CorxLabs/NatureV1-500

NatureV1 — a probabilistic weather and hurricane model built on geometric attention

Status: trained and scored — a research model, not an operational forecast. The first full run is complete and every number in section 4 was measured on data the model never trained on, including an end-to-end test on the 2023 hurricane season (a strong El Niño year no part of the model ever saw). It beats physics-only steering and straight-line extrapolation on hurricane track at every lead, but it is several times less accurate than the National Hurricane Center and the leading global models, it misses rapid intensification, and a red-team pass (section 4.8) found failure modes you should know before using any output. Do not use it for real decisions — for those, use the National Hurricane Center.

Training took about one week of wall-clock time on a single GPU in a hosted notebook (molab), including session restarts and re-staging; the rollout stage alone was 74 GPU-hours.

Version 0.11 adds stage three — storm-centred infrared satellite imagery for the hurricane heads — and fixes what the red team found: calibrated probabilities, an input monitor, and a forecast that can no longer state impossible structure (section 4.9). training_record.json says which stage the released weights come from.

Version 0.12 (code ready, not yet trained) rebuilds the satellite path around the red team's findings and moves the storm heads from the Atlantic to every basin — see section 4.10. The released weights do not use it until it has been trained and has beaten them on the same test storms.

Version 0.13 adds naturev1.cyclone: 39 modules of tropical-cyclone physics that need no neural network, measured on 4,447 forecasts of 407 storms in every basin in seasons they were never fitted on (2018, 2020-2022). The physics consensus beats straight-line extrapolation at every lead from 6 to 120 hours (+12% to +38%, every interval clear of zero) and beats CLIPER at every lead. It does not beat GraphCast, Pangu-Weather, HRES, Aurora, FGN (WeatherNext 2), FuXi or GenCast past 6 hours; combined with any of them it is never worse and is better at 6-12 hours. Plus genesis detection (68% of formations flagged a median 24 h ahead), multi-teacher distillation, data assimilation and a 0.25-degree decoder — section 4.12. The swarm sandbox takes satellite fixes minute by minute and maps impacts parish by parish across the whole Caribbean. On unseen seasons its stall probabilities are skilful, its cone is not better than the fixed cone, and on Hurricane Melissa it kept western Jamaica at risk but far too low — section 4.13. 0.13.1 steers the track with a dynamical model's forecast winds (GFS live, HRES in the hindcasts) and blends in the model's own track. Held-out track errors fall by 12% to 65% (72 h: 512 → 184 km), slightly ahead of HRES alone to 72 h. On Melissa the track now curves north into Jamaica, but the intensity is still far too low — section 4.14. 0.14 blends the consensus with the equal-weight mean of several models (live: GFS, ECMWF IFS and AIFS, GraphCast-GFS, GEFS), which cuts held-out errors another 11% at 24 h and 19-23% at 48-120 h (72 h: 142 km), sizes the cone per forecast, and makes the swarm's worlds each follow one model — section 4.15.

NatureV1 is an 89-million-parameter model of the atmosphere that forecasts global weather out to five days and, for tropical cyclones, where a storm will go, how strong it will get, whether it will intensify rapidly, and whether it will make landfall. Every number it produces comes with an uncertainty. It is built on iHELIX, an attention engine that works on the physical geometry of the planet rather than on a flat grid, and trained by a single, resumable, self-verifying pipeline that lives in one notebook cell. The whole stack — engine, model, training pipeline, verification — is open and written by one person.

• Code and training pipeline: pip install naturev1[all] — naturev1 on PyPI
• Engine: pip install ihelix — ihelix on PyPI
• Author: Nathan. License: Apache-2.0.

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1. What it does

Given six frames of the atmosphere (the last 30 hours of ERA5 reanalysis: 89 channels — 11 surface fields and 6 variables on 13 pressure levels — on a 1.5° global grid), NatureV1 produces:

Global weather, at 6, 12, 18, 24, 36, 48, 72, 96 and 120 hours

• A full-state rollout: the whole atmosphere — all 86 prognostic channels, surface to 50 hPa — stepped forward 6 hours at a time on its own forecast, with mass conservation, out to 72 hours, as an ensemble. This is the weather output with measured skill (section 4.2).
• 2 m temperature, mean sea-level pressure, 10 m wind and precipitation directly at each lead, as a mean and a 90% interval. These direct surface heads were not updated after the rollout stage and have no skill in this release; use the rollout.
• A weather-type category head exists but was never trained, so it is never shown.

For a tropical cyclone, given its current centre

• Track as scenarios, not a line: six weighted trajectories ("38% recurves offshore, 27% tracks the coast…"), each with a tilting uncertainty ellipse per lead, so the cone of uncertainty is drawn from the model, not from a lookup table.
• A multi-model consensus track: the learned track, a physics-only steering-flow track, and straight extrapolation, blended with per-lead weights fitted on held-out seasons — the way the National Hurricane Center's consensus beats every single model in it, done inside one model. Every member is reported alongside the blend.
• Intensity: maximum wind and minimum central pressure per lead, with intervals and the Saffir–Simpson category.
• Rapid intensification: the probability of a 25, 30 and 35 kt gain in 24 hours, plus the expected change. It ranks risk well but its probabilities are far too high (section 4.8).
• Landfall: the probability of landfall by each lead. (The landfall-timing head was never trained and is not shown.)
• Core structure: peak eyewall wind, radius of maximum wind, and 34/50/64 kt wind radii by quadrant, kept physically ordered (34 ≥ 50 ≥ 64 kt; radius of maximum wind inside the gale radius).
• A cone drawn from the whole scenario mixture (track_cone: the radius holding 50% and 90% of the mixture per lead), which on held-out storms held the truth as often as it claims to.
• What the satellite sees (0.11, after stage three). Storm-centred 11-micron infrared — now and six hours earlier — from HURSAT-B1, GridSat-B1 or a live GOES scene, read by a small branch aimed at intensity.
• The storm's environment, read from the model's own atmosphere: deep-layer steering, 200–850 hPa shear, mid-level humidity, ocean temperature — the predictors operational statistical schemes (SHIPS) are built on.

A local forecast for any point on Earth, in physical units, from the gridded fields.

What it refuses to do

This is as much a part of the model as the outputs above.

• An output whose head has never received a training step is never shown. It is replaced by {"available": false, "reason": ...}. The training record travels inside the checkpoint.
• A forecast run from an input path the model was never trained on (today, the satellite path) is marked trustworthy: false and the live satellite forecast is refused outright.
• An input monitor (0.11) compares the storm features with what training looked like; a forecast from inputs unlike anything it learned from — corrupted data, noise, zeros — is marked trustworthy: false.
• check_forecast tests every scenario track, the consensus and the cone, intensity, eyewall and RI value against physical bounds, and checks that landfall never becomes less likely with time and wind radii stay ordered: no 400 kt hurricane, no pressure outside 850–1100 hPa, no cone wider than an ocean, no probabilities that do not sum to one. It reports problems; it does not block the forecast, so a caller must act on what it returns. Section 4.8 lists what it does not catch.
• The pipeline publishes only if the model beats persistence somewhere on held-out data and demonstrably changes its answer when the weather changes. That gate is weak (precipitation alone can pass it); this release was published after the full scorecards and red-team below were reviewed.

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2. How it works

2.1 The engine: iHELIX, attention over physical space

Most weather transformers flatten the globe into tokens and let attention learn geography from scratch. iHELIX keeps the geometry:

• Geometry axes. A domain is composed from spherical, periodic, linear and logarithmic axes. Geometry.globe() is the Earth's surface; Geometry.atmosphere() is a spherical shell whose vertical axis is log-pressure, so that 1000→500 hPa is the same distance as 500→250 hPa. Every point carries a local east/north/up frame, so "20 km north" means the same thing everywhere.
• FieldGrid: data, not architecture. The points data lives on — ERA5's 240×121 grid, a 4,096-point Fibonacci mesh, a satellite scan's pixel footprints — with true area weights. The same model reads any of them.
• GeodesicAttention. Every attention head has a physical radius in kilometres with compact support: heads from 120 km (fronts, convection) to 1,600 km (synoptic scale). Attention is over great-circle distance.
• IndexAttention. A region tree with beam search lets a point reach distant points (teleconnections) without paying for the whole globe.
• TemporalStrand. A gated delta-rule recurrence carries state across the six input frames at linear cost — inherited from HELIX, a linear-context language model this engine grew out of.
• Encode → process → decode. Any source grid is read onto a shared 4,096-point mesh, processed by 17 blocks, and decoded onto any output grid.

2.2 The model: NatureV1

Parameters	89.45 M: 17 iHELIX blocks 84.67 M, input encoders 2.42 M, decoder 0.79 M, storm heads 1.23 M, time embedding 0.13 M, other output heads (field, weather type, noise, ENSO) 0.11 M, state head 0.09 M, norms + mesh seed ~3 k
Hidden size / heads	512 / 8 heads (4 key-value heads), head dim 64, MLP 2048
Latent mesh	4,096 points, 48 neighbours, cluster 64
Head radii	120 km to 1,600 km
History	6 frames × 6 h
Inputs	ERA5 analysis (89 channels + observation masks, padded to 96); calendar features (solar angle, season) given explicitly; optional satellite and environment encoders; per-member noise for ensembles
Outputs	gridded fields with log-variance; full-state residual with log-variance; track mixture (6 modes × 9 leads × 5 parameters); intensity; landfall; RI; eyewall; ENSO
Precision	bf16 mixed precision; gradient checkpointing

The storm path pools the processed mesh around the storm centre with a 500 km Gaussian and, since 0.9, a second 1,000 km pool (the ridge that steers a storm sits a thousand kilometres from the eye). It adds the storm's own state (wind, pressure, 12 h motion, 12 h wind change — what a 1.5° reanalysis cannot show), the storm's position (Coriolis and beta drift), and the physical environment computed from the state tensor. The track head predicts the residual from a steering-flow track, which is a far easier target than the whole track: beta drift, trough interactions, what steering alone gets wrong.

Everything new starts at exactly zero effect. The state head opens as persistence, the ensemble noise as nothing, the environment inputs as nothing. Adding a capability can never make an existing checkpoint worse, and uncertainties open at climatological spread rather than at a confident guess.

2.3 The physics inside the model

• Channel roles. Every input channel is prognostic (evolved), forcing (incoming solar radiation, recomputed each step from orbital geometry) or static (land mask, orography, observation masks, padding). A static field marked prognostic lets a model slowly move a coastline; this is what prevents it.
• Rollout. The whole atmosphere advances 6 h at a time on the model's own forecast, with surface-pressure mass conservation and a GraphCast-style curriculum from one step to twelve.
• Ensembles. Per-point noise is spread spatially by the geodesic blocks; a fair CRPS loss grows the spread only as far as the data justifies; spread/skill is reported.
• Hurricane physics (naturev1.steering): thickness-weighted 850–200 hPa steering over the 200–800 km ring around the centre, 200–850 hPa shear, 700 hPa specific humidity, SST versus 26.5 °C; advection with the correct longitude scaling and climatological beta drift; a steering track from today's analysis held steady, or from the model's own rolled-out atmosphere step by step. The steering track needs no training at all.

2.4 Training, in stages

The whole run took about one week of wall-clock time on one RTX PRO 6000 (96 GB) in a hosted notebook. The GPU time was roughly three to four days; the rest was hosted-session overhead — sessions end after 12 hours or 90 idle minutes and the disk is wiped, so each restart re-pulled checkpoints and staged data from this repository before training resumed. Every stage is resumable from a one-minute checkpoint, so no restart lost more than a minute of training.

1. Stage one — pretraining on reanalysis. Every surface channel at every lead, Gaussian negative log-likelihood, area-weighted, on years of ERA5. This is where the backbone learns what the atmosphere does, from about 2×10¹¹ supervised values.
2. Stage 1b — full-state rollout. The residual state head is trained to roll the whole atmosphere forward, curriculum to 12 steps (72 h), 2-member CRPS ensemble.
3. Stage two — hurricane heads on HURDAT2. The backbone is frozen; only ~1.2 M parameters ever see a best-track label. The frozen backbone runs once per storm into a cached feature bank; the heads then train in seconds per epoch with early stopping on seasons never trained on. Afterwards the consensus weights are fitted on the held-out seasons.
4. Stage three — the satellite (0.11). Every storm sample gets two storm-centred infrared images (now and six hours earlier; 256 × 256 pixels at 0.07°, about 18° across): HURSAT-B1 for 1979–2016, GridSat-B1 after — the same ISCCP B1 record on the same grid (on Katrina at landfall they agree with correlation 0.989). A small network (0.84 M parameters: a CNN plus the Dvorak technique's own radial profile of cloud-top temperature) is added to the hurricane heads with its output at exactly zero, then fine-tuned with the backbone frozen. The model it starts from is the score to beat on held-out storms; if the satellite does not beat it, that model is kept unchanged. Then landfall and rapid-intensification probabilities are calibrated on held-out seasons, the input monitor is fitted, and the rollout's tendency statistics are stored with the weights.

2.5 Data

• ERA5 via WeatherBench 2, 1.5°, 240×121, six-hourly, 13 pressure levels. Split by time over 1959–2021 (train to 2015, validation 2016–2019, test 2020–2021); this run staged the last five training years, 2011–2015 (7,300 global states, ~38 GB), and validated on 2016. A random split would leak tomorrow's answer into training.
• HURDAT2 Atlantic best tracks, 1979 onward (the satellite era). Split by season (validation 2017, 2019, 2021; test 2018, 2020). Labels are paired with the reanalysis by timestamp, not row index; off-synoptic landfall specials are dropped rather than snapped; scarce labels (radius of maximum wind exists on under 5% of points) arrive as NaN and are masked, never imputed.
• Normalisation per flat channel with log and asinh transforms for spiky fields (precipitation, vertical velocity) and observation masks for gappy ones (sea-surface temperature).

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3. Verification and safety

The model is scored the way operational centres score: against the baselines a forecaster would actually use, on data it never saw, in physical units.

• WeatherBench-style scorecards: area-weighted RMSE and anomaly correlation for t2m, mslp, u10, v10, precipitation and for Z500 / T850 rollouts, against persistence and climatology on identical batches, with a 1% margin before anything is called skill.
• Storm scorecard on held-out seasons: great-circle track error of the learned track, the physics-only steering track, the consensus (scored leave-one-season-out), a storm that stays put, and straight extrapolation; intensity MAE against persistence. Beating extrapolation and persistence is the bar; beating steering is what the learned part is for.
• Hindcast: a held-out hurricane (Dorian 2019) forecast from its real analysis, every member against what happened, with wind forecast versus actual.
• Training watchdog: raises on a non-finite loss, warns on divergence and on collapse; held-out validation every 500 steps with an explicit over-fitting flag.
• Preflight: grid alignment, normalisation spikes, grid weights and device agreement are checked before step one, and the run halts if anything fails.
• Does it respond to the weather? A probe confirms different inputs give different outputs.

Resilience is part of safety for a multi-day run: atomic checkpoint writes every minute with snapshots and a second copy elsewhere; the optimizer, schedule, scaler and random states travel with the weights; damaged checkpoints fall back to older ones and incompatible ones are quarantined rather than force-loaded; a supervised background process restarts the run on crash, out-of-memory or stall; every file the run reads back is written atomically; and on a hosted notebook everything expensive is mirrored to this repository so a wiped disk costs minutes.

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4. Results

All numbers below come from the published weights. Track errors are great-circle kilometres; "steering" is the physics-only steering-flow track (no training), "straight" is extrapolation of the last 12 hours, "stay-put" is a storm that does not move, and wind "persistence" is "it stays as strong as it is now". The raw outputs are in results/ and the scripts that produced them in eval/.

4.1 Training, in numbers

Stage	What trained	Steps	Notes
One — reanalysis pretraining	backbone + surface heads	7,275 (8 epochs)	ERA5 2011–2015, Gaussian NLL
1b — full-state rollout	backbone + state head	4,000	curriculum to 12 steps (72 h), 2-member CRPS; 74.3 GPU-hours (4,459 min)
Two — hurricane heads	storm heads only, backbone frozen	best epoch 3 of 28	584 storms / 16,219 samples, 1979+; feature banks ~2 h, heads minutes; early-stopped on held-out seasons

About one week end to end (three to four GPU-days plus hosted-notebook restarts), one RTX PRO 6000 (96 GB). The full per-output training record is in training_record.json; outputs with zero steps (weather type, landfall timing, RI onset, ENSO, satellite and environment encoders) are never shown.

4.2 Global weather (held-out data)

From the run's own WeatherBench-style scorecard, on identical batches for every baseline:

• Full-state rollout: beats climatology by more than 1% on 84 of 84 field-lead pairs, and has skill against both persistence and climatology out to +72 h on msl, q700, t2m, t850, u10, v10 and z500. The ensemble spread/skill ratio at +24 h is 1.08 (1.0 is perfectly calibrated).
• The direct multi-lead surface heads do not have skill (they beat persistence on 6 of 45 field-lead pairs, all precipitation). They were trained in stage one and not updated when the rollout retrained the backbone under them; use the full-state rollout for weather. The complete tables are in logs/train.log.

4.3 Hurricane track and intensity — held-out seasons 2017, 2019, 2021

59 Atlantic storms (including Harvey, Irma, Maria, Dorian, Lorenzo, Ida) that neither the backbone nor the storm heads trained on. Consensus weights scored leave-one-season-out.

Lead	n	NatureV1 consensus	learned track	steering	straight	stay-put	wind error	persistence
6 h	1589	39	42	54	53	140	6.2 kt	3.4 kt
12 h	1530	75	84	107	121	275	7.8 kt	6.6 kt
24 h	1412	163	180	233	283	527	11.0 kt	11.8 kt
48 h	1187	421	457	572	628	977	16.1 kt	18.8 kt
72 h	997	739	844	978	1002	1369	19.5 kt	24.2 kt
120 h	677	1373	1576	1779	1828	2081	22.8 kt	31.6 kt

Track beats steering and straight-line extrapolation at every lead; wind beats persistence from 24 h on.

4.4 End to end on an unseen El Niño season — the 2023 hurricanes

2023 was a strong El Niño year and is outside everything the model saw. ERA5 for 2023 was rebuilt at WeatherBench 2's 1.5° grid from ARCO-ERA5 with area-weighted conservative regridding — checked against the WeatherBench 2 store on an overlapping date, where it agrees to rounding precision (0.03 Pa in sea-level pressure) — and every forecast ran through the full model, raw weather in. All seven hurricanes, one forecast per day at 00Z (96 forecasts), with the shipped consensus weights and no refitting.

Lead	n	NatureV1	steering	straight	stay-put	wind error	persistence	2017/19/21 for comparison
6 h	96	38	47	53	125	6.5 kt	2.9 kt	39
12 h	95	74	99	128	248	7.5 kt	5.8 kt	75
24 h	89	167	231	309	476	10.7 kt	11.9 kt	163
48 h	82	503	689	719	866	14.7 kt	18.7 kt	418
72 h	75	810	1146	1132	1211	15.8 kt	21.5 kt	735
120 h	61	1487	2028	1868	1807	16.1 kt	28.0 kt	1374

Storm (peak)	24 h	48 h	72 h
Lee (145 kt)	100 (steering 120)	240 (378)	325 (635)
Margot	84 (167)	350 (522)	678 (926)
Tammy	125 (223)	441 (601)	838 (1295)
Don	169 (222)	439 (577)	858 (1031)
Idalia	165 (245)	534 (718)	1049 (1373)
Franklin	211 (262)	680 (944)	827 (1263)
Nigel	292 (369)	727 (924)	1111 (1429)

Out to 24 h the El Niño season scored the same as the held-out neutral/La Niña seasons; from 48 h the errors are larger, but the margin over physics steering grew (29% better at 72 h, against 25%). It beat steering for every storm at every one of these leads. One season, seven storms, 00Z only: encouraging, not conclusive.

4.5 Landfall, rapid intensification and structure (2017/19/21)

Output	Result	Verdict
Landfall probability	Brier skill over the base rate +4% (6 h) to +29% (72 h); AUC 0.81–0.86. 2023: +30 to +42% from 72 h, AUC 0.81–0.95	skilful
Rapid intensification (3 thresholds)	ranks risk well (AUC 0.82–0.84) but probabilities are too high (Brier worse than the base rate)	needs calibration before use
Peak wind (eyewall head)	MAE 6 / 11 / 19 kt at 6 / 24 / 72 h vs 22–26 kt for the climatological mean	beats climatology
34/50/64 kt wind radii	MAE 32–37 n mi vs 47–49 for the mean	about 30% better
Radius of maximum wind	28 vs 29 n mi (6 h), loses by 72 h	no skill

4.6 Individual forecasts

Maria 2017, issued 18 Sep 00Z east of the Lesser Antilles, the full model from raw ERA5 (results/maria_2017_end_to_end.txt): miss 14 / 26 / 15 / 65 / 118 / 343 km at 6 h / 1 / 2 / 3 / 4 / 5 days, against 33 / 91 / 101 / 136 / 181 / 245 km for steering. Wind forecast about 70 kt against an observed 145–150 kt.

Dorian 2019, issued 30 Aug 18Z, from the run's hindcast:

Lead	6 h	24 h	48 h	72 h	120 h
learned track (top scenario 26%)	24	99	336	688	1034
consensus	12	106	355	669	935
steering	14	177	382	546	531
straight	17	161	397	651	1012

Good to two days; Dorian then stalled over the Bahamas, which steering handled better.

4.7 In context

For scale only: the National Hurricane Center's official Atlantic track error averaged about 66 km at 24 h and 168 km at 72 h over 2018–2022, and the leading global AI models (GraphCast, Pangu-Weather, FuXi) and ECMWF are in the same league. NatureV1's 163 km and 739 km are 2.5–4.5× larger. It is a 1.5° model trained on five years of data with a few GPU-days of compute; those systems use 0.25°, decades of data and orders of magnitude more compute. Intensity is the weakest output: like every 1.5° model it cannot see an eyewall, and it forecasts about 70 kt for storms that reach 145–160 kt.

4.8 Red team: where it breaks

A deliberate attempt to break the published model: physically impossible inputs, calibration against what actually happened, removing one input at a time, logical consistency, a data-leak audit, and the hardest storm we could find. Everything here is on held-out data unless noted; scripts in eval/.

Data leakage — none found. Storm-head training seasons are 1979–2016; held-out 2017/2019/2021 and test 2018/2020/2022 never appear in training; the weather backbone trained on 2011–2015 only. 2023 is outside everything.

Calibration — is the uncertainty honest? (2017/19/21; 2023 in brackets)

Output	Claimed	Actually
Track, full 6-scenario mixture, 50% region	50%	47–53% (32–55%) — honest
Track, full mixture, 90% region	90%	87–92% (81–93%) — honest, slightly tight at 4–5 days in 2023
Track, top scenario's "95%" cone (what a single cone shows)	95%	60–87% — over-confident; the other scenarios carry the rest
cone_radius_km_68 field	68%	it is the 1-sigma ellipse, which holds 39% in two dimensions — mislabelled
Wind, 90% interval	90%	85–93% — honest
Landfall by 72 h	18% / 39% / 61% / 79%	10% / 31% / 51% / 79% — too high below 70%
Rapid intensification (+30 kt/24 h)	21% / 39% / 55%	1% / 10% / 38% — far too high; do not read these as probabilities

Intensity is biased low, and worse for stronger storms (forecast minus actual, held-out):

Current strength	24 h	72 h
Tropical storm (<64 kt)	−3 kt	−6 kt
Category 1–2	−7 kt	−15 kt
Category 3–5	−10 kt	−18 kt

What the hurricane heads actually rely on (remove one input, held-out error change):

Removed	Track 24 h	Track 72 h	Wind 24 h
Physics steering-track prior	+240%	+40%	0%
All backbone features	+30%	+13%	+18%
Backbone features from a different storm	+29%	+12%	+43%
1,000 km far pool	+10%	+3%	+5%
Physical environment (shear, steering, humidity, SST)	+14%	+4%	+2%
Current wind and pressure	0%	0%	+58%
Last 12 h of motion	+10%	+15%	−1%

The track is the physics steering track plus a learned correction worth about 30% at 24 h. The intensity forecast leans on the storm's current wind; the shear/humidity/SST inputs built to help intensity barely move it.

Inputs the safety checks do not catch.

• Garbage in, plausible out. Random noise in place of the backbone features produced a normal-looking forecast (22–45 kt, a sensible track) with zero check failures. There is no out-of-distribution detector.
• A corrupted steering prior passes straight through. Shifting the prior by 30° moved the forecast 30° with zero check failures.
• The consensus track is not bounds-checked — a centre near the pole gave consensus latitudes above 90°; only the scenario tracks were flagged.
• A missing (NaN) storm centre is flagged on the track, but intensity and RI are still produced as if valid.
• Caught correctly: a 400 kt current wind (forecast 370 kt → flagged), positions off the planet, cones wider than an ocean, and the untrained satellite path (trustworthy: false). The dateline and Southern Hemisphere beta drift are handled correctly.
• Bug: build_forecast without a training record crashes on outputs that carry no ENSO field.

Logical consistency.

• Landfall is "probability of landfall by this lead", which can never fall as the lead grows. It falls in 20% of forecasts (by up to 12 points).
• A 50 kt or 64 kt wind radius exceeds the 34/50 kt radius in 21% of forecasts, and the radius of maximum wind exceeds the 34 kt radius in 17% — both physically impossible.
• Consistent: the three RI thresholds are always ordered, and the two intensity heads agree to 1.5 kt on average.

The hardest case: Hurricane Otis, 2023 (East Pacific — outside the Atlantic the storm heads trained on; full model from raw ERA5, 5 forecasts). Otis went from 50 kt to a 130 kt Category 5 in 24 hours and struck Acapulco. From 24 Oct 00Z NatureV1 forecast 45 kt — a slight weakening — and gave rapid intensification 44%, about what it said on the quiet days before (34–38%). Track: 104 km at 24 h (steering 156 km), but at 72 h it kept Otis at the same latitude while it moved 5° north. It cannot warn of explosive intensification.

Reproducibility gap. The full-state rollout scales its residuals by per-channel tendency statistics measured from the training data; they are not shipped in this release, so reproducing the weather rollout exactly means re-measuring them from ERA5 2011–2015 (64 evenly spaced training windows).

Outside the Atlantic — the Southern Hemisphere (full model from raw ERA5; the storm heads only ever saw Atlantic storms):

Storm	n	24 h: NatureV1 / steering / straight	72 h: NatureV1 / steering / straight	72 h north–south: forecast vs actual
Seroja 2021 (South Indian)	10	249 / 180 / 338 km	682 / 788 / 962 km	−6.4° vs −6.6°
Niran 2021 (South Pacific)	9	209 / 181 / 277 km	976 / 1125 / 1246 km	−3.2° vs −2.6°

It sends Southern Hemisphere storms poleward — south — as it should, and beats steering at 72 h, but at 24 h the learned correction, fitted only to Atlantic storms, makes the track worse than physics steering alone. Outside the Atlantic, trust the steering member at short range.

Still running at the time of writing: four more storms outside the Atlantic (West and East Pacific) and a 10-day rollout to test stability beyond the 72 h trained horizon. They will be added here.

4.9 Fixed in 0.11, measured on the same held-out storms

Red-team finding	Fix	Measured after the fix
RI probabilities far too high (Brier 74% worse than the base rate)	Platt calibration fitted on held-out seasons	+12% Brier skill over the base rate, each season calibrated without itself; says 16% → 12% happen, 38% → 44%
Landfall over-forecast below 70%	same	says 20% → 21% happen, 39% → 44%; Brier skill unchanged at +29%
Garbage inputs gave a plausible forecast	input monitor (feature z-score and length)	random noise and all-zero inputs flagged 100%; real held-out storms flagged 0%
Landfall "by this lead" fell with lead in 20%	reported as a running maximum	0%
Wind radii out of order in 21%; RMW beyond the gale radius in 17%	structure made consistent when decoded	0%
Consensus track not bounds-checked; cone_radius_km_68 mislabelled	checked; renamed cone_radius_km_39; track_cone from the full mixture	—
Rollout tendency statistics not shipped	stored in the weights (state_tendency)	—
No storm centre still produced intensity and RI	every storm section withheld	—

Not fixed, and why: a corrupted steering prior still passes through (it comes from the model's own analysis, and a 30° shift is not physically impossible on its own); intensity remains biased low until the satellite stage has been trained and scored — its results will be added here.

4.10 0.12: the satellite path rebuilt, and every basin (code ready, not yet trained)

Every red-team finding mapped to a change. None of these has results yet — they are trained on 8x B300 by b300_naturev1.py, and this section will report what they measured on the test seasons (2018, 2020), next to the released model on the same storms. The release is replaced only if the new model beats it.

What went wrong	0.12
Intensity 10–18 kt too weak for majors; Otis 50→130 kt called 45 kt	SatNet-Storm (21.8M parameters): a four-frame loop (now, −3, −6, −9 h) of storm-centred 11 µm and 6.7 µm imagery → intensity, central pressure, wind radii, RMW, 12–72 h intensity change, motion; trained on ~230,000 fixes in every basin since 1980. Plus a per-lead intensity bias correction fitted on held-out seasons
RI nearly invisible	RI 2.0: the SHIPS-RII thresholds (25/30/35/40 kt in 24 h, 45/36 h, 55/48 h, 65/72 h) as one ordinal family (P(≥40) ≤ P(≥35) ≤ …), fed the predictors that carry RI signal — distance below maximum potential intensity, shear, mid-level moisture, ocean temperature, persistence — and SatNet's reading of the inner core; focal loss; calibrated afterwards
A storm-centre position was required	SatNet is given a first guess wrong by up to 150 km in training and must find the centre; a vortex tracker proposes first guesses from the model's own sea-level pressure where there is no advisory
Southern hemisphere worse than physics; poleward turns missed (Otis, Rai)	heads work in a poleward frame (southern storms mirrored in, mirrored out — an exact mirror, tested); labels from every basin (IBTrACS, ~4,500 storms vs 584); two new consensus members from the model's own rollout: the storm steered by the forecast flow, and the low followed through the forecast pressure field
"Satellites do not see the whole atmosphere"	the retrieval never pretends to: it brings a 6–48 h old state up to date from a three-frame global satellite loop (window + water vapour, conservative quarter-degree regridding that keeps each cell's coldest pixel and spread, cloud-motion vectors, satellite and view angle per pixel) and starts as exactly the stale state; its score is the share of the change since the stale state it recovers
Heads trained on perfect reanalysis only	stage B trains the heads and the backbone's last 4 blocks with 30% of samples' newest frame replaced by the retrieval, so the model learns from what it gets in real time; the next-step state loss and a pull back to the starting weights keep it a weather model
GridSat read naively is 99.95% masked	decoded by hand; QC removes single-pixel glitches but keeps sharp cloud edges; files under half observed rejected and recorded

Engine: iHELIX 0.6 adds conservative regridding, seam-free spherical convolution and grid-to-mesh pooling. Training: data-parallel on 8 GPUs with a learning-rate schedule driven by the clock (it ends exactly when the budget does) and every checkpoint pushed to this repository under checkpoints/<run>/ as it is written.

4.11 0.12: physics, wind and a wider consensus (code ready, not yet trained)

No single change here is promised to help. The approach is to give the forecast many independent ways to be right and let the held-out seasons decide how much each one counts: every member below enters a consensus whose weights are fitted on 2017/2019/2021 and can go to zero, and nothing is scored until the test seasons.

Area	Added in 0.12
Thermodynamics (naturev1.thermo)	Bister–Emanuel potential intensity from the model's own sounding (reversible CAPE, iterated eyewall pressure, Ck/Cd 0.9); Tang–Emanuel ventilation index and entropy deficit; Emanuel–Nolan genesis potential; Hart cyclone phase space (B, −VTL, −VTU) for tropical / hybrid / extratropical; 200 hPa divergence, 850 hPa vorticity, mid/low humidity, boundary-layer θe, core rain, land share — 23 storm predictors fed to every head and to RI 2.0
Steering	the steering layer depends on intensity (Velden & Leslie: 850–500 hPa for weak storms up to 850–200 for majors) and beta drift scales with storm size
Tracking (naturev1.tracker)	multi-field centre fix (sea-level pressure, 850/700 hPa vorticity and geopotential, weighted by agreement); intensity and phase read along the rollout; a rollout ensemble member with its spread; an analog member (nearest storms in 45 years of best tracks, in the poleward frame); the satellite centre fix iterates — each pass reads a loop cut at the better centre
Wind (naturev1.windfield)	an asymmetric Holland wind field (B from Vickery–Wadhera or fitted to the 34 kt radius per quadrant, Willoughby RMW climatology, Phadke inflow angle, Lin–Chavas motion asymmetry, land roughness, gusts); NHC-style wind-speed probabilities (34/50/64 kt) and gale arrival times by Monte Carlo over the forecast, at points or on a 0.25° map; Kaplan–DeMaria inland decay; R-CLIPER rain totals
Intensity consensus (naturev1.statistical)	a SHIPS-style regression, an LGEM-style logistic growth model bounded by potential intensity, climatology–persistence, the rollout's own intensity, SatNet and the analogs — combined with the network's heads by weights and biases fitted per lead on held-out seasons
Track consensus	8 members (two head summaries, steering, extrapolation, rollout-steered, rollout vortex, rollout ensemble, analogs), a per-lead bias correction in the poleward frame, and a Goerss-style predicted consensus error cone that widens when the members disagree
RI	a stacked RI consensus over RI 2.0, the satellite network, the statistical models and the rollout
Training	intensity loss rebalanced by class (square-root inverse frequency, capped: a major hurricane counts ~4× a tropical storm, the loss keeps its size); an average of the weights (EMA 0.999) is what is evaluated and released
Forecast time	a test-time rotation ensemble: the whole planet turned by the golden angle and run again — the storm, its latitude and its surroundings unchanged, the arithmetic different — merged as a mixture (disagreement widens the uncertainty). Used only if it beats a single pass on the held-out seasons

4.12 0.13: hurricane physics, measured on seasons it never saw

Technical report: Hurricane tracks without a neural network: a physics consensus scored on four unseen seasons.

naturev1.cyclone forecasts a storm's track from one 1.5-degree analysis and the best track so far, with no neural network: 13 members (extrapolation, a rebuilt CLIPER, track-shape analogs, steering trajectories through the vortex-removed analysis with beta drift that depends on the storm's outer circulation, a flow that keeps evolving the way it was evolving, a flow that relaxes to the 1981-2010 climatology as its anomaly loses memory, the vorticity-budget motion, a physics ensemble, a limited-area barotropic model) blended by along- and cross-track weights per lead. Every constant was fitted on 1980-2014 best tracks or the 2016/2017/2019 hindcasts; the table below is the four seasons never used for anything: 2018, 2020, 2021, 2022, every basin (NA, EP, WP, SI, SP), forecasts from every 00/12 UTC tropical or subtropical fix, verified while the system stays tropical (NHC rules), homogeneous samples, 90% intervals from a bootstrap over whole storms.

track error (km)	6 h	12 h	24 h	36 h	48 h	72 h	96 h	120 h
forecasts	4,217	3,983	3,559	3,177	2,826	2,200	1,677	1,262
strongest extrapolation (best of 6 h / 12 h / great-circle, per lead)	33	74	179	303	442	751	1,086	1,417
CLIPER (rebuilt, 1980-2014)	32	70	163	268	378	589	769	914
NatureV1 physics consensus	29	59	127	207	301	515	719	884
skill against extrapolation	+12%	+21%	+29%	+32%	+32%	+31%	+34%	+38%

Against the teachers, on their own years and the same storms (each tracked through its own WeatherBench 2 forecast at 1.5 degrees from the same starting position; tracking at 1.5 degrees costs every teacher a little at 6-12 hours, and they ran at 0.25):

km	6 h	12 h	24 h	48 h	72 h	120 h
NatureV1 physics (2018, 2020)	28	58	126	299	511	914
GraphCast	49	54	67	102	162	296
physics + GraphCast, lead-wise selected (weights never see the scored season)	26	47	67	102	162	296
Pangu-Weather (2018-2022)	49	58	69	101	151	278
physics + Pangu	27	44	69	101	151	278
HRES (2018-2022)	49	60	79	123	187	326
Aurora (2022) / FGN-WeatherNext 2 (2022)	46 / 45	55 / 51	66 / 61	92 / 82	146 / 111	313 / 199

So: the physics alone is far better than extrapolation and climatology and far worse than a modern global model past 6 hours; what it adds to a global model is the first 12 hours. Distilling those models into NatureV1 (below) is the route to their long-range skill; the physics is then the short-range half of the consensus.

Intensity, on the same unseen seasons (SHIFOR, a SHIPS-style regression, a logistic growth model with Kaplan-DeMaria land and terrain decay, all fitted on 2016/2017/2019 and blended per lead; mean absolute error of the peak wind, kt):

kt	6 h	12 h	24 h	36 h	48 h	72 h	96 h	120 h
persistence	4	8	14	19	23	28	31	32
NatureV1 intensity consensus	4	6	11	14	17	20	21	22
skill against persistence	+14%	+21%	+24%	+25%	+26%	+29%	+31%	+31%

Every interval is clear of zero and the consensus beats each of its members at every lead. That is the standard statistical-dynamical bar; operational models do better, and rapid intensification is still missed.

Hurricane Dorian (2019, a tuning season; weights fitted on 2016-2017 only): 21/49/99/164/249/480/656/810 km at 6-120 h against extrapolation's 23/52/131/237/365/641/897/1173 -- and 230 km against 341 at 48 h during the stall over the Bahamas -- while HRES scored 64 km at 24 h and Pangu 63.

Synthetic hard cases (naturev1.cyclone.synthetic: a Dorian-type col where the ridge fades and the trough stays away, ridge breakdown, trough capture, a loop, a Fujiwhara pair, a centre reformation, a sharp turn, a southern recurvature; truth integrated through the evolving flow, the forecast sees only the start): the physics beats extrapolation at 48 and 72 h in all nine (Dorian stall 344 vs 552 km at 48 h and 471 vs 961 at 72 h, the loop 56 vs 416 at 48 h), loses at 24 h in four, and loses at 120 h in four, where the scenario's flow is unlike Earth's climatology (CLIPER and the analogs pull toward real climatology). The stall is not flagged at the initial time when the col only forms later.

Genesis (naturev1.cyclone.genesis, northern hemisphere June-November, fitted on 2016/2017/2019, scored on 2018/2020-2022, 259 formations): Brier skill +0.22 over climatology, well calibrated (top third: forecast 12%, observed 13%); at a 30% threshold it flags 68% of formations a median 24 hours ahead with 52% false alarms.

Also new in 0.13, code ready and tested, not yet run on a GPU: multi-teacher distillation (naturev1.distill: every teacher resampled into NatureV1's grid, levels, steps and channels before any loss; skill-weighted mixture targets with an honest variance; rollout loss with an ERA5 anchor and extra weight near active cyclones), data assimilation for live inputs (naturev1.assimilation: bias correction, gross/background/buddy checks, local optimal interpolation with NatureV1's own predicted variance as the background error), and a 0.25-degree decoder (naturev1.highres) that reads the latent mesh directly. A one-GPU runbook runs all of it and publishes only if the distilled model beats the physics-only consensus.

4.13 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 (it follows the storm's intensity and wanders) and time. It is integrated in micro-segments of a few minutes and carries its own physics: steering-layer depth, beta drift, how far the flow's recent trend persists, how fast its departure from climatology fades, non-divergent steering perturbations, and a short-memory wobble.

The satellite path comes from NHC's fix deck: Dvorak fixes from GOES imagery, microwave, scatterometer, SAR, reconnaissance and radar centre fixes. Each fix has its own uncertainty. Fixes stream in at their own minute, and each one re-weights the worlds. Worlds that disagree with the storm are pruned and the survivors are resampled with genealogy. Fixes that arrive after the analysis re-weight the forecast itself.

The swarm is then painted onto the ground. The map holds every Caribbean country and territory, split into its parishes, provinces and districts: 309 units on a 3 km grid, with terrain. Each world contributes the asymmetric Holland wind field, gusts, and R-CLIPER rain with orographic enhancement on windward slopes. Every unit gets probabilities of tropical-storm, 50 kt and hurricane-force wind (and gusts), rain totals, a flash-flood signal on steep ground, and an arrival time. A million worlds run on one GPU. On a 4-core CPU it manages about 15,000 120-hour worlds a second, and 1,000 worlds painted over a Jamaica landfall take a minute.

Measured on the same unseen seasons (2018 and 2020-2022, 4,447 forecasts).

• Track: the swarm's own mean track beats extrapolation from 12 h (+2% to +22%), loses at 6 h (−9%), and is well behind the consensus. So the consensus stays the track and the swarm is re-centred on it.
• Cone: calibrated on the tuning seasons, the swarm's cone covers 57-64% of positions, against 60-65% for the fixed cone, at about the same size. It is not better yet: its spread barely predicts the consensus's error (rank correlation 0.06-0.13).
• Scenarios: what it adds is these. The probability of a Dorian-type stall has Brier skill +0.08 over climatology, and the probabilities line up with outcomes: forecast 5% → stalled 8%, 17% → 25%, 33% → 38%. Loop probabilities are reliable (forecast 2.2%, observed 2.1%). Recurvature and steady-track probabilities are no better than climatology.

Hurricane Melissa (2025), replayed with only what was known at the time. The inputs were the GFS analysis, the best track to then, and the 21 merged satellite, recon, microwave and scatterometer fixes of the previous 24 hours.

• From 00 UTC on 27 October, about 41 h before the Category 5 landfall, the consensus missed the northward turn and took the storm west-south-west of Jamaica.
• The swarm still put western Jamaica at risk: Westmoreland, St Elizabeth, Hanover, Manchester and St James were the most threatened parishes, at 13-20% for hurricane-force wind and 55-70% for tropical-storm wind, with the heaviest rain on St Elizabeth's and Manchester's slopes. That is where the worst damage was.
• It was far too low. Melissa's best track puts hurricane-force wind over 12 of the 14 parishes and 250-480 mm of rain over them, against forecasts of 110-175 mm. The intensity consensus forecast 111-125 kt for a storm that reached 160 kt: rapid intensification to Category 5 is beyond these statistical models.
• From 26 October, extrapolation beat the consensus from 12 to 48 h while Melissa crawled.

Section 4.14 shows the same forecast after the 0.13.1 upgrade, which fixes the missed turn.

One notebook cell runs all of this for every active NHC storm, or replays any storm since 2021, on one GPU. Research model, not an operational forecast: storm surge is not modelled. Boundaries are from geoBoundaries (OpenStreetMap and others; attribution travels with the map) and terrain from the Terrarium tiles on AWS Open Data.

4.14 0.13.1: the turns, and rapid intensification

A storm turns when its steering changes: a trough digs in, a ridge erodes. The analysis, even with its 12-hour trend, cannot see a trough that is still 2,000 km and two days away. A dynamical model's forecast can. 0.13.1 uses that forecast the way NHC's Beta and Advection Model does, and blends in the model's own track:

• Forecast-flow member. The storm is carried through the model's forecast 850-400 hPa winds, every 12 hours to 120 h, plus beta drift and the part of its present motion those winds do not explain. At each forecast hour, the model's own copy of the storm is found in its pressure field and removed from its winds, so the storm is steered by the environment rather than by itself.
• Model blend. The consensus, now with the forecast-flow member, is pulled toward the model's own track by one weight per lead, fitted on the tuning seasons: 0.2 at 6 h, 0.7 at 24 h and 0.9 by day 3. One weight per lead transferred cleanly between seasons. Fifteen free per-member weights did not, at 96-120 h.
• Live, the model is GFS: GFSAnalysis.forecast_flow reads its forecast winds and pressure from NOAA's bucket, about 150 MB per storm, cached. In the hindcasts it is ECMWF HRES from WeatherBench 2, at 1.5 degrees in both cases.

Track, held-out seasons 2018 and 2020-2022 (4,188 forecasts at 6 h, 1,103 at 120 h; every gain over the old consensus has its whole 90% storm-bootstrap interval above zero):

lead (h)	6	12	24	36	48	72	96	120
0.13.0 consensus (km)	29	59	127	207	301	512	711	874
HRES's own track (km)	49	60	79	100	123	187	251	326
0.13.1 consensus (km)	26	45	72	96	120	184	249	326
gain over 0.13.0	12%	24%	43%	54%	60%	64%	65%	63%
gain over HRES alone	48%	25%	8%	4%	2%	2%	1% (n.s.)	0% (n.s.)

• Storms that turned. On the 561 forecasts whose true track turned by more than 45 degrees between 24 and 72 h, errors fell from 131 / 326 / 601 / 1,048 km to 71 / 119 / 209 / 363 km at 24 / 48 / 72 / 120 h.

• Cone. Recalibrated for the new consensus (27 km at 6 h to 413 km at 120 h), it covers 63-70% of held-out positions against a 67% target.

• Swarm scenarios. The swarm's worlds are now steered by the same forecast winds, which markedly improves its scenario probabilities. Measured on 1,200 held-out forecasts (287 storms with a complete 120-hour truth):

  Brier skill vs climatology	recurve	stall	steady	loop
  swarm, analysis steering	+0.05	+0.09	+0.01	+0.01
  swarm, forecast steering	+0.26	+0.20	+0.14	−0.25

  Recurvature probabilities are now reliable: forecasts of 33% verified 41% of the time, and 63% verified 67%. Loops got worse. The swarm now forecasts them three times too often (6.4% against 2.1% observed), so treat its loop probability as unreliable. The swarm's cone still sizes uncertainty no better than the fixed one (rank correlation with error 0.09-0.22).

Intensity: a rapid-intensification switch. A logistic model gives the probability of a 30 kt rise in 24 hours from SHIPS-RII-style predictors: recent change, intensity, headroom below potential intensity, shear, humidity, ocean heat, latitude and land. On the held-out seasons its Brier skill over climatology is +0.10 and its AUC 0.81, and it is reliable up to about 50%. When it reaches 15%, the intensity consensus switches to weights fitted on such storms. Those lean on LGEM and a new trend member, which carries the last 24 hours' change forward with a 24-hour memory, capped at the potential intensity and decayed over land.

On all held-out storms the switch lowers the mean absolute error by 0.9-2.6% from 6 to 72 h, every lead significant, and is neutral at 96-120 h. On the 72 forecasts with P(RI) ≥ 30% it lowers the error by 5-10% from 6 to 36 h. physics_forecast now also returns ri_probability and intensity_regime.

Melissa, replayed again with only what was known at the time:

track error (km), lead (h)	6	12	24	36	48	72	96	120
from 27 Oct 00Z, 0.13.0	2	12	35	187	392	892	1,834	3,383
from 27 Oct 00Z, 0.13.1	5	17	91	55	79	246	369	1,011
from 26 Oct 00Z, 0.13.0	14	29	69	149	236	588	992	1,794
from 26 Oct 00Z, 0.13.1	17	28	69	140	215	294	394	375

• From 27 October, about 41 hours before landfall, the track now curves north into Jamaica. The forecast puts the storm at 18.0N 78.0W at 36 h, against an actual 17.5N 78.1W.
• Parishes. Every parish now gets a 24-47% chance of hurricane-force wind, up from 13-20%. St Elizabeth, Manchester and Westmoreland are highest. The four parishes the best track gave only tropical-storm winds (St Andrew, St Thomas, Kingston and Portland) are the four lowest.
• Rain. The forecast is 165-261 mm per parish, against a best-track swath of 146-431 mm (it was 110-175 mm in 0.13.0).
• From 26 October, extrapolation still wins to 48 h while Melissa crawled, because GFS turned it north too early that day.
• Intensity is still missed. From 26 October, P(RI) was 26% and the rapid weights were used, yet the forecast was 107 kt at 24 h against 125 kt observed, and 100 kt at 48 h against 155. Taking an already intense storm to Category 5 is still beyond these statistical models.

What to keep in mind. Much of the new track skill comes from a dynamical model: HRES in these hindcasts, GFS live. GFS has historically tracked storms somewhat less accurately than HRES, so live errors will likely be larger than this table, and the cone may run slightly narrow. Without GFS's forecast, for example if NOAA's bucket is unreachable, the forecast falls back to the 0.13.0 consensus and cone, and the run says so.

4.15 0.14: several models at once, a cone sized per forecast, and a swarm on several models

Why the long-range errors were what they were. After 0.13.1 the consensus had become, from 72 h on, essentially the one model it was blended with (HRES in the hindcasts, GFS live): 184 / 249 / 326 km at 72 / 96 / 120 h against HRES's own 187 / 251 / 326. One model's error is the floor you reach that way. Two ideas that sounded right were measured and turned out wrong, so they are not in the release: anchoring the model's track to the observed position (NHC's "interpolated" models) made the blend worse at 6-24 h on the held-out seasons, because it makes the model's short-range error correlated with the physics consensus's and the averaging benefit disappears; and shrinking the model's weight when it disagrees with the forecast-flow member was worse at every lead, because when they disagree the model is still the better of the two.

What does work is the oldest result in track forecasting: several independent models, averaged with equal weight.

Held-out seasons 2018 and 2020-2022, forecasts with at least two archived models (4,205 of 4,447; the models are HRES, Pangu-Weather, GraphCast, FuXi, Aurora and FGN, whichever WeatherBench 2 holds for the date; no weight fitted to them):

lead (h)	6	12	24	36	48	72	96	120
0.13.1: consensus blended with HRES (km)	26	45	72	96	120	184	249	326
equal-weight model mean alone (km)	44	51	64	79	93	140	195	256
0.14: consensus blended with the model mean (km)	25	42	64	81	96	142	200	263

Every gain from 24 h on has its whole 90% storm-bootstrap interval above zero. The physics still earns its place at 6-12 h, where it beats the models' mean by 18-43%; from 24 h on the forecast is mostly the models' mean. That is the honest shape of it: the physics knows the next day, the models know the week.

Live, the models are GFS, ECMWF IFS and AIFS Single (ECMWF open data, CC-BY-4.0), NOAA's GraphCast-GFS and the GEFS ensemble mean (with its spread as a diagnostic), each read by byte range from its public bucket into the same 1.5-degree boxes the physics was fitted on (naturev1.swarm.models). Any model not yet published for a cycle is skipped. For replays older than about four days the ECMWF models come from the AWS mirror, which throttled every request from this session's network, so the Melissa replay below uses the three NOAA models.

A cone sized for this forecast. The cone is now a regression of the consensus's error on how far the physics members spread, how far the model mean sits from the physics consensus, how far the forecast-flow member sits from the model, the storm's speed, latitude and intensity (Goerss's GPCE idea), fitted on the tuning seasons and scaled to 67% coverage. On the held-out seasons its radius ranks the actual errors with a correlation of 0.17-0.38 (the fixed cone, by construction, 0; the swarm's own spread 0.09-0.22) at 64-71% coverage, about 5-10% wider on average than the fixed cone it replaces. The fixed cone is still returned alongside it.

The swarm: a tuning that did not survive the held-out test. With forecast steering the swarm's spread had been three times the consensus's error at 72-120 h, and that excess motion looked like the reason it forecast loops three times too often. Cutting the steering-error and residual perturbations to a quarter did bring its spread to within 12-24% of the error on the tuning seasons and raised every scenario's skill there. On the held-out seasons it did the opposite: the quieter swarm was over-confident (where it said 72% stall, 43% stalled), stall skill fell from +0.20 to +0.02, steady from +0.14 to +0.06, and the loop over-forecast got worse. The spread that is right for the swarm's positions is not the spread that is right for its scenarios, because the swarm is re-centred on a consensus that is better than its own mean. So 0.14 keeps the 0.13 priors, and the 0.13.1 scenario scores stand: recurvature +0.26, stall +0.20, steady +0.14, loops unreliable.

What did change: each world now follows one model's forecast winds, drawn with equal probability (live: the models read for that cycle), so the swarm's futures carry the disagreement between models the way an ensemble does. Checked on the 2019 tuning season with HRES and Pangu-Weather as the two models (120 forecasts, 33 storms with a full five-day truth): the two-model swarm's spread and scenario skill were the same as the one-model swarm's to within noise, because at 1.5 degrees those two models' layer-mean steering is nearly identical (correlation 0.999 at 24 h). The latent only matters when models disagree, which the live set does more often (on Melissa, below, GraphCast-GFS and the GEFS mean parted by 300 km at 72 h). It is not yet scored on the held-out seasons.

Intensity: the models' own deepening. The one thing the statistical intensity members cannot know is what a dynamical model does with the storm. 0.14 reads each model's central pressure along its own track, takes the change in its pressure deficit (central minus environmental pressure) from the analysis, and uses the models' mean deepening twice: as a sixth intensity member (V0 plus 0.7 kt per hPa at 6 h rising to 2.4 kt per hPa at 48 h, fitted on the tuning seasons, capped at the potential intensity and decayed over land) and as three more predictors of the rapid-intensification probability. In the hindcasts the model is HRES at 1.5 degrees; live it is the mean over the models read.

Held-out seasons, mean absolute intensity error (kt), the 0.13.1 regime consensus against the same with the model member (every lead significant):

lead (h)	6	12	24	36	48	72	96	120
0.13.1	4.1	6.4	10.6	14.0	16.7	20.3	21.4	22.5
0.14	4.1	6.3	10.1	13.1	15.5	19.1	20.6	21.8
gain	0.9%	1.8%	4.8%	6.3%	7.2%	5.9%	3.5%	3.1%

The rapid-intensification probability improves from Brier skill +0.096 / AUC 0.813 to +0.123 / AUC 0.840. Where it says 30% or more (98 held-out forecasts), 39% intensified rapidly; above 50% (23 forecasts) only 26% did, so the top of the scale is over-confident. On those 98 forecasts the point forecast itself is no better than 0.13.1's: the member helps on the broad population of storms, not yet on the extreme ones.

Category probabilities. physics_forecast now returns P(≥ 64 / 96 / 113 / 137 kt) at every lead, from the forecast plus the empirical distribution of the consensus's out-of-sample errors on the tuning seasons (25 quantiles per lead, separately for the normal and the rapid regime). Held-out Brier skill over climatology:

threshold	24 h	48 h	72 h	120 h
hurricane (≥ 64 kt)	+0.65	+0.45	+0.38	+0.36
major (≥ 96 kt)	+0.48	+0.30	+0.26	+0.17
Category 4 (≥ 113 kt)	+0.36	+0.23	+0.17	+0.10
Category 5 (≥ 137 kt)	+0.18	+0.10	+0.11	−0.01 (19 cases)

Skilful everywhere except Category 5 at day 5, where there were nineteen cases to score on.

Melissa, replayed a third time with only what was known at the time. The ECMWF models could not be fetched for October 2025 from this session's network, so the models are GFS, GraphCast-GFS and the GEFS mean.

track error (km), lead (h)	6	12	24	36	48	72	96	120
from 27 Oct 00Z, 0.13.0	2	12	35	187	392	892	1,834	3,383
from 27 Oct 00Z, 0.13.1 (GFS)	5	17	91	55	79	246	369	1,011
from 27 Oct 00Z, 0.14 (three models)	3	13	56	46	69	194	274	700
the three models' mean alone	18	13	66	60	100	238	264	590
from 26 Oct 00Z, 0.13.1 (GFS)	17	28	69	140	215	294	394	375
from 26 Oct 00Z, 0.14 (three models)	14	23	44	85	150	261	362	271

• From 27 October the models disagreed usefully: GraphCast-GFS had the track to 198 km at 96 h, the GEFS mean to 284 km at 120 h, GFS to 971 km; their mean, blended with the physics, beat each of them to 72 h. The cone sized for this forecast (12 / 48 / 138 / 232 / 814 km at 6 / 24 / 48 / 72 / 120 h) contained the truth at every lead but 24 h, where the error was 56 km against a 48 km radius.
• From 26 October, GraphCast-GFS alone was remarkable (25 km at 36 h, 123 km at 72 h); GFS and the GEFS mean turned the storm north a day too early, and the blend landed between them.
• Parishes from 27 October: 30-43% for hurricane-force wind over the western and central parishes the storm crossed (St Elizabeth 43%, Manchester 41%, Westmoreland 39%), 22-25% over the eastern parishes it spared -- about where 0.13.1 had them, because the swarm's spread, not the consensus track, sets these probabilities. Rain 153-243 mm per parish against 146-431 mm observed.
• Intensity is still the miss: 114 kt at 24 h from 27 October against 155 kt observed; from 26 October the rapid regime was used (P(RI) 22%) and the forecast reached 109 kt against 145. At 1.5 degrees the models deepened Melissa by only 3-13 hPa, so the new deepening member had little to say here; it earns its keep on the broad population of storms, not on this one.

What to keep in mind. The held-out gains were measured with the models WeatherBench 2 archives; live, the set is different (GFS, IFS, AIFS, GraphCast-GFS, GEFS mean), and the blend weight was fitted for one model. The cone regression did not see inter-model spread in training, since the tuning seasons had one model. The model-deepening member was fitted on HRES's pressure at 1.5 degrees; other models deepen storms differently at that resolution. Everything here degrades gracefully: with no model readable, the forecast is the 0.13.0 one and says so.

4.16 0.15: the ocean's depth, storm size, and the benchmark table

Track: what 0.14 beats, on each reference's own held-out cases (2018 and 2020-2022; mean error in km, reference → NatureV1 0.14; * = the whole 90% storm-bootstrap interval of the improvement is above zero).

reference	n (24 h)	12 h	24 h	48 h	72 h	120 h
extrapolation (6 h motion)	3,559	71 → 41 (+42%*)	179 → 66 (+63%*)	440 → 100 (+77%*)	747 → 149 (+80%*)	1,417 → 301 (+79%*)
CLIPER (rebuilt)	3,559	67 → 41 (+39%*)	163 → 66 (+59%*)	376 → 100 (+74%*)	587 → 149 (+75%*)	910 → 301 (+67%*)
NatureV1 0.13.0 (physics only)	3,559	56 → 41 (+27%*)	127 → 66 (+48%*)	299 → 100 (+67%*)	512 → 149 (+71%*)	879 → 301 (+66%*)
NatureV1 0.13.1 (one model)	3,559	43 → 41 (+4%*)	73 → 66 (+10%*)	122 → 100 (+18%*)	190 → 149 (+22%*)	373 → 301 (+19%*)
ECMWF HRES	3,504	56 → 40 (+27%*)	79 → 65 (+18%*)	122 → 96 (+22%*)	185 → 140 (+24%*)	324 → 260 (+20%*)
Pangu-Weather	3,456	52 → 40 (+24%*)	69 → 63 (+9%*)	101 → 94 (+6%*)	151 → 139 (+8%*)	278 → 254 (+8%*)
GraphCast	1,862	48 → 40 (+17%*)	67 → 65 (+4%*)	102 → 97 (+5%*)	162 → 143 (+11%*)	294 → 260 (+11%*)
FuXi	734	49 → 39 (+19%*)	69 → 64 (+7%*)	93 → 94 (−1%)	154 → 146 (+5%)	295 → 279 (+6%)
Aurora	786	49 → 41 (+18%*)	66 → 62 (+6%*)	92 → 84 (+9%*)	146 → 123 (+16%*)	312 → 249 (+20%*)
FGN (WeatherNext 2)	787	47 → 41 (+13%*)	61 → 63 (−2%)	81 → 86 (−7%)	111 → 118 (−7%)	199 → 209 (−5%)

Read it plainly. NatureV1 now beats every archived model it was compared with at 12 h, beats HRES, Pangu, GraphCast and Aurora at every lead to day 5, and is level with FuXi past 24 h. It does not beat FGN, the model behind WeatherNext 2, past 12 h: on FGN's 787 cases (2022) FGN alone is 5-7% better than the blend from 24 h on, which is what an equal-weight mean does when one member is clearly the best -- it is diluted by the others. Two caveats carry over from 4.15: the blend contains these models' own tracks, so this is a product comparison, not a physics-versus-model one; and live the model set is different (GFS, IFS, AIFS, GraphCast-GFS, GEFS), with the blend weight fitted for one model.

Landfall, answered the way a parish needs it. naturev1.swarm.landfall turns the swarm and the consensus into: when the centre comes ashore (the median and the 10-90% range over the worlds, with dates, in UTC), which parish it crosses first and with what probability, the intensity at the consensus landfall time with its calibrated 10-90% band, the peak intensity and when it comes, and for every parish the expected peak sustained wind, peak gust, the 90th percentile of the peak over the worlds, rain, and the times tropical-storm force and hurricane force arrive and the peak passes. plot.landfall_figure draws it; the molab cell shows it for LANDFALL_COUNTRY. The wind field is now sized to the storm's observed 34-kt radius from the best track, and the worlds' intensities are drawn from the forecast's own calibrated error distribution for the storm's regime instead of a fixed ±8%.

Observations that survive a landfall. naturev1.swarm.observations holds two operators for feeds this package does not yet read: a vortex fitted to any set of barometer readings (phones, watches, home stations -- pressure goes through walls) gives a centre fix with its uncertainty, a central pressure and a wind, which the swarm filters like a satellite fix; and point wind observations are blended into the painted wind map by optimal interpolation. Both are checked on constructed storms (300 phone-grade readings place a 935 hPa centre to within 12 km and 1 hPa). No telecom signal-loss or crowd-sourced pressure data was available to train on, so nothing here claims to infer wind from it; the physics that would use such data is in place. A terrain boundary-layer term (windward speed-up, lee sheltering, Jackson-Hunt scaling) is in ImpactSettings.terrain_speedup_per_slope, off by default, because it has not been verified against station winds here.

The ocean's depth: what the measurement said. Melissa's lesson was that a storm crawling over 120 m of 26 C water does not cool its own ocean the way one over 30 m does, so 0.15 brought in the World Ocean Atlas climatology of the 26 C depth and the heat potential, let the wake cooling scale with that depth, let this year's sea-surface anomaly deepen or shoal the climatological layer, and put the heat potential and the storm's observed size into the SHIPS and rapid-intensification predictors. Each piece was then chosen on the tuning seasons by cross-validation, and the cooling term lost: with no depth dependence at all the LGEM member's 12-72 h error was 15.32 kt; with any depth exponent (0.25-1.0) or any anomaly coefficient it was 15.43-15.56 kt, and the same held on the 349 forecasts over water more than 1 C warmer than the climatology. A monthly 1-degree climatology does not know the water under one storm well enough to improve on the surface temperature the analysis already has. The depth term is in the code with its exponent set to zero by the fitted coefficients; the heat potential and the size are scored below as predictors. Intensity: each release's shipped tables on the same held-out cases (2018 and 2020-2022, 4,215 forecasts of 407 storms at 6 h; mean absolute error in kt; skill = % lower error than the row above it, * = the whole 90% storm-bootstrap interval above zero).

	6 h	12 h	24 h	36 h	48 h	72 h	96 h	120 h
persistence	4.4	8.1	14.3	18.9	23.0	28.3	30.9	32.2
SHIFOR (climatology + persistence)	4.0	6.9	11.7	15.5	18.3	21.2	22.3	22.8
NatureV1 0.13.1 (5-member regime consensus)	3.8	6.4	10.8	14.3	17.0	20.1	21.3	22.3
NatureV1 0.14 (+ model deepening)	3.7	6.2	10.1	13.1	15.5	18.9	20.6	21.8
NatureV1 0.15 (+ ocean heat content, size, basin bias)	3.7	6.1	9.9	13.0	15.5	18.9	20.6	21.7
0.15 vs 0.14	+0.9%*	+1.3%*	+1.3%*	+0.8%	+0.4%	−0.4%	+0.0%	+0.3%
0.15 vs SHIFOR	+6.6%*	+10.7%*	+15.5%*	+16.1%*	+15.1%*	+10.9%*	+7.7%*	+4.7%*
0.15 vs persistence	+16.2%*	+24.8%*	+30.7%*	+32.5%*	+32.7%*	+33.2%*	+33.4%*	+32.6%*

Where the ocean and the size earned their place is the rapid-intensification probability, not the mean: held-out Brier skill 0.094 (0.13.1) → 0.122 (0.14) → 0.154 (0.15), AUC 0.813 → 0.840 → 0.864; of the 107 forecasts that put P(RI) at 30% or more, 46% verified (39% in 0.14). On the held-out forecasts over the warmest, deepest water (slow storms over more than 80 kJ/cm², 54 cases) the mean error fell 4-9% at 6-36 h. The per-basin bias was fitted on the tuning seasons and then shrunk to zero wherever the three seasons did not agree on its sign: what survives is +0.6 to +3.7 kt in the Atlantic and −0.5 to −2.4 kt in the west Pacific at 6-48 h. Honest footnote: the unshrunk Atlantic bias (up to +4.2 kt) made the held-out Atlantic worse (−0.2 to −3.5% at 36-72 h) -- the under-forecast of the tuning seasons' Atlantic was situational, not a constant -- and the unshrunk table would have scored +1.7%* and +2.7%* at 96 and 120 h overall on the strength of a south Indian Ocean term the seasons disagreed on. The shrunk version is what ships.

Why it under-forecasts the wind, measured. The complaint about Melissa -- the consensus held 103-124 kt while the storm went to 160 -- is not a bias. Over all held-out cases the 0.15 forecast is 0 to +3 kt high in the Atlantic. It is conditional (bias = forecast − truth, kt, at 12 / 24 / 36 / 48 h):

the storm then...	n	12 h	24 h	36 h	48 h
intensified ≥ 30 kt in 24 h (rapid)	272	−10.9	−25.5	−26.4	−21.3
intensified 20-30 kt	332	−5.2	−10.9	−13.4	−13.5
held steady (±5 kt)	891	+0.7	+3.5	+5.7	+7.3
weakened ≥ 20 kt	328	+7.8	+14.2	+17.4	+17.9

The forecast maximum over the next five days sits 30 kt under the true maximum for the 620 held-out forecasts of storms that went on to reach 113 kt. A consensus that minimises the mean error regresses toward the middle; no weighting fixes that, and every attempt to move the mean toward the rapid intensifiers' path in proportion to P(RI) came back with a weight of zero on the tuning seasons (and would have cost the 4,173 held-out cases that did not intensify rapidly 2-3 times their error). Two things do help, and both ship:

• The rapid-intensification path as a scenario (intensity_if_ri, coefficients.RI_PATH): the mean change of the 217 tuning-season storms that did intensify rapidly (+9/+19/+40/+44/+37 kt at 6/12/24/36/48 h), capped at the potential intensity along the track and decayed over land. On the 272 held-out forecasts of storms that did go rapid it beats the consensus by 21%, 35%, 60%, 37% and 8% at 6-48 h; on the ones that did not it is 2-3 times worse. It is therefore issued beside the consensus with its probability, never blended into it. Mixing it into the category probabilities was tried and switched off: better at ≥96 and ≥113 kt at 24 h, worse at ≥137 kt and at every threshold from 48 h on.

• The peak-intensity probability (peak_probability, coefficients.PEAK): P(the storm's peak within the next 120 h reaches 64 / 96 / 113 / 137 kt), a logistic on the analysis intensity, the consensus's rise and maximum, the warm-ocean headroom, heat content, shear, humidity, P(RI), the model's deepening and the land ahead. Held-out, for storms below each threshold at analysis time (Brier skill against climatology; the second number is the best a user had before, the maximum over leads of the per-lead category probability):

  threshold	n	base rate	peak logistic	per-lead maximum	reliability (forecast → observed)
  ≥ 64 kt (hurricane)	1,969	0.41	0.32	0.26	0.15→0.13, 0.40→0.31, 0.60→0.56, 0.84→0.84
  ≥ 96 kt (major)	2,472	0.22	0.31	0.22	0.15→0.09, 0.39→0.37, 0.59→0.60, 0.82→0.80
  ≥ 113 kt (category 4)	2,616	0.16	0.28	0.15	0.14→0.15, 0.25→0.25, 0.39→0.41, 0.59→0.53, 0.83→0.82
  ≥ 137 kt (category 5)	2,785	0.05	0.28	0.16	0.07→0.06, 0.14→0.15, 0.24→0.34, 0.40→0.54

  The landfall report now opens with it ("chance the storm peaks at or above: hurricane 100%, major 62%, category 4 31%, category 5 8%"), which is the sentence a parish needs when the point forecast says 107 kt.

The track, fed its own recent error. A model track's error persists from one cycle to the next: the previous cycle's forecast for the time now being analysed, minus the analysis, is known at analysis time, and a fitted share of it is subtracted from the new blended track (apply_track_feedback, coefficients.TRACK_FEEDBACK; pass the previous cycle's result as previous=). Fitted on the tuning seasons' HRES blends, the share is 0.25-0.34 at 24-48 h for a 24 h gap and zero beyond 48 h, where it did harm. Held-out, on the multi-model blend: +0.2%, +1.1%, +1.2%*, +0.4% and +0.2% at 6-48 h. Small and significant, and the honest size of what "learning from the storm's own behaviour" is worth once the blend already removes the initial-position offset (on the raw HRES track the same idea is worth 5-11% at 6-24 h, which is that offset).

Rain, calibrated against radar. R-CLIPER (Tuleya et al. 2007) was run along the observed track of 24 US landfalls -- so track and intensity error are removed and only the rain model is tested -- against NOAA MRMS gauge-corrected radar storm totals on 0.05°, over land within 300 km of the track: 8 tuning storms (Hermine, Matthew, Harvey, Irma, Nate, Barry, Imelda, Dorian; 137,177 cells) and 16 held-out (Gordon, Florence, Michael, Hanna, Isaias, Laura, Sally, Delta, Claudette, Elsa, Fred, Henri, Ida, Nicholas, Ian, Nicole; 329,416 cells; Zeta lost a radar day). As published, R-CLIPER delivers about half the observed rain: the tuning storms' observed/forecast ratio is 1.91 (per storm 0.9-2.8), the area over 100 mm is a third of the observed, the area over 250 mm a sixth. The multiplier is set so the tuning storms' total is unbiased, ×1.95 (coefficients.RAIN_SCALE, ImpactSettings.rain_scale). Held-out:

	cell MAE (mm)	bias (mm)	area ≥ 100 mm, forecast ÷ observed	area ≥ 250 mm	99.5th pct	CSI ≥ 100 mm	CSI ≥ 250 mm	MAE where ≥ 100 mm fell
as published (×1.0)	31.3	−15.3	0.39	0.15	0.58	0.204	0.115	97
MAE-optimal on tuning (×1.2)	31.3	−9.4	0.55	0.36	0.70	0.239	0.180	88
shipped (×1.95)	38.4	+13.1	1.41	1.87	1.10	0.285	0.291	72

So the heavy rain is found far more often (the threat score for 100 mm rises from 0.20 to 0.29, for 250 mm from 0.12 to 0.29, in 13 of the 16 held-out storms) and the error where 100 mm or more actually fell drops by a quarter, at the price of too much rain in the light-rain cells (the held-out storms were less under-forecast than the tuning storms: ratio about 1.5 against 1.9), which is where the overall MAE and the +13 mm bias come from. A multiplier cannot fix R-CLIPER's shape -- too concentrated near the core, nothing for the outer bands and the remnant low -- and that is the next thing to build. One consequence was handled by hand: the US storms have no mountains, so the multiplier was calibrated with the orographic term at 1, and stacking it under the old orographic cap of 4 doubled the wettest cells of a perfect-track Melissa painting against Jamaica's 13 parish gauge maxima; the cap is now 2 (a 1.5-2.5x enhancement is what the literature finds on windward slopes). That is a choice informed by Melissa, not a verification, and it is marked as such. The parish numbers also changed form: the swarm-mean rain is diluted by every world that misses, so the landfall report now gives the rain if the parish is hit, its 90th percentile over the worlds, and the parish's wettest cell if hit (the number a rain gauge reports), next to the mean. Satellite rain was checked as a reference and rejected: CHIRPS put Melissa's 27-29 October total over Jamaica at a maximum of 158 mm against 817 mm in the gauges.

The swarm, sized to the forecast. The worlds' raw spread was never the calibrated one: cone_scale in the swarm tables (0.27-0.70 for the forecast-steered swarm) corrected the reported cone, but the strike probabilities, the landfall probability and timing and every parish number are made from the raw worlds, which on the held-out cases were 1.4 to 3.2 times (median, 6 to 120 h) wider than the flow-dependent cone. 0.15 rescales every world's displacement about the consensus so the swarm's own 67% radius equals the cone sized for this forecast (CONE_FLOW: tight when the models agree, wide when they do not; swarm_products(target_cone_km=...), the affine rescale_worlds). Verified on 396 held-out forecasts of 2018 and 2020 (HRES-steered swarm, 4,096 worlds; the share of the truth inside the swarm's own 50 / 67 / 90% radii about the consensus, 6 h → 120 h):

	50% radius	67% radius	90% radius
raw worlds (0.14)	0.69 → 0.98	0.81 → 0.99	0.93 → 1.00
sized to the cone (0.15)	0.50, 0.51, 0.58, 0.56, 0.53, 0.59, 0.63, 0.63	0.65, 0.64, 0.70, 0.71, 0.69, 0.73, 0.74, 0.75	0.87, 0.87, 0.86, 0.87, 0.90, 0.89, 0.89, 0.89

The 67% coverage is the flow-dependent cone's own (0.64-0.72 on the same cases), the 50% and 90% radii fall where they should, and the swarm's shape (its 50% and 90% radii are 0.79 and 1.47 times its 67% one) matches the truth's (0.64-0.79 and 1.50-1.66). Before this the swarm was spreading a Jamaica landfall over the whole western Caribbean; a world that misses by 300 km at 24 h no longer counts against the parish in its path.

Melissa, replayed cycle by cycle with 0.15. GFS, GraphCast-GFS and the GEFS mean (the ECMWF mirror is throttled from this network); a 20,000-world swarm; each cycle fed the previous cycle's track. What was issued, against what happened (landfall near New Hope, Westmoreland, 18.09N 77.97W, about 17 UTC on 28 October at 160 kt; peak 165 kt at 12 UTC):

forecast from	before landfall	P(landfall, Jamaica)	centre ashore, median (10-90%)	consensus landfall	intensity then (10-90%)	the RI branch (its probability)	P(peak ≥ cat 4 / cat 5)	track error 24 / 48 / 72 h
26 Oct 00 UTC	65 h	74%	28 Oct 03 UTC (27 Oct 18 → 28 Oct 15)	28 Oct 03 UTC, Clarendon	104 kt (72-140)	125 kt at landfall, peak 134 (24%)	63% / 29%	42 / 158 / 277 km
26 Oct 12 UTC	53 h	80%	28 Oct 15 UTC (06 → 21)	28 Oct 13 UTC, St Elizabeth	110 kt (79-146)	152 kt, peak 155 (20%)	100% / 32%	19 / 57 / 161 km
27 Oct 00 UTC	41 h	76%	28 Oct 15 UTC (09 → 21)	28 Oct 14 UTC, St Elizabeth, 18.12N 77.88W	110 kt (90-133)	153 kt, peak 162 (8%)	100% / 23%	43 / 74 / 215 km

Where it is now right: the landfall point (10 km from the actual at 41 h out), the landfall time (the median two hours early with the actual inside a 12-hour band, where 0.14 had put it eight hours early inside a 30-hour band), the parish ranking (at 27 Oct 00 UTC the ten parishes the best-track swath gave hurricane-force wind are the top ten by P(HU): St Elizabeth 84%, Westmoreland 77%, Manchester 72%, St James 71%, Trelawny 71%, Hanover 64%, Clarendon 56%, St Ann 53%, St Catherine 33%, St Mary 20%; the eastern parishes 9-15%; Brier 0.061 against the swath), and the landfall probability itself (76% where 0.14 said 41% from the same cycle -- the swarm sized to the cone, 4.16 above). Where it is still wrong, said plainly: the consensus intensity, 125 → 116 → 106 kt over the first 48 h against 135 → 155 → 165 → 105, is the under-forecast of section 4.16's table made flesh -- a storm in the top few percent of intensification over the deepest warm water in the basin. The branch that was the storm -- 153 kt at landfall, peak 162 -- was on the page from 26 October with its probability (24%, 20%, 8%), and the chance of a category-5 peak sat at 23-32% through all three cycles; a reader of the report had the right scenario and a fair probability for it, not a point forecast that said so. Parish timing ran 3-4 hours early (hurricane force into St Elizabeth at 09:20 UTC, the peak at 13:17, against an eyewall that arrived mid-afternoon), because the consensus moved the storm faster than the crawl it actually made. Rain, if hit / wettest cell against the NHC gauge maximum: Manchester 563 / 747 against 817 mm, St Elizabeth 547 / 787 against 508, Clarendon 483 / 668 against 530, St Catherine 432 / 593 against 668, Kingston 424 against 567 -- the right magnitude in the centre and south, now that the multiplier is in; too much in the far west, where the storm crossed quickest (Westmoreland 689 against 309, Hanover 603 against a single gauge at 146), and too little in the east (Portland 397 against 536), because R-CLIPER puts the rain under the strongest wind and Melissa's two days of crawling south of the island fed the Blue Mountains and St Catherine instead. melissa_jamaica.png shows the four releases side by side from 27 October 00 UTC.

4.17 0.16: the official guidance as members, the model's own rain, and the answer key

The NHC's public a-deck carries every operational aid's track and intensity for a cycle within minutes of the synoptic time. 0.16 reads it (naturev1.swarm.adeck) and blends the aids in with tables fitted on the tuning seasons (naturev1.cyclone.aids, coefficients.ADECK_TRACK / ADECK_INTENSITY). Everything below is on the held-out seasons 2018 and 2020-2022, Atlantic cases where the guidance exists, homogeneous across the rows (749 / 703 / 626 / 554 / 490 / 374 / 281 / 206 cases at 6 / 12 / 24 / 36 / 48 / 72 / 96 / 120 h; 79 storms); * marks a whole 90% storm-bootstrap interval above zero. The 6 h column of every aid is an interpolation between its analysis and its 12 h point, so it flatters nobody but us; read the aids from 12 h on.

Track (mean error, km). The rule chosen on the tuning seasons -- with our own track cross-fitted by season so that it was scored out of sample like the aids -- was the plain mean of our multi-model blend and HCCA; the fitted simplex over HCCA, TVCN, the GEFS mean and the GFS came within 0.2% of it there, so the mean ships.

	6 h	12 h	24 h	36 h	48 h	72 h	96 h	120 h
NatureV1 0.14 blend	22.1	40.1	62.2	82.3	95.5	168.7	260.5	365.1
NatureV1 0.16 = mean(0.14 blend, HCCA)	21.5	35.7	54.1	72.5	89.4	149.6	227.7	318.7
0.16 against 0.14	+2.8%	+11.0%*	+13.0%*	+11.9%*	+6.4%*	+11.4%*	+12.6%*	+12.7%*
HCCA (HFIP corrected consensus)	29.9	40.7	60.3	80.7	104.6	170.5	253.8	363.9
TVCN (track consensus)	29.8	41.8	62.7	84.5	109.5	170.0	248.8	346.5
OFCL (NHC official forecast)	27.6	42.4	64.1	84.9	109.2	169.4	241.6	334.4
0.16 against the official forecast	+22.0%*	+15.9%*	+15.5%*	+14.6%*	+18.1%*	+11.7%*	+5.8%	+4.7%

On the tuning seasons the same mean gained 2% -- there our blend leaned on HRES, which HCCA also contains; on the held-out seasons the blend is a six-model AI-heavy mean whose errors are more independent of HCCA's, and the gain is five times larger. Two things to read with it: HCCA reaches the a-deck about two and a half hours after the synoptic time (our cycle waits for the GFS analysis anyway, which is later), and the official forecast is written by forecasters from this same guidance, so the last row is a product comparison, not a claim about who sees the atmosphere better.

Intensity (mean absolute error, kt). Smooth-L1 simplex weights per lead over our 0.15 consensus and the early-cycle aids; leave-one-season-out on the tuning seasons the blend gained 13-28% at 24-96 h in 2016, 2017 and 2019 alike. HAFS-A and HAFS-B take the HWRF and HMON slots when those are absent, a stand-in by lineage that the archive could not verify and that the record reports.

	6 h	12 h	24 h	36 h	48 h	72 h	96 h	120 h
NatureV1 0.15 consensus	3.4	6.0	9.6	12.2	13.9	16.2	18.4	18.8
NatureV1 0.16 = 0.15 + aids	3.3	5.4	7.1	8.5	9.5	10.5	12.5	12.8
0.16 against 0.15	+2.9%*	+9.9%*	+26.0%*	+30.6%*	+31.4%*	+35.1%*	+32.0%*	+32.3%*
IVCN (intensity consensus)	4.3	5.5	7.2	8.5	9.4	10.7	12.7	13.8
HCCA	4.3	5.5	7.2	8.7	9.6	11.1	12.5	13.0
HWRF (HWFI)	4.6	6.2	8.0	9.4	10.6	13.3	15.3	16.3
SHIPS with decay (DSHP)	4.5	6.1	8.4	10.2	11.6	13.4	16.3	18.3
LGEM	4.5	6.4	9.0	11.1	12.2	13.3	15.8	17.5
OFCL (NHC official forecast)	3.6	5.0	7.4	8.8	10.1	11.2	12.4	13.4
0.16 against the official forecast	+6.4%	−7.9%	+4.9%	+4.5%	+5.9%*	+6.1%	−0.7%	+4.6%

The weights say what the archive thinks of us: our consensus carries 78% of the blend at 6 h, 54% at 12 h, 20% at 24 h and nothing from 48 h on, where HCCA, IVCN and the hurricane models take over. The one thing the aids do not fix is the thing this roadmap started from: on the 39 held-out cases that intensified by 30 kt or more in the next day, the bias at 24 h moves from −23 kt (ours) to −21 kt (the blend), with the official forecast at −19 kt -- every mean forecast under-forecasts the explosive cases, which is why the calibrated peak quantiles and the RI branch (4.16) stay in the report beside the headline.

Rapid intensification, the NHC's probabilities beside ours. The SHIPS text carries the SHIPS-RII, logistic, Bayesian, DTOPS and consensus probabilities of +30 kt in 24 h; the season archive's e-deck carries the same after the fact -- but only from 2020, so there is no tuning-season sample and nothing here was chosen on one. On 2020-2022 (481 cases with the consensus, 453 with DTOPS; 25 and 24 events): ours Brier skill 0.125 (AUC 0.866), the SHIPS-RII consensus 0.068 (0.847), the deterministic SHIPS-RII 0.020, the logistic −0.070, the Bayesian 0.074, DTOPS 0.171 (0.866); the equal-weight mean of ours and the consensus 0.133, of ours and DTOPS 0.199. The mean with DTOPS is reported as ri_probability_combined in the cycle record and the cell with that caveat; ours stays the headline and the regime switch until a tuning-season sample exists.

The rest of the roadmap, briefly (ROADMAP_0.16.md has the matrix): the GFS's own accumulated rain travels with every world as half of its rain -- against gauge-corrected radar on US landfalls, Ida 23 vs 45 mm mean error, Nicholas 17 vs 55, Fred 21 vs 36, Ian level; the calibrated peak quantiles (coverage 0.53 / 0.77 / 0.91 / 0.95 at 50 / 75 / 90 / 95%, q90 four kt above the true peak of the category-5 storms where the consensus max sits 37 kt under) and E[peak | RI] (+0.6 kt bias on the storms that went rapid); the arrival-time window (3.6 h at 24 h overall, 7.3 h for storms under 3 m/s; no along-track bias found, so nothing is nudged); the cycle record and the previous cycle's feedback found automatically. Rejected on the tuning seasons and listed as such: the stall-over-water penalty, a translation-speed rain factor, a 115-kt rain saturation, nonlinear rain transforms, dynamic per-storm model weighting.

The answer key. benchmark_heldout_atlantic_2018_2020_2022.csv.gz in this repository holds the 849 held-out Atlantic cases with the best-track truth at every lead and every reference's forecast or error on them: NatureV1 0.14 and 0.16 tracks, 0.15 and 0.16 intensities, the official forecast and the aids (HCCA, TVCN, IVCN, HWRF, HMON, SHIPS, LGEM, GFS, GEFS mean), the archived models' track errors (HRES, Pangu, GraphCast, FuXi, Aurora, FGN), CLIPER and extrapolation. naturev1.cyclone.verify.compare scores a new forecast against it on the same storms with the storm-block bootstrap. One long table, one scoring function: a claim about a hurricane model can be checked on it.

Melissa replayed with 0.16 (the same three cycles as 4.16; the GFS rain member and the NHC guidance in, 20,000-world swarm; "own" is our blend before the aids, "official" the NHC forecast from the same cycle):

forecast from	before landfall	P(landfall, Jamaica)	centre ashore, median (10-90%)	consensus landfall	intensity then (10-90%)	the RI branch (its probability)	P(peak ≥ cat 4 / cat 5)	track error 24 / 48 / 72 h: 0.16 (own; official)
26 Oct 00 UTC	65 h	72%	28 Oct 09 UTC (27 Oct 21 → 28 Oct 21)	28 Oct 06 UTC, Clarendon	96 kt (64-132)	124 kt at landfall, peak 130 (23%)	62% / 28%	44 / 121 / 195 km (42 / 158 / 277; 34 / 123 / 124)
26 Oct 12 UTC	53 h	83%	28 Oct 12 UTC (06 → 21)	28 Oct 11 UTC, St Elizabeth	101 kt (71-136)	151 kt, peak 152 (19%)	100% / 31%	42 / 72 / 147 km (15 / 53 / 161; 40 / 54 / 73)
27 Oct 00 UTC	41 h	83%	28 Oct 15 UTC (09 → 21)	28 Oct 14 UTC, St Elizabeth, 18.06N 77.72W	98 kt (78-121)	149 kt, peak 160 (8%)	100% / 23%	54 / 71 / 212 km (38 / 69 / 215; 79 / 79 / 164)

What moved against 4.16: the landfall probability (76 → 83% at 41 h), the far-west rain (Westmoreland 413 mm if hit against the 309 mm gauge where 0.15 said 689; Hanover 407 against 146 where 0.15 said 603; Manchester 584 / 865 against 817, St Catherine 468 / 666 against 668, Kingston 466 against 567 -- the GFS's own rain pulls the total off the fast western crossing and onto the parishes that got it), the landfall point and time (14 UTC against about 17, the median 15 UTC inside a 12-hour band, as before). What moved the wrong way, said plainly: Melissa was not the archive. On the two earlier cycles the NHC guidance was worse than our standalone blend at 24-48 h -- at 26 Oct 12 UTC HCCA sat 70 km off at 24 h where our blend had 15 km, so the mean sat at 42; the intensity aids were all low on this storm and pulled the 48 h intensity from 110 to 100 kt (26 Oct 12 UTC) and from 106 to 85 kt (27 Oct 00 UTC) against a truth of 165 and 105 -- and the mean inherits what its members do. That is the price of a rule that lowers the error 11-13% over 626 held-out cases; the parish Brier against the swath went from 0.061 to 0.073 at 41 h. The averaging penalty, taken to the archive (the table below), and what ships for it, is in the next paragraph. The branch that was the storm -- 149-151 kt at landfall, peak 152-160 -- stayed on the page from 26 October with its probability, and the 95% peak quantile sat at 133-140 kt against the 165 kt that happened: the explosive case is still a tail event to this engine, as to the official forecast (140 kt at 24 h against 155). Parish timing still ran about four hours early (hurricane force into St Elizabeth at 08:20 UTC, the peak at 12:42, against an eyewall that arrived mid-afternoon), as the arrival window in the report now says it can. melissa_jamaica.png shows the four releases side by side.

The averaging penalty. A fixed 50/50 mean drags a member that caught a turn toward one that did not -- the 26 Oct 12 UTC cycle above. Whether that is the rule or the exception is a question for the archive, not for one storm. On the held-out Atlantic cases, split by how far our blend and HCCA sit apart at 24 h:

held-out cases	n	ours alone	HCCA	TVCN	50/50 mean	ours closer than HCCA	ours the outlier against TVCN
all with HCCA	641	62 km	60	63	54	--	--
the 20% that disagree most (≥ 92 km apart)	159	133	93	95	94	31%	97%
the 10% that disagree most (≥ 128 km apart)	80	220	101	106	138	16%	100%

When the two disagree strongly it is our standalone that is wrong two times in three, and the mean is a hedge that costs little when ours is right and saves a great deal when it is not. Every remedy that trusts the standalone in a disagreement was tried on the tuning seasons and lost there (ours 2/3, a disagreement gate toward ours, the median and the trimmed mean of ours, HCCA and TVCN). Two rules survived and ship in ADECK_TRACK: (1) weights earned from the previous cycle -- at issue time the previous cycle's forecasts of ours and of HCCA are verified against the position just analysed, and the split follows sigmoid(0.5 · log(e_HCCA / e_ours)) within 25-75% at 6-24 h (chosen per lead on the tuning seasons; nothing to earn beyond 24 h, so the split stays fixed there); (2) the outlier gate -- once the two sit more than 1.5 cone radii apart, up to 10% of the pair's weight moves away from whichever of them is further from TVCN (a tie with the plain mean on the tuning seasons, a loss at 6 h in every season, so it starts at 12 h). Together on held-out: 1.4% / 2.5% / 1.1% / 0.7% / 1.0% / 1.9% / 2.3% lower error at 12 / 24 / 36 / 48 / 72 / 96 / 120 h, every lead significant; in the most-disagreeing fifth, 94 → 89 km at 24 h. For the Melissa cycle that raised the question the earned split would have given ours 54% at 24 h (its previous 12 h forecast was 22 km off, HCCA's 33) and the gate nothing (the two were less than 1.5 cone radii apart) -- a few km back, not the 27 km lost, because the archive says that cycle was the exception. The disagreement is now reported per lead (aids_track["disagreement_km"]), the cell says when the two sit further apart than the cone, and both tracks are in the record for the forecaster who has reason to believe the standalone this time.

5. Limitations

• Resolution. 1.5° (~165 km) cannot resolve an eyewall, so intensity is the weakest output. The explicit environment inputs (shear, humidity, SST) were added to compensate; the red team shows they barely move the intensity forecast (section 4.8).
• Not operational. It runs on reanalysis, which is available days after the fact. There is no real-time analysis feed, and the satellite input path exists but is untrained.
• Verification is internal. Three held-out seasons plus the 2023 season, scored by this project's own scripts; no independent party has verified it.
• Intensity. Biased low, by 10–18 kt for major hurricanes; misses explosive intensification entirely (Otis). Rapid-intensification probabilities are calibrated in 0.11 but carry only modest skill; radius of maximum wind has no skill. The satellite stage targets this; its effect is measured when it is trained.
• Uncertainty display. The full scenario mixture is well calibrated; a single scenario's cone is over-confident. Use track_cone, drawn from the mixture.
• Input checks are statistical. The monitor catches inputs unlike training; a plausible but wrong input (another storm's features, a shifted steering prior) is not detectable this way.
• Other basins. At 24 h the learned track correction is worse than physics steering outside the Atlantic.
• Surface heads are stale. The direct multi-lead surface fields were not retrained after the rollout stage; use the full-state rollout for weather.
• Small data. Five years of reanalysis at 1.5°, and the storm heads start memorising after about three epochs.
• Atlantic only for the storm heads, 1979 onward; other basins are out of distribution.
• Training cost. About one week wall-clock on one GPU in a hosted notebook; most of the overhead was session restarts. A machine that keeps its disk would cut it to three or four days.
• Tornadoes, hail, flash floods are far below this resolution and out of scope.

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6. Using it

Install and train, or score, from one cell (marimo, Colab, Jupyter or a plain script):

pip install "naturev1[all]"            # 0.16 from PyPI
pip install "naturev1[all] @ git+https://github.com/Wisk-inc/transformers@claude/linear-context-architecture-a35c6h#subdirectory=natureweather"   # the development branch

The complete pipeline is one notebook cell; it installs what it needs, stages the data, trains in stages, scores itself, and only publishes if it earned it. Every setting is at the top.

Load the released model (weights, config and the normalisation statistics it was trained with):

from naturev1.hub import from_pretrained

model, config, normalizer = from_pretrained("CorxLabs/NatureV1-500")
print(model.trained_heads())      # steps each output has received; 0 = never trained, never shown

With satellite imagery (0.11, once stage three has been trained), from a live GOES ABI band 13 file:

import numpy as np
import torch
from naturev1.stormsat import encode_bt, goes_patch

now = goes_patch("C13_now.nc", (lat, lon))                  # storm-centred 0.07-degree patch, kelvin
earlier = goes_patch("C13_6h_ago.nc", (lat_6h, lon_6h))     # where the storm was six hours ago
codes = torch.from_numpy(encode_bt(np.stack([now, earlier])))[None]
outputs = model(..., storm_satellite=(codes, torch.tensor([[True, True]])))

The weights are also provided as model.safetensors. To reproduce the results in section 4, see eval/: elnino2023.py rebuilds 1.5° ERA5 for any date from ARCO-ERA5 and runs the full model on a season's storms.

build_forecast(outputs, config.lead_times_hours, issued, storm_center=(lat, lon), trained=model.trained_heads()) turns a forward pass into the forecast bundle: track scenarios with cones, consensus with members, landfall, intensity, rapid intensification, eyewall, and a point forecast, in physical units with 90% intervals, with every untrained section marked unavailable.

The hurricane path (0.13-0.16; the physics, the swarm, the guidance, the parishes) is one call, live or replayed as it was known at the time:

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
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
# 0.16: the NHC a-deck is read by default (guidance=False switches it off) and its aids blended in; the official
# forecast, the aids used and our own forecast before the blend:
print(run["guidance"]["ofcl"], run["result"]["aids_track"], run["result"]["aids_intensity"], run["result"]["intensity_ours"])
print(run["guidance"]["nhc_ri"], run["guidance"].get("ri_probability_combined"))   # the NHC's RI guidance beside ours

Files in this repository

model.safetensors                 the released weights (89.45 M parameters), safetensors format
model.safetensors.pt              the same weights as a PyTorch state dict (what from_pretrained loads)
config.json, normalizer.json      model configuration and the training normalisation statistics
training_record.json              steps per output, parameter count, stage-two state
results/                          every scorecard and test in section 4, as produced
eval/                             the scripts that produced them
checkpoints/stage1|rollout|stage2 full training checkpoints (with optimizer state) for resuming or fine-tuning
checkpoints/stage3                stage three: satellite branch, calibration, input monitor (0.11)
checkpoints/storm_bank_*.pt       frozen-backbone features for the storm heads
checkpoints/satellite_bank_*.pt   storm-centred infrared for every storm sample (one byte per pixel)
staging/                          the normalised ERA5 staging, so a new session needs no re-download
logs/train.log                    the complete training log, including every scorecard

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7. Why it is built this way

Three convictions run through the whole stack.

Geometry is not something a weather model should have to learn. Distances, areas, the sphere, the vertical: these are known. iHELIX gives attention physical radii and true area weights so the parameters go on the atmosphere, not on rediscovering the globe.

Scarce labels must be spent on few parameters. There are 55,230 Atlantic best-track points in history and no engineering makes more. The backbone learns from 10¹¹ free reanalysis values; the hurricane heads, about a million parameters, learn from the labels on top of a frozen backbone, with the physics handed to them explicitly.

A forecast that cannot say "I don't know" is dangerous. Every output carries an uncertainty, every untrained head is hidden, the physical bounds are checked, the model is scored against persistence before anyone is allowed to believe it, and it has been red-teamed so its failures are written down (section 4.8). The light bulb was not made in one shot; this one is instrumented so that when it fails, it fails visibly.

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NatureV1, iHELIX and the training pipeline are by Nathan, Apache-2.0. This card describes the first full training run of version 0.10 of the pipeline (about one week of training, completed October 2026). ERA5 data: Copernicus Climate Change Service; HURDAT2: NOAA National Hurricane Center.