Ensemble Graph Neural Networks for Probabilistic Sea Surface Temperature Forecasting via Input Perturbations

Accurate regional ocean forecasting requires models that are both computationally efficient and capable of representing predictive uncertainty. This work investigates ensemble learning strategies for sea surface temperature (SST) forecasting using Graph Neural Networks (GNNs), with a focus on how input perturbation design affects forecast skill and uncertainty representation. We adapt a GNN architecture to the Canary Islands region in the North Atlantic and implement a homogeneous ensemble approach inspired by bagging, where diversity is introduced during inference by perturbing initial ocean states rather than retraining multiple models. Several noise-based ensemble generation strategies are evaluated, including Gaussian noise, Perlin noise, and fractal Perlin noise, with systematic variation of noise intensity and spatial structure. Ensemble forecasts are assessed over a 15-day horizon using deterministic metrics (RMSE and bias) and probabilistic metrics, including the Continuous Ranked Probability Score (CRPS) and the Spread-skill ratio. Results show that, while deterministic skill remains comparable to the single-model forecast, the type and structure of input perturbations strongly influence uncertainty representation, particularly at longer lead times. Ensembles generated with spatially coherent perturbations, such as low-resolution Perlin noise, achieve better calibration and lower CRPS than purely random Gaussian perturbations. These findings highlight the critical role of noise structure and scale in ensemble GNN design and demonstrate that carefully constructed input perturbations can yield well-calibrated probabilistic forecasts without additional training cost, supporting the feasibility of ensemble GNNs for operational regional ocean prediction.

💡 Research Summary

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This paper addresses the need for computationally efficient yet uncertainty‑aware regional ocean forecasts by introducing a lightweight ensemble framework built on a single trained Graph Neural Network (GNN). The authors adapt the SeaCast GNN, originally designed for the Mediterranean, to the Canary Islands region of the North Atlantic, where strong upwelling and complex coastline demand high spatial resolution. The model operates on a hierarchical mesh graph, using an encoder‑processor‑decoder architecture with interaction‑network message passing. During training the network learns to predict one day ahead; at inference time it is rolled forward autoregressively to produce a 15‑day forecast.

Instead of training multiple independent models, diversity is generated solely at inference by perturbing the initial sea‑surface temperature (SST) field. Three families of perturbations are examined: (i) unstructured Gaussian noise added independently to each grid point, (ii) spatially coherent Perlin noise generated at low resolutions (e.g., 4 × 4, 8 × 8) and interpolated to the full grid, and (iii) fractal Perlin noise that combines multiple octaves to introduce multi‑scale variability. For each family the authors systematically vary the noise amplitude (σ = 0.1, 0.3, 0.5 K) and spatial resolution, yielding nine distinct ensemble configurations.

The dataset comprises daily SST from the CMEMS Level‑4 reanalysis (0.05° × 0.05°, 1982‑2023), daily mean 10 m wind components from ERA5, and high‑resolution bathymetry from NOAA’s ETOPO. All variables are interpolated onto the same regular latitude‑longitude grid before being mapped onto the mesh graph.

Performance is assessed with deterministic metrics (RMSE, bias) and probabilistic metrics drawn from WeatherBench: Continuous Ranked Probability Score (CRPS) and the spread‑skill ratio (ensemble spread divided by RMSE). Results show that deterministic skill is essentially unchanged across all ensembles, confirming that perturbations do not degrade the core predictive ability of the GNN. However, the probabilistic skill varies markedly with the type of perturbation. Pure Gaussian noise yields the largest ensemble spread but leads to over‑dispersed forecasts, especially beyond day 10, resulting in higher CRPS values. In contrast, low‑resolution Perlin noise produces a moderate spread that respects the spatial correlation scales of the ocean, delivering the lowest CRPS across the 15‑day horizon and a spread‑skill ratio close to unity, indicating good calibration. Fractal Perlin noise offers multi‑scale variability but can become over‑dispersed when the amplitude is high, slightly worsening CRPS compared with the simple Perlin case.

The study therefore demonstrates that (1) inference‑time input perturbations are sufficient to generate a useful probabilistic ensemble without the need for multiple model trainings, dramatically reducing computational cost; (2) the spatial structure of the perturbation is far more important than its raw magnitude for achieving calibrated uncertainty estimates; and (3) for regional ocean applications, spatially coherent, low‑resolution Perlin perturbations strike the best balance between diversity and physical realism.

The authors discuss practical implications for operational forecasting: the ensemble can be generated on‑the‑fly from a single GNN, enabling near‑real‑time probabilistic SST forecasts on modest hardware. They also outline future work, including incorporating observation‑based error statistics into the perturbation design, extending the approach to additional ocean variables (e.g., salinity, currents), and exploring joint perturbations of atmospheric forcings. Overall, the paper provides a clear, empirically validated pathway to bring probabilistic, machine‑learning‑based ocean forecasting into operational settings.