Link Between Stochastic Grid Perturbation and Location Uncertainty Framework

This paper investigates the relationship between a Stochastic Grid Perturbation (SGP) and Location Uncertainty (LU) in the context of ocean modeling. 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.