Diabatic Balance Model for the Equatorial Atmosphere
Bibliographic record
Abstract
Abstract Using an asymptotic expansion, a balance model is derived for the shallow-water equations (SWE) on the equatorial β plane that is valid for planetary-scale equatorial dynamics and includes Kelvin waves. In contrast to many theories of tropical dynamics, neither a strict balance between diabatic heating and vertical motion nor a small Froude number is required. Instead, the expansion is based on the smallness of the ratio of meridional to zonal length scales, which can also be interpreted as a separation in time scale. The leading-order model is characterized by a semigeostrophic balance between the zonal wind and meridional pressure gradient, while the meridional wind υ vanishes; the model is thus asymptotically nondivergent, and the nonzero correction to υ can be found at the next order. Importantly for applications, the diagnostic balance relations are linear for winds when inferring the wind field from mass observations and the winds can be diagnosed without direct observations of diabatic heating. The accuracy of the model is investigated through a set of numerical examples. These examples show that the diagnostic balance relations can remain valid even when the dynamics do not, and the balance dynamics can capture the slow behavior of a rapidly varying solution.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".