The full view retains the technical content, figures and sources. The plain-language explanation introduces the ideas without changing the findings.
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.
Could several local models reconstruct the atmosphere together while keeping one agreed record of every transfer across their shared boundaries?
D-LEGOS divides space and time into local blocks. A transfer leaving one block enters its neighbour with the opposite sign. The paper derives properties of that accounting and specifies experiments that would test a restricted atmospheric reconstruction.
Analytical examples and small numerical checks establish properties of the stated graphs and scalar systems. They also show that balanced accounting does not identify every hidden flow or guarantee accurate uncertainty. The separate component studies help define the tests, but they do not complete the atmospheric experiment.
The atmospheric reconstruction remains proposed. It must recover observations deliberately withheld from fitting, withstand missing data and biased background information, and be compared with methods receiving the same inputs and computing budget.
Use the full view for the complete technical discussion, figures, interactive elements and sources.
P7 · INTERACTIVE 3D COMPANION
Follow heat across touching cells. Change the number of cubes, exchange strength or circulation, then inspect what conservation can and cannot tell you.
Loading the 3D scene…
A 2D fallback may appear in its place. You can also follow the study with these steps and the full paper.
Change the number of touching cells: 2–5 along each axis. The model replays the same elapsed time on the new lattice.
Assumed coupling in the constructed heat graph.
Assumed transfer around a closed cycle of the toy graph. It changes the face transfers without changing storage tendencies.
Fraction of synthetic sensor markers made visible; the hidden-state interpolation diagnostic changes with this selection.
Drag to rotate. Focus the scene to zoom with the wheel; arrow keys rotate and + / − zoom. Click a cell to inspect its transfers.
What does exact conservation tell you about the physical state inside connected cells? Watch the local stored quantities and the shared transfers between them.
Synthetic shared-flux system; the atmospheric reconstruction described in P7 remains proposed.
This scene evolves variable-count unequal-capacity heat reservoirs on a cyclic graph. It is not a completed three-dimensional atmospheric solver, and the graph differs from the manuscript’s manufactured chain.
The circulation control adds a divergence-free cycle transfer. The observation control changes visible sensors and a hidden-state interpolation diagnostic; it does not refit the predicted state. Neither control measures atmospheric circulation or formal reconstruction uncertainty.
P7’s executed manufactured chain and the separate browser demonstration are evidence of their specified numerical behaviour, not proof of accurate Caribbean reconstruction.
The browser uses a cubic lattice with 2–5 cells per edge. Every transfer joins face-sharing neighbours. Equal cube widths represent the topology; unequal heat capacities are material properties. The closed-cycle marker shows an added divergence-free transfer around one four-cell face loop. It is not an air parcel or a measured travel time.
dm/dt = −BF + s; 1ᵀB = 0
This equation defines B as positive at the sending cell and negative at the receiving cell, the opposite sign convention to P7. A shared transfer F leaves one cell and enters its neighbour. Internal exchanges cancel; external sources s remain.
Incidence form in P7Bc = 0 can hold for non-zero circulation c
A graph cycle can carry a transfer that leaves cell storage changes unchanged. Cancellation does not identify every flux.
Limits of conservation in P7Terrain 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
D-LEGOS: space-time control volumes, shared-face flux ledgers and the limits of what conservation proves
Select a term to read its meaning in this study.
A defined piece of space used to keep track of what enters, leaves, is stored or is produced inside it.
A piece of space together with a time interval. Its spatial faces carry transfers, while its beginning and ending describe the stored state.
The rate at which a quantity crosses a surface. A transfer over a time interval is the accumulated amount that crosses it.
Whether the available observations can distinguish different possible explanations. Several hidden flows can produce the same measured change in storage.
A measurement deliberately excluded from fitting or reconstruction so that it can provide an independent check.