Articles | Volume 33, issue 4
https://doi.org/10.5194/npg-33-521-2026
https://doi.org/10.5194/npg-33-521-2026
Research article
 | 
20 Oct 2026
Research article |  | 20 Oct 2026

A physically grounded input distance resolves longitude-encoding ambiguity but not specification dependence in ensemble persistent homology of cyclone trajectories

Rongzhen Dai

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This preprint is open for discussion and under review for Biogeosciences (BG).
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Cited articles

Adams, H., Emerson, T., Kirby, M., Neville, R., Peterson, C., Shipman, P., Chepushtanova, S., Hanson, E., Motta, F., and Ziegelmeier, L.: Persistence images: a stable vector representation of persistent homology, J. Mach. Learn. Res., 18, 1–35, 2017. 
Adams, H. and Moy, M.: Topology applied to machine learning: from global to local, Front. Artif. Intel. Ap., 4, 668302, https://doi.org/10.3389/frai.2021.668302, 2021. 
Bauer, U.: Ripser: efficient computation of Vietoris–Rips persistence barcodes, J. Appl. Comput. Topol., 5, 391–423, https://doi.org/10.1007/s41468-021-00071-5, 2021. 
Bendich, P., Marron, J. S., Miller, E., Pieloch, A., and Skwerer, S.: Persistent homology analysis of brain artery trees, Ann. Appl. Stat., 10, 198–218, https://doi.org/10.1214/15-AOAS886, 2016. 
Benjamini, Y. and Hochberg, Y.: Controlling the false discovery rate: a practical and powerful approach to multiple testing, J. Roy. Stat. Soc. B, 57, 289–300, https://doi.org/10.1111/j.2517-6161.1995.tb02031.x, 1995. 
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Tests that summarise the shape of a cloud of storm positions can give different answers depending on choices the analyst makes but rarely reports. Using three benchmark geomagnetic storms, we show that measuring distance along the Earth surface removes one such choice, and we measure how much the answer still moves with the others. Averaging over those choices rather than selecting one, we report a directional residual: neither a detection nor evidence that no effect is there.
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