On the Limits of Univariate Deep Learning for Significant Wave Height Forecasting
Authors: Yilin Zhai, Hongyuan Shi, Zaijin You
Organizations: Shandong Key Laboratory Of Estuary And Coast & Nuclear Environment, Ludong University, Shandong, 264025, Yantai, China · School of Hydraulic and Civil Engineering, Ludong University, Shandong, 264025, Yantai, China · Institute of Coastal Research, Ludong University, Yantai, 264025, Shandong, China · Navigation College, Dalian Maritime University, Dalian, 116026, Liaoning, China
This study conducts a systematic hyperparameter search across five deep learning architectures, DLinear, LSTM, PatchTST, ResAttLstm, and Mamba2, and nine context lengths (1-168 h) for single-station significant wave height (Hs) forecasting on NDBC buoy 41009, followed by re-evaluation of the best configurations on a 47-buoy, 37-year corpus. The five families converge to a common performance level on the multi-buoy evaluation (between-family SD = 0.0014 m^2, 0.8% of the grand mean), a spread dwarfed by the 4.83x cross-dataset MSE shift between buoy corpora. All multi-buoy trials beat persistence (mean skill +0.062), but no architecture consistently outperforms the others. On the single-buoy experiment, skill peaks at 12-24 h where five trials fall below persistence, per-family Q4/Q3 test MSE ratios range from 2.4 to 2.6, and deep models underperform persistence for the most extreme 1% of waves. These findings are consistent with the interpretation that persistence already captures the dominant linear-inertial signal in univariate Hs, and that architecture engineering under this univariate input setting has reached diminishing returns: cross-buoy variance, not model class, dominates forecast error. Future work should prioritise atmospheric covariates, zero-shot cross-buoy transfer, and decomposition of Hs into swell and wind-sea components. By establishing a rigorous reference baseline for what univariate Hs models can and cannot achieve, this study provides a benchmark against which future multivariate and physics-informed approaches can be calibrated, and offers practical guidance for lightweight buoy-level forecasting in mid-latitude storm-dominated and swell-mixed environments.
Figures & tables
Figure 1: Overview of the two-phase experimental design. This figure is a conceptual schematic generated with GPT Image 2.0 and contains no scientific data.
Figure 2: Geographic distribution of the 47 NDBC buoys used in the multi-buoy evaluation.
Property
mean ± SD
median
IQR
Q1–Q3
p95
p99
p99.9
max
41009
1.18±0.67 m
1.01 m
0.79 m
0.70 – 1.49 m
2.45 m
3.48 m
5.19 m
9.79 m
47 buoys
1.46±1.01 m
1.21 m
1.08 m
0.78 – 1.86 m
3.44 m
5.10 m
7.35 m
16.91 m
Table 1: Dataset summary. All SWH statistics are computed directly from raw NDBC hourly records.
Figure 3: Schematic of the sliding-window construction. This figure is a conceptual schematic generated with GPT Image 2.0 and contains no scientific data.
Family
Params
Key hyperparameters
DLinear
2
kernel_size [9, 93]; lr [1e-3, 9.9e-3]
LSTM
5
n_layers {2,3}; hidden {64–256}; bidirectional per layer; dropout [0.003, 0.49]; lr [1e-4, 1e-2]
Table 2: Continuous parameters are sampled uniformly (or log-uniform for learning rate). Categorical parameters are enumerated. Batch size was fixed at 4096 for all families.
Family
Test MSE
Persistence skill
p99 MSE
Q4/Q3 ratio
PatchTST
0.0333
+0.043
0.446
2.4
DLinear
0.0335
+0.038
0.459
2.4
LSTM
0.0338
+0.029
0.516
2.5
Mamba2
0.0339
+0.026 ( −0.015 – +0.048 )
0.521
2.5
ResAttLstm
0.0343
+0.014 ( −0.026 – +0.057 )
0.558
2.6
Table 3: Per-family results on station 41009. Mean values across nine context lengths. The overall skill range (min–max across CLs) is shown for the two families with negative-skill trials.
Figure 4: Test MSE distribution across the nine context lengths per family, station 41009. Boxes show median and IQR; whiskers extend to 1.5× IQR. Dashed line: grand mean. Shaded band: ±1 between-family SD.
Figure 5: Persistence skill across context lengths, station 41009
Figure 6: Test MSE distribution across the nine context lengths per family, 47-buoy dataset. Boxes show median and IQR; whiskers extend to 1.5×IQR .
Figure 7: Persistence skill and tail performance on the 47-buoy dataset
Figure 8: Mean seasonal test MSE by family, 47-buoy dataset. Numbers above Q4 bars: per-family Q4/Q3 MSE ratio.
Figure 9: Test MSE versus persistence skill for each (family, context length) cell, 47-buoy dataset. Annotated numbers indicate context length in hours. Circled points mark Pareto-optimal configurations.
Family
Q1
Q2
Q3
Q4
Δ (Q4 − Q3)
DLinear
+0.058
+0.072
+0.081
+0.064
−0.017
LSTM
+0.047
+0.091
+0.090
+0.050
−0.040
PatchTST
+0.064
+0.084
+0.087
+0.070
−0.017
ResAttLstm
+0.040
+0.083
+0.084
+0.044
−0.040
Mamba2
+0.046
+0.085
+0.078
+0.048
−0.030
Grand mean
+0.051
+0.083
+0.084
+0.055
−0.029
Table 4: Seasonal persistence skill by family, multi-buoy evaluation. Values are 9-CL means. All five families exhibit Q4 skill < Q3 skill.
Figure 10: Ratio of multi-buoy to single-buoy test MSE per family and context length. The dashed line marks the grand mean (4.83).
Figure 11: Persistence skill per family and context length. (a) Single-buoy. (b) Multi-buoy.
Family
MSE (0%)
MSE (5%)
MSE (15%)
Skill (0%)
Skill (5%)
Skill (15%)
PatchTST
0.1611
0.1601
0.1565
+0.0727
+0.0730
+0.0737
DLinear
0.1623
0.1613
0.1575
+0.0660
+0.0663
+0.0676
LSTM
0.1633
0.1624
0.1591
+0.0605
+0.0600
+0.0586
Mamba2
0.1640
0.1631
0.1597
+0.0567
+0.0562
+0.0551
ResAttLstm
0.1645
0.1636
0.1603
+0.0538
+0.0532
+0.0516
Table 5: Per-family 9-CL mean test MSE and persistence skill under 0%, 5%, and 15% randomly missing observations with linear interpolation, multi-buoy evaluation.
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