the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 11 Jun 2026
Correlated Geometric Scaling of Tornado Damage Paths in the SPC Database (1950–2024)
Abstract. We investigate the large-scale geometric organisation of tornado damage paths using the NOAA Storm Prediction Center (SPC) tornado database over the period 1950–2024. The analysis focuses primarily on the correlated geometry of tornado path length and width independently of any energetic weighting procedure.
A robust anisotropic scaling relation is identified between tornado path width W and path length L,
W ∼ Lα, α ≈ 0.43,
indicating that longer tornadoes undergo systematic sublinear lateral broadening during propagation. This correlated geometric growth naturally induces a hierarchy for the geometry-only observable
A = LW,
which obeys the scaling law
A ∼ L1+α ≈ L1.43.
Complementary cumulative distribution functions reveal broad heavy-tailed statistics spanning several decades in scale. Finite-size scaling analysis further demonstrates that the geometric hierarchy remains remarkably stable across independent historical periods despite major observational transitions associated with Doppler-radar deployment and evolving survey practices.
Higher-order conditional moments remain predominantly affine and are shown to be fully consistent with the measured width–length scaling relation. Null-model comparisons demonstrate that the observed hierarchy cannot be explained solely by broad marginal distributions or simple algebraic construction effects, but instead reflects genuine correlations linking tornado length and width across scales.
Although the present analysis remains fundamentally statistical, the results suggest that tornado damage geometry may reflect the large-scale statistical imprint of persistent coherent vortex organisation embedded within strongly nonlinear convective dynamics.
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Status: open (until 06 Aug 2026)
- RC1: 'Comment on egusphere-2026-2829', Anonymous Referee #1, 29 Jun 2026 reply
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RC2: 'Comment on egusphere-2026-2829', Anonymous Referee #2, 30 Jun 2026
reply
For reasons relating to both presentation and scientific content, this manuscript cannot be considered for publication in Nonlinear Processes in Geophysics. It falls well short of the journal's academic and scientific standards. The dataset is inadequately described, the methodology is presented in a highly repetitive manner—with the same equations repeated numerous times—and the proposed scaling relationships are not convincingly demonstrated. Most importantly, Figures 1 and 2, which are central to the manuscript's claims, do not provide clear evidence of scaling behaviour.
The manuscript also suffers from a number of major issues regarding its presentation.
- Equations should not appear in the abstract. The abstract should be completely revised to conform to the conventions of scientific writing.
- Throughout the manuscript, equations are not numbered and are systematically following unnecessary blank lines. The equations should be properly numbered and integrated into the text. In many instances, a displayed equation is unnecessary, and the corresponding expression could simply be incorporated into the sentence. The author is encouraged to consult recent papers in the field to become familiar with standard practices for presenting mathematical material in scientific articles.
Regarding the scientific content:
- Lines 87–93: Equations are introduced in the Introduction without defining the notation (e.g. W, L, A, and α). Either these equations should be removed from the Introduction or the notation should be explained. However, if these relationships constitute original results, they do not belong in the Introduction.
- Line 112: The quantities EF0 and EF5 are not defined.
- Section 2.1: The description of the dataset is insufficient. The manuscript should specify how many tornado tracks are included, the spatial resolution of the data, the total number of observations, and, for each of the three study periods (line 124), the corresponding number of tornadoes.
- Line 131: The definition of W is unclear. How is this quantity obtained? Furthermore, the physical or statistical justification for the proposed scaling relationship should be explained.
- The scaling law (W \sim L^{\alpha}) is repeated in the abstract and on lines 88, 131, 141, 231, 277, 295, and 337. It should be introduced only once as a numbered equation and subsequently referred to by its equation number.
- Likewise, the relation A = LW is repeated on lines 91, 136, 143, 225, 287, 293, and 350. The same comment applies.
- Equation on line 209: The parameter (\eta) is never defined.
- Given Equation 169, Equation 171 follows immediately by taking the logarithm. It is unnecessary to state such a trivial mathematical step explicitly in a scientific paper.
- Figures 1 and 2: These figures are not convincing. No clear scaling behaviour is apparent from the data presented, despite the fact that the manuscript's central conclusions rely on these relationships. This is a major weakness of the study.
There are numerous additional issues throughout the manuscript that could also be raised. However, the points listed above are already sufficient to conclude that the manuscript does not currently meet the scientific and editorial standards required for publication in Nonlinear Processes in Geophysics.
Citation: https://doi.org/10.5194/egusphere-2026-2829-RC2 -
RC3: 'Comment on egusphere-2026-2829', Anonymous Referee #3, 30 Jun 2026
reply
Overall Assessment
I found this manuscript interesting and potentially valuable. The identification of a persistent width–length scaling relationship using the long-term SPC tornado database is an intriguing result, and the manuscript is generally well organized and clearly written.
The statistical analyses are carefully conducted and the geometric hierarchy appears robust. My comments mainly concern the physical interpretation of the reported scaling relationship and the extent to which the measured exponent can be considered a universal property of tornadoes rather than an effective climatological average obtained from a heterogeneous population of events.
MAJOR COMMENTS
Major Comment 1
Physical meaning of the scaling exponent
The manuscript identifies a remarkably stable width–length scaling exponent (α ≈ 0.43). However, I found myself wondering what physical meaning should be attached to this exponent.
Is α ≈ 0.43 an intrinsic property of tornado evolution, or is it primarily an emergent climatological statistic resulting from aggregation across many different tornado populations?
Additional discussion regarding the physical interpretation of the exponent would strengthen the manuscript considerably.
Major Comment 2
Potential dependence on tornado intensity
Both tornado path length and tornado path width are known to increase with tornado intensity.
Therefore, I wonder whether the observed width–length scaling may partly reflect a common dependence of both variables on EF rating.
The manuscript itself acknowledges the potential importance of EF1+, EF2+, and EF3+ analyses. If feasible, I believe such sensitivity tests would significantly strengthen the conclusions.
Major Comment 3
Influence of environmental variability
The SPC database spans a wide range of environmental conditions.
I wonder whether the reported scaling relation remains stable across different meteorological environments, such as regions characterized by different levels of vertical wind shear, storm-relative helicity, convective instability, or storm mode.
Without considering these sources of variability, it is difficult to determine whether the measured exponent represents a universal geometric property or a climatological average across diverse environments.
Major Comment 4
Connection between geometric scaling and tornado dynamics
The manuscript provides a convincing statistical description of tornado-path geometry.
However, I would appreciate a stronger discussion connecting the reported geometric hierarchy to tornado dynamics.
For example, tornado path length is closely related to tornado lifetime and translational motion, while path width may reflect vortex structure, mesocyclone organization, or parent-storm evolution.
Strengthening this connection would considerably broaden the meteorological significance of the study.
Major Comment 5
Treatment of tornadoes as a single statistical population
As I understand it, all tornadoes contained within the SPC database are treated as a single statistical population.
However, supercell tornadoes, QLCS tornadoes, landspouts, and weak short-lived tornadoes may not necessarily exhibit identical geometric behavior.
I would appreciate additional discussion regarding whether the reported exponent should be interpreted as a universal property or as an effective climatological exponent obtained from a heterogeneous tornado population.
MINOR COMMENTS
Minor 1
Definition and uncertainty of tornado width
Since width is one of the central variables in the study, additional discussion regarding the definition and observational uncertainty of path-width measurements would be helpful.
(Methods, p.7)
Minor 2
Please consider reporting confidence intervals for the estimated exponent α ≈ 0.43 in the main text and/or Figure 1.
Minor 3
Please specify the number of bootstrap realizations used and briefly describe the resampling procedure. (Appendix B4)
Minor 4
Please report the number of tornadoes included in each historical subset.
(1950–1974, 1975–1999, 2000–2024)
Minor 5
The plateau region in Figure 11 appears to be identified primarily through visual inspection.
A quantitative criterion would improve reproducibility.
Minor 6
Several statements regarding geometric hierarchy / temporal robustness / internal consistency
appear repeatedly throughout the Discussion and Conclusion sections.
The manuscript could be slightly shortened by reducing repetition.
Minor 7
The manuscript discusses temporal observational inhomogeneities.
However, additional discussion regarding possible width-measurement biases during the pre-Doppler era may be useful.
Minor 8
A brief comparison with scaling relationships reported for other atmospheric vortices (e.g., mesocyclones or tropical cyclones) may help place the results within a broader meteorological context.
Minor 9
The measured exponent is close to, but distinct from, 0.5.
I wonder whether the authors have considered whether this difference has any potential physical interpretation or whether it falls within the statistical uncertainty of the estimate.
Minor 10
The future-work section could be expanded slightly to discuss how environmental variables (e.g., CAPE, SRH, storm mode, or parent-storm characteristics) might be incorporated into future scaling analyses.
Citation: https://doi.org/10.5194/egusphere-2026-2829-RC3
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