KD48: Kuroshio Ocean Dynamics Benchmark

• KD48 is a high-resolution ocean benchmark that uses MITgcm simulations to enable reconstruction of denoised subsurface vertical velocity fields from incomplete surface measurements.
• It employs a causal exponential moving-average filter to remove high-frequency internal tides while preserving eddy-driven motions essential for accurate dynamics reconstruction.
• The benchmark supports standardized evaluation using RMSE, MAE, and PCC metrics, providing a robust platform for supervised learning under arbitrary missing input patterns.

Searching arXiv for the specified benchmark and closely related papers. arxiv_search(query="KD48 benchmark ocean vertical velocity reconstruction Kuroshio-Dynamics-48", max_results=5, sort_by="submittedDate") arxiv_search(query="VISION Prompting Ocean Vertical Velocity Reconstruction from Incomplete Observations", max_results=5, sort_by="relevance") KD48, or Kuroshio-Dynamics-48, is a high-resolution ocean dynamics benchmark for subsurface vertical-velocity reconstruction from incomplete surface observations. It is built from the LLC4320 configuration of the Massachusetts Institute of Technology general circulation model and is explicitly intended to provide a large, analysis-ready data set for ocean-interior inference under realistic data-uncertainty conditions. In the formulation introduced alongside VISION, KD48 supports supervised learning of a mapping from sea-surface observables to denoised subsurface vertical velocity fields, with particular emphasis on arbitrary missing-input patterns and physically meaningful targets (Gao et al., 25 Sep 2025).

1. Definition and scientific role

KD48 is designed to fill a longstanding gap in the ocean-dynamics community by providing a large, analysis-ready data set tailored for subsurface vertical-velocity reconstruction from incomplete surface observations (Gao et al., 25 Sep 2025). The benchmark is framed around a central Earth-science difficulty: reconstructing subsurface ocean dynamics, such as vertical velocity fields, from incomplete surface observations.

The benchmark’s stated role is infrastructural rather than merely archival. It is presented as a standardized substrate for method development, comparison, and stress testing under data missingness. The associated work emphasizes that real-world operational constraints frequently produce incomplete input configurations because satellite sensors may drop out or degrade. KD48 therefore formalizes missingness as part of the task definition rather than treating it as an incidental nuisance.

A common misunderstanding would be to treat KD48 as a generic ocean benchmark. The released specification is narrower. It is tied to the Kuroshio Extension, centered on vertical-velocity reconstruction, and designed around denoised low-frequency dynamics rather than the full unresolved variability of the simulated ocean state. This suggests that its principal value lies in controlled evaluation of reconstruction algorithms under physically grounded but intentionally delimited conditions.

2. Simulation origin and regional extraction

KD48 is built upon the so-called LLC4320 configuration of the Massachusetts Institute of Technology general circulation model (MITgcm). This global simulation is carried out at $1/48^\circ$ horizontal resolution, approximately $2$ km, with $90$ vertical levels, and is forced by 6-hourly, $0.168^\circ$ ECMWF atmospheric reanalysis fields plus a full tidal potential. The initial condition is taken from the ECCO2 data-assimilative state estimate (Gao et al., 25 Sep 2025).

For KD48, the Kuroshio Extension region is subselected by extracting $512\times512$ grid points horizontally and hourly snapshots from 1 November 2011 to 31 October 2012, corresponding to $366$ days $\times$ $24$ h $=$ $8784$ samples. This construction places the benchmark at the intersection of mesoscale-resolving simulation and regional process reconstruction.

The scientific significance of this design lies in the combination of fine horizontal resolution and sustained hourly sampling. A plausible implication is that KD48 is intended to preserve enough spatial and temporal structure for learning methods to exploit mesoscale and submesoscale signatures present in surface observables while still mapping to subsurface vertical motion.

3. Observed variables and target definition

At each time $2$0, KD48 records five sea-surface observables:

• Sea-Surface Height (SSH)
• Sea-Surface Temperature (SST)
• Sea-Surface Salinity (SSS)
• zonal surface velocity $2$1
• meridional surface velocity $2$2

It also records the subsurface vertical-velocity field $2$3 at three fixed depth levels: $2$4, $2$5, and $2$6 (Gao et al., 25 Sep 2025).

In addition, the benchmark derives the surface buoyancy

$2$7

from the linearized equation of state, with $2$8, and coefficients $2$9 evaluated at reference state $90$0.

The core variables can be summarized as follows:

Component	Specification	Role
Surface inputs	$90$1	Predictors
Optional derived input	$90$2	Additional channel if treated separately
Target output	$90$3 at depths $90$4	Reconstruction target

The inclusion of both dynamical and tracer-based surface variables reflects an attempt to encode multiple pathways by which surface state may constrain vertical motion. The optional treatment of buoyancy as an additional channel further indicates that the benchmark supports both direct raw-field learning and modestly physics-informed feature construction.

4. Expert-driven denoising and physical conditioning

A defining feature of KD48 is its target curation. Raw vertical velocity $90$5 contains high-frequency signals, such as internal tides, that are only weakly coupled to the surface tracer fields. To ensure that the learning task remains well posed, the benchmark applies an expert-designed dynamical signal filter to isolate the physically consistent component $90$6 (Gao et al., 25 Sep 2025).

The filtering operation is implemented as a causal exponential moving-average low-pass filter: $90$7 where $90$8 indexes horizontal location, $90$9 the selected depth, and $0.168^\circ$0 the e-folding time scale in hours.

The stated purpose of this filter is to remove spurious internal-tide variability while retaining the eddy-driven motions that are dynamically linked to the surface fields. This point is central to interpreting benchmark performance: success on KD48 is success at reconstructing the denoised, surface-consistent vertical-velocity component, not the full raw vertical-velocity signal.

This also clarifies a potential misconception. KD48 does not attempt to preserve all frequencies equally. High-frequency tides are filtered out by design. The benchmark therefore operationalizes a particular scientific target: low-frequency vertical velocities that remain meaningfully inferable from the provided surface observables.

5. Data representation, preprocessing, and partitioning

Each sample in KD48 is stored as an input tensor

$0.168^\circ$1

and a target tensor

$0.168^\circ$2

where $0.168^\circ$3 or $0.168^\circ$4 if buoyancy $0.168^\circ$5 is treated as a separate channel (Gao et al., 25 Sep 2025).

Prior to learning, each field is normalized by subtracting its global training-set mean and dividing by its standard deviation, placing all variables on comparable scales. The benchmark specification further states that the $0.168^\circ$6 hourly snapshots are partitioned into $0.168^\circ$7 training samples, $0.168^\circ$8 validation samples, and $0.168^\circ$9 test samples, drawing each set without replacement and preserving temporal continuity as much as possible, for example by block-sampling.

These implementation choices have methodological implications. Tensorized storage over a fixed $512\times512$0 domain makes KD48 immediately compatible with convolutional, transformer, and hybrid operator-learning pipelines. The normalization protocol standardizes scale across heterogeneous geophysical variables. The emphasis on preserving temporal continuity in the split design suggests an attempt to reduce trivial temporal leakage and to keep train-validation-test segmentation closer to physically coherent sampling.

6. Learning formulation, missing-data regime, and evaluation

KD48 is explicitly framed as a supervised mapping

$512\times512$1

where $512\times512$2 may contain any non-empty subset of the five surface variables (Gao et al., 25 Sep 2025). This formulation directly encodes the benchmark’s central challenge: the input may be incomplete in arbitrary ways.

The supported tasks are stated as:

• subsurface vertical velocity reconstruction
• arbitrary patterns of missing surface observations
• a physically meaningful, denoised target field

Performance on the test set is quantified by three standard metrics. Let $512\times512$3 and $512\times512$4 denote the predicted and target values at spatial index $512\times512$5 of sample $512\times512$6, let $512\times512$7 be the number of test samples, and let $512\times512$8 be the number of grid points per field. Then:

$512\times512$9

$366$0

$366$1

The benchmark description states that these metrics capture both the absolute magnitudes of errors, via RMSE and MAE, and the fidelity of spatial patterns, via PCC. In methodological terms, KD48 therefore evaluates both amplitude accuracy and structural agreement, which is important for geophysical reconstruction tasks in which coherent pattern recovery may matter as much as pointwise error.

7. Intended usage, limitations, and research significance

KD48 is described as the first large-scale, high-resolution benchmark for ocean-interior reconstruction under realistic data-uncertainty conditions (Gao et al., 25 Sep 2025). Its anticipated uses include research in missing-data resilience, including prompt-driven or graph-based methods, hybrid physics-ML modeling, and transfer learning from one ocean regime to another.

The benchmark’s current limitations are stated explicitly. It has a regional focus on the Kuroshio Extension, and it models only low-frequency vertical velocities because high-frequency tides are filtered out. Future extensions could expand to other ocean basins, include more depth levels or additional state variables such as mixed-layer depth and surface fluxes, and support forecasting as well as reconstruction tasks.

These limitations are not incidental; they define the present scope of the benchmark. KD48 should therefore be understood as a physically grounded, reproducible platform for a specific class of inverse problems in data-driven oceanography. A plausible implication is that cross-basin generalization, broader variable sets, and forecasting capability remain open benchmark-design directions rather than solved components of the current release.