Variational Assimilation of Surface Wave Data for Bathymetry Reconstruction. Part II: Second Order Adjoint Sensitivity Analysis
Bibliographic record
Abstract
Data assimilation methods have been proposed as a technique for reconstructing ocean bathymetry from observations of surface waves. To better understand this technique, we use second order adjoint (SOA) variational analysis to derive the sensitivity of the surface wave error to perturbations in the observations (such as their number, spacing and position relative to bathymetry profiles), given the reconstructed bathymetry. We apply SOA to the data assimilation scheme for the one-dimensional shallow water equations for bathymetry detection introduced in Khan and Kevlahan (2021). We derive the Hessian of a cost function J representing the error between forecast surface wave and the observations. We then use SOA to derive the sensitivity of the surface wave error given the reconstructed bathymetry to perturbations in the observations for both a compactly supported Gaussian bathymetry, and a sandbar profile bathymetry. We investigate the correlation between (i) low sensitivity of the surface wave given the reconstructed bathymetry, to the observations, and (ii) the error in the bathymetry reconstruction, as well as the sensitivity of the data assimilation scheme to perturbations of its parameters. Additionally, we determine whether the conclusions in Khan and Kevlahan (2021) for bathymetry reconstruction can be verified by the present sensitivity analysis. We observe that relatively large errors in the bathymetry reconstruction and large relative amplitudes of the Gaussian and sandbar bathymetry profiles are associated with higher sensitivity of the surface wave reconstruction error to the observations. However, sensitivity decreases when the observation network has a greater coverage of the bathymetry. Significantly, the sensitivity of the surface wave to the observations is orders of magnitude lower than the bathymetry reconstruction error itself. These results suggest optimal configurations of surface wave observations, help minimise costs for making observations, and could enhance the accuracy of tsunami models.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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".