Global Ocean Dynamics (global-ocean-3D)

One line description of the data: 243 3D, 100-year global ocean simulations with realistic bathymetry on 15 depth levels.

Longer description of the data: A primitive-equation ocean simulation configured from the MITgcm global_ocean.cs32x15 verification case. It features realistic bathymetry, Levitus hydrographic initial conditions and monthly surface restoring, Trenberth wind-stress climatology, shi/ncep heat and freshwater fluxes, GM/Redi mesoscale-eddy parameterisation, and GGL90 vertical mixing. We track potential temperature, salinity, velocity, and sea level. The ocean is non-autonomous: both the surface restoring fields and the atmospheric fluxes are subject to annual cycles, meaning the same instantaneous state can map to different 30-day snapshots, depending on the hidden seasonal phase. The presence of these seasonality patterns poses an additional challenge for learned models, since it tests their capability to forecast non-autonomous dynamical systems with complex boundary conditions. We vary the GM/Redi background diffusivity ${\kappa }_{\mathrm{G}\mathrm{M}}\backslash kappa\_\{\backslash rm\; GM\}$, the horizontal viscosity $A_{h}A\_h$, the vertical diffusivity $K_{v}K\_v$, and the surface restoring timescales for temperature ${\tau }_T\backslash tau\_T$ and salinity ${\tau }_S\backslash tau\_S$, spanning weak, standard, and strong mixing regimes.

Code or software used to generate the data: MITgcm, starting from the global_ocean.cs32x15 verification experiment.

Visualization:

About the data

Dimension of discretized data: 1189 snapshots per trajectory (~99 model years, every 30 days) on a cubed-sphere grid with six $32\times 3232\; \backslash times\; 32$ faces and 15 depth levels, plus sea-surface height.

Fields available in the data:

HDF5 path	Shape	Units	Description
t0_fields/theta	(1, 1189, 15, 6, 32, 32)	°C	Potential temperature $\theta \backslash theta$
t0_fields/salt	(1, 1189, 15, 6, 32, 32)	psu	Salinity $SS$
t0_fields/u, t0_fields/v	(1, 1189, 15, 6, 32, 32)	m/s	Horizontal velocity components on the C-grid, in each cube face's local $xx$ and $yy$ directions (not east/north)
t0_fields/eta	(1, 1189, 1, 6, 32, 32)	m	Sea-surface height $\eta \backslash eta$
scalars/{gm_background_k, visc_ah, diff_kr, tau_theta_relax_days, tau_salt_relax_days}	()	m²/s, days	Run parameters ${\kappa }_{\mathrm{G}\mathrm{M}},A_h,K_v,{\tau }_T,{\tau }_S\backslash kappa\_\{\backslash rm\; GM\},\; A\_h,\; K\_v,\; \backslash tau\_T,\; \backslash tau\_S$
dimensions/{time, level, face, y, x}	—	s, —, —, —, —	Coordinates (level is the index 1–15, not depth)
aux_coords/{depth, xc, yc}	(15,), (6, 32, 32)	m, °, °	Cell-center depth, longitude, latitude
grid.h5: mask_c_3d, mask_w_3d, mask_eta, angle_cs, angle_sn, hfac_c	(15, 6, 32, 32) / (6, 32, 32)	—	Static grid file at the dataset root (not in the run files): tracer and velocity masks, surface mask, rotation angles to east/north, partial-cell fractions

Temperature and salinity use the level-dependent tracer mask mask_c_3d (wet cell centers, one mask per level $k=1,\dots ,15k\; =\; 1,\; \backslash ldots,\; 15$). The velocities use mask_w_3d, which marks cells whose west face (for u) and south face (for v) are both open; it is a subset of mask_c_3d, and u, v are also 0.0 at closed faces of wet cells. The sea-surface height $\eta \backslash eta$ uses the column mask mask_eta, which marks any column with at least one wet level. Land cells are stored as 0.0. When computing normalization statistics, losses, or metrics, one should mask accordingly, so that models are scored only on real ocean.

Number of trajectories: 243: $3^{5}3^5$ parameter combinations, one run each, split 194/24/25 into data/{train,valid,test}/.

Estimated size of the ensemble of all simulations: 248 GB (compressed HDF5).

Storage format: One HDF5 file per run plus the static grid.h5. stats.yaml holds the normalization statistics used in the paper (mean and std of each field and of its one-step differences), one entry per field and level (theta_k01 … v_k15) plus eta. They are computed on the train split over wet cells only, using the masks above, on the native cubed-sphere values (u and v in face-aligned directions).

Grid type: Cubed-sphere with six $32\times 3232\; \backslash times\; 32$ faces and 15 depth levels (depths at cell centers range from 25 m to 4855 m). Fields are stored on the native grid as (trajectory, time, level, face, y, x). In the paper they are regridded to a $64\times 12864\; \backslash times\; 128$ lat-lon grid at training time (inverse-distance weighting over the 4 nearest cells, after imputing land), and only 6 of the 15 levels are used, $k=1,3,5,7,10,13k\; =\; 1,\; 3,\; 5,\; 7,\; 10,\; 13$; vector rotation from face-aligned to geographic east/north uses the static $(\cos \alpha ,\sin \alpha )(\backslash cos\backslash alpha,\; \backslash sin\backslash alpha)$ angles supplied by MITgcm.

Initial conditions: Runs start from the pickup.0000072000 file shipped with the tutorial, i.e. after a warm-up of roughly 200 model years initialised from Levitus 3D temperature and salinity.

Boundary conditions: Realistic bathymetry; non-linear free surface (representing a real fresh-water flux). Surface forcing by Levitus monthly surface restoring of temperature and salinity, Trenberth wind stress, and shi/ncep heat and freshwater fluxes, all following an annual cycle.

Simulation time-step $(\mathrm{\Delta }t)(\backslash Delta\; t)$: 1 day.

Data are stored separated by $(\delta t)(\backslash delta\; t)$: 30 days.

Total time range $(t_{min}(t\_\{min\}$ to $t_{max})t\_\{max\})$: The production run consists of 100 years (36,000 steps, 360-day model years). The first 12 snapshots are dropped, accounting for ≈ 1 model year of parameter-change adjustment transient, leaving 1189 snapshots covering ~99 model years. The time coordinate is shifted so that t[0] = 0.

Set of coefficients or non-dimensional parameters evaluated:

• ${\kappa }_{\mathrm{G}\mathrm{M}}\in \{250,1000,2500\}{\mathrm{m}}^2{\mathrm{s}}^{-1}\backslash kappa\_\{\backslash rm\; GM\}\; \backslash in\; \backslash \{250,\; 1000,\; 2500\backslash \}\backslash ,\backslash mathrm\{m^2\backslash ,s^\{-1\}\}$, the GM/Redi background diffusivity
• $A_h\in \{1.5\times {10}^5,3\times {10}^5,5\times {10}^5\}{\mathrm{m}}^2{\mathrm{s}}^{-1}A\_h\; \backslash in\; \backslash \{1.5\; \backslash times\; 10^5,\; 3\; \backslash times\; 10^5,\; 5\; \backslash times\; 10^5\backslash \}\backslash ,\backslash mathrm\{m^2\backslash ,s^\{-1\}\}$, the horizontal viscosity
• $K_v\in \{1\times {10}^{-5},3\times {10}^{-5},1\times {10}^{-4}\}{\mathrm{m}}^2{\mathrm{s}}^{-1}K\_v\; \backslash in\; \backslash \{1\; \backslash times\; 10^\{-5\},\; 3\; \backslash times\; 10^\{-5\},\; 1\; \backslash times\; 10^\{-4\}\backslash \}\backslash ,\backslash mathrm\{m^2\backslash ,s^\{-1\}\}$, the vertical diffusivity
• ${\tau }_T\in \{30,60,120\}\backslash tau\_T\; \backslash in\; \backslash \{30,\; 60,\; 120\backslash \}$ days, the surface restoring timescale for temperature
• ${\tau }_S\in \{90,180,360\}\backslash tau\_S\; \backslash in\; \backslash \{90,\; 180,\; 360\backslash \}$ days, the surface restoring timescale for salinity

The original $A_{h}A\_h$ grid included $A_h={10}^6{\mathrm{m}}^2{\mathrm{s}}^{-1}A\_h\; =\; 10^6\backslash ,\backslash mathrm\{m^2\backslash ,s^\{-1\}\}$, leading to the model crossing CFL = 1. The grid was then tightened to the values above, all below the unstable boundary; a 365-step preflight on the new grid showed max ${\mathrm{a}\mathrm{d}\mathrm{v}\mathrm{c}\mathrm{f}\mathrm{l}}_{\mathrm{w}\mathrm{v}\mathrm{e}\mathrm{l}}\approx 0.094\backslash mathrm\{advcfl\}\_\{\backslash rm\; wvel\}\; \backslash approx\; 0.094$.

Approximate time to generate the data: Per-run wall-time of ~25–30 minutes for a full 100-year trajectory.

Hardware used to generate the data: Single CPU core per run.

Loading

It's important to load hdf5plugin before h5py to make sure the filters are registered properly.

Download one run (≈1.1 GB) plus the static grid file and read them with h5py:

import hdf5plugin  # registers the LZ4 filter, must come before reading
import h5py
from huggingface_hub import hf_hub_download

repo = "sada-group/global-ocean-3D"
path = hf_hub_download(repo, "data/test/run_0006.h5", repo_type="dataset")
grid = hf_hub_download(repo, "grid.h5", repo_type="dataset")

with h5py.File(path, "r") as f, h5py.File(grid, "r") as g:
    theta = f["t0_fields/theta"][0]        # (1189, 15, 6, 32, 32): time, level, face, y, x
    eta = f["t0_fields/eta"][0, :, 0]      # (1189, 6, 32, 32)
    params = {k: f["scalars"][k][()] for k in f["scalars"]}
    wet = g["mask_c_3d"][:]                # (15, 6, 32, 32), True on ocean cells
    sst = theta[:, 0][:, wet[0]]           # surface temperature on wet cells only

To download a subset, e.g. the 25 test runs (≈27 GB), use snapshot_download with allow_patterns:

from huggingface_hub import snapshot_download

root = snapshot_download(
    "sada-group/global-ocean-3D",
    repo_type="dataset",
    allow_patterns=["data/test/*", "grid.h5", "stats.yaml"],  # drop allow_patterns for everything
)

Please cite the associated paper if you use this data in your research:

@misc{muser2026dandelionsphericalflowerneural,
      title={Dandelion: A Spherical Flower for Neural Simulation of Planetary Dynamics}, 
      author={Till Muser and Giovanni Abati and Ivan Dokmanić},
      year={2026},
      eprint={2608.27521},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2608.27521}, 
}

as well as the solver and its cubed-sphere implementation:

@article{marshall1997finite,
  title={A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers},
  author={Marshall, John and Adcroft, Alistair and Hill, Chris and Perelman, Lev and Heisey, Curt},
  journal={Journal of Geophysical Research: Oceans},
  volume={102},
  number={C3},
  pages={5753--5766},
  year={1997},
  publisher={Wiley Online Library}
}

@article{adcroft2004implementation,
  title={Implementation of an atmosphere--ocean general circulation model on the expanded spherical cube},
  author={Adcroft, Alistair and Campin, Jean-Michel and Hill, Chris and Marshall, John},
  journal={Monthly Weather Review},
  volume={132},
  number={12},
  pages={2845--2863},
  year={2004}
}