The Regional Fractional Energy Balance Equation: Projections to 2100
Bibliographic record
Abstract
We present the fractional energy balance equation (FEBE) which is a generalization of the standard EBE. The FEBE can be derived either from Budyko–Sellers models or phenomenologically by applying the scaling symmetry to energy storage processes. It is easily implemented by changing the integer order of the storage (derivative) term in the EBE to a fractional value near 1/2. The model used a Bayesian framework based on historical temperatures and natural and anthropogenic forcing series for parameter estimation. Significantly, the error model was not ad hoc, rather predicted by the model itself: the internal variability response to white noise internal forcing, a fraction Relaxation noise (fRn). Due to computational constraints, we employ a block bootstrapping method to calculate the likelihoods of our parameters in the Bayesian scheme. Notably we estimate the regional relaxation time directly from empirical data, generally it is calculated for various discrete surface types using heat capacities or globally from fitting a two-box model to GCM outputs, which to the authors knowledge has not been estimated prior to this study. The FEBE historical reconstructions (1880–2020) closely follow observations (notably during the “slowdown”, 1998–2015). We also reproduce the internal variability with the FEBE and statistically validate this against centennial scale temperature observations. We show the FEBE to plausibly reproduce the annual cycle at monthly resolution, in particular to explain the lag between the temperature maximum and the maximum in the radiative forcing. Using the calibrated FEBE we made temperature projections to 2100 using both the Representative Carbon Pathways (RCP) and Shared Socioeconomic Pathways (SSP) scenarios, shown alongside the Coupled Model Intercomparison Project Phase (CMIP) 5 and 6 multi-model ensemble (MME) at global and regional scales.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".