the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 03 Sep 2026
DEN-SURGE: High-frequency and multi-decadal Danish storm surge reconstruction integrating hydrodynamic modelling, observations, and machine learning
Abstract. Assessing coastal hazards and planning robust defence infrastructure under a changing climate requires long-term, high-frequency sea-level records. However, historical tide gauge records are often temporally fragmented, while raw hydrodynamic hindcasts tend to systematically underestimate sub-hourly storm surge peaks due to spatial model resolution limitations. This paper introduces ReSEML v1.0 (Residual Surge Ensemble Machine Learning), a machine learning framework designed to reconstruct continuous, sub-hourly extreme sea-level catalogues across complex coastlines. By training a stacked deep learning ensemble (LSTM + TCN) to exclusively predict the local physical residual between sub-hourly tide gauge observations and a hydrodynamic model baseline, we build the continuous 64-year DEN-SURGE catalogue (1961–2024) across 50 Danish stations. By eliminating sensor malfunctions, closing multi-year monitoring gaps, and correcting numerical peak underestimations, DEN-SURGE delivers an AI-ready benchmark whose quality and physical completeness surpass both raw simulations and fragmented gauge records. Due to regional characteristics, corrections are applied by partitioning the coastline into 10 clusters. Out-of-sample validation shows that ReSEML reduces nationwide mean bias during high water events to within ± 0.4 cm and lowers Root Mean Squared Errors (RMSE) for the same events below 10 cm. Cross-referencing against independent historical storm surge lists confirms the framework's reliability in capturing historical peaks and recovering missing extremes. Extending the continuous record back to 1961 stabilises Extreme Value Analysis (EVA) curves, reducing 95 % confidence intervals for the 100-year return level by on average 46 %. While focused here on historical catalogue homogenisation, this work also provides a methodological bridge for downscaling future climate simulations, establishing a consistent framework to quantify evolving climate risks in coastal planning.
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Status: open (until 23 Oct 2026)
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RC1: 'Comment on essd-2026-693', Anonymous Referee #1, 23 Sep 2026
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AC1: 'Reply on RC1', Jian su, 02 Oct 2026
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We sincerely thank Referee #1 for her/his positive evaluation of our results and for raising constructive questions during this Open Discussion phase. Below, we provide an immediate, detailed clarification addressing the three conceptual and methodological points raised by the referee. These clarifications will be fully integrated into our final revised manuscript and formal point-by-point response letter once the open discussion is closed.Referee comment: The results are actually quite good. I'd like to ask, why use the LSTM algorithm? It's a bit old, and it's mainly for time-series forecasting. Why not choose the latest time-series forecasting model?Author response: From our perspective, the LSTM architecture is not obsolete. While natural language processing (NLP) has largely moved on to attention-based foundation models, LSTMs remain a top-tier choice in physical sciences, hydrological modelling, and oceanography. Recent benchmark studies (e.g., in catchment hydrology and coastal dynamics, such as Kratzert et al., 2019; Daramola et al., 2025) repeatedly demonstrate that properly regularised recurrent networks often match or outperform large transformers on medium-length geophysical sequences while offering superior training stability, lower computational cost, and robust convergence across diverse regional clusters.Moreover, modern long-sequence forecasting architectures, e.g., Informer (Zhou et al., 2021), PatchTST (Nie et al., 2022), and iTransformer (Liu et al., 2024), excel when trained on continuous, stationary multi-year sequences with sequence horizons exceeding thousands of steps (L > 10^4). In contrast, our reconstruction framework operates on targeted, event-scale slices (±24 h around identified peaks, comprising 288 steps at 10-minute resolution). On finite event windows with scarce extreme-tail samples, self-attention mechanisms lack intrinsic inductive temporal locality and require massive sample volumes to avoid overfitting on rare extreme events. Furthermore, patch-based and cross-channel attention architectures introduce substantial parameter overhead without performance gains on localised, 288-step residual learning problems.As stated in Section 2.3 of the manuscript, our choice of base learners is rooted in the different physical dynamics of regional shallow-water surges. In the revised manuscript, we will add the above points to the Methods section.References:
Zhou, H., Zhang, S., Peng, J., Zhang, S., Li, J., Xiong, H., & Zhang, W. (2021). Informer: Beyond efficient transformer for long sequence time-series forecasting. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 35, No. 12, pp. 11106-11115).
Nie, Y., Nguyen, N. H., Sinthong, P., & Kalagnanam, J. (2022). A time series is worth 64 words: Long-term forecasting with transformers. arXiv preprint arXiv:2211.14730.
Liu, Y., Hu, T., Zhang, H., Wu, H., Wang, S., Ma, L., & Long, M. (2024). iTransformer: Inverted transformers are effective for time series forecasting. In International Conference on Learning Representations (ICLR).
Kratzert, F., Klotz, D., Herrnegger, M., Sampson, A. K., Hochreiter, S., & Nearing, G. S. (2019). Toward improved predictions in ungauged basins: Exploiting the power of machine learning. Water Resources Research, 55, https://doi.org/10.1029/2019WR026065.
Daramola, S., Muñoz, D. F., Muñoz, P., Saksena, S., & Irish, J. (2025). Predicting the evolution of extreme water levels with long short-term memory station-based approximated models and transfer learning techniques. Water Resources Research, 61, e2024WR039054.
Referee comment: From Figure 7, there appears to be a systematic error in panel (a). What is the main reason for this?Author response: We thank the reviewer for noting the systematic error in Fig. 7(a). Such discrepancies can be partly attributed to error patterns, such as bathymetric smoothing inside narrow channels and wind-forcing deficiencies, which have been extensively studied in the literature for numerical modelling. However, a detailed quantitative attribution of the internal errors of the numerical model is beyond the scope of this study. Instead, panel (a) merely illustrates the baseline systematic deficit of raw numerical hindcasts, directly motivating our paradigm and illustrating how the ReSEML framework successfully removes these persistent errors.Referee comment: The red crosses in Figure 8 represent model miss. Why would there be model misses? As I understand it, only observations can be missing.Author response: We thank the referee for this question. First, a "model miss" is possible and is the standard categorical verification metric (False Negative) in POT analysis: an extreme surge was in the official event list (eta_obs >= threshold), but the numerical hindcast did not reach that threshold (eta_model < threshold) during the event window.Diagnostic checking across the stations shows that these misses are largely from four different sources: (1) spurious historical artefacts or unflagged gauge shifts in older POT lists (as discussed for Køge); (2) unresolved bathymetric bottlenecks in narrow fjords and estuaries (e.g., Randers Fjord, Odense Fjord) damping simulated setup; (3) temporal phase lags and basin seiche offsets causing peaks to fall outside the matching window; and (4) atmospheric wind-forcing deficits under-resolving peak drag in high-energy coastal zones.A comprehensive, event-by-event examination of all 790 missed events at the 36 stations would be a very significant effort outside the scope of this paper, but we will summarise these four underlying mechanisms in the revised manuscript.Citation: https://doi.org/10.5194/essd-2026-693-AC1
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AC1: 'Reply on RC1', Jian su, 02 Oct 2026
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Data sets
DEN-SURGE v1.0: a machine-learning-reconstructed, 10-minute continuous extreme sea-level catalog for 50 Danish coastal stations (1961-2024) Jian Su https://doi.org/10.5281/zenodo.21719179
Model code and software
ReSEML v1.0: Residual stacking ensemble for coastal sea level reconstruction Jian Su https://doi.org/10.5281/zenodo.21719179
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1.The results are actually quite good. I'd like to ask, why use the LSTM algorithm? It's a bit old, and it's mainly for time-series forecasting. Why not choose the latest time-series forecasting model?
2. From Figure 7, there appears to be a systematic error in panel (a). What is the main reason for this?
3. The red crosses in Figure 8 represent model miss. Why would there be model misses? As I understand it, only observations can be missing.