Barotropic Jets (barotropic-jets)

One line description of the data: 160 rotating shallow-water simulations on the sphere, initialized with balanced zonal jets and a localized height perturbation triggering barotropic instability.

Longer description of the data: Barotropic Jets is a parametric ensemble based on a bi-hemispheric extension of the Galewsky et al. (2004) shallow-water test case. Each simulation starts with two zonal jets at opposite latitudes, with a surface-height profile that balances the zonal flow. A localized height perturbation is added only to the northern jet, breaking hemispheric symmetry and triggering barotropic instability. The resulting dynamics include cyclone rollup, filament formation, and cross-equatorial Rossby-wave propagation. We vary the jet strength, jet latitude, perturbation amplitude, and mean fluid depth. Simulations are performed in a polar-aligned frame, then each trajectory is rotated during postprocessing so that the physical rotation axis is not aligned with the output grid's poles. The dataset provides a setting for learning nonlinear jet dynamics on a sphere without a fixed alignment between the flow and the computational grid.

Code or software used to generate the data: Dedalus v3, an MPI-parallel spectral PDE solver using spin-weighted spherical harmonics through SphereBasis. Biharmonic hyperviscosity is applied to both velocity and surface height for grid-scale dissipation.

Visualization:

About the data

Dimension of discretized data: 167–169 snapshots per trajectory (varies by run, see below) on a $256\times 512256\; \backslash times\; 512$ (lat × lon) grid.

Fields available in the data:

HDF5 path	Shape	Units	Description
t0_fields/h	(1, T, 256, 512)	m	Surface-height perturbation about the mean fluid depth $HH$; total depth is $H+hH+h$
t1_fields/velocity	(1, T, 256, 512, 2)	m/s	Horizontal velocity; last axis is [u_phi, u_theta] = [eastward, southward] in the rotated output grid's local basis
scalars/{u_max, lat_center, h_hat, H}	()	m/s, °, m, m	Run parameters
dimensions/{time, lat, lon}	(T,), (256,), (512,)	s, °, °	Coordinates
$T\in \{167,168,169\}T\; \backslash in\; \backslash \{167,\; 168,\; 169\backslash \}$ is the number of snapshots in that run. All fields are stored as float32. The time coordinate is stored as float64. Relative vorticity is not included; it can be recomputed from the velocity.

The spatial rotation applied to each trajectory can be reproduced with rotation_from_seed(source_run_id) from datagen/galewsky/so3.py in the code repository, using the source_run_id attribute stored in each file.

Number of trajectories: 160: $5\times 4\times 2\times 45\; \backslash times\; 4\; \backslash times\; 2\; \backslash times\; 4$ physical parameter combinations, each represented by one orientation. The split is 128 training, 16 validation, and 16 test trajectories, with no physical configuration shared between splits.

Estimated size of the ensemble of all simulations: Approximately 35 GB (HDF5).

Storage format: One gzip-compressed HDF5 file per trajectory, data/{train,valid,test}/run_XXXX.h5 with run IDs run_0000 to run_0159. Each file stores its run parameters under scalars/, and stats.yaml holds the normalization statistics computed on the train split.

Grid type: $256\times 512256\; \backslash times\; 512$ equiangular, pole-excluding latitude–longitude grid. Latitude centers are ${\varphi }_j=-90\mathrm{°}+(j+0.5)\cdot 180\mathrm{°}\mathrm{/}256\backslash phi\_j\; =\; -90°\; +\; (j\; +\; 0.5)\; \backslash cdot\; 180°/256$; longitude centers are ${\lambda }_k=k\cdot 360\mathrm{°}\mathrm{/}512\backslash lambda\_k\; =\; k\; \backslash cdot\; 360°/512$, stored in degrees. The native solver uses a Gauss–Legendre grid in colatitude with 256 nodes and 512 equispaced longitudes, with a $3\mathrm{/}23/2$ dealiasing factor. Snapshots are resampled to the regular grid by cubic-spline interpolation in colatitude. During the subsequent spatial rotation, scalar fields are interpolated at back-rotated grid points and velocity components are transformed into the output grid's local east/south basis.

Initial conditions: Two compact-support zonal jets centered at $\pm \mathtt{l}\mathtt{a}\mathtt{t}\mathtt{\_}\mathtt{c}\mathtt{e}\mathtt{n}\mathtt{t}\mathtt{e}\mathtt{r}\backslash pm\backslash mathtt\{lat\backslash \_center\}$, each with a half-width of ${20}^{\circ }20^\backslash circ$ and a peak velocity of u_max. The initial meridional velocity is zero. The surface-height profile is obtained from geostrophic and cyclostrophic balance, followed by area-mean subtraction. A bi-Gaussian height perturbation of amplitude h_hat is added only to the northern jet, centered at longitude zero and latitude lat_center in the canonical frame, with fixed meridional and zonal width parameters $\alpha =1\mathrm{/}3\backslash alpha\; =\; 1/3$ and $\beta =1\mathrm{/}15\backslash beta\; =\; 1/15$ rad. A spin-up period of 4 simulation days is discarded.

Boundary conditions: Spherical.

Simulation time-step $(\mathrm{\Delta }t)(\backslash Delta\; t)$: CFL-adaptive, initialized at 120 s and capped at 600 s.

Data are stored separated by $(\delta t)(\backslash delta\; t)$: ≈4 hours. Snapshots are written at adaptive solver steps, so they fall within about ±80 s of each 4-hour mark and the spacing varies between 14,267 and 14,537 s. Use dimensions/time for actual times.

Total time range $(t_{min}(t\_\{min\}$ to $t_{max})t\_\{max\})$: ≈0–28 days, corresponding to simulation days 4–32 after discarding the first 4 days as spin-up. The time coordinate is stored in seconds since day 4. Depending on where the snapshots near day 4 and day 32 fall, the first snapshot is at $t\approx 0t\; \backslash approx\; 0$ or $t\approx 4t\; \backslash approx\; 4$ h and the last at $t\approx 27.83t\; \backslash approx\; 27.83$ or $2828$ days, giving 167–169 snapshots per run.

Set of coefficients or non-dimensional parameters evaluated:

• u_max $\in \{60,70,80,90,100\}\backslash in\; \backslash \{60,\; 70,\; 80,\; 90,\; 100\backslash \}$ m/s, the peak velocity of each jet
• lat_center $\in \{30,40,50,60{\}}^{\circ }\backslash in\; \backslash \{30,\; 40,\; 50,\; 60\backslash \}^\backslash circ$, the northern jet's central latitude; the southern jet is centered at its negative
• h_hat $\in \{60,240\}\backslash in\; \backslash \{60,\; 240\backslash \}$ m, the amplitude of the localized height perturbation
• H $\in \{8000,10000,12000,14000\}\backslash in\; \backslash \{8000,\; 10000,\; 12000,\; 14000\backslash \}$ m, the mean fluid depth

The sphere radius is fixed at $R=6.37122\times {10}^{6}R\; =\; 6.37122\; \backslash times\; 10^6$ m, the rotation rate at $\mathrm{\Omega }=7.292\times {10}^{-5}\backslash Omega\; =\; 7.292\; \backslash times\; 10^\{-5\}$ rad/s, and gravitational acceleration at $g=9.80616g\; =\; 9.80616$ m/s².

Approximate time to generate the data: Approximately 40–50 minutes per original simulation.

Hardware used to generate the data: One sciCORE compute node at the University of Basel per simulation, using 16 MPI ranks on AMD EPYC / Intel Xeon-class CPUs, with one rank per core and OMP_NUM_THREADS=1. Simulations use float64; output fields are downcast to float32 during postprocessing.

Loading

No extra plugin is needed: the files use gzip compression, which h5py reads natively.

Download a single run (≈235 MB) and read it with h5py:

import h5py
from huggingface_hub import hf_hub_download

path = hf_hub_download("sada-group/barotropic-jets", "data/test/run_0014.h5", repo_type="dataset")
with h5py.File(path, "r") as f:
    h = f["t0_fields/h"][0]                                  # (T, 256, 512)
    u_east, u_south = f["t1_fields/velocity"][0].transpose(3, 0, 1, 2)
    t = f["dimensions/time"][:]                              # seconds; spacing is not exactly 4 h
    params = {k: f["scalars"][k][()] for k in f["scalars"]}

To download a whole split (or the full 35 GB dataset), use snapshot_download with allow_patterns:

from huggingface_hub import snapshot_download

root = snapshot_download(
    "sada-group/barotropic-jets",
    repo_type="dataset",
    allow_patterns=["data/test/*", "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 original benchmark and the solver:

@article{galewsky2004,
  title={An initial-value problem for testing numerical models of the global shallow-water equations},
  author={Galewsky, Joseph and Scott, Richard K. and Polvani, Lorenzo M.},
  journal={Tellus A: Dynamic Meteorology and Oceanography},
  volume={56},
  number={5},
  pages={429--440},
  year={2004},
  doi={10.3402/tellusa.v56i5.14436}
}

@article{burns2020dedalus,
  title={Dedalus: A flexible framework for numerical simulations with spectral methods},
  author={Burns, Keaton J. and Vasil, Geoffrey M. and Oishi, Jeffrey S. and Lecoanet, Daniel and Brown, Benjamin P.},
  journal={Physical Review Research},
  volume={2},
  number={2},
  pages={023068},
  year={2020},
  doi={10.1103/PhysRevResearch.2.023068}
}