A New Spatial-Scale Decomposition of the Brier Score: Application to the Verification of Lightning Probability Forecasts
Bibliographic record
Abstract
Abstract A new scale decomposition of the Brier score for the verification of probabilistic forecasts defined on a spatial domain is introduced. The technique is illustrated on the Canadian Meteorological Centre (CMC) lightning probability forecasts. Probability forecasts of lightning occurrence in 3-h time windows and 24-km spatial resolution are verified against lightning observations from the North American Lightning Detection Network (NALDN) on a domain encompassing Canada and the northern United States. Verification is performed for lightning occurrences exceeding two different thresholds, to assess the forecast performance both for modest and intense lightning activity. Observation and forecast fields are decomposed into the sum of components on different spatial scales by performing a discrete 2D Haar wavelet decomposition. Wavelets, rather than Fourier transforms, were chosen because they are locally defined, and therefore more suitable for representing discontinuous spatial fields characterized by the presence of a few sparse nonzero values, such as lightning. Verification at different spatial scales is performed by evaluating Brier score and Brier skill score for each spatial-scale component. Reliability and resolution are also evaluated on different scales. Moreover, the bias on different scales is assessed, along with the ability of the forecasts to reproduce the observed-scale structure.
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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 | 0.000 |
| 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 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".