Bibliographic record
Abstract
Abstract Balance equations (BEs) which describe the balance constraints among balanced variables have wide applications in data assimilation and diagnosing balanced motions. In the applications an additional equation serving as an interface to connect the balanced variables and full fields (data assimilation analyses or fields of primitive equations) is required for the inversion of BEs to obtain the balanced variables. The interface equation is often constructed through the potential vorticity (PV) based on the argument that PV of the full fields should be preserved in the balanced motion. However, it is not clear that for the given balance constraints this prescribed PV‐based interface equation can lead to the optimal solutions for the BEs. To search for the interface equation which can produce the optimal solutions for the BEs under given balance constraints, the variational approach is proposed to derive instead of ‘prescribing’ the interface equation by minimizing an energy‐like norm under both geostrophic and Charney balance constraints. The derived interface equations are compared against the PV‐based interface equation for the two‐dimensional (2D) shallow‐water model and three‐dimensional (3D) baroclinic system. Analytical results show that the two kinds of interface equation are different in general but are close when the Rossby number and the departure of geopotential/temperature from its reference value are small. The accuracy associated with the derived interface equation is examined by comparing the balanced variables obtained by inverting the BEs with the derived and PV‐based interface equations numerically in a hemisphere shallow‐water system. The results show that under the same balance constraint the derived interface equation leads to better global accuracy of balanced variables.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".