CloudSat Cloud Length, Thickness Distributions Again Confirm the 23/9 (2.55 D) Scaling, Stratified, Turbulence Model
Bibliographic record
Abstract
Nearly 100 years ago, Richardson proposed that his “scaling first”, 4/3 law of turbulent advection holds from dissipation up to planetary scales. Starting in the 1960s - due primarily to its theoretical simplicity - the atmosphere was instead modelled as an “isotropy first” hybrid of isotropic 2D and isotropic 3D turbulence. In the 1980's Schertzer and Lovejoy pointed out that since the atmosphere is stratified, scaling first implies different horizontal and vertical scaling exponents and proposed the ratio = 5/9 implying an in-between dimension$D=2+5/9= 23/9=2.55\ldots$. By 2013 (the review [1]), the (meagre) aircraft support for the isotropic first model had been shown to be spurious, while numerous scaling first analyses (precipitation, aerosols, cloud densities, horizontal wind) vindicated Richardson and confirmed the 23/9D model over most of the horizontal and vertical ranges. I discuss new analyses of CloudSat cloud length distributions up to ≈ 2000 km (data from [2]) that yield the estimate$D=2.53\pm 0.02$giving even more support for Richardson and the 23/9D model and excluding the (still) fashionable isotropy first ($D=2$, large,$D=3$, small) model at the level of many, many, many standard deviations. Applications to remote pollution modelling and measurements are also discussed.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.002 |
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".