On dynamically unresolved oceanic mesoscale motions

Berloff, Pavel; Ryzhov, Eugene A.; Shevchenko, Igor

doi:10.1017/jfm.2021.477

Cited by 15 publications

(16 citation statements)

References 49 publications

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“…It is worth looking for the ways of imposing physical constraints, such as energy/mass conservation, into the emulators, for example, using an appropriate penalizing term in the loss function. Second, the results obtained here are directly relevant for emulation of various complex and multi-scale fields in the context of eddy parameterizations and test the alternative definitions of eddies investigated recently (Agarwal et al, 2021;Berloff et al, 2021). Finally, a possible sequel to this work is including more stochastic and deep-learning methods, or a mixture of both, for example, the Stochastic Neural Networks (Guillaumin & Zanna, 2021).…”

Section: Discussionmentioning

confidence: 78%

A Comparison of Data‐Driven Approaches to Build Low‐Dimensional Ocean Models

Agarwal

Kondrashov

Dueben

et al. 2021

J Adv Model Earth Syst

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We present a comprehensive inter‐comparison of linear regression (LR), stochastic, and deep‐learning approaches for reduced‐order statistical emulation of ocean circulation. The reference data set is provided by an idealized, eddy‐resolving, double‐gyre ocean circulation model. Our goal is to conduct a systematic and comprehensive assessment and comparison of skill, cost, and complexity of statistical models from the three methodological classes. The model based on LR is considered as a baseline. Additionally, we investigate its additive white noise augmentation and a multi‐level stochastic approach, deep‐learning methods, hybrid frameworks (LR plus deep‐learning), and simple stochastic extensions of deep‐learning and hybrid methods. The assessment metrics considered are: root mean squared error, anomaly cross‐correlation, climatology, variance, frequency map, forecast horizon, and computational cost. We found that the multi‐level linear stochastic approach performs the best for both short‐ and long‐timescale forecasts. The deep‐learning hybrid models augmented by additive state‐dependent white noise came second, while their deterministic counterparts failed to reproduce the characteristic frequencies in climate‐range forecasts. Pure deep learning implementations performed worse than LR and its simple white noise augmentation. Skills of LR and its white noise extension were similar on short timescales, but the latter performed better on long timescales, while LR‐only outputs decay to zero for long simulations. Overall, our analysis promotes multi‐level LR stochastic models with memory effects, and hybrid models with linear dynamical core augmented by additive stochastic terms learned via deep learning, as a more practical, accurate, and cost‐effective option for ocean emulation than pure deep‐learning solutions.

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Section: Discussionmentioning

confidence: 78%

A Comparison of Data‐Driven Approaches to Build Low‐Dimensional Ocean Models

Agarwal

Kondrashov

Dueben

et al. 2021

J Adv Model Earth Syst

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“…This is often necessary in studies of eddy parameterisation [e.g. 1,2,3,4,5,6] as a way of identifying the 'eddy forcing' that quantifies the effects of missing scales that are not resolved in low-resolution model runs. The dynamical flow decomposition method [1,3] uses the results of a high-resolution model run as the reference 'truth'; the coarse-grid model run is then corrected towards the coarse-grained truth and the amount by which the solution needs to be corrected gives the eddy forcing; the statistical properties of the eddy forcing can then be used to configure a stochastic parameterisation [2].…”

Section: Introductionmentioning

confidence: 99%

“…1,2,3,4,5,6] as a way of identifying the 'eddy forcing' that quantifies the effects of missing scales that are not resolved in low-resolution model runs. The dynamical flow decomposition method [1,3] uses the results of a high-resolution model run as the reference 'truth'; the coarse-grid model run is then corrected towards the coarse-grained truth and the amount by which the solution needs to be corrected gives the eddy forcing; the statistical properties of the eddy forcing can then be used to configure a stochastic parameterisation [2]. Another approach is used in [4], in which the eddy forcing is calculated by considering the differences between the advection and diffusion terms when calculated on the coarse-grid from the coarse-grained fields, and the coarse-grained versions of the fine-grid advection and viscosity terms.…”

Section: Introductionmentioning

confidence: 99%

“…However, the way in which coarse-graining is performed is not unique. The simplest choice is to project variables directly [3], which may be done if every point in the coarse grid is also contained in the fine grid. Another approach is given in [4], in which the coarse-grained field is obtained by an average over neighbouring grid points.…”

Section: Introductionmentioning

confidence: 99%

“…However, if we use arbitrary coarse-grainings then there is no guarantee that w = w. We can, however, choose to perform the coarsegrainings of w and u in such a way as to allow this condition to hold. This is particularly important when applying the dynamical decomposition method [1,3] to PE because in that case the horizontal velocities of the coarse grid model are corrected online towards the coarse-grained reference solution; the vertical velocity is then calculated diagnostically from the 'corrected' horizontal velocities. We should therefore aim to correct towards a horizontal velocity field that gives the correct vertical velocity.…”

Section: Introductionmentioning

confidence: 99%

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On Divergence- and Gradient-Preserving Coarse-Graining for Finite Volume Primitive Equation Ocean Models

Patching

2021

Preprint

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We consider the problem of coarse-graining in finite-volume fluid models. Projecting a variable on a fine grid onto a coarser grid will in general cause some information about the solution to be lost. In particular, horizontal divergences and gradients will not be the same when calculated on the coarse grid from a projected solution as when they are calculated on the fine grid. Therefore, it is necessary to choose the method of coarse-graining carefully via a weighted average so that these properties will be conserved in the resulting field. We derive general conditions on the averaging weights that allow these properties to be preserved. We then take the particular case of a regular triangular mesh in which the fine-grid resolution is some integer multiple N of the coarse-grid resolution. For this case we particular values for the averaging weights preserve the divergence for general N , and different weights that preserve the gradient for the case N = 2. These coarse-grainings are applied to data from FESOM2 simulations and we demonstrate that using this coarse-graining gives a significant improvement over other methods.

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