On post-glacial sea level - II. Numerical formulation and comparative results on spherically symmetric models
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Bibliographic record
Abstract
Theoretical approaches to computing gravitationally self-consistent sea-level changes in consequence of ice growth and ablation are comprised of two parts. The first is a mapping between variations in global sea level and changes in ocean height (required to define the surface load), and the second is a method for computing global sea-level change arising from an arbitrary surface loading. In Mitrovica & Milne (2003) (Paper I) we described a new, generalized mapping between sea-level change and ocean height that takes exact account of the evolution of shorelines associated with both transgression and regression cycles and time-dependent marine-based ice margins. The theory is valid for any earth model. In this paper we extend our previous work in three ways. First, we derive an efficient, iterative numerical algorithm for solving the generalized sea-level equation. Secondly, we consider a special case of the new sea-level theory involving spherically symmetric earth models. Specifically, we combine our iterative numerical formulation with viscoelastic Love number theory to derive an extended pseudo-spectral algorithm for solving the new sea-level equation. This algorithm represents an extension of earlier methods developed for the fixed-shoreline case to precisely incorporate shoreline migration processes. Finally, using this special case, we quantitatively assess errors incurred in previous efforts to extend the traditional (fixed shoreline) sea-level equation of Farrell & Clark (1976) to treat time-dependent shorelines. We find that the approximations adopted by Johnston (1993) and Milne (1998) to treat transgression and regression at shorelines introduce negligible (∼1 per cent) error into predictions of post-glacial relative sea-level histories. In contrast, the errors associated with the Peltier (1994) sea-level equation are an order of magnitude larger, and comparable to the error incurred using the traditional sea-level theory. Furthermore, our numerical tests verify the high accuracy of the Milne (1998) approximation for treating the influence of grounded, marine-based ice.
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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 | 0.000 | 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 it