The Role of the Nonlinearity of the Stefan–Boltzmann Law on the Structure of Radiatively Forced Temperature Change
Bibliographic record
Abstract
Abstract The Stefan–Boltzmann law governs the temperature dependence of the blackbody emission of radiation: . A consequence of this nonlinearity is that a cold object needs a greater increase in temperature than a hot object in order to reach the same increase in radiation emitted. Therefore, this nonlinearity potentially has an impact on the structure of radiatively forced atmospheric temperature change in both the horizontal and vertical directions. For example, it has previously been argued to be a cause of polar amplification (PA) of surface air warming. Here, the role of this nonlinearity is investigated by 1) assessing the magnitude of its effect on PA compared to spatial variations in CO 2 ’s radiative forcing for Earth’s atmosphere and 2) linearizing in a gray radiation atmospheric general circulation model (GCM) with an interactive hydrological cycle. Estimates for Earth’s atmosphere show that the combination of the Planck feedback and forcing from CO 2 would produce a tropically amplified warming if they were the only means of changing the Earth’s energy balance. Contrary to expectations, climate change simulations with linearized radiation do not have reduced polar amplification of surface air warming relative to the standard GCM configuration. However, simulations with linearized radiation consistently show less warming in the upper troposphere and more warming in the lower troposphere across latitudes. The lapse rate feedbacks from pure radiative and radiative–convective configurations of the model are used to show that the “cold-altitudes-warm-more” effect of the nonlinearity carries across this model hierarchy.
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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 | 0.000 | 0.003 |
| 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 | 0.001 |
| 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".