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

1Why a physics baseline

A learned hurricane model is only worth something if it beats the forecasts that cost nothing: straight-line extrapolation of the last 6 or 12 hours of motion, and CLIPER, the climatology-and-persistence regression that has been the skill floor for official forecasts since the 1970s [1, 2]. At 6-12 hours extrapolation is hard to beat at all, because a storm's motion changes slowly. NatureV1's learned track head already beats a steering-only track and extrapolation on the held-out 2017, 2019 and 2021 Atlantic seasons. This report describes a second, independent answer to the same question: how far can hand-written physics alone go, with every constant fitted on past seasons and nothing learned by gradient descent? The result is naturev1.cyclone, 39 Python modules, and the consensus it produces is now the physical prior that the learned model and its distillation targets are measured against.

2Data and verification

Analyses. Each forecast starts from one ERA5 [3] analysis on the WeatherBench 2 [4] 1.5-degree grid (13 pressure levels, the analysis 12 hours earlier for tendencies) and the best track so far (IBTrACS [5]): position, intensity and the last 48 hours of motion. Cases. Every 00 and 12 UTC fix of a tropical or subtropical system in every basin. Verification follows NHC practice: a forecast is verified only while the system remains tropical, errors are great-circle distances, and every comparison uses a homogeneous sample (the same cases for every method at a given lead). 90% confidence intervals come from a bootstrap that resamples whole storms, since forecasts of the same storm are not independent.

Splits. CLIPER, SHIFOR and the analog database were fitted on 1980-2014 best tracks. Everything else (consensus weights, the cone, the genesis model) was tuned on 2016, 2017 and 2019. The four seasons 2018, 2020, 2021 and 2022 were not used for any choice and are reported once. The baseline at each lead is the strongest of three extrapolations (6-hour, 12-hour and great-circle), chosen per lead after the fact, which flatters the baseline rather than the model.

3Thirteen members

Every member predicts the full track to 120 hours. The physics members share one preprocessing step: the storm's own circulation is removed from the analysis by inverting its vorticity and divergence inside 600 km (a Biot-Savart / Poisson inversion with a 300 km taper), so the remaining flow is the environment that steers it [6].

The thirteen members of the shipped consensus: xtrp6, cliper, analog, budget_mix, evo12, med_anom48, int_anom48, budget_anom96, evo_anom48, evo_anom96, ens48_mean, baro_res12, baro.

Consensus

Members are combined in along-track and cross-track coordinates relative to a reference member, with a separate weight vector per lead for each direction [10]. Weights are constrained to the simplex and fitted by accelerated projected gradient descent (FISTA [11]) with an exact Lipschitz step; an unconstrained fit diverged once more than eight members were present. Regime-specific and selective variants were tried and were worse in leave-one-season-out cross-validation, so one global set of weights ships.

4Results on four unseen seasons

Figure 1. Mean track error on the held-out 2018, 2020, 2021 and 2022 seasons, all basins, homogeneous sample.

Table 1. Every 90% interval of the improvement over extrapolation excludes zero, and the consensus also beats CLIPER at every lead. On the tuning seasons, in cross-validation, the same consensus scored 27/55/123/202/289/482/673/828 km, so there is no sign of overfitting to them.

Against global AI and physics models

Each teacher was tracked through its own WeatherBench 2 forecast, regridded to 1.5 degrees and started from the same position. Tracking at 1.5 degrees costs every teacher a little at 6-12 hours; they ran at 0.25 degrees.

Table 2. The physics is far better than extrapolation and climatology and far worse than a modern global model beyond 6 hours. Combined, with weights that never see the scored season, it is never worse than the global model and is better at 6-12 hours. Distilling those models into NatureV1 is the route to their long-range skill.

Hurricane Dorian (2019)

With weights fitted on 2016-2017 only, the consensus scored 21/49/99/164/249/480/656/810 km at 6-120 hours against 6-hour extrapolation's 23/52/131/237/365/641/897/1173. During the stall over Grand Bahama, where the Bermuda High weakened and drifted east while the next trough stayed too far north to pick the storm up, its 48-hour error was 230 km against 341. The stall diagnostic (Newton search for saddle points of the steering flow) flags such cols explicitly.

Synthetic hard cases

Nine constructed scenarios (a Dorian-type col, ridge breakdown, trough capture, a loop, a Fujiwhara pair, a centre reformation, a sharp turn, a southern-hemisphere recurvature and a straight runner), with truth integrated through the evolving flow and the forecast shown only the start: the physics beats extrapolation at 48 and 72 hours in all nine (the Dorian stall 344 vs 552 km at 48 h and 471 vs 961 at 72 h; the loop 56 vs 416 at 48 h). It loses at 24 hours in four and at 120 hours in four, where the scenario's flow is unlike Earth's climatology and the climatological members pull the wrong way. A stall that only forms later is not flagged at the initial time.

Genesis

Candidate disturbances are vorticity maxima found in the analysis. Each is scored by a logistic model with all pairwise and squared terms over thirteen features: 850 and 600 hPa vorticity and its 24-hour change, the Okubo-Weiss parameter, 600 hPa humidity, deep-layer shear, SST, the depth of the low, a warm-core measure, a genesis potential index, the candidate's age and latitude, and the closedness of its wave-relative pouch [14]. On the four unseen seasons (northern hemisphere, June-November, 259 formations) its Brier skill over climatology is +0.22, it is well calibrated (top third: forecast 12%, observed 13%), and at a 30% threshold it flags 68% of formations a median 24 hours ahead, with 52% of alarms false.

5Limitations

• One 1.5-degree analysis cannot see an eyewall. Track at 6-12 hours is limited by the best track's own uncertainty.
• Beyond 12 hours every modern global model is far better. The physics is a baseline and a short-range partner, not a replacement.
• The 67th-percentile cone covers 60-65% of held-out positions, slightly narrower than intended.
• This report covers track and genesis. Intensity members (SHIFOR, a SHIPS-style regression, a logistic growth model with Kaplan-DeMaria land decay [15, 16, 17]) ship in the same package and are verified separately.

6Availability

pip install naturev1
from naturev1.cyclone import physics_forecast
out = physics_forecast(case, env, climatology, analogs)   # track, members, cone, stall, ridge, regime, intensity

Code, fitted coefficients and the hindcast harness are Apache-2.0 at pypi.org/project/naturev1; the model card is at huggingface.co/CorxLabs/NatureV1-500.

References

1. Neumann, C. J. (1972). An alternate to the HURRAN tropical cyclone forecast system. NOAA Tech. Memo. NWS SR-62.
2. Aberson, S. D. (1998). Five-day tropical cyclone track forecasts in the North Atlantic basin. Weather and Forecasting, 13, 1005-1015.
3. Hersbach, H., et al. (2020). The ERA5 global reanalysis. Q. J. R. Meteorol. Soc., 146, 1999-2049.
4. Rasp, S., et al. (2024). WeatherBench 2: A benchmark for the next generation of data-driven global weather models. JAMES, 16, e2023MS004019.
5. Knapp, K. R., et al. (2010). The International Best Track Archive for Climate Stewardship (IBTrACS). BAMS, 91, 363-376.
6. Galarneau, T. J., and C. A. Davis (2013). Diagnosing forecast errors in tropical cyclone motion. Mon. Wea. Rev., 141, 405-430.
7. Velden, C. S., and L. M. Leslie (1991). The basic relationship between tropical cyclone intensity and the depth of the environmental steering layer in the Australian region. Weather and Forecasting, 6, 244-253.
8. Holland, G. J. (1983). Tropical cyclone motion: Environmental interaction plus a beta effect. J. Atmos. Sci., 40, 328-342.
9. Arakawa, A. (1966). Computational design for long-term numerical integration of the equations of fluid motion. J. Comput. Phys., 1, 119-143.
10. Goerss, J. S. (2000). Tropical cyclone track forecasts using an ensemble of dynamical models. Mon. Wea. Rev., 128, 1187-1193.
11. Beck, A., and M. Teboulle (2009). A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci., 2, 183-202.
12. Lam, R., et al. (2023). Learning skillful medium-range global weather forecasting. Science, 382, 1416-1421.
13. Bi, K., et al. (2023). Accurate medium-range global weather forecasting with 3D neural networks. Nature, 619, 533-538.
14. Dunkerton, T. J., M. T. Montgomery, and Z. Wang (2009). Tropical cyclogenesis in a tropical wave critical layer: easterly waves. Atmos. Chem. Phys., 9, 5587-5646.
15. DeMaria, M., and J. Kaplan (1994). A Statistical Hurricane Intensity Prediction Scheme (SHIPS) for the Atlantic basin. Weather and Forecasting, 9, 209-220.
16. DeMaria, M. (2009). A simplified dynamical system for tropical cyclone intensity prediction. Mon. Wea. Rev., 137, 68-82.
17. Kaplan, J., and M. DeMaria (1995). A simple empirical model for predicting the decay of tropical cyclone winds after landfall. J. Appl. Meteor., 34, 2499-2512.