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REVIEW 3 major objections 5 minor 139 references

Global Estimation of Subsurface Eddy Kinetic Energy of Mesoscale Eddies Using a Multiple-input Residual Neural Network

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A two-branch residual neural network reconstructs monthly mean, 1-degree-filtered eddy kinetic energy down to 2000 m across most of the global ocean, outperforming earlier networks and mode-based physical reconstructions.

desk verdict Capable ML study with a circularity problem in the deep-ocean skill claim; deserves review but needs a reframe. read the letter →

arxiv 2412.10656 v1 pith:7GJRWM6D submitted 2024-12-14 physics.ao-ph cs.LG

Chenyue Xie , An-Kang Gao , Xiyun Lu This is my paper · ORCID
classification physics.ao-phcs.LG
keywords eddykineticenergymesoscaleeddiesresidualneuralnetworktop-hatspatialfiltersatellitealtimetrysubsurfacereconstructiontransferlearningoceanreanalysis
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Mesoscale eddy kinetic energy (EKE) is the standard measure of eddy intensity and a key ingredient in ocean-climate eddy parameterizations, yet its subsurface form has been hard to measure because Argo-style observations are sparse. This paper claims that a multiple-input residual neural network (MI-ResNet) can reconstruct monthly mean, 1-degree-filtered EKE in the upper 2000 m over the 10°S-60°S and 10°N-60°N bands from satellite sea surface fields plus sparse subsurface climatological profiles, and that it does so more accurately than surface-only networks and physics-based baroclinic/surface-mode reconstructions. On the 2017-2020 test period, the paper reports global R² of about 0.86 at the surface and 0.78 at 2000 m using reanalysis inputs, with comparable skill after transfer learning to observational inputs. If the claim holds, it offers a practical way to generate global subsurface EKE fields for eddy parameterization without waiting for dense in-situ coverage.

What carries the argument

The load-bearing object is the multiple-input residual neural network (MI-ResNet): a two-branch architecture whose surface branch processes a 17×17×10 tensor of satellite-derived variables around the target column and whose subsurface branch processes a vertical profile of density, geostrophic velocities, and velocity gradients at five depths. The theoretical thread that ties the inputs to the target is the Taylor-series expansion of the filtered product, $\overline{ab}-\bar{a}\bar{b}\approx \alpha \frac{\partial a}{\partial x_k}\frac{\partial b}{\partial x_k}$, which the paper uses to motivate why filtered velocity gradients should carry most of the information needed to predict EKE. In the multiple-input models, those gradients are supplied at exactly the depths where EKE is predicted, so the network is effectively learning a local regression from the pieces of the target itself plus surface information.

What would settle it

Retrain MI-ResNet holding out, from both inputs and outputs, all filtered velocity and gradient data at the deepest target level (for example, 2000 m), so the network must predict that level from surface fields and shallower profiles; if R² at 2000 m falls toward the surface-only ResNet's value rather than staying near 0.78, the claimed deep skill traces to the network reading the target itself.

Watch

Extended reading notes

Core claim

The paper's central claim is that spatially filtered EKE, defined by a top-hat filter at 1 degree as $\mathrm{EKE}=\frac{1}{2}(\overline{uu}+\overline{vv}-\bar{u}\bar{u}-\bar{v}\bar{v})$, is learnable as a function of sea surface variables (SSH, SST, bathymetry, surface geostrophic velocities and their gradients) combined with sparse vertical profiles of density, geostrophic velocity, and velocity gradients. Using the Taylor-series relation $\overline{ab}-\bar{a}\bar{b}\approx \alpha \frac{\partial a}{\partial x_k}\frac{\partial b}{\partial x_k}$, the authors argue that filtered velocity gradients are the natural bridge between the inputs and the target. The proposed MI-ResNet integrates a surface branch that reads a 17×17 spatial tensor around each location with a subsurface branch that reads vertical profiles at five depths, and it is trained on five high-EKE regions of the GLORYS12V1 reanalysis. The reported result is that this model outperforms the surface-only FCNN and ResNet, the multiple-input FCNN, and the first baroclinic mode (BC1) and first surface mode (SM1) reconstructions in every tested region, with global test-period R² of 0.859 at the surface and 0.775 at 2000 m, and that transfer learning preserves most of this skill when the inputs are switched to satellite and ISAS20 observational fields.

Load-bearing premise

The load-bearing premise is that it is legitimate to feed the model filtered subsurface velocities and their gradients at exactly the depths where EKE is predicted; since EKE is defined from those velocities, the deep inputs are near-deterministic proxies of the target, and if the intended task is reconstruction from independent surface observables this premise fails.

Editorial extensions

If this is right

  • If the MI-ResNet result is right, monthly maps of 1-degree-filtered EKE down to 2000 m can be produced for the global ocean outside the tropics from data that already exist: satellite SSH and SST plus gridded Argo climatology.
  • The reported improvement over BC1 and SM1 means that mode-decomposition reconstructions, which lose skill in the deep ocean, can be replaced by a data-driven vertical structure that keeps R² above roughly 0.6-0.8 at 2000 m.
  • Transfer learning from the reanalysis-trained network to observational inputs would let the method be applied without retraining from scratch in regions where only altimetry and Argo products are available.
  • Because the same inputs are global, the model can supply EKE fields to GM-style and backscatter eddy parameterizations, including estimates of the vertical structure of eddy mixing.
  • The paper's own discussion extends the framework to other subsurface variables such as temperature, salinity, currents, subgrid stress, and biochemical tracers.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the subsurface branch supplies velocity gradients at the target depths, a natural next test, not reported here, is to retrain with those gradients withheld and see how much deep skill remains; that experiment would separate genuine surface-driven reconstruction from local regression of the target.
  • The same architecture should transfer to other filtered quadratic quantities, since any product of filtered variables has the same Taylor-series structure; filtered enstrophy or tracer variance would be plausible candidates.
  • For practical deployment, the pointwise R² and relative-error numbers should be accompanied by uncertainty maps, because eddy parameterizations respond nonlinearly to EKE magnitude and confidence intervals matter for climate use.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes multiple-input neural network models (MI-FCNN and MI-ResNet) to estimate spatially filtered subsurface eddy kinetic energy (EKE) from sea surface variables together with vertical profiles of subsurface density and geostrophic velocities, motivated by a Taylor-series expansion of EKE. The models are trained on five regions of a global eddy-resolving reanalysis (GLORYS12V1) over 2001-2016, tested on 2017-2020 and on non-training regions, and transferred to observational inputs. The authors report that MI-ResNet outperforms surface-input FCNN/ResNet and physics-based first-mode models, with test-period R2 around 0.86 at the surface and 0.78 at 2000 m globally.

Significance. If the central claim were valid, the paper would provide a practical tool for mapping filtered subsurface EKE from satellite and gridded Argo data, with useful implications for eddy parameterizations. The study has clear strengths: a held-out temporal test period, evaluation on non-training regions, comparison with several baselines, transfer-learning experiments, and deposit of the main code at Zenodo. However, the validity of the central claim is undermined by the construction of the subsurface input branch, which supplies contemporaneous filtered velocities and gradients at exactly the depths where EKE is predicted; because EKE is defined from those same velocities (Eq. 5) and locally approximated by products of the gradients (Eq. 6), the reported deep-ocean skill largely reflects fitting a local target-proxy mapping rather than reconstructing unobserved EKE from independent observables.

major comments (3)
  1. [§3.2.2, Table 3, Eqs. (5)–(6)] The subsurface branch supplies ρ, u_g, v_g, and their horizontal gradients at exactly the five depths where EKE is output (0, -500, -1000, -1500, -2000 m). Since Eq. (5) defines EKE as a quadratic functional of the filtered velocities and Eq. (6) states that ab - \bar a \bar b ≈ α (∂a/∂x_k)(∂b/∂x_k), the filtered velocity gradients at depth are an approximate deterministic proxy for the target EKE at the same depth. The network can therefore learn a fitted local closure from near-target fields, and the deep-ocean R² values in Fig. 12 (e.g., 0.775 at 2000 m globally) do not measure the ability to reconstruct unobserved EKE from independent surface and Argo data. This also invalidates the comparison against the FCNN/ResNet models, which are deliberately denied this near-target channel, and undermines the headline claim in the Abstract and §5. Please remove the contemporaneous subsurface velocity/gradient inputs, use genuine climatological (long-term mean) fields, or explicitly reframe the contribution as a subgrid-scale EKE closure; a control experiment with the subsurface branch withheld at test time is needed to quantify the leakage.
  2. [Abstract; §3.2.3, Table 3] The abstract and Table 3 describe the subsurface inputs as 'climatological variables,' but §3.2.3 states that the monthly mean subsurface filtered velocities and gradients are calculated at 1/2° resolution from the same reanalysis period as the target, and the evaluation uses monthly fields contemporaneous with each EKE month. These are not climatological fields. The distinction matters because the interpretation of the transfer-learning results depends on whether the subsurface branch carries time-varying target information. Please correct the terminology and clearly specify which fields (contemporaneous monthly versus long-term climatology) are used in each experiment.
  3. [§4, MI-ResNet (Obs.) transfer-learning experiments] The observational transfer-learning experiments do not describe how the subsurface velocities u_g, v_g and their gradients in Table 3 are obtained from the observational data (SSH, SST, ISAS20 temperature and salinity). Argo measures temperature and salinity, not velocity; the only description in §2.1 is that vertical profiles of velocities can be derived from the thermal wind relation using surface geostrophic velocities as references, but no equation or implementation detail is given for the observational branch. Without this information, the MI-ResNet (Obs.) results in Figures 4-9 and Figure 12 are not reproducible. Please specify the derivation, including the choice of reference velocity and how the gradients are computed after interpolation to the common grid.
minor comments (5)
  1. [Eq. (14)] The text calls the statistic 'volume-weighted' R², but the displayed definition uses a spatial average ⟨•⟩ over the region; please clarify whether vertical weighting is included or whether the metric is computed separately at each depth.
  2. [§3.1] The term 'Strurm-Liouville problem' is a typo and should be 'Sturm-Liouville problem.'
  3. [Figure 11 caption] The caption refers to 'EKEResNet GLORYS,' which should presumably be 'EKEMI-ResNet GLORYS'; the PDF panels also appear to be missing axis labels and units.
  4. [§2.2] The sentence 'Although a fixed filter kernel is used at all locations, Only the water area is considered...' has an awkward capitalization and word order; please rephrase for clarity.
  5. [Figure 12 caption] The legend labels 'GLORYS' and 'Observation' are not defined in the caption; please state explicitly that these denote the input-data source for the MI-ResNet model.

Circularity Check

2 steps flagged · score 7.0 of 10

MI models receive filtered subsurface velocities and gradients at the same five depths where EKE is predicted, so the reported deep-ocean skill largely reduces to a learned local Taylor closure on near-deterministic proxies of the target.

  1. self definitional [Section 3.2.2 (Table 3); Equations (5)-(6)]
    "the subsurface variables include the vertical profiles of density 𝜌, subsurface filtered velocities (𝑢𝑔,𝑣𝑔), and subsurface filtered velocity gradients (∂𝑢𝑔/∂𝑥, ∂𝑢𝑔/∂𝑦, ∂𝑣𝑔/∂𝑥, ∂𝑣𝑔/∂𝑦) ... the vertical profiles of inputs and EKE are re-interpolated into five vertical layers from surface to 2000 m depth with 500 m intervals. EKE= 1/2(𝑢𝑢+𝑣𝑣−𝑢𝑢−𝑣𝑣) ... 𝑎𝑏−𝑎𝑏=𝛼 ∂𝑎/∂𝑥𝑘 ∂𝑏/∂𝑥𝑘+···"

    The MI models receive filtered velocities and their horizontal gradients at exactly the five depths at which EKE is output. Equation (5) defines EKE as a quadratic functional of those same filtered velocity fields, and Equation (6), which the paper uses to justify the inputs, approximates EKE by products of the filtered velocity gradients. The network can therefore learn a fitted local version of the Taylor formula essentially from fields that nearly determine the target. The reported deep skill, such as R2=0.78 at 2000 m globally, measures how well the network inverts a local velocity-gradient closure, not how well unobserved subsurface EKE is reconstructed from independent observables.

  2. fitted input called prediction [Abstract; Section 3.2.3; Section 5]
    "a multiple-input neural network approach is proposed to reconstruct the subsurface monthly mean EKE from sea surface variables and subsurface climatological variables (e.g., horizontal filtered velocity gradients) ... The monthly mean subsurface filtered velocity gradients are calculated at 1/2◦ resolution, the same horizontal resolution as the gridded Argo float observations ... The MI-ResNet model outperforms the FCNN, ResNet, and MI-FCNN models, and traditional physics-based models in both regional and global reconstruction of subsurface EKE in the upper 2000 m."

    The headline 'reconstruction' claim is presented as estimating subsurface EKE from surface data plus sparse subsurface profiles, but the actual subsurface branch inputs are contemporaneous monthly filtered velocities and gradients at the five output depths, not independent climatological constraints. The comparison with FCNN, ResNet, and BC1/SM1 is therefore biased, because those baselines are deliberately denied the near-target subsurface channel. What the MI models demonstrate is that a flexible network can emulate the Taylor relation of Equation (6) from target-related fields; that is a legitimate subgrid-scale closure but not a reconstruction of unobserved EKE.

full rationale

The central circularity is confined to the multiple-input models. The surface-only FCNN and ResNet models are genuinely predictive: their inputs are SSH, SST, H, β_t, and surface geostrophic velocities and gradients, none of which is the target, and their moderate deep skill (R2 around 0.3-0.4 at 2000 m) is an honest surface-to-interior inference. The MI models, however, add a subsurface branch whose inputs are the filtered velocities and gradients at the same five depths as the EKE output (Table 3). Since EKE is defined from those velocity fields (Equation 5), and Equation (6) approximates it by the same gradients, the network can reproduce deep EKE by learning a local Taylor-like closure from near-deterministic proxies. The abstract's 'subsurface climatological variables' phrasing does not cure this: Section 3.2.3 states the inputs are monthly mean filtered velocity gradients, contemporaneous with the monthly EKE target. The comparison with FCNN/ResNet and BC1/SM1 is also unfair because those baselines are deliberately denied the near-target channel. The paper's self-citations (C. Xie et al. 2021, 2023a, 2023b, 2024) are methodological or data-repository citations and are not load-bearing. If reframed as learning a subgrid-scale closure for filtered EKE from local velocity-gradient fields, the MI result is legitimate and non-circular; as a claim of reconstructing unobserved subsurface EKE, the result partially reduces by construction to the inputs.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on reanalysis-as-ground-truth, geostrophic balance outside the tropics, the Taylor-style approximation of EKE by velocity-gradient products, and the assumption that same-depth filtered velocity gradients are acceptable inputs. The free parameters are mostly architecture and training choices; no new physical entities are introduced.

free parameters (5)
  • Network architecture hyperparameters = layer widths 64/256/128, kernel 5x5, dropout 0.3, L2 1e-5, initial LR 1e-3, decay 0.8 per 10 epochs, batch size 512…
    Chosen by hand in §3.2.1-3.2.3; central performance comparisons depend on these choices.
  • Filter width Δ = 1 degree
    Selected in §2.2 as the spatial scale defining EKE; not fitted to data but a modeling choice that shapes the target.
  • Vertical discretization = 5 layers at 0, 500, 1000, 1500, 2000 m
    Interpolation choice in §3.2.2; coarsens the vertical profiles fed to the MI models.
  • Validity floor for N = 1e-5 s^-1
    Imposed for computing BC1/SM1 vertical modes in §3.1, following Stanley et al. (2020); not fitted by this paper.
  • Training region selection = 5 regions covering ~14.5% of the global ocean
    Choice in §3.2.3; generalization claims are conditioned on this selection and are tested outside the selected regions.
assumptions (6)
  • domain assumption Geostrophic balance is valid outside the 10-degree equatorial band.
    Equations (1)-(2) derive surface velocities from SSH; §2.1 explicitly restricts the analysis to latitudes beyond 10 degrees.
  • domain assumption Eddy-resolving GLORYS reanalysis provides trustworthy 'ground truth' EKE.
    All R2 and Er scores are computed against GLORYS EKE (§2.2, Eq. 14), not against direct subsurface observations.
  • standard math Top-hat spatial filter with land mask implements the intended scale decomposition.
    Equation (4); used to define EKE and inputs, following prior coarse-graining literature.
  • domain assumption Taylor-series expansion (Eq. 6) is a valid local approximation for EKE.
    Used in §2.2 and §3.2.2 to justify adding filtered velocity gradients as inputs.
  • domain assumption Surface and subsurface geostrophic velocities can be derived from SSH and density via geostrophy and thermal wind.
    §2.1 and §3.2.2; the observational implementation of the inputs relies on these relations.
  • domain assumption EKE vertical structure follows the separable form EKE = EKE_s Φ^2(z) for the physics baselines.
    Equation (11) is used for BC1 and SM1 models; it is not used by the neural networks but underpins the comparison baselines.

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Cite this review

Pith. "Pith review of Global Estimation of Subsurface Eddy Kinetic Energy of Mesoscale Eddies Using a Multiple-input Residual Neural Network." pith.science (2026). https://pith.science/paper/7GJRWM6D

@misc{pith2026241210656,
  author       = {Pith},
  title        = {Pith review of: Global Estimation of Subsurface Eddy Kinetic Energy of Mesoscale Eddies Using a Multiple-input Residual Neural Network},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7GJRWM6D}},
  note         = {Machine review of arXiv:2412.10656}
}
read the original abstract

Oceanic eddy kinetic energy (EKE) is a key quantity for measuring the intensity of mesoscale eddies and for parameterizing eddy effects in ocean climate models. Three decades of satellite altimetry observations allow a global assessment of sea surface information. However, the subsurface EKE with spatial filter has not been systematically studied due to the sparseness of subsurface observational data. The subsurface EKE can be inferred both theoretically and numerically from sea surface observations but is limited by the issue of decreasing correlation with sea surface variables as depth increases. In this work, inspired by the Taylor-series expansion of subsurface EKE, a multiple-input neural network approach is proposed to reconstruct the subsurface monthly mean EKE from sea surface variables and subsurface climatological variables (e.g., horizontal filtered velocity gradients). Four neural networks are trained on a high-resolution global ocean reanalysis dataset, namely, surface-input fully connected neural network model (FCNN), surface-input Residual neural network model (ResNet), multiple-input fully connected neural network model (MI-FCNN), and multiple-input residual neural network model (MI-ResNet). The proposed MI-FCNN and MI-ResNet models integrate the surface input variables and the vertical profiles of subsurface variables. The MI-ResNet model outperforms the FCNN, ResNet, and MI-FCNN models, and traditional physics-based models in both regional and global reconstruction of subsurface EKE in the upper 2000 m. In addition, the MI-ResNet model performs well for both regional and global observational data based on transfer learning. These findings reveal the potential of the MI-ResNet model for efficient and accurate reconstruction of subsurface oceanic variables.

Figures

Figures reproduced from arXiv: 2412.10656 by the authors.

Figure 1
Figure 1. The multiple-year averaged surface EKE and meridional velocity (𝑢) as functions of longitude and latitude using the eddy-resolving GLORYS reanalysis and altimetric data for the period 2001-2020: (a) EKE𝑠 Truth, (b) EKE𝑠 Obs. , (c) u𝑠 Truth, (d) u𝑠 Obs. . The latitude region between 10◦S and 10◦N is shaded in grey. Gray dashed lines in (a) and (b) denote the isopleths of EKE with 0.01 m2 /s 2 . The five representativ… view at source ↗
Figure 2
Figure 2. Schematic diagram of the MI-ResNet structure used in this study for estimating subsurface EKE. The first branch of inputs (Input 1) denotes sea surface variables, the second branch of inputs (Input 2) denotes the vertical profiles of variables, and the output of the network is the profile of EKE. 3.2.3 Training and validation details The training process is presented in detail after introducing the four neural netwo… view at source ↗
Figure 3
Figure 3. a shows that the training converges effectively after 200 epochs, and is terminated around 250 epochs. 0 100 200 300 Global iterations 0 0.1 0.2 0.3 L o s s (a) Training loss Validation loss 2000 2005 2010 2015 2020 time (year) 0 0.2 0.4 0.6 0.8 1 R 2 (b) Surface -500m -1000m -1500m -2000m 2000 2005 2010 2015 2020 time (year) (c) [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: The temporally averaged coefficients of efficiency 𝑅 2 of EKE produced by different models (BC1, SM1, FCNN, ResNet, MI-FCNN, and MI-ResNet) for the test dataset (2017-2020): (a) GSR, (b) KR, (c) AR, (d) BMCR. 0 0.2 0.4 0.6 0.8 1 ErjE K E (a) BC1 SM1 FCNN ResNet MI-FCNN…
Figure 5
Figure 5. Figure 5: The temporally averaged relative error 𝐸𝑟 of EKE produced by different models (BC1, SM1, FCNN, ResNet, MI-FCNN, and MI-ResNet) for the test dataset (2017-2020): (a) GSR, (b) KR, (c) AR, (d) BMCR [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: The time series of the regional average EKE diagnosed from the eddy-resolving GLORYS re￾analysis data and reconstructed from the MI-ResNet model with both eddy-resolving GLORYS reanalysis and observational data: (a) GSR, (b) KR, (c) AR, (d) BMCR. The dashed black lines…
Figure 7
Figure 7. Figure 7: The time series of the EKE diagnosed from the eddy-resolving GLORYS reanalysis data and reconstructed from the MI-ResNet model with both eddy-resolving GLORYS reanalysis and observational data at different locations: (a) GSR (43◦N, 53◦W), (b) KR (36◦N, 158◦E), (c) AR (…
Figure 8
Figure 8. Figure 8: The temporally averaged coefficients of efficiency 𝑅 2 and relative error 𝐸𝑟 of EKE over the SPOR produced by different models (BC1, SM1, FCNN, ResNet, MI-FCNN, and MI-ResNet) for the test dataset (2017-2020): (a) 𝑅 2 , (b) 𝐸𝑟 . Figures 9a and b present the time series…
Figure 9
Figure 9. Figure 9: The time series of EKE diagnosed from the eddy-resolving GLORYS reanalysis data and recon￾structed from the MI-ResNet model with both eddy-resolving GLORYS reanalysis and observational data at SPOR: (a) region-weighted mean EKE, (b) Single location (32◦S, 154◦W). The d…
Figure 10
Figure 10. Figure 10: The contours of temporal averaged EKE over 2017 to 2020 years at different depths around the global ocean: (a) Ground truth (0 m), (b) MI-ResNet (GLORYS, 0 m), (c) MI-ResNet (Observation, 0 m), (d) Ground truth (-1000 m), (e) MI-ResNet (GLORYS, -1000 m), (f) MI-ResNet…
Figure 11
Figure 11. Figure 11: The probability density functions of EKETruth, EKEResNet GLORYS, and EKEResNet Obs. in the training region (TR) and global ocean (GO): (a) TR: surface, (b) TR: -1000 m, (c) TR: -2000 m, (d) GO: surface, (e) GO: -1000 m, (f) GO: -2000 m. –19– [PITH_FULL_IMAGE:figures/…
Figure 12
Figure 12. Figure 12: The temporally averaged coefficients of efficiency 𝑅 2 and relative error 𝐸𝑟 of EKE over the global ocean produced by the MI-ResNet model based on the eddy-resolving GLORYS reanalysis and observational data: (a) 𝑅 2 (MI-ResNet: GLORYS), (b) 𝑅 2 (MI-ResNet: Observation…

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Works this paper leans on

139 extracted references · 78 canonical work pages

  1. [1]

    apacite url apacite =6pt Acknowledgments. 6pt 1sp \@dates Received \@recvdate\@empty\@rcvaccrule \@recvdate \@revisedate\@empty ; revised \@revisedate; \@accptdate\@empty \@revisedate\@empty; accepted \@accptdate \@pubdate\@empty. ; published \@pubdate. -2pt \@authaddrs @list\@empty =.15in @list 1sp @list =9pt plus 2pt minus 6pt \@sluginfo width 4pc =3000...

    2001

  2. [2]

    gc" journal option for G-Cubed Nov 3, 2003 M Kelly, fixed noindent in subsubsubsection titles and for all sections in rog option Oct 2, 2003 M Kelly, added

    \@ifstar \@figbox \@figbox \@figbox#1#2#3 to !#1! #3 [#1][c] !#2!#3 \@tempdima#2 \@tempdima by2 \@tempdima by- \@tempdima by- \@height\@tempdima\@depth\@tempdima\@width @ to @ #3 Bib ??? ??? ??? =0 =0 = @figure=0 @table=0 #1 --#1 -24pt -2ex #1 0= #1 to 0 #1 I NDEX T ERMS: #1 #1 Citation: #1 Feb 9, 2009 Changed name and references to name from agu2001 to a...

    2009

  3. [3]

    , " * write output.state after.block = add.period write newline

    ENTRY address archive author booktitle chapter doi edition editor eid eprint howpublished department institution journal key month note number organization pages publisher school series title type url volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 '...

  4. [4]

    write newline

    " write newline "" before.all 'output.state := FUNCTION if.digit duplicate "0" = swap duplicate "1" = swap duplicate "2" = swap duplicate "3" = swap duplicate "4" = swap duplicate "5" = swap duplicate "6" = swap duplicate "7" = swap duplicate "8" = swap "9" = or or or or or or or or or FUNCTION n.separate 't := "" #0 'numnames := t empty not t #-1 #1 subs...

  5. [5]

    APACrefauthors \ 2019

    Aluie-2019 APACrefauthors Aluie, H. APACrefauthors \ 2019 . Convolutions on the sphere: Commutation with differential operators Convolutions on the sphere: Commutation with differential operators . GEM-International Journal on Geomathematics 10 9 1-30

    2019

  6. [6]

    , Hecht, M

    Aluie-2018 APACrefauthors Aluie, H. , Hecht, M. \ Vallis, G K. APACrefauthors \ 2018 . Mapping the energy cascade in the North Atlantic Ocean: The coarse-graining approach Mapping the energy cascade in the north atlantic ocean: The coarse-graining approach . Journal of Physical Oceanography 48 2 225–244

    2018

  7. [7]

    \ Eakins, B W

    Amante-2009 APACrefauthors Amante, C. \ Eakins, B W. APACrefauthors \ 2009 . ETOPO1 1 Arc-minute global relief model: P rocedures, data sources and analysis. NOAA Technical Memorandum NESDIS NGDC-24, National Geophysical Data Center, NOAA. Etopo1 1 arc-minute global relief model: P rocedures, data sources and analysis. noaa technical memorandum nesdis ngd...

    2009

  8. [8]

    , Melnichenko, O

    Amores-2017 APACrefauthors Amores, A. , Melnichenko, O. \ Maximenko, N. APACrefauthors \ 2017 . Coherent mesoscale eddies in the North Atlantic subtropical gyre: 3-D structure and transport with application to the salinity maximum Coherent mesoscale eddies in the north atlantic subtropical gyre: 3-d structure and transport with application to the salinity...

    2017

Show all 139 references
  1. [9]

    \ Zanna, L

    Anstey-2017 APACrefauthors Anstey, J A. \ Zanna, L. APACrefauthors \ 2017 . A deformation-based parameterization of ocean mesoscale eddy reynolds stresses A deformation-based parameterization of ocean mesoscale eddy reynolds stresses . Ocean Modelling 112 99--111

    2017

  2. [10]

    , Filoche, A

    Archambault-2024 APACrefauthors Archambault, T. , Filoche, A. , Charantonis, A. , B \'e r \'e ziat, D. \ Thiria, S. APACrefauthors \ 2024 . Learning sea surface height interpolation from multi-variate simulated satellite observations Learning sea surface height interpolation f...

    2024

  3. [11]

    APACrefauthors \ 2019

    Bachman-2019 APACrefauthors Bachman, S D. APACrefauthors \ 2019 . The GM + E closure: A framework for coupling backscatter with the Gent and McWilliams parameterization The gm + e closure: A framework for coupling backscatter with the gent and mcwilliams parameterization . Oce...

    2019

  4. [12]

    , Smith, T M

    Banzon-2016 APACrefauthors Banzon, V. , Smith, T M. , Chin, T M. , Liu, C. \ Hankins, W. APACrefauthors \ 2016 . A long-term record of blended satellite and in situ sea-surface temperature for climate monitoring, modeling and environmental studies A long-term record of blended...

    2016

  5. [13]

    , Alvera-Azc \'a rate, A

    Barth-2020 APACrefauthors Barth, A. , Alvera-Azc \'a rate, A. , Licer, M. \ Beckers, J M. APACrefauthors \ 2020 . DINCAE 1.0: a convolutional neural network with error estimates to reconstruct sea surface temperature satellite observations DINCAE 1.0: a convolutional neural ne...

    2020

  6. [14]

    , Sandwell, D T

    Becker-2009 APACrefauthors Becker, J J. , Sandwell, D T. , Smith, W H F. , Braud, J. , Binder, B. , Depner, J. Weatherall, P. APACrefauthors \ 2009 . Global bathymetry and elevation data at 30 Arc seconds resolution: SRTM30\_PLUS Global bathymetry and elevation data at 30 arc ...

    2009

  7. [15]

    , Rackow, T

    Beech-2022 APACrefauthors Beech, N. , Rackow, T. , Semmler, T. , Danilo, S. , Wang, Q. \ Jung, T. APACrefauthors \ 2022 . Long-term evolution of ocean eddy activity in a warming world Long-term evolution of ocean eddy activity in a warming world . Nature Climate Change 12 910--917

    2022

  8. [16]

    \ Zanna, L

    Bolton-2019 APACrefauthors Bolton, T. \ Zanna, L. APACrefauthors \ 2019 . Applications of deep learning to ocean data inference and subgrid parameterization Applications of deep learning to ocean data inference and subgrid parameterization . Journal of Advances in Modeling Ear...

    2019

  9. [17]

    , Storer, B A

    Buzzicotti-2023 APACrefauthors Buzzicotti, M. , Storer, B A. , Khatri, H. , Griffies, S M. \ Aluie, H. APACrefauthors \ 2023 . Spatio-temporal coarse-graining decomposition of the global ocean geostrophic kinetic energy Spatio-temporal coarse-graining decomposition of the glob...

    2023

  10. [18]

    APACrefauthors \ 2008

    Cessi-2008 APACrefauthors Cessi, P. APACrefauthors \ 2008 . An energy--constrained parameterization of eddy buoyancy flux An energy--constrained parameterization of eddy buoyancy flux . Journal of Physical Oceanography 38 8 1807--1819

    2008

  11. [19]

    \ Charantonis, A A

    Chapman-2017 APACrefauthors Chapman, C. \ Charantonis, A A. APACrefauthors \ 2017 . Reconstruction of subsurface velocities from satellite observations using iterative self-organizing maps Reconstruction of subsurface velocities from satellite observations using iterative self...

    2017

  12. [20]

    , Schlax, M G

    Chelton-2011 APACrefauthors Chelton, D B. , Schlax, M G. \ Samelson, R M. APACrefauthors \ 2011 . Global observations of nonlinear mesoscale eddies Global observations of nonlinear mesoscale eddies . Progress in Oceanography 91 2 167-216

    2011

  13. [21]

    , Yang, K

    Chen-2018 APACrefauthors Chen, C. , Yang, K. , Ma, Y. \ Wang, Y. APACrefauthors \ 2018 . Reconstructing the surface temperature field by using sea surface data through self-organizing map method Reconstructing the surface temperature field by using sea surface data through sel...

    2018

  14. [22]

    Guanlan" science mission: China's novel contribution to space oceanography Concept design of the

    Chen-2019 APACrefauthors Chen, G. , Tang, J. , Zhao, C. , Wu, S. , Fangjie, Y. , Ma, C. Wu, L. APACrefauthors \ 2019 . Concept design of the "Guanlan" science mission: China's novel contribution to space oceanography Concept design of the "guanlan" science mission: China's nov...

    2019

  15. [23]

    , Ferziger, J H

    Clark-1979 APACrefauthors Clark, R A. , Ferziger, J H. \ Reynolds, W C. APACrefauthors \ 1979 . Evaluation of subgrid-scale models using an accurately simulated turbulent flow Evaluation of subgrid-scale models using an accurately simulated turbulent flow . Journal of Fluid Me...

    1979

  16. [24]

    , Renault, L

    Contreras-2023 APACrefauthors Contreras, M. , Renault, L. \ Marchesiello, P. APACrefauthors \ 2023 . Understanding energy pathways in the Gulf Stream Understanding energy pathways in the gulf stream . Journal of Physical Oceanography 53 3 719-736

    2023

  17. [25]

    , LaCasce, J H

    Lama-2016 APACrefauthors de La Lama, M S. , LaCasce, J H. \ Fuhr, H K. APACrefauthors \ 2016 . The vertical structure of ocean eddies The vertical structure of ocean eddies . Dynamics and Statistics of the Climate System 1 1 dzw001

    2016

  18. [26]

    , Liu, H

    Ding-2024 APACrefauthors Ding, M. , Liu, H. , Lin, P. , Meng, Y. \ Yu, Z. APACrefauthors \ 2024 . Evaluating westward and eastward propagating mesoscale eddies using a 1/10 ^ global ocean simulation of CAS-LICOM3 Evaluating westward and eastward propagating mesoscale eddies us...

    2024

  19. [27]

    \ Greatbatch, R J

    Eden-2008 APACrefauthors Eden, C. \ Greatbatch, R J. APACrefauthors \ 2008 . Towards a mesoscale eddy closure Towards a mesoscale eddy closure . Ocean Modelling 20 3 223--239

    2008

  20. [28]

    , Bony, S

    Eyring-2016 APACrefauthors Eyring, V. , Bony, S. , Meehl, G A. , Senior, C A. , Stevens, B. , Stouffer, R J. \ Taylor, K E. APACrefauthors \ 2016 . Overivew of the coupled model intercomparison project phase 6 (CMIP6) experimental design and organization Overivew of the couple...

    2016

  21. [29]

    , Thierry, R

    Fabienne-2016 APACrefauthors Fabienne, G. , Thierry, R. , Virginie, T. , Nicolas, K. \ Karina, v S. APACrefauthors \ 2016 . In-situ based reanalysis of the global ocean temperature and salinity with ISAS: variability of the heat content and steric height In-situ based reanalys...

    2016

  22. [30]

    , Sondak, D

    Fang-2019 APACrefauthors Fang, R. , Sondak, D. , Protopapas, P. \ Succi, S. APACrefauthors \ 2019 . Neural network models for the anisotropic Reynolds stress tensor in turbulent channel flow Neural network models for the anisotropic reynolds stress tensor in turbulent channel ...

    2019

  23. [31]

    , Liu, C

    Feng-2022 APACrefauthors Feng, L. , Liu, C. , K o hl, A. \ Wang, F. APACrefauthors \ 2022 . Seasonality of four types of baroclinic instability in the global oceans Seasonality of four types of baroclinic instability in the global oceans . Journal of Geophysical Research: Ocea...

    2022

  24. [32]

    \ Wunsch, C

    Ferrari-2010 APACrefauthors Ferrari, R. \ Wunsch, C. APACrefauthors \ 2010 . The distribution of eddy kinetic and potential energies in the global ocean The distribution of eddy kinetic and potential energies in the global ocean . Tellus, Series A 62 92-108

    2010

  25. [33]

    , Gagne II, D J

    Foster-2021 APACrefauthors Foster, D. , Gagne II, D J. \ Whitt, D B. APACrefauthors \ 2021 . Probabilistic machine learning estimation of coean mixed layer depth from dense satellite and sparse in situ observations Probabilistic machine learning estimation of coean mixed layer...

    2021

  26. [34]

    , M u nnich, M

    Frenger-2015 APACrefauthors Frenger, I. , M u nnich, M. , Gruber, N. \ Knutti, R. APACrefauthors \ 2015 . Southern Ocean eddy phenomenology Southern ocean eddy phenomenology . Journal of Geophysical Research: Oceans 120 11 7413–7449

    2015

  27. [35]

    , Pavelsky, T

    Fu-2024 APACrefauthors Fu, L L. , Pavelsky, T. , Cretaux, J F. , Morrow, R. , Farrar, J T. , Vaze, P. Dibarboure, G. APACrefauthors \ 2024 . The surface water and ocean topography mission: A breakthrough in radar remote sensing of the ocean and land surface water The surface w...

    2024

  28. [36]

    \ Ubelmann, C

    Fu-2014 APACrefauthors Fu, L L. \ Ubelmann, C. APACrefauthors \ 2014 . On the transition from profile altimeter to swath altimeter for observing global ocean surface topography On the transition from profile altimeter to swath altimeter for observing global ocean surface topog...

    2014

  29. [37]

    Gao-2023 APACrefauthors Gao, X. , Li, Y. , Lin, P. , Zhang, L. , Ren, Q. , Lu, Y. \ Wang, F. APACrefauthors \ 2023 . Origins of multidecadal SST variations in the Southern Atlantic and Indian Oceans since the 1960s Origins of multidecadal sst variations in the southern atlanti...

    2023

  30. [38]

    \ Mcwilliams, J C

    Gent-1990-mixing APACrefauthors Gent, P R. \ Mcwilliams, J C. APACrefauthors \ 1990 . Isopycnal mixing in ocean circulation models Isopycnal mixing in ocean circulation models . Journal of Physical oceanography 20 1 150--155

    1990

  31. [39]

    , Manucharyan, G E

    George-2021 APACrefauthors George, T M. , Manucharyan, G E. \ Thompson, A F. APACrefauthors \ 2021 . Deep learning to infer eddy heat fluxes from sea surface height patterns of mesoscale turbulence Deep learning to infer eddy heat fluxes from sea surface height patterns of mes...

    2021

  32. [40]

    APACrefauthors \ 1992

    Germano-1992 APACrefauthors Germano, M. APACrefauthors \ 1992 . Turbulence: the filtering approach Turbulence: the filtering approach . Journal of Fluid Mechanics 238 325--336

    1992

  33. [41]

    APACrefauthors \ 1982

    Gill-1982 APACrefauthors Gill, A E. APACrefauthors \ 1982 . Atmosphere-ocean dynamics Atmosphere-ocean dynamics . Academic Academic Press

    1982

  34. [42]

    , LaCasce, J H

    Groeskamp-2020 APACrefauthors Groeskamp, S. , LaCasce, J H. , McDougall, T J. \ Rog\' e , M. APACrefauthors \ 2020 . Full-depth global estimates of ocean mesoscale eddy mixing from observations and theory Full-depth global estimates of ocean mesoscale eddy mixing from observat...

    2020

  35. [43]

    , Loose, N

    Grooms-2021 APACrefauthors Grooms, I. , Loose, N. , Abernathey, R. , Steinberg, J M. , Bachman, S D. , Marques, G. E., Y. APACrefauthors \ 2021 . Diffusion-based smoothers for spatial filtering of gridded geophysical data Diffusion-based smoothers for spatial filtering of grid...

    2021

  36. [44]

    , Chen, R

    Guan-2022 APACrefauthors Guan, W. , Chen, R. , Zhang, H. , Yang, Y. \ Wei, H. APACrefauthors \ 2022 . Seasonal surface eddy mixing in the Kuroshio Extension : Estimation and machine learning prediction Seasonal surface eddy mixing in the Kuroshio Extension : Estimation and mac...

    2022

  37. [45]

    \ Zanna, L

    Guillaumin-2021 APACrefauthors Guillaumin, A P. \ Zanna, L. APACrefauthors \ 2021 . Stochastic-deep learning parameterization of ocean momentum forcing Stochastic-deep learning parameterization of ocean momentum forcing . Journal of Advances in Modeling Earth Systems 13 9 e202...

    2021

  38. [46]

    , Bachman, S

    Guo-2022 APACrefauthors Guo, Y. , Bachman, S. , Bryan, F. \ Bishop, S. APACrefauthors \ 2022 . Increasing trends in oceanic surface poleward eddy heat flux observed over the past three decades Increasing trends in oceanic surface poleward eddy heat flux observed over the past ...

    2022

  39. [47]

    \ Czaja, A

    Hausmann-2012 APACrefauthors Hausmann, U. \ Czaja, A. APACrefauthors \ 2012 . The observed signature of mesoscale eddies in sea surface temperature and the associated heat transport The observed signature of mesoscale eddies in sea surface temperature and the associated heat t...

    2012

  40. [48]

    \ Mahadevan, A

    He-2024 APACrefauthors He, J. \ Mahadevan, A. APACrefauthors \ 2024 . Vertical velocity diagnosed from surface data with machine learning Vertical velocity diagnosed from surface data with machine learning . Geophysical Research Letters 51 6 e2023GL104835

    2024

  41. [49]

    , Penduff, T

    Hogg-2022 APACrefauthors Hogg, A M. , Penduff, T. , Close, S E. , Dewar, W K. , Constantinou, N C. \ Martinez-Moreno, J. APACrefauthors \ 2022 . Circumpolar variations in the chaotic nature of Southern Ocean eddy dynamics Circumpolar variations in the chaotic nature of souther...

    2022

  42. [50]

    APACrefauthors \ 1975

    Hoskins-1975 APACrefauthors Hoskins, B J. APACrefauthors \ 1975 . The geostrophic momentum approximation and the semi-geostrophic equations The geostrophic momentum approximation and the semi-geostrophic equations . Journal of the Atmosphere Sciences 32 2 233-242

    1975

  43. [51]

    , Liu, C

    Huang-2020 APACrefauthors Huang, B. , Liu, C. , Banzon, V. , Freeman, E. , Graham, G. , Hankins, B. Zhang, H M. APACrefauthors \ 2020 . Improvements of the Daily Optimum Interpolation Sea Surface Temperature (DOISST) Version 2.1 Improvements of the daily optimum interpolation ...

    2020

  44. [52]

    APACrefauthors \ 1964

    Huber-1964 APACrefauthors Huber, P J. APACrefauthors \ 1964 . Robust estimation of a location parameter Robust estimation of a location parameter . Annals of mathematical statistics 35 1 73--101

    1964

  45. [53]

    , Guan, Y

    Jakhar-2024 APACrefauthors Jakhar, K. , Guan, Y. , Mojgani, R. , Chattopadhyay, A. , Hassanzadeh, P. \ Zanna, L. APACrefauthors \ 2024 . Learning closed-form equations for subgrid-scale closures from high-fidelity data: Promises and challenges Learning closed-form equations fo...

    2024

  46. [54]

    , Adcroft, A

    Jansen-2019 APACrefauthors Jansen, M F. , Adcroft, A. , Khani, S. \ Kong, H. APACrefauthors \ 2019 . Toward an energetically consistent, resolution aware parameterization of ocean mesoscale eddies Toward an energetically consistent, resolution aware parameterization of ocean m...

    2019

  47. [55]

    \ Marotzke, J

    Jayne-2002 APACrefauthors Jayne, S R. \ Marotzke, J. APACrefauthors \ 2002 . The oceanic eddy heat transport The oceanic eddy heat transport . Journal of Physical Oceanography 32 12 3328-3345

    2002

  48. [56]

    , Eric, G

    Jean-Michel-2021 APACrefauthors Jean-Michel, L. , Eric, G. , Romain, B B. \ et al. APACrefauthors \ 2021 . The Copernicus global 1/12 oceanic and sea ice GLORYS12 reanalysis The copernicus global 1/12 oceanic and sea ice glorys12 reanalysis . Frontiers in Earth Science 9 698876

    2021

  49. [57]

    , Danilov, S

    Juricke-2020 APACrefauthors Juricke, S. , Danilov, S. , Koldunov, N. , Oliver, M. \ Sidorenko, D. APACrefauthors \ 2020 . Ocean kinetic energy backscatter parameterization on unstructured grids: Impact on global eddy-permitting simulations Ocean kinetic energy backscatter para...

    2020

  50. [58]

    , Danilov, S

    Juricke-2019 APACrefauthors Juricke, S. , Danilov, S. , Kutsenko, A. \ Oliver, M. APACrefauthors \ 2019 . Ocean kinetic energy backscatter parameterizations on unstructured grids: Impact on mesoscale turbulence in a channel Ocean kinetic energy backscatter parameterizations on...

    2019

  51. [59]

    \ Dawson, C N

    Khani-2023 APACrefauthors Khani, S. \ Dawson, C N. APACrefauthors \ 2023 . A gradient based subgrid-scale parameterization for ocean mesoscale eddies A gradient based subgrid-scale parameterization for ocean mesoscale eddies . Journal of Advances in Modeling Earth Systems 15 2...

    2023

  52. [60]

    , Griffies, S M

    Khatri-2021 APACrefauthors Khatri, H. , Griffies, S M. , Uchida, T. , Wang, H. \ Menemenlis, D. APACrefauthors \ 2021 . Role of mixed-layer instabilities in the seasonal evolution of eddy kinetic energy spectra in a global submesoscale permitting simulation Role of mixed-layer...

    2021

  53. [61]

    Kingma-2014 APACrefauthors Kingma, D P. \ Ba, J. APACrefauthors \ 2014 . Adam: A method for stochastic optimization Adam: A method for stochastic optimization . ArXiv:1412.6980

    2014 arXiv

  54. [62]

    \ Lapeyre, G

    Klein-2009 APACrefauthors Klein, P. \ Lapeyre, G. APACrefauthors \ 2009 . The oceanic vertical pump induced by mesoscale and submesoscale turbulence The oceanic vertical pump induced by mesoscale and submesoscale turbulence . Annual Review of Marine Science 1 1 351-375

    2009

  55. [63]

    APACrefauthors \ 2012

    LaCasce-2012 APACrefauthors LaCasce, J H. APACrefauthors \ 2012 . Surface quasigeostrophic solutions and baroclinic modes with exponential stratification Surface quasigeostrophic solutions and baroclinic modes with exponential stratification . Journal of Physical Oceanography ...

    2012

  56. [64]

    APACrefauthors \ 2017

    LaCasce-2017 APACrefauthors LaCasce, J H. APACrefauthors \ 2017 . The prevalence of oceanic surface modes The prevalence of oceanic surface modes . Geophysical Research Letters 44 21 11097-11105

    2017

  57. [65]

    \ Groeskamp, S

    LaCasce-2020 APACrefauthors LaCasce, J H. \ Groeskamp, S. APACrefauthors \ 2020 . Baroclinic modes over rough bathymetry and the surface deformation radius Baroclinic modes over rough bathymetry and the surface deformation radius . Journal of Physical oceanography 50 10 2835–2847

    2020

  58. [66]

    APACrefauthors \ 2009

    Lapeyre-2009 APACrefauthors Lapeyre, G. APACrefauthors \ 2009 . What vertical mode does the altimeter reflect? O n the decomposition in baroclinic modes and on a surface-trapped mode What vertical mode does the altimeter reflect? O n the decomposition in baroclinic modes and o...

    2009

  59. [67]

    \ Klein, P

    Lapeyre-2006 APACrefauthors Lapeyre, G. \ Klein, P. APACrefauthors \ 2006 . Dynamics of the upper oceanic layers in terms of surface Quasigeostrophy theory Dynamics of the upper oceanic layers in terms of surface quasigeostrophy theory . Journal of Physical oceanography 36 2 165-176

    2006

  60. [68]

    APACrefauthors \ 1975

    Leonard-1975 APACrefauthors Leonard, A. APACrefauthors \ 1975 . Energy cascade in large-eddy simulations of turbulent fluid flows Energy cascade in large-eddy simulations of turbulent fluid flows . Advances in Geophysics 18 237--248

    1975

  61. [69]

    , Peng, S

    Liu-2017 APACrefauthors Liu, L. , Peng, S. \ Huang, R. APACrefauthors \ 2017 . Reconstruction of ocean's interior from observed sea surface information Reconstruction of ocean's interior from observed sea surface information . Journal of Geophysical Research: Oceans 122 2 1042-1056

    2017

  62. [70]

    , Peng, S

    Liu-2014 APACrefauthors Liu, L. , Peng, S. , Wang, J. \ Huang, R. APACrefauthors \ 2014 . Retrieving density and velocity fields of the ocean’s interior from surface data Retrieving density and velocity fields of the ocean’s interior from surface data . Journal of Geophysical ...

    2014

  63. [71]

    , Zheng, Q

    Liu-2021 APACrefauthors Liu, Y. , Zheng, Q. \ Li, X. APACrefauthors \ 2021 . Characteristics of global ocean abnormal mesoscale eddies derived from the fusion of sea surface height and temperature data by deep learning Characteristics of global ocean abnormal mesoscale eddies ...

    2021

  64. [72]

    , Bachman, S

    Loose-2023 APACrefauthors Loose, N. , Bachman, S. , Grooms, I. \ Jansen, M. APACrefauthors \ 2023 . Diagnosing scale-dependent energy cycles in a high-resolution isopycnal ocean model Diagnosing scale-dependent energy cycles in a high-resolution isopycnal ocean model . Journal...

    2023

  65. [73]

    , Kamenkovich, I

    Luyy-2022 APACrefauthors Lu, Y. , Kamenkovich, I. \ Berloff, P. APACrefauthors \ 2022 . Properties of the lateral mesoscale eddy-induced transport in a high-resolution ocean model: Beyond the flux-gradient relation Properties of the lateral mesoscale eddy-induced transport in ...

    2022

  66. [74]

    \ NEMO-team

    Madec2016 APACrefauthors Madec, G. \ NEMO-team. APACrefauthors \ 2016 . NEMO Ocean Engine Nemo ocean engine . Institut Pierre-Simon Laplace Technical Report

    2016

  67. [75]

    , Siegelman, L

    Manucharyan-2021 APACrefauthors Manucharyan, G E. , Siegelman, L. \ Klein, P. APACrefauthors \ 2021 . A deep learning approach to spatiotemporal sea surface height interpolation and estimation of deep currents in geostrophic ocean turbulence A deep learning approach to spatiot...

    2021

  68. [76]

    \ Adcroft, A J

    Marshall-2010 APACrefauthors Marshall, D P. \ Adcroft, A J. APACrefauthors \ 2010 . Parameterization of ocean eddies: Potential vorticity mixing, energetics and Arnold’s first stability theorem Parameterization of ocean eddies: Potential vorticity mixing, energetics and arnold...

    2010

  69. [77]

    , Scott, J R

    Marshall-2017 APACrefauthors Marshall, J. , Scott, J R. , Romanou, A. , Kelly, M. \ Leboissetier, A. APACrefauthors \ 2017 . The dependence of the ocean's moc on mesoscale eddy diffusivities: A model study The dependence of the ocean's moc on mesoscale eddy diffusivities: A mo...

    2017

  70. [78]

    , Manucharyan, G E

    Martin-2023 APACrefauthors Martin, S A. , Manucharyan, G E. \ Klein, P. APACrefauthors \ 2023 . Synthesizing sea surface temperature and satellite altimetry observations using deep learning improves the accuracy and resolution of gridded sea surface height anomalies Synthesizi...

    2023

  71. [79]

    , Manucharyan, G E

    Martin-2024 APACrefauthors Martin, S A. , Manucharyan, G E. \ Klein, P. APACrefauthors \ 2024 . Deep learning improves global satellite observations of ocean eddy dynamics Deep learning improves global satellite observations of ocean eddy dynamics . Geophysical Research Letter...

    2024

  72. [80]

    , Hogg, A M

    Martinez-Moreno-2022 APACrefauthors Martinez-Moreno, J. , Hogg, A M. \ England, M H. APACrefauthors \ 2022 . Climatology, seasonality, and trends of spatially coherent ocean eddies Climatology, seasonality, and trends of spatially coherent ocean eddies . Journal of Geophysical...

    2022

  73. [81]

    , Knight, Z

    McCuen-2006 APACrefauthors McCuen, R H. , Knight, Z. \ Cutter, A G. APACrefauthors \ 2006 . Evaluation of the Nash--Sutcliffe efficiency index Evaluation of the Nash--Sutcliffe efficiency index . Journal of Hydrologic Engineering 11 6 597--602

    2006

  74. [82]

    \ Katz, J

    Meneveau-2000 APACrefauthors Meneveau, C. \ Katz, J. APACrefauthors \ 2000 . Scale-invariance and turbulence models for large-eddy simulation Scale-invariance and turbulence models for large-eddy simulation . Annual Review of Fluid Mechanics 32 1-32

    2000

  75. [83]

    , Yan, C

    Meng-2021 APACrefauthors Meng, L. , Yan, C. , Zhuang, W. , Zhang, W. , Geng, X G. \ Yan, X H. APACrefauthors \ 2021 . Reconstructing high-resolution ocean subsurface and interior temperature and salinity anomalies from satellite observations Reconstructing high-resolution ocea...

    2021

  76. [84]

    , Stewart, A L

    Meng-2024 APACrefauthors Meng, S. , Stewart, A L. \ Manucharyan, G. APACrefauthors \ 2024 . Circumpolar transport and overturning strength inferred from satellite observables using deep learning in an eddying southern ocean channel model Circumpolar transport and overturning s...

    2024

  77. [85]

    \ Hakim, G J

    Mengzl-2024 APACrefauthors Meng, Z. \ Hakim, G J. APACrefauthors \ 2024 . Reconstructing the tropical Pacific upper ocean using online data assimilation with a deep learning model Reconstructing the tropical Pacific upper ocean using online data assimilation with a deep learni...

    2024

  78. [86]

    , Gonz \' a lez-Haro, C

    Miracca-Lage-2022 APACrefauthors Miracca-Lage, M. , Gonz \' a lez-Haro, C. , Napolitano, D C. , Isern-Fontanet, J. \ Polito, P S. APACrefauthors \ 2022 . Can the surface Quasi-Geostrophic (SQG) theory explain upper ocean dynamics in the South Atlantic Can the surface quasi-geo...

    2022

  79. [87]

    , Fu, L L

    Morrow-2019 APACrefauthors Morrow, R. , Fu, L L. , Ardhuin, F. , Benkiran, M. , Chapron, B. , Cosme, E. Zaron, E D. APACrefauthors \ 2019 . Global observations of fine-scale ocean surface topography with the surface water and ocean topography (SWOT) mission Global observations...

    2019

  80. [88]

    \ Sutcliffe, J V

    Nash-1970 APACrefauthors Nash, J E. \ Sutcliffe, J V. APACrefauthors \ 1970 . River flow forecasting through conceptual models part I--A discussion of principles River flow forecasting through conceptual models part I--A discussion of principles . Journal of Hydrology 10 3 282--290

    1970

  81. [89]

    , Zhai, X

    Ni-2023 APACrefauthors Ni, Q. , Zhai, X. , LaCasce, J H. , Chen, D. \ Marshall, D P. APACrefauthors \ 2023 . Full-depth eddy kinetic energy in the global ocean estimated from altimeter and Argo observations Full-depth eddy kinetic energy in the global ocean estimated from alti...

    2023

  82. [90]

    , Annaig, P M

    Nicolas-2023 APACrefauthors Nicolas, K. , Annaig, P M. \ Fabienne, G. APACrefauthors \ 2023 . ISAS temperature, salinity, dissolved oxygen gridded fields Isas temperature, salinity, dissolved oxygen gridded fields . SEANOE

    2023

  83. [91]

    \ Yang, Q

    Pan-2010 APACrefauthors Pan, S J. \ Yang, Q. APACrefauthors \ 2010 . A survey on transfer learning A survey on transfer learning . IEEE Transactions on Knowledge and Data Engineering 22 10 1345--1359

    2010

  84. [92]

    , Ellis, M

    Partee-2021 APACrefauthors Partee, S. , Ellis, M. , Rigazzi, A. , Shao, A E. , Bachman, S. , Marques, G. \ Robbins, B. APACrefauthors \ 2022 . Using machine learning at scale in HPC simulations with SmartSim : An application to ocean climate modeling Using machine learning at ...

    2021

  85. [93]

    , Bachelot, L

    Pauthenet-2022 APACrefauthors Pauthenet, E. , Bachelot, L. , Balem, K. , Maze, G. , Treguier, A M. , Roquet, F. Tandeo, P. APACrefauthors \ 2022 . Four-dimentional temperature, salinity and mixed-layer depth in the Gulf Stream, reconstructed from remote-sensing and in situ obs...

    2022

  86. [94]

    APACrefauthors \ 1987

    Pedlosky-1987 APACrefauthors Pedlosky, J. APACrefauthors \ 1987 . An inertial theory of the Equatorial undercurrent An inertial theory of the equatorial undercurrent . Journal of Physical oceanography 17 11 1978-1985

    1987

  87. [95]

    , Hecht, M

    Rai-2021 APACrefauthors Rai, S. , Hecht, M. , Maltrud, M. \ Aluie, H. APACrefauthors \ 2021 . Scale of oceanic eddy killing by wind from global satellite observations Scale of oceanic eddy killing by wind from global satellite observations . Science Advances 7 eabf4920

    2021

  88. [96]

    , Smith, T M

    Reynolds-2007 APACrefauthors Reynolds, R W. , Smith, T M. , Liu, C. , Chelton, D B. , Casey, K S. \ Schlax, M G. APACrefauthors \ 2007 . Daily high-resolution-blended analyses for sea surface temperature Daily high-resolution-blended analyses for sea surface temperature . Jour...

    2007

  89. [97]

    , B o ning, W., Claus , Greatbatch, R J

    Rieck-2015 APACrefauthors Rieck, J K. , B o ning, W., Claus , Greatbatch, R J. \ Scheinert, M. APACrefauthors \ 2015 . Seasonal variability of eddy kinetic energy in a global high-resolution ocean model Seasonal variability of eddy kinetic energy in a global high-resolution oc...

    2015

  90. [98]

    \ Munoz-Carpena, R

    Ritter-2013 APACrefauthors Ritter, A. \ Munoz-Carpena, R. APACrefauthors \ 2013 . Performance evaluation of hydrological models: Statistical significance for reducing subjectivity in goodness--of--fit assessments Performance evaluation of hydrological models: Statistical signi...

    2013

  91. [99]

    Ross-2023 APACrefauthors Ross, A. , Li, Z. , Perezhogin, P. , Fernandez-Granda, C. \ Zanna, L. APACrefauthors \ 2023 . Benchmarking of machine learning ocean subgrid parameterizations in an idealized model Benchmarking of machine learning ocean subgrid parameterizations in an ...

    2023

  92. [100]

    , Gula, J

    Schubert-2020 APACrefauthors Schubert, R. , Gula, J. , Greatbatch, R J. , Baschek, B. \ Biastoch, A. APACrefauthors \ 2020 . The submesoscale kinetic energy cascade: Mesoscale absorption of submesoscale mixed layer eddies and frontal downscale fluxes The submesoscale kinetic e...

    2020

  93. [101]

    , Penduff, T

    Serazin-2018 APACrefauthors S \' e razin, G. , Penduff, T. , Barnier, B. , Molines, J M. , Arbic, B K. , M \" u ller, M. \ Terray, L. APACrefauthors \ 2018 . Inverse cascdes of kinetic energy as a source of intrinsic variability: a global OGCM study Inverse cascdes of kinetic ...

    2018

  94. [102]

    APACrefauthors \ 1963

    Smagorinsky-1963 APACrefauthors Smagorinsky, J. APACrefauthors \ 1963 . General circulation experiments with the primitive equations I. The basic experiment General circulation experiments with the primitive equations i. the basic experiment . Monthly Weather Review 91 3 99–164

    1963

  95. [103]

    \ Vanneste, J

    Smith-2013 APACrefauthors Smith, K S. \ Vanneste, J. APACrefauthors \ 2013 . A surface-aware projection basis for quasigeostrophic flow A surface-aware projection basis for quasigeostrophic flow . Journal of Physical Oceanography 43 3 548–562

    2013

  96. [104]

    , Stewart, A L

    Solodoch-2023 APACrefauthors Solodoch, A. , Stewart, A L. , Hogg, A M. \ Manucharyan, G E. APACrefauthors \ 2023 . Machine learning-derived inference of the Meridional Overturning Circulation from satellite-observable variables in an ocean state estimate Machine learning-deriv...

    2023

  97. [105]

    , McWilliams, J C

    Srinivasan-2019 APACrefauthors Srinivasan, K. , McWilliams, J C. , Molemaker, M J. \ Barkan, R. APACrefauthors \ 2019 . Submesoscale vortical wakes in the Lee of topography Submesoscale vortical wakes in the lee of topography . Journal of Physical oceanography 49 7 1949-1971

    2019

  98. [106]

    , Bathman, S D

    Stanley-2020 APACrefauthors Stanley, Z. , Bathman, S D. \ Grooms, I. APACrefauthors \ 2020 . Vertical structure of ocean mesoscale eddies with implications for parameterizations of tracer transport Vertical structure of ocean mesoscale eddies with implications for parameteriza...

    2020

  99. [107]

    \ Aluie, H

    Storer-2023 APACrefauthors Storer, B A. \ Aluie, H. APACrefauthors \ 2023 . A coarse-graining utility for geophysical flows on the sphere A coarse-graining utility for geophysical flows on the sphere . Journal of Open Source Software 8 84 4277

    2023

  100. [108]

    , Buzzicotti, M

    Storer-2022 APACrefauthors Storer, B A. , Buzzicotti, M. , Khatri, H. , Griffies, S M. \ Aluie, H. APACrefauthors \ 2022 . Global energy spectrum of the general oceanic circulation Global energy spectrum of the general oceanic circulation . Nature Communications 13 5314

    2022

  101. [109]

    , Mengxuan, A

    Sun-2023 APACrefauthors Sun, W. , Mengxuan, A. , Liu, j. , Liu, J. , Yang, J. , Tan, W. Dong, C. APACrefauthors \ 2023 . Comparative analysis of four types of mesoscale eddies in the North Pacific Subtropical Countercurrent region - part II seasonal variatino Comparative analy...

    2023

  102. [110]

    , Hassanzadeh, P

    Sunyq-2023 APACrefauthors Sun, Y Q. , Hassanzadeh, P. , Alexander, M J. \ Kruse, C G. APACrefauthors \ 2023 . Quantifying 3D gravity wave drag in a library of tropical convection-permitting simulations for data-driven parameterizations Quantifying 3d gravity wave drag in a lib...

    2023

  103. [111]

    , Pahlavan, A., Hamid , Chattopadhyay, A

    Sun-2024 APACrefauthors Sun, Y Q. , Pahlavan, A., Hamid , Chattopadhyay, A. , Hassanzadeh, P. , Lubis, S W. , Alexander, M J. Guan, Y. APACrefauthors \ 2024 . Data imbalance, uncertainty quantification, and transfer learning in data-driven parameterizations: Lessons from the e...

    2024

  104. [112]

    , Cheng, L

    Tian-2022 APACrefauthors Tian, T. , Cheng, L. , Wang, G. , Abraham, J. , Wei, W. , Ren, S. Leng, H. APACrefauthors \ 2022 . Reconstructing ocean subsurface salinity at high resolution using a machine learning approach Reconstructing ocean subsurface salinity at high resolution...

    2022

  105. [113]

    , Waldman, R

    Torres-2023 APACrefauthors Torres, R. , Waldman, R. , Mak, J. \ S \'e f \'e rian, R. APACrefauthors \ 2023 . Global estimation of the eddy kinetic energy dissipation from a diagnostic energy balance Global estimation of the eddy kinetic energy dissipation from a diagnostic ene...

    2023

  106. [114]

    , Deremble, B

    Uchida-2022 APACrefauthors Uchida, T. , Deremble, B. \ Popinet, S. APACrefauthors \ 2022 . Deterministic model of the eddy dynamics for a midlatitude ocean model Deterministic model of the eddy dynamics for a midlatitude ocean model . Journal of Physical Oceanography 52 6 1133–1154

    2022

  107. [115]

    APACrefauthors \ 2017

    Vallis-2017 APACrefauthors Vallis, G K. APACrefauthors \ 2017 . Atmospheric and oceanic fluid dynamics Atmospheric and oceanic fluid dynamics . Cambridge University Press

    2017

  108. [116]

    , Geurts, B

    Vreman-1996 APACrefauthors Vreman, B. , Geurts, B. \ Kuerten, H. APACrefauthors \ 1996 . Large-eddy simulation of the temporal mixing layer using the Clark model Large-eddy simulation of the temporal mixing layer using the clark model . Theoretical and Computational Fluid Dyna...

    1996

  109. [117]

    , Flierl, G R

    Wang-2013 APACrefauthors Wang, J. , Flierl, G R. , LaCasce, J H. , McClean, J L. \ Mahadevan, A. APACrefauthors \ 2013 . Reconstructing the ocean’s interior from surface data Reconstructing the ocean’s interior from surface data . Journal of Physical Oceanography 43 8 1611–1626

    2013

  110. [118]

    , Fu, L L

    Wang-2018 APACrefauthors Wang, J. , Fu, L L. , Qiu, B. , Menemenlis, D. , Farrar, J T. , Chao, Y. Flexas, M M. APACrefauthors \ 2018 . An observing system simulation experiment for the calibration and validation of the surface water Ocean Topography sea surface height measurem...

    2018

  111. [119]

    , Wang, R

    Wangx-2024 APACrefauthors Wang, X. , Wang, R. , Hu, N. , Wang, P. , Huo, P. , Wang, G. Song, J. APACrefauthors \ 2024 . XiHe: A data-driven model for global ocean eddy-resolving forecasting Xihe: A data-driven model for global ocean eddy-resolving forecasting . Arxiv:2402.02995v2

    2024 arXiv

  112. [120]

    \ Wang, Y

    Wei-2021 APACrefauthors Wei, H. \ Wang, Y. APACrefauthors \ 2021 . Full-depth scalings for isopycnal eddy mixing across continental slopes under upwelling-favorable winds Full-depth scalings for isopycnal eddy mixing across continental slopes under upwelling-favorable winds . ...

    2021

  113. [121]

    , Wang, Y

    Wei-2022 APACrefauthors Wei, H. , Wang, Y. , Stewart, A L. \ Mak, J. APACrefauthors \ 2022 . Scalings for eddy buoyancy fluxes across prograde shelf/slope fronts Scalings for eddy buoyancy fluxes across prograde shelf/slope fronts . Journal of Advances in Modeling Earth System...

    2022

  114. [122]

    \ Wunsch, C

    Wortham-2014 APACrefauthors Wortham, C. \ Wunsch, C. APACrefauthors \ 2014 . A multidimensional spectral description of ocean variability A multidimensional spectral description of ocean variability . Journal of Physical oceanography 44 3 944-966

    2014

  115. [123]

    APACrefauthors \ 1997

    Wunsch-1997 APACrefauthors Wunsch, C. APACrefauthors \ 1997 . The vertical partition of oceanic horizontal kinetic energy The vertical partition of oceanic horizontal kinetic energy . Journal of Physical Oceanography 27 8 1770-1794

    1997

  116. [124]

    APACrefauthors \ 1999

    Wunsch-1999 APACrefauthors Wunsch, C. APACrefauthors \ 1999 . A summary of North Atlantic baroclinic variability A summary of north atlantic baroclinic variability . Journal of Physical Oceanography 29 12 3161-3166

    1999

  117. [125]

    , Balwada, D

    Xiao-2023 APACrefauthors Xiao, Q. , Balwada, D. , Jones, C S. , Herrero-Gonzalez, M. , Smith, K S. \ Abernathey, R. APACrefauthors \ 2023 . Reconstruction of surface kinematics from sea surface height using neural networks Reconstruction of surface kinematics from sea surface ...

    2023

  118. [126]

    , Gao, A

    ML_dataset APACrefauthors Xie, C. , Gao, A. \ Lu, X. APACrefauthors \ 2024 12 . Replication Data for: ``Global Estimation of Subsurface Eddy Kinetic Energy of Mesoscale Eddies Using a Multiple-input Residual Neural Network'' [Dataset] . Replication Data for: ``Global Estimatio...

    2024 doi

  119. [127]

    , Wei, H

    Xie-2023b APACrefauthors Xie, C. , Wei, H. \ Wang, Y. APACrefauthors \ 2023 1 . Bathymetry-aware mesoscale eddy parameterizations across upwelling slope fronts: A machine learning-augmented approach Bathymetry-aware mesoscale eddy parameterizations across upwelling slope front...

    2023

  120. [128]

    , Wei, H

    Xie-2023a APACrefauthors Xie, C. , Wei, H. \ Wang, Y. APACrefauthors \ 2023 2 . Impact of parameterized isopycnal diffusivity on shelf-ocean exchanges under upwelling-favorable winds: Offline tracer simulations augmented by artificial neural network Impact of parameterized iso...

    2023

  121. [129]

    , Xiong, X

    Xie-2021 APACrefauthors Xie, C. , Xiong, X. \ Wang, J. APACrefauthors \ 2021 . Artificial neural network approach for turbulence models: A local framework Artificial neural network approach for turbulence models: A local framework . Physical Review Fluids 6 8 084612

    2021

  122. [130]

    , Liu, H

    xiejw-2023 APACrefauthors Xie, J. , Liu, H. \ Lin, P. APACrefauthors \ 2023 . A multifaceted isoneutral eddy transport diagnostic framework and its application in the Southern Ocean A multifaceted isoneutral eddy transport diagnostic framework and its application in the southe...

    2023

  123. [131]

    , Bachman, S

    Yankovsky-2024 APACrefauthors Yankovsky, E. , Bachman, S. , Smith, K S. \ Zanna, L. APACrefauthors \ 2024 . Vertical structure and energetic constraints for a backscatter parameterization of ocean mesoscale eddies Vertical structure and energetic constraints for a backscatter ...

    2024

  124. [132]

    Yao-2023 APACrefauthors Yao, H. , Ma, C. , Jing, Z. \ Zhang, Z. APACrefauthors \ 2023 . On the vertical structure of mesoscale eddies in the Kuroshio-Oyashio Extension On the vertical structure of mesoscale eddies in the kuroshio-oyashio extension . Geophysical Research Letter...

    2023

  125. [133]

    \ Griffies, S M

    Yassin-2022 APACrefauthors Yassin, H. \ Griffies, S M. APACrefauthors \ 2022 . On the discrete normal modes of quasigeostrophic theory On the discrete normal modes of quasigeostrophic theory . Journal of Physical Oceanography 52 2 243–259

    2022

  126. [134]

    , Clune, J

    Yosinski-2014 APACrefauthors Yosinski, J. , Clune, J. , Bengio, Y. \ Lipson, H. APACrefauthors \ 2015 . How transferable are features in deep neural networks How transferable are features in deep neural networks . Advances in Neural Information Processing Systems 27

    2014

  127. [135]

    \ Bolton, T

    Zanna-2020 APACrefauthors Zanna, L. \ Bolton, T. APACrefauthors \ 2020 . Data-driven equation discovery of ocean mesoscale closures Data-driven equation discovery of ocean mesoscale closures . Geophysical Research Letters 47 17 e2020GL088376

    2020

  128. [136]

    , Griffies, S M

    Zhang-2024 APACrefauthors Zhang, W. , Griffies, S M. , Hallberg, R W. , Kuo, Y. \ Wolfe, C L. APACrefauthors \ 2024 . The role of surface potential vorticity in the vertical structure of mesocale eddies The role of surface potential vorticity in the vertical structure of mesoc...

    2024

  129. [137]

    Zhu-2023 APACrefauthors Zhu, R. , Li, Y. , Chen, Z. , Du, T. , Zhang, Y. , Li, Z. Wu, L. APACrefauthors \ 2023 . Deep learning improves reconstruction of ocean vertical velocity Deep learning improves reconstruction of ocean vertical velocity . Geophysical Research Letters 50 ...

    2023

  130. [138]

    Zhu-2022 APACrefauthors Zhu, Y. , Li, Y. , Wang, F. \ Lv, M. APACrefauthors \ 2022 . Weak mesoscale variability in the optimum interpolation sea surface temperature (OISST)-AVHRR-only version 2 data before 2007 Weak mesoscale variability in the optimum interpolation sea surfac...

    2022

  131. [139]

    , Zhang, R H

    Zhuyc-2022 APACrefauthors Zhu, Y. , Zhang, R H. , Moum, J N. , Wang, F. , Li, X. \ Li, D. APACrefauthors \ 2022 . Physcis-informed deep learning parameterization of ocean vertical mixing improves climate simulations Physcis-informed deep learning parameterization of ocean vert...

    2022

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Reviewed August 11, 2026 · model on record in the stance chip above.