storage change = net transport + integrated source
The ledger records how much enters, leaves, grows or decays. It checks the numerical balance, separately from whether the movement and source are physically correct.
Three separate residuals in P5Choose how to read
The full view retains the technical content, figures and sources. The plain-language explanation introduces the ideas without changing the findings.
Separating moving rain from growing rain
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
Rain can move across a map, become stronger or fade. Can a model keep an accurate transfer account while allowing for processes its simplified physical equation leaves out?
How the comparison works
The paper first defines the update and its constraints, then tests small constructed examples with known rules. It compares methods that handle a missing growth term in different ways and checks whether a proposed tolerance helps when the methods receive comparable information.
What the result means
Learning a growth term helps when growth exists in the constructed system. A learned source can also compensate for a wrong transport speed, so a correct-looking map does not prove the hidden flow is correct. The adaptive tolerance does not beat a simpler method given the same information.
Where the evidence stops
No meteorological experiment was run. The constructed one-dimensional test shares important assumptions with its simulator, and the full atmospheric tolerance rule remains to be evaluated.
Use the full view for the complete technical discussion, figures, interactive elements and sources.
P5 · INTERACTIVE 3D COMPANION
Compare rainfall transport and growth
Watch a rain tracer move, grow and fade. Compare a balanced transfer record with the location and intensity of the rain itself.
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 an exactly balanced rain update still produce the wrong rain pattern? The rain tracer moves across a periodic constructed domain.
- The method Shared-face transport moves the tracer. A separate source lets existing rain grow or decay; its estimate is fitted to noisy development examples under a tolerance. Change growth strength or source-prior tolerance while watching the moving pattern.
- Check the result Introduce wind error and compare the forecast pattern with the reference. The ledger can remain balanced while the tracer arrives in the wrong place. Check the difference field as well as the total.
Source strength in the constructed tracer system.
Allowed departure from the toy model’s zero-source prior; not a tuned atmospheric rule.
Assumed relative motion error in the toy forecast.
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 an exactly balanced rain update still produce the wrong rain pattern? The rain tracer moves across a periodic constructed domain.
Synthetic transport-and-growth illustration; it is not the paper’s full benchmark or an atmospheric experiment.
Data, views and methods
Calculated values
What this browser model represents
This periodic two-dimensional tracer scene is a teaching extension of the paper’s one-dimensional mechanism. It fits a source estimate to fixed noisy development replicas, but does not reproduce every benchmark arm, fit or control.
P5 reports mathematical propositions and a completed synthetic experiment. No atmospheric experiment has been run.
A visually useful tolerance setting here is not evidence that the paper’s adaptive rule beats its matched-information comparator.
Method in the paper
penalise departure beyond a fixed tolerance
The proposed nominal-relation penalty has a tolerance set on development data. The full atmospheric rule remains untested.
Evidence-adaptive tolerance in P5Geography 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
CLEAR-PINN: closure-limited, evidence-adaptive residual learning for precipitation nowcasting
Terms explained
Select a term to read its meaning in this study.
PINN
A physics-informed neural network: a learned function trained partly by penalising disagreement with specified equations. A small penalty does not prove that every prediction is physically correct.
Closure
An approximate rule for processes that a model does not represent explicitly. The rule can be useful and still miss important physical effects.
Residual
The amount by which a value fails to satisfy a stated equation or constraint. A small residual checks that relation, not every source of scientific error.
Synthetic experiment
A test using a deliberately constructed system whose rules are known. It can isolate a mechanism, but its results do not establish performance in the real atmosphere.
Flux
The rate at which a quantity crosses a surface. A transfer over a time interval is the accumulated amount that crosses it.