Reflect planet lab

/reflect/ is a static browser energy balance explorer. The earlier terrain experiment remains at /reflect/terrain/; see REFLECT_TERRAIN.md.

Files

_pages/reflect.html: controls and scientific explanation.
assets/css/reflect-globe.css: viewport layout, with shared reflect.css styles.
assets/js/reflect/globe-model.mjs: spherical grid, orbit, radiation, approximate regional temperature pattern, reference seasons and edits.
fair-ebm.mjs: deterministic three-layer FaIR thermal equations in JavaScript.
jin-ocean.mjs: Jin ocean albedo port from SpeedyWeather gm/albedo.
co2-baseline.mjs: editable dated NOAA concentration snapshot.
globe-worker.mjs: persistent worker, bounded batches, pooled snapshots.
globe-render.mjs: native WebGL sphere and capped Canvas fallback.
globe-app.mjs: playback, inspection, Gaussian brushes and CSV history.
model.mjs: unchanged supplied C45 equations shared with the terrain lab.
assets/data/reflect/land-mask.bin: packed Natural Earth coastline raster.
scripts/build_reflect_land_mask.py: stdlib-only offline mask generator.

Grid and geography

Default ~100 km spacing gives 200 latitude rows and 50,932 cells. Reduced longitude counts towards the poles avoid tiny polar cells. Areas use exact spherical cell boundaries and double precision. Every global mean is area weighted. Earth radius is 6,371 km; 200 and 400 km options reduce computation further.

The land mask rasterises public-domain Natural Earth ne_110m_land, repository v5.1.2, at 720 × 360 half-degree cell centres. It occupies 32,400 bytes, with south-to-north rows and least-significant-bit-first packing. Each model cell samples the mask at its centre. Major coastlines and islands are geographic; narrow islands, inland waters and fractional coast cells are simplified. land-mask.json records provenance. To rebuild, download the pinned GeoJSON and run python3 scripts/build_reflect_land_mask.py /path/ne_110m_land.geojson.

Vegetation, snow, sea ice and physical C45 inputs are prescribed illustrative fields. Polar ocean cells have fixed full ice cover; land temperatures and vegetation are not observed maps. Seed varies prescribed input fields, not coastlines.

Orbit, daily radiation and ocean reflection

Kepler’s equation sets orbital speed and distance. Perihelion is near 3 January, with fixed solar longitude 282.94°, eccentricity 0.0167, tilt 23.44° and period 365.2422 days. Changing eccentricity retains that period. Insolation is 1361/r² W/m². Latitude-dependent daily means include polar day/night; a small spatial quadrature correction gives exact global incoming S(r)/4.

The calendar begins in the visitor’s current UTC season. Default playback is one model year in ten seconds. Display rotation makes one turn per model year, with ray-cast lighting kept in viewing coordinates. This is decorative: the physics averages 24-hour rotation and is independent of display orientation. Reduced-motion preferences disable automatic display rotation; selecting a painting/inspection tool also holds the globe still.

C45 coefficients, normalisation and noise quadrature are unchanged. Broadband BRDF coefficients are cached per land cell. Eight-point Gauss–Legendre daylight quadrature averages irradiance-weighted black-sky kernels by latitude; diffuse reflection uses white-sky kernels. Clamping the averaged land albedo rather than each individual solar angle is a daily averaging approximation.

Jin et al. (2011) ocean reflection preserves the coefficients and defaults of SpeedyWeather gm/albedo, commit b5eaa01a76d1ce6b083592a1e4c94f419385c77c: refractive index 1.34, foam reflectance 0.55, volume scattering 0.006 and sea-ice albedo 0.6. The module is an attributed EUPL-1.2 adaptation; its licence is bundled as assets/data/reflect/SpeedyWeather-EUPL-1.2.txt.

Direct reflection is Fresnel reflectance minus the Jin roughness regression. Diffuse reflection uses the branch’s clear/isotropic expression; no cloud option is enabled. The global 10 m wind dial defaults to 5 m/s. Unlike SpeedyWeather, which expects an external roughness field, this app diagnoses the RMS slope using Cox–Munk σ = sqrt(0.003 + 0.00512 U). Whitecaps occupy clamp(2.95e-6 U^3.52, 0, 1). Volume scattering and foam are included in both direct and diffuse components, then mixed with ice and bounded after the final mixture. Eight-point daylight quadrature averages direct ocean albedo before mixing. This is a broadband daily approximation, not a spectral ocean or wave model. User albedo overrides replace both direct and diffuse reflectivities.

Gaussian atmospheric scattering

The global dial multiplies a smooth heterogeneous field. Scattered fractions are clamped to 0–0.95. Scattered irradiance evolves under the spherical heat kernel for τ = (σ/R)² / 2, approaching a Gaussian of standard deviation σ. Widths are 80–200 km; the discrete approximation is coarse at large cell spacing.

A finite-volume neighbor graph wraps longitude and joins overlapping intervals on adjoining latitude rows. Every edge transfers equal and opposite power; explicit substeps satisfy a positivity bound. This conserves the area integral without storing a large Gaussian weight matrix. Scattering redistributes sunlight and changes direct/diffuse surface reflection. It includes no clouds, atmospheric absorption, backscatter to space or thermal diffusion.

FaIR global thermal response

The JavaScript implementation uses FaIR 2.2.4’s deterministic thermal equations, specialised to three layers. It does not import the full Python model, carbon cycle or stochastic forcing process. With time measured in model years:

F = 5.35 ln(CO₂ / 280) + areaMean(ASRexperiment − ASRreference)
C0 dT0/dt = F − λ T0 − k1(T0 − T1)
C1 dT1/dt = k1(T0 − T1) − ε k2(T1 − T2)
C2 dT2/dt = k2(T1 − T2)
N = F − λ T0 + (1 − ε) k2(T1 − T2)
λ = 5.35 ln(2) / ECS

Capacities [3.62, 9.47, 98.66] W yr/m²/K and exchanges [2.39, 0.63] W/m²/K come from the HadGEM2-ES example in FaIR’s n-layer documentation. This app changes the example feedback to ECS 2.5, 3 and 4°C per doubling, and sets ε=1 for conservative exchange. These illustrative configurations are not that model’s calibration or a posterior FaIR ensemble. The shaded range is a sensitivity scenario envelope, not a probabilistic transient interval from IPCC percentiles.

Daily forcing is sampled at the midpoint. A cached 4×4 augmented matrix exponential integrates the three-layer constant-forcing update exactly. The input is the change in absorbed sunlight plus CO₂ forcing: evolving imbalance is never fed back as an additional forcing. Surface edits and orbit changes retain the unchanged reference and temperatures, so their forcing is not recalibrated away.

Startup, seasons and regional temperatures

Automatic startup uses the dated NOAA global trend snapshot in co2-baseline.mjs: 428.00 ppm for 9 October 2026, checked 10 October 2026. The displayed date and “Recent” button refer to this bundled value; there is no live request. Update that file and the HTML fallback when refreshing the value.

All three thermal layers start at equilibrium with the selected CO₂. This is an idealised equilibrium-at-present-CO₂ experiment, not historical climate or observed present-day warming. The unchanged 280 ppm reference uses the original surfaces, wind, orbit and scattering. Its prescribed baseline is Tbase = 14 − 40(sin²(latitude) − 1/3) °C, averaging near 14°C.

Reference annual absorbed sunlight is estimated with 48 samples. The periodic seasonal state is solved analytically at startup, then integrated daily:

Cs dTseason/dt = ASRreference − annualMeanASRreference − λcentral Tseason

A separate local single-layer anomaly supplies an approximate regional pattern, using prescribed capacities 2.1e8 J/m²/K over ocean/ice and 2e7 over land. Its area mean is removed and replaced by FaIR’s central global surface anomaly. The regional map is not a spatial FaIR model or resolved circulation. Absolute temperature is the reference baseline plus seasonal temperature and this adjusted anomaly. Scenario global temperatures share the same reference.

Main imbalance reports the change from the reference; total imbalance includes reference seasonal storage. Heat change is the exact change in reference seasonal heat plus the central FaIR layers’ heat content, converted to ZJ. The trailing 366-day mean uses integrated net fluxes. Monthly scalar history is capped at 1,200 records; CSV exports use ECS-envelope labels and append the current state. No dynamic heat transport, ice feedback, interactive clouds or carbon cycle is included. These assumptions are also visible in the app’s “How it works” dialog.

Lightweight implementation

Numerical state occupies roughly 10 MiB at 100 km, excluding transient graph construction, browser overhead and render buffers. FaIR adds only nine thermal states and three small cached matrices. No per-cell timestep history is retained. Five Float32 fields form each ~1 MiB transferable snapshot, returned to a small pool. At most one advance is in flight, with batches capped at eight requested days. Worker snapshots and DOM updates target at most 12 per second; display rotation is capped near 30 fps and needs no texture upload on the surface view. Slower devices can run below the selected playback speed without skipping daily physics. Hidden pages pause; restart/page exit terminates the worker.

Native WebGL uses one shader and a 720×360 texture. Pixel count is capped at 1.2 million and DPR at 1.5. Canvas fallback ray-casts a reusable 512×384 image. Paused views have no idle animation loop. No runtime libraries, remote textures, API calls or uploads are needed; the coastline mask is a tiny same-origin asset.

Sources

Local preview

bundle exec jekyll build
bundle exec jekyll serve

Open http://127.0.0.1:4000/reflect/. Module workers require HTTP.

Gregory Munday