Data assimilation for the two-dimensional shallow water equations: Optimal initial conditions for tsunami modelling
Bibliographic record
Abstract
Accurate modelling of tsunami waves requires complete boundary and initial data, coupled with the appropriate mathematical model. However, necessary data is often missing or inaccurate, and may not have sufficient resolution to capture the dynamics of such nonlinear waves accurately. We demonstrate that variational data assimilation for the continuous shallow water equations (SWE) is a feasible approach for recovering initial conditions. We showed that the necessary conditions for reconstructing one-dimensional initial conditions in Kevlahan et al. (2019) can be extended to the maximum Euclidean distance between pairwise observations to two-dimensions. We use Sadourny finite-difference finite volume simulations to verify convergence to the true initial conditions can be achieved for observations arranged in multiple configurations, for both isotropic and anisotropic initial conditions, and with realistic bathymetry data in two dimensions. We compare observations arranged in straight lines, in a grid, and along concentric circles, and assess the optimal number and configuration of observation points such that convergence to the true initial conditions is achieved. These idealised results with simplified two-dimensional geometry are a first step towards more physically realistic settings. Recent advances in altimetry observation data now permit much denser measurements of sea surface height than is possible with a fixed buoy network. This provides the opportunity to use the method developed here for more accurate tsunami forecasts in realistic settings.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| 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".