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

Alejandro J. González-Santana; Giovanny A. Cuervo-Londoño; Javier Sánchez

cs.LGMar 6, 2026

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

Authors: Alejandro J. González-Santana, Giovanny A. Cuervo-Londoño, Javier Sánchez

Organizations: Centro de Tecnologías de la Imagen Instituto Universitario de Cibernética, Empresas y Sociedad (IUCES) University of Las Palmas de Gran Canaria, Spain · Oceanografía Física y Geofísica Aplicada Instituto Universitario en Acuicultura Sostenible y Ecosistemas Marinos (ECOAQUA) University of Las Palmas de Gran Canaria, Spain

Abstract

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.

Figures & tables

Parameter	Value
Maximum latitude	34.525º
Minimum latitude	19.55º
Maximum longitude	-5.975º
Minimum longitude	-20.97º

Table 1: Coordinates delimiting the area of study.

Figure 1: Sea Surface Temperature (SST) data in Kelvin for January 1, 2018, in the north-west African coast.

Figure 2: Wind components ( $u$ and $v$ ) at 10 meters above the surface for January 1, 2018.

Figure 3: Processed bathymetry downloaded from ETOPO.

Figure 4: Diagram of autoregressive operation.

Figure 5: Examples of Gaussian noise added to SST, generated with different standard deviations.

Figure 6: Examples of Perlin noise added to SST, generated with different spatial resolutions.

Figure 7: Examples of Perlin Fractal noise with three octaves added to the SST, generated with different spatial resolutions and the same noise scalability. The rest of parameters correspond to default values.

Symbol	Rank	Description
$f$	-	Prediction
$o$	-	Observation
$t$	$1,\ldots,T$	Verification time
$l$	$1,\ldots,L$	Prediction horizon
$i$	$1,\ldots,I$	Latitude index
$j$	$1,\ldots,J$	Longitude index

Table 2: Notation used in the metrics [ 30 ] .

Noise type	Mean ( $\mu$ )	Standard deviation ( $\sigma$ )
Gaussian ( $\mu$ =0, $\sigma$ =0.1)	0.0	0.1
Gaussian ( $\mu$ =0, $\sigma$ =0.05)	0.0	0.05
Gaussian ( $\mu$ =0, $\sigma$ =0.01)	0.0	0.01

Table 3: Gaussian noise configurations used during the tests.

Noise type	Resolution	Repeatable
P_res_2x3x3	(2, 3, 3)	(T, F, F)
P_res_2x12x12	(2, 12, 12)	(T, F, F)

Table 4: Classic Perlin noise configurations used during the tests.

ID	Resolution	Repeatable	Persistence	Octaves	Scale	Lacunarity
A	(15, 15)	(F, T)	0.5	3	0.2	2.0
B	(5, 5)	(F, T)	0.5	3	0.2	2.0
C	(15, 15)	(F, F)	0.5	3	0.2	2.0
D	(15, 15)	(F, T)	0.5	3	0.05	2.0
E	(15, 15)	(F, T)	0.5	3	0.4	2.0

Table 5: Fractal Perlin noise configurations used during the tests. The IDs correspond to: A) PF_res_15x15 ; B) PF_res_5x5 ; C) PF_res_15x15_without_tileable ; D) PF_res_15x15 (

\alpha

=0.05); and E) PF_res_15x15 (

\alpha

=0.4).

Configuration	1 day	5 days	15 days
Deterministic (ref)	0.109	0.308	0.586
Gaussian ( $\mu$ =0, $\sigma=0.01$ )	0.55%	0.03%	0.00%
Gaussian ( $\mu$ =0, $\sigma=0.1$ )	28.96%	5.36%	0.43%
P $\_$ res $\_$ 15x15 ( $\alpha=0.05$ )	1.56%	0.16%	0.02%
P $\_$ res $\_$ 2x12x12	64.01%	15.90%	1.62%
P $\_$ res $\_$ 2x3x3	61.17%	14.83%	1.47%

Table 6: Comparison of the increase RMSE over different time horizons for each noise configuration, with respect to a deterministic prediction without noise.

Figure 8: SST bias maps for one-day forecasts starting on 2 January 2022. Each row corresponds to a different input noise configuration, and each column represents a member of the ensemble, with the last column showing the ensemble mean.

Figure 9: CRPS and its components, averaged for each prediction horizon, comparing the different sets of predictions with Gaussian noise.

Figure 10: Graph of the unbiased spread-skill ratio and its components, averaged for each prediction horizon, comparing different sets of predictions with Gaussian noise introduced.

Figure 11: CRPS and its components, averaged for each prediction horizon, comparing the predictions with Perlin noise introduced.

Figure 12: Unbiased spread-skill ratio and its components, averaged for each prediction horizon, comparing the different sets of predictions with Perlin noise introduced.

Figure 13: RMSE averaged by prediction horizon, comparing the performance of unifying Perlin noise configurations.

Figure 14: CRPS, unbiased RMSE, and spread-skill ratio averaged by prediction horizon, comparing the different sets of predictions with added noise, evaluated on the complete test data set.

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