Intercomparison of the primal and dual formulations of variational data assimilation
Bibliographic record
Abstract
Abstract Two approaches can be used to solve the variational data assimilation problem. The primal form corresponds to the 3D/4D‐Var used now in many operational NWP centres. An alternative approach, called dual or 3D/4D‐PSAS, consists in solving the problem in the dual of observation space. Both forms use the same basic operators so that once one method is developed, it should be possible to obtain the other easily provided these operators have a modular form. It has been shown that, with proper conditioning of the minimization problem, the two algorithms should have similar convergence rates and computational performances. In the presence of nonlinearities, the incremental form of 3D/4D‐Var extends the equivalence to the so‐called 3D/4D‐PSAS. The first objective of this paper is to present results obtained with the variational data assimilation of the Meteorological Service of Canada to show the equivalence between the 3D‐Var and the PSAS systems. This exercise has forced us to have a close look at the modularity of the operational 3D/4D‐Var which then makes it possible to obtain the 3D‐PSAS scheme. This paper then focuses on these two quadratic problems that show similar convergence rates. However, the minimization of 3D‐PSAS is examined more thoroughly as some parameters are shown to be determining elements in the minimization process. Lastly, preconditioning properties are studied and the Hessians of the two problems are shown to be directly related to one another through their singular vectors, which makes it possible to cycle the Hessian of the PSAS form. Copyright © 2008 Royal Meteorological Society
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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 | 0.003 | 0.005 |
| 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 | 0.001 |
| Open science | 0.001 | 0.002 |
| 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".