Data of the Stochastic Grid Perturbation comparison with Location Uncertainty framework

Description

Abstract (English)

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.

Technical info (English)

USAGE:

Once the archive is extracted, put the folder "outputs" in the code repository. The figures are then ready to be computed, e.g. by launching the command "python3 exploit_results.py fig_visualise_perturbation" 

Table of contents (English)

FILE TREE:

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.

Series information (English)

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.