BridgeCast: Bridging Ocean Wave Forecasts to Reanalysis via Flow Matching with Exogenous Variables

Siyu Gan; Dongsheng Luo; Kunxiaojia Yuan; Dongjin Song; Jingchao Ni

physics.ao-phSep 27, 2026

BridgeCast: Bridging Ocean Wave Forecasts to Reanalysis via Flow Matching with Exogenous Variables

Authors: Siyu Gan, Dongsheng Luo, Kunxiaojia Yuan, Dongjin Song, Jingchao Ni

Organizations: Johns Hopkins University · Singapore Management University · University of Houston · University of Connecticut

Abstract

Ocean wave forecasting is essential for maritime safety, offshore operations, and coastal resilience, yet remains challenging due to systematic biases in physics-based models. Physical models, while widely used, rely on approximations and parameterizations that limit their accuracy under complex ocean-atmosphere conditions. To enhance ocean wave forecasting, we propose BridgeCast, within a physics-AI hybrid framework for bias correction. BridgeCast is a probabilistic model based on conditional flow matching (CFM) that learns to transform physical model forecasts into reanalysis-like fields. It treats physical forecasts as corrupted observations and employs a continuous-time generative process to bridge their distribution toward that of reanalysis data. BridgeCast is parameterized by a Transformer-based architecture that enables spatiotemporal modeling, incorporation of exogenous atmospheric variables, and flexible inference via both ordinary and stochastic differential equation formulations. Extensive experiments on real-world datasets demonstrate that BridgeCast consistently outperforms state-of-the-art baselines across regions and forecast lead times.

Figures & tables

Figure 1: An illustration of BridgeCast ’s process of bridging GFS-WW3 ’s forecasts to the reanalysis data of ERA5 in (a) Gulf of Mexico, and (b) North Sea. The numbers in brackets are RMSEs. $\tau$ is flow time. “Ours” is BridgeCast , which resembles ERA5 with less errors than GFS-WW3 .

Figure 2: An illustration of the BridgeCast Architecture. (a) is an overview of the architecture with a zoom-in of the BridgeCast block. (b) illustrates the four modules in the BridgeCast block. $\tau$ is the flow time. $T_{l}$ is the lead time. $\boldsymbol{\alpha}$ ’s, $\boldsymbol{\beta}$ ’s, $\boldsymbol{\gamma}$ ’s are scaling and shifting parameters.

Dataset	Region	$N_{\text{train}}$	$N_{\text{val}}$	$N_{\text{test}}$	Dimension
GFS	Gulf of Mexico	193,944	2,904	2,904	$33\times 47$
	North Sea	193,896	2,904	2,904	$32\times 48$
	California Coast	192,240	2,904	2,904	$35\times 41$
IFS	Gulf of Mexico	29,520	17,376	17,184	$33\times 47$
	North Sea	29,520	17,376	17,184	$32\times 48$
	California Coast	29,520	17,376	17,184	$35\times 41$

Table 3

		Gulf of Mexico					North Sea					California Coast
	Model	RMSE ↓	CRPS ↓	CSI ↑	HSS ↑	twCRPS ↓	RMSE ↓	CRPS ↓	CSI ↑	HSS ↑	twCRPS ↓	RMSE ↓	CRPS ↓	CSI ↑	HSS ↑	twCRPS ↓
Short-Term	GFS-WW3	0.2351	0.1583	0.6950	0.8096	0.0130	0.4657	0.2851	0.7457	0.8404	0.0434	0.2300	0.1600	0.6510	0.7695	0.0149
	FlowMatch	0.3025	0.1404	0.3776	0.5229	0.0261	0.7739	0.4334	0.3358	0.4287	0.0830	0.2966	0.1553	0.4571	0.5881	0.0148
	U-Net	0.1688	0.1101	0.6986	0.8127	0.0156	0.3563	0.2656	0.7297	0.8299	0.0401	0.3386	0.2504	0.5309	0.6604	0.0293
	EarthFormer	0.1939	0.1173	0.6692	0.7913	0.0187	0.3410	0.2353	0.7092	0.8118	0.0437	0.2314	0.1793	0.6044	0.7298	0.0161
	EarthFarseer	0.1734	0.1096	0.6889	0.8061	0.0164	0.2728	0.1998	0.7775	0.8633	0.0304	0.2128	0.1609	0.6281	0.7515	0.0145

Table 1: Performance comparison on GFS ’s dataset.

\uparrow

(

\downarrow

) indicates a larger (smaller) value is better. Red ( Blue ) values indicate the best (second-best) values per forecasting term.

Figure 3: CRPS comparison w.r.t. different lead times across different regions.

	Short-Term				Mid-Term				Long-Term
Model	RMSE ↓	CRPS ↓	CSI ↑	HSS ↑	RMSE ↓	CRPS ↓	CSI ↑	HSS ↑	RMSE ↓	CRPS ↓	CSI ↑	HSS ↑
BridgeCast -o	0.1348	0.0678	0.7620	0.8574	0.1551	0.0797	0.6610	0.7860	0.2916	0.1460	0.4433	0.5864
(a) - Exogenous variables $\mathcal{Z}$	+0.1403	0.0689	0.7514	0.8523	0.1558	0.0819	0.6602	0.7880	0.2908	0.1466	0.4522	0.6013
Improvement	-4.08%	-1.62%	-1.39%	-0.59%	-0.44%	-2.76%	-0.13%	+0.25%	+0.26%	-0.41%	+2.03%	+2.54%
(b) - Spatial attention module	0.1517	0.0732	0.7451	0.8479	0.1603	0.0774	0.6459	0.7768	0.3019	0.1372	0.4204	0.5667
Improvement	-12.52%	-7.93%	-2.22%	-1.11%	-3.31%	+2.89%	-2.29%	-1.17%	-3.56%	+6.04%	-5.17%	-3.35%

Table 2: Ablation Analysis of BridgeCast -o on GFS ’s dataset in Gulf of Mexico.

\uparrow

(

\downarrow

) indicates a larger (smaller) value is better. “Improvement” of each ablation is relative to BridgeCast -o.

Figure 4: Qualitative comparison of BridgeCast and other baselines on GFS ’s data in North Sea region (lead time 24h) when there was a storm event.

Data	Model	Gulf (s)	NS (s)	Cali (s)
GFS	BridgeCast -o	0.714	0.681	0.636
GFS	BridgeCast -s	0.743	0.710	0.665
IFS	BridgeCast -o	0.951	0.914	0.840
IFS	BridgeCast -s	0.980	0.942	0.874

Table 3: Inference Time of BridgeCast .

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

		Gulf of Mexico					North Sea					California Coast
	Model	RMSE ↓	CRPS ↓	CSI ↑	HSS ↑	twCRPS ↓	RMSE ↓	CRPS ↓	CSI ↑	HSS ↑	twCRPS ↓	RMSE ↓	CRPS ↓	CSI ↑	HSS ↑	twCRPS ↓
Short-Term	IFS-Wave	0.2110	0.1397	0.6829	0.8015	0.0133	0.4328	0.2771	0.6630	0.7855	0.0202	0.2342	0.1676	0.6385	0.7659	0.0181
	U-Net	0.1564	0.0936	0.6889	0.8076	0.0123	0.2687	0.1944	0.5982	0.7229	0.0178	0.1908	0.1302	0.6596	0.7836	0.0130
	EarthFormer	0.1738	0.1067	0.6049	0.7380	0.0152	0.2940	0.2111	0.5712	0.6992	0.0213	0.2030	0.1412	0.6088	0.7357	0.0146
	EarthFarseer	0.1372	0.0874	0.6808	0.8014	0.0118	0.2559	0.1794	0.6006	0.7274	0.0176	0.1820	0.1274	0.6578	0.7799	0.0124
	SimVP	0.1758	0.1117	0.6398	0.7698	0.0136	0.3256	0.2387	0.6331	0.7615	0.0171	0.2122	0.1560	0.6696	0.7897	0.0130

Appendix

Table 4: Performance comparison on IFS ’s dataset.

\uparrow

(

\downarrow

) indicates a larger (smaller) value is better. Red ( Blue ) values indicate the best (second-best) values per forecasting term.

		Gulf of Mexico		North Sea		California Coast
	Model	CRPS-MWP (s)	CRPS-MWD ( ∘ )	CRPS-MWP (s)	CRPS-MWD ( ∘ )	CRPS-MWP (s)	CRPS-MWD ( ∘ )
Short-Term	GFS-Wave	1.1789	18.1443	2.1466	23.6186	3.1095	24.5094
	U-Net	0.3038	9.6514	0.5430	15.6090	0.7313	14.2569
	EarthFormer	0.3223	10.1632	0.4402	11.7093	0.5345	9.9825
	EarthFarseer	0.3196	10.7905	0.4456	11.5879	0.5360	10.3003
	SimVP	0.3373	12.6680	0.4635	12.7184	0.5787	11.2427

Appendix

Table 5: Mean-wave-period (MWP) and mean-wave-direction (MWD) CRPS on GFS ’s dataset. Red ( Blue ) values indicate the best (second-best) per column. MWP CRPS in seconds (Gaussian CRPS for ensembles,

|

mean

-y|

MAE for

M{=}1

); MWD CRPS in degrees (mean angular distance, regardless of

M

). Lead bands as in Table 1 .

		Gulf of Mexico		North Sea		California Coast
	Model	CRPS-MWP (s)	CRPS-MWD ( ∘ )	CRPS-MWP (s)	CRPS-MWD ( ∘ )	CRPS-MWP (s)	CRPS-MWD ( ∘ )
Short-Term	IFS-Wave	0.4825	10.3872	0.5160	10.7447	0.8127	6.9564
	U-Net	0.2638	8.9300	0.3395	8.5967	0.3518	7.4276
	EarthFormer	0.2891	9.7657	0.3694	9.7133	0.3569	7.8750
	EarthFarseer	0.2586	8.8383	0.3528	8.6533	0.3606	7.4498
	SimVP	0.3209	10.5803	0.4212	12.4824	0.3845	9.2524

Appendix

Table 6: Mean-wave-period (MWP) and mean-wave-direction (MWD) CRPS on IFS ’s dataset. Red ( Blue ) values indicate the best (second-best) per column. MWP CRPS in seconds (Gaussian CRPS for ensembles,

|

mean

-y|

MAE for

M{=}1

); MWD CRPS in degrees (mean angular distance, regardless of

M

). Lead bands as in Table 4 .

Figure 5: Sensitivity to the training-time perturbation scale

\sigma

for BridgeCast -o on the GFS Gulf of Mexico validation set.

Figure 6: SDE-noise sweep on the validation set. Each panel shows validation CRPS as a function of $\varepsilon_{\text{SDE}}$ , with separate curves for Short-Term, Mid-Term, Long-Term, and Overall. Rows correspond to forecast systems ( GFS , IFS ), and columns correspond to regions (Gulf of Mexico, North Sea, California). Stars mark the minimum of each curve.

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