Covariate-based stochastic parameterization of baroclinic ocean eddies

Abstract

Abstract:In this study we investigate a covariate-based stochastic approach to parameterize unresolved turbulent processes within a standard model of the idealised, wind-driven ocean circulation. We focus on vertical instead of horizontal coarse-graining, such that we avoid the subtle di culties of horizontal coarsegraining. The corresponding eddy forcing is uniquely de ned and has a clear physical interpretation related to baroclinic instability. We propose to emulate the baroclinic eddy forcing by sampling from the conditional probability distribution functions of the eddy forcing obtained from the baroclinic reference model data. These conditional probability distribution functions are approximated here by sampling uniformly from discrete reference values. We analyze in detail the di erent performances of the stochastic parameterization dependent on whether the eddy forcing is conditioned on a suitable ow-dependent covariate or on a timelagged covariate or on both. The results demonstrate that our non-Gaussian, non-linear methodology is able to accurately reproduce the rst four statistical moments and spatial/temporal correlations of the stream function, energetics, and enstrophy of the reference baroclinic model.

Introducing VECMAtk - Verification, Validation and Uncertainty Quantification for Multiscale and HPC Simulations

“…More specifically, we aim for statistically representative, data-driven surrogate models that account for the uncertainties in subgrid-scale responses due to their internal nonlinear and possibly chaotic dynamics. The surrogates are to be constructed from a (limited) set of reference data, with the goal of accurately reproducing long-term statistics, in line with the approach from [17,18].…”

Reduced Model-Error Source Terms for Fluid Flow

“…One possible course of action, explored in e.g. [17,10], is to directly create a full-field surrogate r (x, y; t) ∈ R N ×N , using a database reference snapshots in time of the exact eddy forcing (7). Here, N is the number of grid points in one spatial direction, typically 2 7 , 2 8 or higher.…”

“…Here, N is the number of grid points in one spatial direction, typically 2 7 , 2 8 or higher. Constructing a full-field, dynamic surrogate of a quantity as complex as the eddy forcing is a challenging task, and storing a potentially large amount of reference snapshots can lead to high memory requirements [17]. We therefore propose to precede the surrogate construction step with a procedure that significantly compresses the training data.…”

“…In this study, we also consider a stochastic surrogate method [17,16], and as a performance indicator we use the degree by which it is able to capture energy and enstrophy statistics. However, we refrain from an approach that is purely data-driven, i.e.…”

Reducing data-driven dynamical subgrid scale models by physical constraints

“…Early contributions to this topic in the context of ocean modelling includes the work of [6] , where the eddy-forcing is replaced by a spacetime correlated random-forcing process. Furthermore, in [7] a conditional data resampling scheme is proposed to replace the unresolved scales of an ocean model. Other notable examples include the work of [8][9][10] .…”