A practical scheme of the sigma‐point Kalman filter for high‐dimensional systems
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Bibliographic record
Abstract
Abstract While applying a sigma‐point Kalman filter (SPKF) to a high‐dimensional system such as the oceanic general circulation model (OGCM), a major challenge is to reduce its heavy burden of storage memory and costly computation. In this study, we propose a new scheme for SPKF to address these issues. First, a reduced rank SPKF was introduced on the high‐dimensional model state space using the truncated single value decomposition (TSVD) method (T‐SPKF). Second, the relationship of SVDs between the model state space and a low‐dimensional ensemble space is used to construct sigma points on the ensemble space (ET‐SPKF). As such, this new scheme greatly reduces the demand of memory storage and computational cost and makes the SPKF method applicable to high‐dimensional systems. Two numerical models are used to test and validate the ET‐SPKF algorithm. The first model is the 40‐variable Lorenz model, which has been a test bed of new assimilation algorithms. The second model is a realistic OGCM for the assimilation of actual observations, including Argo and in situ observations over the Pacific Ocean. The experiments show that ET‐SPKF is computationally feasible for high‐dimensional systems and capable of precise analyses. In particular, for realistic oceanic assimilations, the ET‐SPKF algorithm can significantly improve oceanic analysis and improve ENSO prediction. A comparison between the ET‐SPKF algorithm and EnKF (ensemble Kalman filter) is also tribally conducted using the OGCM and actual observations.
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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 | 0.001 |
| 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 it