Σⱼ wⱼ pⱼ = c
The fine-cell predictions p are weighted by area fractions w to match the supplied parent mean c. This states the aggregate constraint; it does not identify the correct fine pattern.
Three output rules in P1Choose how to read
The full view retains the technical content, figures and sources. The plain-language explanation introduces the ideas without changing the findings.
Rainfall totals and the detail inside a map
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
Suppose the rainfall total for a large area is already known. Can a neural network divide that rain among smaller areas more accurately if it must preserve the original total?
How the comparison works
The study uses monthly CHIRPS rainfall over Jamaica. It compares otherwise matched networks with no exact total constraint, a penalty for mismatching the total, and a rule that preserves it exactly. A simpler method distributes rain using the usual seasonal pattern learned from earlier years.
What the result means
The exact rule improves the tested network, but the seasonal method has lower error. Preserving a total makes the pieces add up; it does not tell the model where every piece belongs. If the supplied total is wrong, a perfectly balanced detailed map still inherits that error.
Where the evidence stops
The model receives the observed total for the month it reconstructs, so this is not a forecast of that month. Most scores compare one CHIRPS field with another, and the station check is too small to establish broad real-world accuracy.
Use the full view for the complete technical discussion, figures, interactive elements and sources.
P1 · INTERACTIVE 3D COMPANION
Allocate rainfall across smaller cells
Watch one coarse rainfall total split into smaller cells. Change the spatial pattern and the supplied total, then compare the maps.
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 Can a model distribute a known rainfall total accurately among smaller cells? Watch the broad rainfall field and the finer cells beneath it.
- The method The constrained allocator adjusts fine-cell values so their weighted total matches the supplied coarse value. Compare the fine pattern with the constructed reference; a matching total can hide a different pattern.
- Check the result Change the coarse-total bias and switch between prediction, baseline and difference. Look for a balanced aggregate alongside a visible spatial error. The reference reveals what accounting alone cannot check.
Assumed multiplicative bias in this synthetic example; 0.20 means a 20% increase.
Size of added distortion in the synthetic fine pattern. The underlying allocation can already differ from the reference at zero.
How strongly the toy allocation is pulled towards the supplied total.
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
Can a model distribute a known rainfall total accurately among smaller cells? Watch the broad rainfall field and the finer cells beneath it.
Synthetic rainfall allocation; the displayed maps and errors are not the paper’s CHIRPS results.
Data, views and methods
Calculated values
What this browser model represents
This scene constructs a rainfall field and competing allocations in the browser. It does not load CHIRPS, run the paper’s neural networks or replay their prediction arrays.
The three sliders are teaching parameters. Their values are not fitted parameters from the paper.
The study evaluates conditional downscaling with the observed target-month coarse rainfall supplied. It does not establish prospective rainfall forecast skill.
Method in the paper
aggregate error ≠ spatial accuracy
The driver-error analysis separates a wrong parent total from the remaining within-parent pattern error.
Driver error and aggregation floor in P1Geography 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
Exact volume conservation in neural rainfall downscaling over Jamaica: a conditional CHIRPS benchmark with a driver-error bound
Terms explained
Select a term to read its meaning in this study.
Downscaling
Estimating a finer map from information supplied on a coarser grid. Drawing smaller cells does not by itself provide new measurements.
Conservation
Keeping an exact account of a specified quantity. If a transfer leaves one cell, the same transfer must enter the next; any external source or sink must also be recorded.
CHIRPS
Climate Hazards Group InfraRed Precipitation with Station data. A rainfall dataset that combines satellite information, station observations and a long-term rainfall pattern. A value represents a grid cell rather than a direct measurement at every place inside it.
Climatology
A summary of past conditions for a season or date. In these experiments it provides a simple comparison using the training record.
RMSE
Root-mean-square error. It measures the size of prediction errors and gives larger errors extra weight. Lower is better when the data and units are the same.