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.

0.8: the whole atmosphere, and an audit

The model now predicts and evolves every prognostic channel — 13 pressure levels included — as a residual from persistence, with solar forcing computed from orbital geometry, mass conserved, a pressure- and area-weighted loss, and fair-CRPS ensembles. Storm heads pool around the storm and are given its current intensity and motion. Stage two runs the frozen backbone once per storm and trains the heads on the cached features, which turned days per epoch into seconds.

A full read of the code found and fixed, among others: a GPU memory leak on every training step with DataLoader workers; hurricane lead targets at the wrong valid time on 10.9% of samples (92% of them on landfalling stretches); a rollout loop that never rolled out; a publish gate that could never open; and untrained heads printed as forecasts. Each has a regression test in tests/test_fixes_080.py.

0.12: the satellite path rebuilt, every basin, 8x B300

Built from what the trained model and its red team showed: intensity biased low, rapid intensification missed, southern-hemisphere tracks worse than physics, poleward turns missed, a storm centre required.

• naturev1.ibtracs — every basin since 1980 (IBTrACS), wind normalised to one-minute, ~230,000 labelled fixes.
• naturev1.satstage — GridSat-B1 1980-2021 (4-6 TB) staged into quarter-degree global frames (mean, coldest pixel, spread, coverage, satellite, view angle) and 320 px storm loops; hand-decoded, quality-controlled, resumable.
• naturev1.satnet — SatNet-Storm (intensity, centre fix from a 150 km-wrong guess, radii, intensity change, ordinal RI, motion; hemisphere-mirrored) and the satellite retrieval (stale state + satellite loop + cloud motion → full state, starting exactly at the stale state).
• naturev1.stormtrain — stage B: heads + the backbone's last blocks on every basin, retrieval in the loop, RI 2.0, poleward frame; banks with two rollout track members; consensus, calibration, intensity bias correction; scored on test seasons against the model it started from.
• naturev1.tracker — vortex tracking through rollouts, storm detection.
• naturev1.engine — DDP on N GPUs, bf16, a clock-driven schedule, every checkpoint pushed to the Hub in order.
• b300_naturev1.py — the runbook: preflight, staging, stage A (3 h, both satellite networks side by side), stage B, and a publish step that only replaces the release if the new model beat it.

Then more ways to be right, each weighted by the held-out seasons (weights may be zero):

• naturev1.thermo — potential intensity (Bister-Emanuel), ventilation, entropy deficit, genesis potential, cyclone phase space and SHIPS-like predictors from the model's own atmosphere, fed to every storm head.
• naturev1.windfield — asymmetric Holland wind field, NHC-style 34/50/64 kt probabilities and arrival times (points or a 0.25 degree map), inland decay, gusts, R-CLIPER rain.
• naturev1.statistical — SHIPS-style regression, LGEM-style logistic growth, climatology-persistence, an intensity consensus with per-lead weights and biases, track bias correction, a predicted-error cone, an RI consensus.
• naturev1.tracker — multi-field centre fix, intensity and phase along the rollout, rollout-ensemble and analog track members; the satellite centre fix iterates to convergence.
• Training and forecast time: intensity loss rebalanced by class, an average of the weights (EMA), and a test-time rotation ensemble used only if it beats a single pass on held-out seasons.

Tested end to end on CPU, including two-process data parallelism; not yet run on B300 hardware.

0.13: hurricane physics that beats extrapolation -- measured, not promised

Technical report: Hurricane tracks without a neural network (CorX Labs report 05, also as a PDF).

naturev1.cyclone -- 39 modules, each one idea, no neural network -- forecasts a storm's track and intensity from one analysis and the best track so far, and detects storms before they form. Every constant was fitted on 1980-2014 best tracks or the 2016/2017/2019 seasons. On the held-out seasons (2018, 2020, 2021, 2022; 4,447 forecasts, 407 storms, every basin; storm-bootstrap 90% intervals):

Intensity (SHIFOR + SHIPS-style + logistic growth, blended per lead): mean absolute error 4/6/11/14/17/20/21/22 kt at 6-120 h against persistence's 4/8/14/19/23/28/31/32 -- +14% to +31%, every interval clear of zero.

It beats extrapolation and CLIPER at every lead, and loses to every modern global model (GraphCast, Pangu, HRES, Aurora, FGN/WeatherNext 2, FuXi, GenCast) past 6 hours; combined with one of them, lead by lead, it is never worse than that model and better at 6-12 hours. Genesis: 68% of formations flagged a median 24 hours ahead (52% false alarms), Brier skill +0.22.

from naturev1.cyclone import physics_forecast       # track, members, cone, regime, Dorian-type stall warning,
fc = physics_forecast(case, environment)            # shear profile, intensity along the track

Also in 0.13: naturev1.distill (multi-teacher distillation with spatial / vertical / temporal alignment of every teacher into NatureV1's space), naturev1.assimilation (bias correction, quality control, local optimal interpolation for live inputs), naturev1.highres (decoding the latent mesh at 0.25 degrees). Distillation and the 0.25-degree decoder are tested on CPU, not yet trained.

0.13: the swarm sandbox, the satellite path and Caribbean impacts

naturev1.swarm (idea: Nathan) runs alongside the physics. It is a particle filter over possible futures. Each world is a 4D worldline (longitude, latitude, steering depth, time) with its own physics, integrated in micro-segments and re-weighted minute by minute by NHC's satellite, recon and radar centre fixes. Its wind and rain are then painted onto every parish, province and district of the Caribbean: 309 units, with terrain.

from naturev1.swarm.geography import CARIBBEAN, RegionMap
from naturev1.swarm.landfall import format_landfall, landfall_summary
from naturev1.swarm.live import forecast_storm
region = RegionMap.build(CARIBBEAN)                                   # once; cached
earlier = forecast_storm("al132025", when="2025-10-26T12", archive=True, particles=100_000, region=region)
run = forecast_storm("al132025", when="2025-10-27T00", archive=True,  # Melissa as it was known then
                     particles=100_000, region=region,
                     previous={"time": "2025-10-26T12", "track": earlier["result"]["track"]})   # 0.15: its error feeds back
# 0.16: the NHC a-deck is read by default (guidance=False switches it off); the official forecast and the aids used:
print(run["guidance"]["ofcl"], run["result"]["aids_track"], run["result"]["aids_intensity"], run["result"]["intensity_ours"])
print(run["impact"].table())                                          # parish-by-parish probabilities
print(format_landfall(landfall_summary(region, run["result"], run["case"], run["impact"], "Jamaica",
                                       analysis_time="2025-10-27T00")))  # when, where, how strong; rain if hit
print(run["result"]["peak_probability"])                              # P(peak within 5 days >= 64/96/113/137 kt)
print(run["result"]["intensity_if_ri"], run["result"]["ri_probability"])   # the rapid-intensification branch

On unseen seasons, its stall probabilities are skilful (Brier +0.08 over climatology) and its loop probabilities are reliable. Its cone is not better than the fixed one, and its own mean track is worse than the consensus, which stays the track. On Melissa the consensus missed the northward turn. The swarm kept western Jamaica at risk, but at 13-20% for hurricane-force wind where the storm brought it to most of the island, because a 160 kt Category 5 was forecast at 111-125 kt.

0.13.1: the turns, and rapid intensification

The track now uses a dynamical model's forecast winds, the way NHC's Beta and Advection Model does. They come from GFS live and from ECMWF HRES in the hindcasts. The model's own storm is removed at every forecast hour. The consensus is then blended with the model's own track, one weight per lead. That lets the track see a trough two days out, which the analysis cannot. Held-out seasons 2018 and 2020-2022, km:

On storms that turned by more than 45 degrees, the 72 h error fell from 601 to 209 km. The swarm, steered by the same forecast, now gives skilful recurvature probabilities: Brier skill +0.26, up from +0.05. Its loop probabilities got worse (−0.25), so treat them as unreliable.

For intensity, a rapid-intensification probability (Brier skill +0.10, AUC 0.81) switches the intensity consensus to weights fitted on such storms. That lowers the error by 1-3% overall and by 5-10% when P(RI) ≥ 30%, at 6-36 h.

On Melissa from 27 October, the track now curves north into Jamaica: 55 / 79 / 246 km errors at 36 / 48 / 72 h, against 187 / 392 / 892 km before. Every parish gets a 24-47% chance of hurricane-force wind, up from 13-20%. The intensity is still far too low (118 kt at 24 h against 155 kt). The live track leans on GFS, which has historically erred somewhat more than HRES. Details are in section 4.14 of the model card.

0.14: several models at once, a cone sized per forecast, a swarm on several models

The consensus is now blended with the equal-weight mean of several models' tracks, not one model's. Live they are GFS, ECMWF IFS and AIFS (open data), GraphCast-GFS and the GEFS mean, each read by byte range from its public bucket (naturev1.swarm.models); any model not yet published is skipped. On the held-out seasons, with the archived models WeatherBench 2 holds (HRES, Pangu, GraphCast, FuXi, Aurora, FGN) and no weight fitted to them:

Also: a cone sized per forecast from member spread, model disagreement, speed, latitude and intensity (held-out rank correlation with the error 0.17-0.38, the fixed cone 0); each swarm world follows one model's forecast winds. Three ideas measured and rejected on the held-out seasons: anchoring the model track to the observed position, shrinking the model's weight when it disagrees with the physics, and a quieter swarm (its spread matched the error on the tuning seasons, but its scenario probabilities became over-confident on the held-out ones).

Intensity gains the models' own deepening (their central-pressure-deficit change along their tracks) as a member and as a rapid-intensification predictor: held-out error down 4.8% at 24 h, 6.3% at 36 h and 7.2% at 48 h, every lead significant; P(RI) Brier skill +0.12, AUC 0.84; and calibrated P(≥ 64 / 96 / 113 / 137 kt) at every lead (Brier skill +0.65 / +0.48 / +0.36 / +0.18 at 24 h).

On Melissa from 27 October, with GFS, GraphCast-GFS and the GEFS mean: 56 / 46 / 69 / 194 / 274 km at 24-96 h (0.13.1: 91 / 55 / 79 / 246 / 369). The intensity is still far too low (114 kt at 24 h against 155). Each world of the swarm now follows one model; the parish probabilities are about where 0.13.1 had them. Details and every caveat are in section 4.15 of the model card.

0.15: the ocean's depth, landfall parish by parish, and the benchmark table

The intensity now knows how deep the warm water is: the depth of the 26 C isotherm and the heat potential from the World Ocean Atlas climatology (packaged), deepened or shoaled by this year's sea-surface anomaly, size the cold wake and enter the SHIPS and rapid-intensification predictors with the storm's observed size. Landfall is answered the way a parish needs it (naturev1.swarm.landfall): when the centre comes ashore with its 10-90% range and dates, which parish first, the intensity then and at peak, and each parish's peak wind, gust, rain and arrival times. The wind field is sized to the observed 34-kt radius, the worlds' intensities drawn from the forecast's own calibrated error distribution. naturev1.swarm.observations fits a vortex to barometer readings (a centre fix with uncertainty and a central pressure) and blends point winds into the map -- operators for feeds not yet read here. The track benchmark against every archived model is in section 4.16 of the model card. Measured on the held-out seasons (2018, 2020-2022), none of it tuned there. Intensity: 0.15's tables lower the error 0.9-1.3% at 6-24 h over 0.14 (16-33% over persistence, 5-16% over SHIFOR at every lead), and lift the rapid-intensification Brier skill from 0.122 to 0.154 (AUC 0.840 → 0.864). The under-forecast of the wind is conditional, not a bias: −25 kt at 24 h on the storms that intensify rapidly, +14 kt on those that weaken fast, and the forecast peak sits 30 kt under the true peak of the storms that reach 113 kt. Two products answer that: the rapid-intensification path issued beside the consensus with its probability (60% better than the consensus at 24 h on the storms that did go rapid, 2-3 times worse on those that did not, hence never blended), and a peak-intensity probability -- P(peak within 5 days ≥ 64 / 96 / 113 / 137 kt) -- with held-out Brier skill 0.32 / 0.31 / 0.28 / 0.28 against 0.26 / 0.22 / 0.15 / 0.16 for the best per-lead category probability. Track: the previous cycle's error fed back into the new blend is worth +1.1-1.2% at 12-24 h (significant) and nothing past 48 h. Rain: R-CLIPER along the observed track of 24 US landfalls against gauge-corrected radar delivered half the observed rain; a ×1.95 multiplier set on 8 tuning storms raises the held-out threat score for 100 mm from 0.20 to 0.29 and for 250 mm from 0.12 to 0.29, at the cost of a +13 mm bias in the light-rain cells. Parish rain is now reported if the parish is hit and as its wettest cell, not only as the swarm mean that every missing world dilutes. The swarm itself is now sized to the flow-dependent cone: its raw worlds were 1.4-3.2 times too wide on held-out cases (the truth sat inside its 67% radius 81-99% of the time); rescaled about the consensus they cover 64-75%, with the 50% and 90% radii where they should be, so strike, landfall and parish probabilities stop being diluted by worlds that miss by hundreds of km. Full tables in the model card, section 4.16.

Melissa, 27 October 00 UTC, 41 hours before landfall: Jamaica landfall probability 76% (0.14: 41%), the consensus ashore at 18.12N 77.88W on 28 October 14 UTC (actual: New Hope, 18.09N 77.97W, about 17 UTC), the swarm's median 15 UTC inside a 12-hour band; St Elizabeth 84%, Westmoreland 77%, Manchester 72% for hurricane-force wind, the eastern parishes 9-15%; 110 kt at landfall with the rapid-intensification branch at 153 kt (actual 160) and a 23% chance of a category-5 peak; Manchester's wettest cell 747 mm against the 817 mm gauge.

0.16: the official guidance as members, the model's own rain, and the answer key

The forecast now reads what the forecasters read. naturev1.swarm.adeck fetches the NHC's public a-deck for the cycle -- every operational aid's track and intensity, minutes after the synoptic time -- and naturev1.cyclone.aids blends the aids in with tables fitted on the tuning seasons: the track is the plain mean of our multi-model blend and HCCA (the HFIP corrected consensus), the intensity a simplex over our consensus, IVCN, HWRF, HMON, SHIPS, LGEM, the GFS and HCCA, lead by lead. Weights renormalise over the aids present, HAFS-A/B stand in for HWRF/HMON and TVCN for HCCA when those are absent (and the record says so), and our own track and intensity stay beside the blend (track_ours, intensity_ours). The NHC's rapid-intensification guidance (SHIPS-RII, logistic, Bayesian, DTOPS, consensus) is read from the SHIPS text and reported beside ours. The GFS's own accumulated rain travels with every world as half of its rain (fetch_qpf), so the moisture and the model's orography enter the parish totals. The peak quantiles, E[peak | RI] and the arrival-time window of the 0.16 roadmap are in the landfall report, and every cycle is saved and fed back (naturev1.swarm.bulletin). ROADMAP_0.16.md has the deficit matrix with what was tried, what shipped and what was rejected.

Measured on the held-out seasons (2018, 2020-2022), none of it tuned there; Atlantic cases, where the NHC guidance exists (626 at 24 h, 71 storms). Track: the mean with HCCA takes the error from 62 to 54 km at 24 h, 96 to 89 at 48 h, 169 to 150 at 72 h and 365 to 319 at 120 h (11-13% lower than 0.14 at 12-120 h, every lead significant), and sits 12-22% under the NHC official forecast at 6-72 h and 5-6% under it at 96-120 h -- on the tuning seasons the same rule gained 2%, so the held-out gain is larger than the fit promised, not smaller. Intensity: the aid blend takes the mean error from 9.6 to 7.1 kt at 24 h, 13.9 to 9.5 at 48 h, 16.2 to 10.5 at 72 h and 18.8 to 12.8 at 120 h (26-35% lower than 0.15 from 24 h on, every tuning season agreeing in leave-one-season-out), and it is 4-6% under the official forecast at 24-72 h and level with it at 96-120 h (the official forecast is itself made from this guidance three hours later, so read it as a product comparison). What the aids do not fix: the under-forecast on the storms that intensify rapidly moves only from -23 to -21 kt at 24 h (the official forecast: -19), which is why the peak quantiles and the RI branch remain the answer to the explosive cases. Rapid intensification: the archive's e-decks carry no RI probabilities before 2020, so nothing could be chosen on the tuning seasons; on 2020-2022 ours has Brier skill 0.13, the SHIPS-RII consensus 0.07, DTOPS 0.17 and the equal-weight mean of ours and DTOPS 0.20 -- that mean is reported as ri_probability_combined with this caveat, and ours stays the headline. Rain: the GFS member against gauge-corrected radar on US landfalls -- Ida 23 vs 45 mm mean error, Nicholas 17 vs 55, Fred 21 vs 36, Ian level. Rejected on the tuning seasons and said so: a stall-over-water penalty (its sign flips between seasons; the fixed rule is 45-122% worse on the stall cases), a translation-speed rain factor, a 115-kt rain saturation, nonlinear rain transforms, dynamic per-storm model weighting. Timing: no systematic along-track bias was found, so the arrival-time error (3.6 h at 24 h, 7.3 h for storms under 3 m/s) is reported as a window rather than corrected. The held-out case list with every reference's forecast on it is published as benchmark_heldout_atlantic_2018_2020_2022.csv.gz on the model repository, with the scoring code, so that a new model can be checked on the same storms. Full tables in the model card, section 4.17.

Melissa, 27 October 00 UTC, 41 hours before landfall, replayed with 0.16: Jamaica landfall probability 83% (0.15: 76%), the consensus ashore at 18.06N 77.72W on 28 October 14 UTC (actual: New Hope, 18.09N 77.97W, about 17 UTC), the swarm's median 15 UTC inside a 12-hour band; St Elizabeth 77%, Manchester 69%, Westmoreland 60%, Clarendon 54% for hurricane-force wind, the eastern parishes 10-15%; the far-west rain that 0.15 overdid is now near the gauges (Westmoreland 413 mm if hit against 309, Hanover 407 against 146) with Manchester 584 / 865 against 817 and St Catherine 468 / 666 against 668. Said plainly, this storm was not the archive: on the two earlier cycles the NHC guidance was worse than our standalone blend at 24-48 h (26 Oct 12 UTC: HCCA 70 km off at 24 h where our blend had 15 km, so the mean sat at 42; the aids pulled the 48 h intensity from 110 to 100 kt against a truth of 165), and the mean inherits that -- the price of a rule that is 11-13% better over 626 held-out cases. The averaging penalty was then taken to the archive: on the fifth of held-out cases where our blend and HCCA disagree most at 24 h, ours alone is 133 km off, HCCA 93 and the mean 94 -- ours is the one that is wrong in 69% of them (84% in the most extreme tenth, where TVCN sides with HCCA every time), so no rule that trusts the standalone in a disagreement survives. Two rules do, and ship: the split between ours and HCCA is earned from the previous cycle's verified errors at 6-24 h (the member that caught the last turn keeps more of its vote), and beyond 1.5 cone radii of disagreement up to 10% of the pair's weight moves away from whichever member stands alone against TVCN; together 1.4-2.5% lower held-out error at 12-36 h and 1-2% at 48-120 h, every lead significant, and the disagreement itself is reported per lead with both tracks in the record.

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.