A Nonlinear Schrödinger Equation Model of the Intraseasonal Oscillation
Bibliographic record
Abstract
The nonlinear Schrödinger (NLS) equation was used to explore possible mechanisms responsible for the intraseasonal oscillation phenomenon occurring in the atmosphere. An NLS equation depicts such a scenario that in a narrowbanded wave packet, the balance between nonlinearity and dispersion results in either a focusing of the wave packet appearing as a solitary envelope or a defocusing in the form of a superlinear envelope. The occurrence of either case depends on the signs of the dispersion coefficient and the Landau constant. Application of this concept to the intraseasonal oscillation was motivated by observational evidence that the large-scale eastward propagation of large cloud clusters with a recurrence period of 40–50 days is concurrently accompanied by mesoscale westward propagations of smaller cloud clusters. The small clusters are actually embedded in the large clusters and exhibit themselves in a well-organized wave train form. In the context of an NLS equation, the eastward propagation of large clusters could be an envelope propagation of the small cluster wave train at the group velocity. In order to examine this hypothesis, a theoretical framework was established in this study. An NLS equation was derived from the nonlinear shallow water equation forced by the internal atmospheric heating, such as that due to cumulus clouds. Two types of wave trains that may resemble dynamical behaviors of the intraseasonal oscillation were investigated: mixed Rossby–gravity wave trains and Rossby wave trains. For mixed Rossby–gravity wave trains, only a superlinear envelope is possible. For Rossby wave trains, the occurrence of a solitary envelope or a superlinear envelope depends on the wavelength. Eventually, the current NLS equation model is still too crude to reproduce quantitative characteristics of the intraseasonal oscillation, for example, the propagation speed of the large cloud clusters.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".