Each file pq_[X].npz contain the time "t" (year) pressure field "p"(m²s⁻²), the vorticity field "q" (which is actually q/f0), the perturbation "dx" and "dy" (m). Note that "dx" and "dy" are not the space steps but a possible negative perturbation of the grid. In some simulations where the stochastic perturbation is not applied, the "dx" and "dy" fields are not included as they would be zero. The shape of the numpy arrays is (n_ens=30, nlayer=3, nx=97, ny=121) for the low-resolution and (n_ens=30, nlayer=3, nx=385, ny=481) for the deterministic 10km-resolution case. n_ens is the number of member in the ensembles, nlayer is the number of stacked isopycnal layers, and (nx, ny) is the horizontal grid size. The shape of the arrays in moments_u.npy, moments_q.npy is (n_exp=6, n_moments=4, n_time=92, n_ens=30)The experiments are in the order: (LU_enstrophy, det_HR, det, Perturbed_points, Without_compensation, Perturbed_steps)The moments are in increasing order: (mean, standard deviation, skewness, kurtosis)The moments were computed for each ensemble member in n_time=92 occurences, i.e. once every four days. The jet-centered moments were computed on the restricted horizontal area defined by (nx/5 : 3*nx/5, ny/3 : 2*ny/3).

The related paper investigates the relationship between a Stochastic Grid Perturbation (SGP) and Location Uncertainty (LU). The LU formulation, which introduces random velocity fluctuations, has shown efficacy in organizing large-scale flow and replicating long-term statistical characteristics. SGP was created as a simpler approach which perturbs the computational grid for ensemble members, aiming to simulate small uncertainties in high-resolution predictability studies.We aim to clarify the link between SGP and LU. After introducing the LU formalism, we derive the SGP method and discuss its connection to LU.Correlated noise in time is introduced in the SGP method to preserve the structure of the original grid.A compensating advection term is shown to preserve LU properties despite the latter correlated noise.Numerical experiments on a 3-layer Quasi-Geostrophic model compare various SGP implementations with an explicit LU implementation, highlighting the importance of the compensating advection term to achieve strict equivalence.

FILE TREE OF outputs/: outputs/ det/ param.pth pq_[X].npz det_10km/ param.pth pq_[X].npz LU_enstrophy/ param.pth pq_[X].npz Perturbed_points/ param.pth pq_[X].npz Perturbed_steps/ param.pth pq_[X].npz Without_compensation/ param.pth pq_[X].npz where X is the day count, 0<=X<=365. To avoid unnecessary data storage, only the pq_[X].npz files that are used in the statistical analyses (1 day out of 4) are included in this dataset. The linked code actually produces more data. FILE TREE OF tmp_moments/: tmp_moments/ moments_q.npy moments_u.npy tmp_moments_jet_centered/ moments_q.npy moments_u.npy

The archive outputs.tar.xz contain the outputs of the code which performs a Stochastic Grid Perturbation on a Quasi-Geostrophic model; The archive tmp_moments.tar.xz and tmp_moments_jet_centered.tar.xz contain the first four standarized spatial moments of the state variables. They are exploited in the paper "Link between Stochastic Grid Perturbation and Location Uncertainty framework".

USAGE: Once the archives are extracted, put the folders "outputs", "tmp_moments" and "tmp_moments_jet_centered" in the code repository. The figures are then ready to be computed, e.g. by launching the command "python3 exploit_results.py radar_chart".