Uncertainty and predictability in geophysics: Chaos and multifractal insights
Bibliographic record
Abstract
"Uncertainty and error growth are crosscutting geophysical issues. Since the ""chaos revolution"" the dominant paradigm has been the ""butterfly effect"": the dependence on initial conditions is so sensitive that errors grow exponentially fast with characteristic times. This was the outcome of studying superficially simple caricatures of more involved systems. We critically analyze the physical relevance of these models and the mathematical generality of this effect. We emphasize that the atmosphere, oceans, rain etc., are spatially extended turbulent systems, with wide ranges of spatial scales. Turbulent phenomenology already shows that errors grow only slowly across these scales; they follow power laws, there are no characteristic times. An important recent realization is that in spite of strong anisotropies the dynamically significant range of scales is much larger than previously thought and that the role of intermittency is drastic and yields much more frequent extremes. The focus is now on time-space geophysical scaling behavior: their multifractality. It is found quite generally - not only for turbulent fields- that an infinite hierarchy of exponents is required to characterize the predictability decay from average to extreme events. Nevertheless, these laws are meaningful over the whole time range from short to long term; we give their explicit expression. This multifractal predictability suggests the advantages of stochastic rather than deterministic sub-grid parametrizations, and makes stochastic forecasting very attractive."
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.012 | 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".