---
license: cc-by-4.0
task_categories:
  - time-series-forecasting
tags:
  - weather
  - climate
  - graphcast
  - data-assimilation
  - initial-conditions
  - atmospheric-science
pretty_name: GraphCast 1.0° Optimal Initial Conditions
size_categories:
  - n<1K
---

# 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](#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

```python
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.

```bibtex
@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}
}
```