactly computable. Its hyperbolic cosine is an algebraic number over the field encoding the coefficients of the hyperbolic isometries defining the surface.

cs.CG↗