Addressing cross-dependence in gravity coefficients for improved terrestrial water storage estimation
Bibliographic record
Abstract
The conventional univariate Kalman filtering (UKF) applied to gravity field coefficients introduces a dependence bias that is driven by the inter-dependence between cosine and sine components of the gravity field. Such bias, when accumulated over time, can lead to significant distortions in regional total water storage anomalies (TWSA). This study proposes a methodological advancement via a multivariate Kalman filter (MKF) framework to mitigate this bias, refining the dependency structure. We analyse the bias introduced by UKF, demonstrate its impact on TWS estimates, and present a correction using the MKF approach. When tested in application to high latitudinal basins, the proposed MKF reduces the annually aggregated bias introduced by UKF, yet the improvements appear to be minor at basin-scale. Bias reductions become more pronounced in the basins’ high-latitudinal regions for grid-TWSA at ≈1° grid resolution. Findings suggest that in polar regions which are challenged by complex mass change patterns, MKF still yields a substantial improvement in dependence bias over UKF, implying its potential in reducing long-term bias equally well or more effectively in the tropics. Restoring the temporal dependence in perturbed ensemble predictions via temporal shuffling can further exploit the MKF’s predictive advantage. Overall, the study highlights the necessity of incorporating coefficients’ cross-dependencies in Kalman filtering frameworks for enhancing GRACE-based gravity field solutions for hydrological and geodetic applications. • Geoid coefficients of same degree and order inherit cross-dependence between them. • This cross-dependence can be captured in a multivariate Kalman filter framework. • The multivariate framework-based geoid coefficients exhibit reduced uncertainties. • The framework reduces long-term dependence bias in terrestrial water storage.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 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".