Joint horizontal‐vertical anisotropic scaling, isobaric and isoheight wind statistics from aircraft data
Bibliographic record
Abstract
Aircraft measurements of the horizontal wind have consistently found transitions from roughly k−5/3 to k−2.4 spectra at scales Δxc ranging from about 100–500 km. Since drop sondes find k−2.4spectra in the vertical, the simplest explanation is that the aircraft follow gently sloping trajectories (such as isobars) so that at large scales, they estimate vertical rather than horizontal spectra. In order to directly test this hypothesis, we used over 14500 flight segments from GPS and TAMDAR sensor equipped commercial aircraft. We directly estimate the joint horizontal‐vertical (Δx, Δz) wind structure function finding ‐ for both longitudinal and transverse components ‐ that the ratio of horizontal to vertical scaling exponents isHz ≈ 0.57 ± 0.02, close to the theoretical prediction of the 23/9D turbulence model which predicts Hz = 5/9 = 0.555…. This model also predicts that isobars and isoheight statistics will diverge after Δxc; using the observed fractal dimension of the isobars (≈1.79 ± 0.02), we find that the isobaric scaling exponents are almost exactly as predicted theoretically and Δxc ≈ 160, 125 km, (transverse, longitudinal). These results thus give strong direct support to the 23/9D scaling stratification model.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".