Analytical Infrared Delta-Four-Stream Adding Method from Invariance Principle
Bibliographic record
Abstract
Abstract The single-layer solutions using a four-stream discrete ordinates method (DOM) in infrared radiative transfer (IRT) have been obtained. Two types of thermal source assumptions—Planck function exponential and linear dependence on optical depth—are considered. To calculate the IRT in multiple layers with a vertically inhomogeneous atmosphere, an analytical adding algorithm has been developed by applying the infrared invariance principle. The derived adding algorithm of the delta-four-stream DOM (δ-4DDA) can be simplified to work for the delta-two-stream DOM (δ-2DDA). The accuracy for monochromatic emissivity is investigated for both δ-2DDA and δ-4DDA. The relative error for the downward emissivity can be as high as 15% for δ-2DDA, while the error is bounded by 2% for δ-4DDA. By incorporating δ-4DDA into a radiation model with gaseous transmission, δ-4DDA is much more accurate than δ-2DDA. Also, δ-4DDA is much more efficient, since it is an analytical method. The computing time of δ-4DDA is about one-third of the corresponding inverse matrix method.
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How this classification was reachedexpand
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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 teacher head, 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".