NatureV1

A probabilistic weather and hurricane-track model that treats satellite imagery as geolocated samples on a sphere, not a rectangle of pixels.

pip install "naturev1[all]"

Why not a ViT or CNN over the image

Three things break when you crop a GOES scene, divide by 255 and hand it to a vision backbone:

1. A GOES pixel is not a fixed size. ABI scans in fixed angular steps from geostationary orbit. Measured off a real scene, the limb pixel covers 64× the ground area of the nadir pixel. A convolution weights them equally and silently over-counts the stretched edge of the disk.
2. An array index is not a place. Nothing in image[400, 1200] says 24.7°N 81.3°W.
3. Normalizing to 0–1 destroys the physics. Channel 13 is a brightness temperature: 180 K is an overshooting top, 300 K is warm ocean. Per-image rescaling erases exactly what was measured.

NatureV1 solves the fixed-grid projection for every pixel's latitude/longitude (validated against the file's own metadata — it recovers 2.07 km at nadir where nominal C13 resolution is 2 km), computes each pixel's true ground footprint and uses it as a quadrature weight, and keeps brightness temperature in kelvin. Satellite and analysis data then fuse without either being resampled onto the other's grid.

Every output is a distribution

Track comes out as weighted scenarios, each a full trajectory with a tilting uncertainty ellipse. Collapsing them to one line scores 116 under the mixture likelihood where keeping both branches scores 8.2 — because the average of "recurves offshore" and "hits the coast" is a track through somewhere the storm was never going. Fields carry per-point variance, landfall a probability per lead time, intensity a Saffir-Simpson category with an interval.

It trains twice, because the labels are 4 orders of magnitude too few

An 88M-parameter model fitted to the Atlantic best-track archive is not a weather model. The archive is 55,230 points — 1,167 landfalls, 1,839 rapid intensifications, 2,587 with a radius of maximum wind. That is 0.0006 supervised values per parameter, and what you get back is an expensive lookup table for storms that already happened.

So the backbone never sees it.

Stage one is self-supervised on ERA5 reanalysis, where the label is free: given the atmosphere now, predict it at +6 through +120 hours. The WeatherBench 2 six-hourly store is 92,040 timesteps from 1959 to 2021 — 1.6×10¹⁰ supervised values, 180 per parameter, and nobody annotates anything.

Stage two fine-tunes the storm heads with the backbone frozen. 0.96M parameters of 89M — 1.1% — ever see a best track. Those 24,585 paired storm points can fit 0.96M parameters; they cannot fit 89M.

from naturev1 import ERA5Window, StormWindow, pair_tracks_with_reanalysis

pretrain = ERA5Window(era5, indices=splits["train"], lead_steps=offsets)   # free labels
starts, targets, _ = pair_tracks_with_reanalysis(tracks, store_times, offsets)
finetune = StormWindow(ERA5Window(era5, indices=starts), targets)          # real outcomes
model.freeze_backbone(True)

Longitude rotation is an exact augmentation here, not an approximation: on an equiangular grid, rotating the globe by a whole number of cells is a roll of the array, and this architecture is exactly equivariant to it. 240 valid atmospheres, free, nothing resampled.

Four things the obvious implementation gets wrong

Each of these ran clean on shapes, ranges and a falling loss while the data was wrong, so the regression tests assert on physics and geometry instead:

1. Dimension order. WeatherBench 2 stores (time, longitude, latitude); the coordinate mesh is latitude-major. Read untransposed you get the right point count, sane values, and every sample bound to the wrong place on Earth. Correlation of temperature against its assigned latitude: ~0 → −0.873.
2. Cell weights. cos(latitude) gives the pole row 6.1e-17 — zero in float32 — deleting the poles from every area-weighted sum. True spherical cell area makes a pole cell 306× lighter, not 10¹⁶×.
3. Precipitation. 15% of the grid is exactly zero and the max sits 30σ out, so a z-score trains the model to predict zero everywhere. log1p(x/0.1mm) brings it to 4.5σ and inverts exactly.
4. Missing is not average. Sea-surface temperature is absent over 27.9% of the grid; filling it with the ocean mean asserts warm water over Kansas. Gappy variables get an observation channel.

Heads start at climatology, not at zero

A linear head emits about zero, so asked for central pressure in hPa it opens 1000 off — a squared error of a million. Measured on a real fine-tuning step, the intensity term was 119,191 of a 60,565 total, with a gradient norm of 207,018. Anchoring each head at Atlantic climatology and starting each log-variance at the observed spread (rather than claiming ±1 kt about peak wind) brings the same step to total 58, intensity 4, eyewall 5, gradient norm 13 — with no architecture change. The RI classifier opens at the measured 4.11% base rate, not at even odds.

Built for a runtime that dies

Checkpoints go down on a wall-clock interval, written to a temp file and renamed into place, so a killed cell leaves the previous checkpoint intact. Resume restores optimizer moments, LR schedule, scaler and RNG state — not just weights.

Not trained

No weights here have seen real data. The architecture, losses, ingest and training loop are complete and exercised end to end on real GOES-19 imagery, but nothing here should inform a decision about a real storm. The National Hurricane Center is the authoritative source for tropical cyclone forecasts.

Made by Nathan.