Numerical discretization causing error variance loss and the need for inflation
Bibliographic record
Abstract
Abstract The effects of model discretization errors on the propagation of error covariance have a more complex nature than the effect on the state variable. The analysis is carried out for the advection transport equation, where the continuous (in space and time) propagation of the related error covariance function can be written, solved and compared with the discrete model applied to the covariance matrix. The numerical analysis of the problem is carried out with a 1D‐problem, but is also illustrated with a 3D chemical transport model (CTM) used for chemical data assimilation. It is shown that variance loss (compared to the continuous propagation solution) depends on the covariance function itself as well as the numerical discretization scheme. The variance loss is particularly sensitive to the correlation length. In a simple first‐order discretization, an analytical expression is obtained and is used to derive an analytical expression for inflation. Experiments show, for example, that following an analysis over a dense network of observations (with spatially uncorrelated errors) a significant variance loss occurs in the propagation step. With the (variance) inflation scheme, we are able to restore the variance lost at each grid point, and at each timestep, during the entire integration. The variance inflation scheme applied to an EnKF can be formulated to change the variance spread of the ensemble or to act directly on the state.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".