Spatial and temporal stochastic cascade structure of deterministic numerical models of the atmosphere
Bibliographic record
Abstract
Statistical analyses of numerical models of the atmosphere have traditionally concentrated on classical turbulent fluxes, especially the energy and enstrophy. Theoretically, this has been justified by isotropic theories and through hypothetical isotropic cascades. However due to gravity, the atmosphere and its models are strongly anisotropic (stratified) so that these theories are quite unrealistic. Our starting point are empirical findings that the stratification is scaling so that the atmospheric dynamics (and as we show here, their models) can be governed by anisotropic cascades governed by nonstandard turbulent fluxes. In this generalized scaling framework we expect scaling relations of the (generalized) Kolmogorov form to hold: F(L) = ?(L) LH, where F(L) is the fluctuation in a field at scale L and H is a scaling exponent and ?(L) is the underlying resolution L flux. We use this approach to estimate ?(L) and then to systematically degrade it to lower and lower resolutions. The cascade hypothesis predicts that qhigher than = (Louter/L)K(q) where here L is the resolution of the flux, Louter is the outer scale of the cascade (where it starts) and K(q) is a scaling exponent function describing all the statistical properties as a function of scale. In this presentation we test this anisotropic cascade framework on the horizontal east-west wind, temperature, and humidity fields at 5 different pressure levels for both (three years of) the ERA40 reanalysis as well as (eleven months of) the Canadian Meteorological Centre Global Environmental Multiscale (CMC GEM) model. Our results indicate that over most of the range of scales (essentially planetary scales down to 2-3 pixels; below this the hyperviscosity breaks the scaling), that the spatial stochastic structure predicted by phenomenological cascade models is obeyed to within ±1%. We also examine the cascade sructure in the temporal domain; we find that it has a break in the scaling between the meteorological (less than ~20 days) and climate (greater than ~ 100 days) regimes. The temporal behaviour is also discussed with the aid of space-time (Stommel diagrams) to which we give a rigorous interpretation. We discuss how to exploit stochastic cascade structure to improve current forecasting methods, including applications to stochastic parametrisations.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".