Brier score = mean (p − y)²
Here p is the predicted event probability and y is zero or one. The paper compares calibrated probabilities on held-out times and cells.
Models, calibration and scoring in P8Choose how to read
The full view retains the technical content, figures and sources. The plain-language explanation introduces the ideas without changing the findings.
Testing whether physical features travel between islands
How to use this companion
Use the controls to inspect the relationship described by the paper. The interactive display is explanatory; it does not rerun the archived training experiment or supply independent evidence of forecast skill. Read the linked full manuscript for the executed comparison.
What the study asks
Do physically meaningful descriptions of atmospheric moisture help a rainfall model when it is tested at a Caribbean location excluded from training?
How the comparison works
Models predict the chance of next-day heavy rain at six grid cells. One uses temperature and dew point directly; another transforms them into specific humidity and saturation deficit. Training, probability calibration and testing use different periods.
What the result means
The moisture transformation changes the average score only slightly, with an uncertainty interval that includes no improvement. A simple model using season and the previous day’s rainfall performs better than either boosted alternative. Physical meaning alone does not guarantee additional predictive information.
Where the evidence stops
Each island is represented by one selected grid cell, and targets come from a gridded product. The result is a bounded negative finding about this comparison, not proof that atmospheric physics is unhelpful in every rainfall model.
Use the full view for the complete technical discussion, figures, interactive elements and sources.
P8 · INTERACTIVE 3D COMPANION
Test rainfall probabilities at withheld cells
Watch a synthetic probability field built from moisture and rainfall history. Change the weights and calibration to see how the displayed risk changes.
The question
Real geographic contextCalculated synthetic fields
ReferenceEstimate
Loading the 3D scene…
The WebGL 3D view is unavailable
A 2D fallback may appear in its place. You can also follow the study with these steps and the full paper.
- The question Does a physical change of variables help a probability model when it moves to a cell it did not learn from? The markers represent a small constructed cross-cell comparison, not island-wide observations.
- The method Logistic models learn from invented rainfall and moisture records, with each target cell excluded from training and calibration. Change the moisture or rainfall-memory weights, then shift calibration and watch the predicted probabilities respond.
- Check the result Compare the predicted probabilities with generated event outcomes and the rainfall-history baseline. Brier scores measure probability errors on these invented outcomes. A meaningful physical variable does not by itself guarantee a better score.
Multiplier on fitted moisture-feature coefficients in the synthetic logistic model; not a coefficient fitted in the paper.
Multiplier on the synthetic model’s fitted previous-rainfall coefficient.
Assumed offset on the log-odds scale; not a measured calibration estimate.
Drag to rotate. Focus the scene to zoom with the wheel; arrow keys rotate and + / − zoom. Click a cell to inspect its transfers.
The question
Does a physical change of variables help a probability model when it moves to a cell it did not learn from? The markers represent a small constructed cross-cell comparison, not island-wide observations.
Synthetic statistical-method illustration; probabilities are not the six-cell pilot’s measured predictions or validated climate forecasts.
Data, views and methods
Calculated values
What this browser model represents
The browser calculates specific humidity and saturation deficit from invented temperature and dew point. It fits logistic models on synthetic data, excluding each target cell from both training and intercept calibration. These are not the paper’s boosted classifiers, data or Brier scores.
The predicted surface shows probabilities. The reference layer interpolates generated zero-or-one event outcomes; it is not a known true-probability surface. Height is neither terrain nor rainfall depth, and the difference layer is probability minus outcome.
The actual pilot compares equal-budget raw and thermodynamic features, with seasonal and rainfall-history controls. Six selected grid cells do not represent island-wide forecasting skill.
Method in the paper
exclude the target cell from training and calibration
The transfer design asks whether a model works at a cell absent from both development stages.
Target information and splits in P8Geography and figure design
Terrain is a sampled Mapzen/Tilezen elevation mesh, with a 62.5 m display spacing over an 8 km square. Source tiles have approximately 36 m pixel spacing at this latitude; display spacing does not establish survey accuracy. Colours show the calculated field, while terrain heights provide location context. WebGL displays a 129 × 129 terrain grid; the CPU compatibility view resamples the same elevations to 33 × 33 for responsiveness. Neither display resolution is an accuracy claim. The location selector does not change the numerical model. P6 soil columns and P7 touching heat cells use diagram dimensions. Changing the cube count changes the synthetic lattice and replays the elapsed scenario; it does not refine an atmospheric forecast. P8 markers use requested pilot coordinates, with illustrative model values. P1 column heights repeat rainfall, or absolute error in Difference view, at diagram scale; they are not millimetres on the terrain. P8 column heights repeat the probability or absolute error; their signs come from the colour scale and inspector. P6 shows zero in the reference column when displaying error. Coastline extrusion, sensor shapes, heat-volume sizes and particle speeds are explanatory symbols; they are not surveyed buildings, physical parcel sizes or measured motion.
Sources: Mapzen/Tilezen Terrain Tiles; USGS and NOAA terrain attribution; Natural Earth, public domain. Regional outlines are at 1:10 million, displayed with an equirectangular projection at 17°N. Terrain uses a local equirectangular display. Elevation exaggeration is shown above the scene.
Sequential field colours follow viridis; signed errors use a centred blue–orange scale. The colour limits stay fixed as the example runs; values outside them are counted in the legend. The plan view removes perspective. Figure design follows Crameri et al. (2020); pause and reduced motion follow WCAG motion guidance. The browser export retains a source caption. No atmospheric model skill follows from this animation.
Asset versions and checksums · Coordinate definitions · Numerical model source
Source sections
A cross-island test of thermodynamic features for next-day heavy-rain probabilities: a bounded negative result
Terms explained
Select a term to read its meaning in this study.
Specific humidity
The mass of water vapour divided by the total mass of moist air. It describes how much water vapour is present.
Saturation deficit
How much water vapour would need to be added to reach saturation under the stated temperature and pressure conditions.
Brier score
The average squared difference between an event probability and its outcome, recorded as one for an event and zero otherwise. Lower is better on the same cases.
Transfer
Using a model at a new location or on a different task. Success on its original training locations does not establish success after that move.
Bootstrap interval
A range calculated by repeatedly resampling the observed record. Resampling whole years or blocks preserves some dependence, but does not include every source of uncertainty.