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: final response (author comments only)
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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
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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RC2: 'Comment on essd-2026-693', Anonymous Referee #2, 22 Oct 2026
The preprint by Su and others presents a storm surge dataset based on various data sources and machine learning.
My main concerns are related to the model description and validation, purpose and applicability of the framework, and the format of the contents on zenodo, as I explain in the comments below.
The comment on the non-stationarity (line 71) is clashing to that at line 75; are you implying that ML is able to manage the non-stationarity?
It seems that an East-West and North-South gradient in model performances is present. The authors should comment such aspects more critically, which may be done by showing the cluster in maps (especially if these clusters are regional or dependent on exposition; in this case, this should be shown too).
I am confused by the choice of sequence extraction for training. I understand a period of 48 hours is used, but I guess events might exceed that. Moreover, no dynamic information other than sea level is used-the authors should explain if other variables might be useful. What happens in case? Moreover, if the correction muted for non-storm periods, i.e., the simulation is unaltered?
The description of models used is poor. Unless I missed, hyperparameters (and how these are set) are not specified, both for RF and DL models. What is the needed hardware and resources to run this?
The structure of the zenodo repository needs improvement. The supplementary figure file returns a worrisome message when unpacked: "error: invalid zip file with overlapped components (possible zip bomb)". Probably this is due to an enormous number of files within (8 GBs of images!); please organize them differently (e.g., in panels) and ensure this works across platforms.
Some information on the continuity of the underlying hydrodynamic simulation at the UERRA/DMI system in 2018/2019 should be presented; other possible discontinuities commented as well.
The use of the solid line with different purposes between Fig. 7 and 9 is unfortunate. Please keep consistency to avoid confusion.
I find the paragraph starting at 409 to be confusing. The EVA results seems very different for the bottom two stations; does this indicate poor reliability of the reconstruction?
The final part of Section 1 seems to suggest that the framework acts to bias-correct model simulations; I would like to understand if this is the case, and the advantage over existing datasets e.g. https://cds.climate.copernicus.eu/datasets/sis-water-level-change-timeseries-cmip6?tab=overview
In general, context with respect existing resources is scarce. Please consider the literature (e.g. https://doi.org/10.5194/sp-3-slre1-4-2024) to identify relevant works and alternative datasets for which yours would be superior.
Line-by-line comments
7 undefined acronyms
134 "precise" meaning nearest pixel of the simulation output?
151 I wonder if the information can be propagated somehow into Fig 1, to inform the reader. Is clustering regional?
173 and following with "exclusion" you mean that sequences are dropped, substituted or missing values are inserted? Please specify better this cleaning step
222 and following acronyms for networks already introduced, right? On the other hand, the reference papers for them are not cited?
228 OK, but this is not done here?
329 please comment on the tendency for 0 difference in the early portion of each sequence
364 please explain if x=0 or y=0 are removed from your model output due to the ML correction or simply the QC procedure
490 it would be nice to generate some synthetic corrupted cases within the test set and see how the model perform in such controlled circumstances, for which you also have a withheld ground truth
554 I think it's not proper to speak about AI-ready datasets, since your are not delivering something immediately useful for other modellers, right?
635 why citing a preprint version? Consider https://os.copernicus.org/articles/20/21/2024/
576 shouldn't information on the format be added? As far as I can see, data organized in .csv files reporting model/bias/reconstruction. How can one understand if the data is reconstructed or simulation-based? There is a large number of digits, is the precision of observations so high (10^-14 cm) to support that? It would be useful to include information on the QC ground truthCitation: https://doi.org/10.5194/essd-2026-693-RC2 -
AC2: 'Reply on RC2', Jian su, 29 Oct 2026
We sincerely thank Referee #2 for his/her constructive, thorough, and insightful review of our manuscript. Below, we address each point raised by the referee and summarise our revision strategy. These replies 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 comment on the non-stationarity (line 71) is clashing to that at line 75; are you implying that ML is able to manage the non-stationarity?
Response: Thank you for the referee's notes. We do not suggest that multi-decadal climatic non-stationarity, like mean sea-level rise or vertical land movement, can be solved by machine learning. Rather, the ReSEML framework solely concentrates on learning the stationary, non-linear physical relationships governing event-scale wind setup, shallow-water resonance, and timing errors; long-term trends are eliminated before model training by referencing all records to the Danish national geodetic datum (DVR90) and eliminating local sea-level trends. To identify long-term SLR trends from event-scale hydrodynamic dynamics, we will rework lines 71–75 in the updated text.
Referee Comment: It seems that an East-West and North-South gradient in model performances is present. The authors should comment such aspects more critically, which may be done by showing the cluster in maps (especially if these clusters are regional or dependent on exposition; in this case, this should be shown too).
Response: These spatial performance patterns align directly with distinct Danish coastal hydrodynamic regimes, spanning the macrotidal, wind-setup-dominated North Sea and Wadden Sea, the topographically transition straits in the Belts and Kattegat, and the microtidal Western Baltic dominated by post-storm seiche oscillations. In the revised manuscript, we will add a dedicated geographical map displaying the regional cluster distributions alongside coastal exposure characteristics and expand the Discussion Section to critically evaluate the physical drivers behind these East-West and North-South performance gradients.
Referee Comment: I am confused by the choice of sequence extraction for training. I understand a period of 48 hours is used, but I guess events might exceed that. Moreover, no dynamic information other than sea level is used-the authors should explain if other variables might be useful. What happens in case? Moreover, is the correction muted for non-storm periods, i.e., the simulation is unaltered?
Response: The 48-hour event window (±24 h around the surge peak, comprising 288 steps at 10-minute resolution) was chosen because storm surges in Danish waters are primarily driven by fast-moving synoptic low-pressure systems, meaning a 48-hour duration adequately captures the complete pre-surge setup, peak crest, and water level drainage phase. One fjord system (Limfjord) experiencing elevated sea level sustained for several days was excluded from this study. We utiilise modelled sea level as the primary input feature because the numerical hydrodynamic model already acts as a dynamic physical integrator of surface wind stress, barometric pressure, and astronomical tides; relying on sea-level residuals avoids the severe dimensionality and overfitting pitfalls of ingesting multi-level meteorological fields into finite extreme event records. For non-storm periods, the baseline numerical simulation remains unaltered because the correction is designed specifically for extreme and near-extreme threshold exceedances, and we will clarify this windowing sensitivity, the trade-offs of omitted meteorological variables, and non-storm data treatment in the revised manuscript.
Referee Comment: The description of models used is poor. Unless I missed, hyperparameters (and how these are set) are not specified, both for RF and DL models. What is the needed hardware and resources to run this?
Response: We agree that the technical specifications of our architecture should be explicitly documented. We will add a dedicated hyperparameter table in Section 2 to the revised manuscript, showing the configurations for the base LSTM (2 layers, 64 hidden units, learning rate = 0.001, early stopping patience = 12), the TCN (3 residual blocks with 32, 64, and 128 channels, kernel size = 3, causal padding, dropout = 0.2), and the Random Forest meta-learner (100 estimators, maximum tree depth = 6). We also provide details of computational hardware and resource requirements. Training over all regional clusters takes less than 12 hours on a single desktop GPU (i.e. NVIDIA A40).
Referee Comment: The structure of the zenodo repository needs improvement. The supplementary figure file returns a worrisome message when unpacked: "error: invalid zip file with overlapped components (possible zip bomb)". Probably this is due to an enormous number of files within (8 GBs of images!); please organize them differently (e.g., in panels) and ensure this works across platforms.
Response: The warning message is triggered by unpacking heuristics detecting an excessive number of individual image files within an uncompressed 8 GB directory structure. To resolve this completely, we are restructuring the Zenodo repository by compiling individual station plots into one packages (< 1 GB each). It will be released under an updated Zenodo version and DOI for the revised manuscript.
Referee Comment: Some information on the continuity of the underlying hydrodynamic simulation at the UERRA/DMI system in 2018/2019 should be presented; other possible discontinuities commented as well.
Response: The underlying hydrodynamic model configuration, bathymetric grid, and vertical reference datum remained identical across the transition from UERRA reanalysis atmospheric forcing to the operational DMI system in 2018/2019. In the revised manuscript, we will incorporate a quantitative overlap evaluation comparing bias, variance, and datum continuity during the overlapping transition months to confirm that no artificial step changes or statistical discontinuities were introduced into the multi-decadal series.
Referee Comment: The use of the solid line with different purposes between Fig. 7 and 9 is unfortunate. Please keep consistency to avoid confusion.
Response: Thanks. We will harmonise all line styles, markers and colour palettes in Figures 7, 8 and 9 in the revised manuscript to provide a consistent visual representation of observations, raw model runs and reconstructed surge trajectories throughout the paper.
Referee Comment: I find the paragraph starting at 409 to be confusing. The EVA results seems very different for the bottom two stations; does this indicate poor reliability of the reconstruction?
Response: We thank the referee for pointing out this in the discussion. It is a good point. The divergence observed in the bottom two stations does not indicate poor reconstruction skill, but rather reflects severe sampling uncertainty in the observational record: these specific tide gauges possess short observational time series (fewer than 15–20 years), leading to large statistical uncertainty when fitting empirical return periods. Extending the record using the 64-year reconstructed series provides a physically consistent sample that stabilises the tail behaviour of the GPD distribution, and we will thoroughly rewrite the paragraph starting at line 409 to clearly decouple observational sampling uncertainty from reconstruction accuracy.
Referee Comment: The final part of Section 1 seems to suggest that the framework acts to bias-correct model simulations; I would like to understand if this is the case, and the advantage over existing datasets e.g. https://cds.climate.copernicus.eu/datasets/sis-water-level-change-timeseries-cmip6?tab=overview. In general, context with respect existing resources is scarce. Please consider the literature (e.g. https://doi.org/10.5194/sp-3-slre1-4-2024) to identify relevant works and alternative datasets for which yours would be superior.
Response: We appreciate this constructive suggestion to contextualise DEN-SURGE within existing pan-European climate services and recent sea-level literature. Unlike traditional static bias-correction methods (e.g., quantile mapping) that adjust aggregate probability distributions without fixing temporal misalignments or phase errors, ReSEML executes dynamic, high-frequency residual reconstruction that preserves temporal surge progression, peak sharpness, and shallow-water seiche decay. Also, although pan-European services such as the Copernicus CDS water level datasets provide valuable information at the continental-scale, their coarser spatial resolutions are not able to resolve complex Danish fjords, inner Danish straits, and local barrier islands, nor do they provide the 10-minute resolution and local geodetic datum harmonisation (DVR90) offered by DEN-SURGE, which we will articulate thoroughly in the Introduction and Discussion alongside the recommended references.
We thank Referee #2 again for the minor comments, and we will address them all in our revised manuscript.
Citation: https://doi.org/10.5194/essd-2026-693-AC2
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AC2: 'Reply on RC2', Jian su, 29 Oct 2026
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.