tvonich/graphcast_1.0-deg_optimal_initial_conditions

GraphCast 1.0° Optimal Initial Conditions

Gradient-optimized initial conditions for DeepMind's GraphCast weather model (1.0° / GraphCast_small configuration). Each file is the optimized model input state for a single forecast, produced by backpropagating the forecast error at a fixed target lead time through the (frozen) GraphCast network and updating the input fields. These are optimal initial conditions: the input state that, when rolled out, most closely reproduces the verifying analysis at the target lead.

These data accompany Vonich & Hakim (2026), Atmospheric Predictability Beyond 30 Days with Machine Learning (see Citation).

Contents

Subset	Files	Precision	Target lead	Init dates (2020)
14day_f32/	732	float32	56 steps (14 days)	every 12 h (00Z & 12Z)
32day_f64/	61	float64	128 steps (32 days)	~every 6 days

• 14day_f32 — 12-hourly initialization across the full year, optimized to a 14-day target. Single precision. (Filenames carry a BEST_ prefix.)
• 32day_f64 — longer 32-day optimization horizon, carried out and stored in double precision (float64) because single-precision gradients stall at long lead times. Initialized every ~6 days across all of 2020 (complete: 61 members). (Filenames carry a BEST64_ prefix.)

File format

One NetCDF (.nc) file per initialization, named:

14day_f32/BEST_<YYYY-MM-DDTHH>_56_target_lead.nc     (e.g. 14day_f32/BEST_2020-03-13T00_56_target_lead.nc)
32day_f64/BEST64_<YYYY-MM-DDTHH>_128_target_lead.nc  (e.g. 32day_f64/BEST64_2020-03-13T00_128_target_lead.nc)

The numeric token in the filename is the optimization target lead in 6-hour steps (56 = 14 days, 128 = 32 days).

Each file holds the two input timesteps GraphCast requires (t − 6 h and t):

Dimension	Size	Notes
batch	1	single case
time	2	input frames at −6 h and 0 h
level	13	50–1000 hPa
lat	181	−90 … 90, 1.0° spacing
lon	360	0 … 359, 1.0° spacing

Pressure levels (hPa): 50, 100, 150, 200, 250, 300, 400, 500, 600, 700, 850, 925, 1000

Variables (GraphCast _small input set):

• Surface / single-level: 2m_temperature, 10m_u_component_of_wind, 10m_v_component_of_wind, mean_sea_level_pressure, total_precipitation_6hr
• Atmospheric (per level): geopotential, temperature, specific_humidity, u_component_of_wind, v_component_of_wind, vertical_velocity
• Static / forcing: geopotential_at_surface, land_sea_mask, toa_incident_solar_radiation, year_progress_{sin,cos}, day_progress_{sin,cos}

Provenance

• Model: GraphCast (Lam et al., 2023), GraphCast_small (1.0°, 13 levels).
• Baseline state: ERA5 reanalysis, regridded to the GraphCast 1.0° grid.
• Optimization: Adam-based gradient descent on the input state with the GraphCast weights held fixed; loss is the rollout error against ERA5 at the target lead time. The 32day_f64 subset uses double precision throughout to avoid the floating-point precision floor that limits long-lead optimization.

Note on small-scale noise

These optimal initial conditions can contain spurious fine-scale (grid-point) noise. This is expected rather than a defect: GraphCast damps such small-scale structure within the first few forward steps, so it has essentially no effect on the forecast at the target lead and is therefore effectively unconstrained by the optimization. The fields released here come from the original, unregularized optimization. Newer iterations of the method add regularization options that remove this noise while preserving the physically meaningful correction.

Usage

import xarray as xr
from huggingface_hub import hf_hub_download

path = hf_hub_download(
    repo_id="tvonich/graphcast_1.0-deg_optimal_initial_conditions",
    filename="14day_f32/BEST_2020-03-13T00_56_target_lead.nc",
    repo_type="dataset",
)
ds = xr.open_dataset(path)
print(ds)

Citation

If you use this dataset, please cite:

Vonich, P. T., and G. J. Hakim, 2026: Atmospheric Predictability Beyond 30 Days with Machine Learning. Artif. Intell. Earth Syst., e260009, https://doi.org/10.1175/AIES-D-26-0009.1, in press.

and the original GraphCast model:

Lam, R., et al. (2023). Learning skillful medium-range global weather forecasting. Science, 382(6677), 1416–1421.

@article{vonich2026predictability,
  title   = {Atmospheric Predictability Beyond 30 Days with Machine Learning},
  author  = {Vonich, Peter T. and Hakim, Gregory J.},
  journal = {Artificial Intelligence for the Earth Systems},
  year    = {2026},
  pages   = {e260009},
  doi     = {10.1175/AIES-D-26-0009.1},
  note    = {in press}
}

@article{lam2023graphcast,
  title   = {Learning skillful medium-range global weather forecasting},
  author  = {Lam, Remi and Sanchez-Gonzalez, Alvaro and Willson, Matthew and
             Wirnsberger, Peter and Fortunato, Meire and Alet, Ferran and
             Ravuri, Suman and Ewalds, Timo and Eaton-Rosen, Zach and Hu, Weihua
             and Merose, Alexander and Hoyer, Stephan and Holland, George and
             Vinyals, Oriol and Stott, Jacklynn and Pritzel, Alexander and
             Mohamed, Shakir and Battaglia, Peter},
  journal = {Science},
  volume  = {382},
  number  = {6677},
  pages   = {1416--1421},
  year    = {2023},
  doi     = {10.1126/science.adi2336}
}