Reconstruction of Extreme Sea Levels in coastal China using Multiple Deep Learning models

Abstract

We present a 1970–2020 dataset of daily maximum coastal water levels reconstructed for 23 tide gauges along China’s coast. The product combines storm-surge residuals predicted with an Informer-based deep learning workflow (benchmarked against LSTM, CNN-LSTM, and ConvLSTM) with astronomical tides estimated by UTide from historical observations. Predictors are drawn from ERA5 reanalysis and multi-source tide-gauge records are used for training and validation. For each station, the model with best validation skill generates residuals combined with tidal harmonics to form daily maxima. Across stations, the reconstruction attains a mean correlation coefficient of 0.81 and RMSE of 11.7 cm for daily maxima; for events above the 95th percentile, the mean correlation is 0.68 and RMSE is typically below 20 cm. The release includes metadata, data splits, and skill metrics for transparency and reuse. This dataset enables spatiotemporal analyses of extreme coastal water levels and coastal hazard mitigation in regions with sparse observations. Daily maxima are computed as the sum of the maximum tide and maximum surge. This serves as an upper bound, as the peaks of tide and surge rarely coincide. Using hourly data, we estimate a mean non-coincidence bias of 14.9 cm (14.8%). Additionally, station-specific statistics are provided for user adjustment.

Background & Summary

China experiences frequent tropical cyclone landfalls that generate damaging extreme sea levels. Storm surges (abnormal sea-level fluctuations driven by cyclones and synoptic systems) combine with astronomical tides to produce hazardous extremes, causing widespread economic losses and secondary impacts such as saline intrusion^1–5. Despite this risk, publicly accessible multi-decadal tide-gauge records along China’s coastline are sparse and unevenly distributed. Only 12 GESLA-3 stations exceed 19 years of observations, with many series terminating by 1997⁶. These limitations restrict robust assessment of spatial heterogeneity and long-term variability in extreme sea levels across coastal China. Two complementary approaches are commonly used to simulate storm surges and extreme sea levels. Dynamical models (e.g., ADCIRC, Delft3D, MIKE) solve hydrodynamic equations and explicitly represent tide–surge interactions, bathymetric friction, and air-sea coupling effects, but require high-resolution geospatial datasets and substantial computational resources^5,7–10. Data-driven methods learn relationships between atmospheric predictors and water-level variables at lower computational cost, spanning statistical regression and empirical formulations^11–14 to machine-learning algorithms including support vector machines, decision trees, random forests, and gradient boosting^15,16. Recent deep-learning advances capture spatial and temporal dependencies through convolutional neural networks (CNNs), long short-term memory networks (LSTMs), convolutional LSTMs (ConvLSTMs), and attention mechanisms^17–24. Existing storm surge reconstruction products provide valuable global coverage but exhibit variable performance in coastal China. Statistical and machine-learning reconstructions from reanalysis data offer extended temporal coverage but may lack regional accuracy^25,26. Hydrodynamic model outputs provide physically consistent simulations but are computationally intensive and depend on bathymetric data quality^8,9. Recent studies have applied deep learning to storm surge prediction using diverse input resolutions and methodologies, demonstrating improved skill in capturing nonlinear relationships between atmospheric drivers and surge responses^17,20,22,23. Beyond these standard architectures, recent research has explored more advanced techniques to capture complex temporal dynamics. For instance, Temporal Convolutional Networks (TCNs) and hierarchical deep networks have been applied to model long-range dependencies and multi-scale interactions in time series^27,28. Similarly, physics-informed neural networks (PINN)²⁹ and related physics-guided surrogate approaches, which explicitly embed shallow-water dynamics into neural networks, offer promising avenues to ensure physical consistency in predictions. In this context, our study adopts the Informer architecture, a Transformer-based model optimized for long-sequence forecasting, to balance computational efficiency with accuracy. We present a comprehensive dataset of reconstructed daily maximum coastal water levels for 23 tide gauges along China’s coast spanning 1970–2020. The reconstruction integrates data-driven storm-surge modeling with tidal harmonic analysis to provide continuous daily maximum water-level time series where observational records are incomplete or unavailable. Non-tidal residuals are predicted from sea-level pressure and 10-m wind components from ERA5 reanalysis^30,31 using multiple deep-learning architectures: LSTM, CNN-LSTM, ConvLSTM, and Informer models. We systematically evaluate model performance across stations and select the optimal architecture for each location based on validation metrics. Storm surge predictions incorporate 24-hour lagged meteorological features and attention mechanisms to capture temporal dependencies and nonlinear atmospheric-ocean interactions.Astronomical tides are estimated using UTide harmonic analysis³² applied to available observational records from each station. UTide effectively handles irregular temporal sampling and provides confidence interval estimates, enhancing the reliability of tidal reconstructions. Daily maximum water levels are synthesized by combining model-predicted storm surges with corresponding astronomical tide values, ensuring physical consistency between surge and tidal components.The dataset includes station-level metadata (coordinates, record spans, data quality flags), model selection information, and validation statistics to support transparency and reuse. We provide comprehensive performance evaluation using correlation coefficients, root-mean-square errors, and mean absolute errors computed across all stations and for high-percentile events (≥95th percentile). Model validation employs temporal holdout testing with approximately 20% of each station’s record reserved as an independent test set. We compare reconstruction skill against three existing global storm surge products: GTSMv3 hydrodynamic simulations^8,33, and statistical reconstructions based on 20th Century Reanalysis and ERA-20 C reanalysis data^25,26. Performance evaluation demonstrates robust skill across stations, with average correlation coefficients exceeding 0.8 for daily maxima and substantial improvements over existing products, particularly for extreme events. The reconstruction captures both magnitude and timing of storm surge peaks during major typhoon events, providing enhanced representation of extreme coastal water levels compared to coarser global products.This dataset addresses critical data gaps for extreme sea-level analysis in coastal China, where sparse observational networks limit comprehensive risk assessment. The multi-decadal, station-level reconstructions enable analyses of temporal variability, return period estimation, and trend detection that would not be possible with short or discontinuous observational records alone.

Methods

Data sources

The predictors were obtained from the ERA5 reanalysis product^30,31. The ERA5 dataset covers coastal China region with a horizontal resolution of 0.25° × 0.25° and temporal resolution of 1 hour. This study employs atmospheric variables spanning 1970–2020, including mean sea level pressure (SLP) and 10-meter wind components (U10 and V10).

A total of 23 tide gauge stations along China’s coast were selected for analysis, with their spatial distribution and temporal spans illustrated in Fig. 1. Among them, there are 16 tide gauges with hourly records that were derived from the Global Extreme Sea Level Analysis dataset (GESLA-3)^6,34. The remaining 7 tide gauges (TG6-TG10, TG12-13), obtained from the Zhejiang Provincial Department of Water Resources, have a time series ranging from 2005 to 2020. These observational data are not publicly available due to data-sharing restrictions; therefore, the reconstruction results for these stations cannot be independently reproduced. To isolate storm surge components at each station, the following sequential processing was applied to observed water level data: (1) Detrending: removal of annual mean sea level variations using linear regression; (2) Harmonic tidal analysis: decomposition of residual signals into tidal constituents and storm surge residuals via least-squares harmonic fitting; (3) Peak extraction: identification of daily maximum storm surge magnitudes from detided residuals.

Fig. 1.

(a) Distribution of the 23 tide gauges used in this study. The numbers correspond to the station list on the right. (b) Observation time span for each station.

Reconstruction methodology

This study aims to reconstruct the daily maximum water level series along the Chinese coast from 1970 to 2020 using deep learning methods. The research methodology primarily comprises four key steps (Fig. 2). First, we collected predictors and observations. Next, we performed targeted operations during data processing, including data quality control, standardization, and outlier handling. Finally, by establishing nonlinear relationships between the daily maximum storm surge (predictand) and the surrounding atmospheric circulation fields (predictors), we evaluated and compared the performance of four deep learning models (LSTM, CNN-LSTM, ConvLSTM, and Informer) in storm surge prediction. During the model training and evaluation phase, multiple statistical metrics were employed to systematically assess the predictive capabilities of the four deep learning models. Attention mechanisms and 24-hour lagged features were incorporated to enhance model performance. After identifying the optimal model, the model was utilized to reconstruct daily maximum storm surges throughout the study period. These reconstructed storm surges were then superimposed onto the astronomic tides reconstructed using UTide to obtain the reconstructed daily maximum water level series for the Chinese coastal region.

Fig. 2.

Research framework.

Data processing

This study employed three variables as predictors: zonal wind speed at 10 meters (U10), meridional wind speed at 10 meters (V10), and mean sea level pressure (SLP). For sensitivity analysis, we also tested other variables such as sea surface temperature (SST). but the predicted results were not improved. Consequently, U10, V10, and SLP were ultimately selected as the predictors.

Predictors were extracted from a 10° × 10° spatial domain centered on each tide-gauge station, following Dang et al.¹⁸ and Tadesse et al.²⁵, who demonstrated that such a domain effectively captures the synoptic-scale atmospheric circulation systems influencing storm surges in the Western North Pacific and global coasts. The domain for each station comprised 40 × 40 data grid points, with time span ranging from 1970 to 2020. To further support this choice, we performed a brief sensitivity test (Supplementary Table S8) comparing the 10° × 10° baseline with a reduced 5° × 5° domain. The 10° × 10° setting shows modestly better performance and offers a practical balance between physical coverage and computational cost.

To incorporate temporal dependencies, lagged features were investigated. Predictors from different preceding intervals (3 h, 6 h, 12 h, 24 h) were evaluated for forecasting the daily maximum storm surge. The results of this comparative experiment are provided in the Supplementary Materials. Among different lag options (3 h, 6 h, 12 h, 24 h), a 24-hour lag configuration was selected based on superior validation performance (see Supplementary Materials) It was determined that incorporating a 24-hour lag was optimal. Specifically, atmospheric variables from 24-hour periods spanning both the preceding and current days were used to predict the maximum storm surge on the current day.

Regarding preprocessing of the predictand (daily maximum storm surge), outlier detection and missing value handling were performed while maintaining data integrity. Specifically, when missing values were identified in the predictand observations, the corresponding predictor data for those time steps were concurrently excluded from the dataset to ensure consistency.

Deep learning models and model training

This study evaluates four deep learning architectures for storm surge prediction: LSTM, CNN-LSTM hybrid, ConvLSTM, and Informer. LSTM captures temporal dependencies through gated mechanisms and has proven effective for hydrometeorological forecasting^35,36. CNN-LSTM combines convolutional spatial feature extraction with LSTM temporal modeling, demonstrating strong performance in multivariate water level prediction³⁷. ConvLSTM embeds memory mechanisms within convolutional operations for integrated spatiotemporal modeling²⁴. Informer incorporates ProbSparse self-attention mechanisms for efficient long-sequence processing³⁸.

To reduce computational complexity and address multicollinearity, Principal Component Analysis (PCA) is applied^11,12,39. The original four-dimensional feature tensor (48 × 3 × 40 × 40) representing 48 time steps, 3 variables, and 40 × 40 spatial grid is restructured and compressed. PCA reduces spatial dimensions to 400 principal components, yielding a 48 × 400 matrix while preserving maximum spatial variability. The first 400 components together explain more than 99.8% of the total variance across all stations (see Supplementary Table S6), indicating that nearly all atmospheric information was retained after dimensionality reduction.To avoid data leakage, PCA was fitted exclusively on the training data, and the resulting component loadings were subsequently applied to the test sets.

Temporal features are constructed using basic time units (year, month, day, weekday) enhanced with trigonometric transformations to capture periodic characteristics. These features undergo min-max normalization for consistent scaling. Spatial and temporal components are concatenated to form a final feature matrix of dimensions 48 × 411.

Dataset partitioning allocates 80% for training and 20% for testing. To accommodate varying observational spans across stations, approximately 20% of each station’s record (e.g., ~5 years from a 26-year series) is reserved as a continuous independent test period. This temporal holdout approach evaluates generalization on unseen time periods.

Model training employs the AdamW optimizer with early stopping to prevent overfitting and learning rate decay for improved convergence. For each station, the architecture achieving the best validation performance is selected for final reconstruction, ensuring optimal skill across the diverse coastal environments represented in the dataset.

Data reconstruction

This study reconstructs daily maximum water level time series by integrating reconstructed storm surges with astronomical tides. Specifically, for each tide gauge station, tidal harmonic analysis is performed on observational data using the UTide package to extract principal tidal constituents and reconstruct the astronomical tide time series. The UTide package offers advantages for this application, including the ability to handle data with irregular time intervals and provide confidence interval estimates, thereby enhancing the reliability of the astronomical tide reconstruction. Subsequently, the daily maximum storm surge is combined with the corresponding astronomical tide for each day to derive a comprehensive daily maximum water level time series. Concretely, the daily maximum total water level is calculated by summing the highest astronomical tide and the highest storm-surge residual for each individual day. Notably, since these two peaks rarely coincide in time, this summed value should be interpreted as an upper bound of the actual daily maximum water level. To quantify the potential overestimation introduced by this summation method, for days with available hourly observational data, we compare the summed value (i.e., the upper bound) with the actual highest combined water level recorded within the same day. The station-specific average differences (expressed both in centimeters and as a percentage) are reported in Supplementary Table S5.

Data Records

The reconstructed coastal water level dataset⁴⁰ is publicly available through Figshare. The dataset comprises comprehensive daily maximum water level reconstructions for 23 tide gauge stations along China’s coast spanning 1970–2020. The repository is organized into two main directories: ChainWL and Code.

The repository is organized into two primary directories: ChainWL and Code. The ChainWL directory contains the core dataset components, including validation metrics and reconstructed time series for daily maximum storm surges, astronomical tides, and total water levels across 23 stations from 1970 to 2020. The Code directory provides the complete computational workflow, comprising scripts for ERA5 data acquisition, preprocessing, and model training (e.g., Informer, LSTM), along with pre-trained weights to ensure full reproducibility of the results.

Technical Validation

Validation metrics and approach

Model performance is assessed using three standard metrics: Pearson correlation coefficient (PCC), root-mean-square error (RMSE), and mean absolute error (MAE):

$${\mathrm{Pearson}\prime \mathrm{s}(r}_{\mathit{xy}})=\frac{\sum _{i=1}^n(x_i-\overline{x}\left)\right(y_i-\overline{y})}{\sqrt{\sum _{i=1}^n{(x_i-\overline{x})}^2}\sqrt{\sum _{i=1}^n{(y_i-\overline{y})}^2}}$$ 1

$$\mathit{RMSE}=\sqrt{\frac{\sum _{i=1}^n{(y_i-x_i)}^2}{n}}$$ 2

$$\mathit{MAE}=\frac{\sum _{i=1}^n|y_i-x_i|}{n}$$ 3

$$\mathit{Bias}=\frac{1}{n}\sum _{i=1}^n\left(y_i-x_i\right)$$ 4

$$\mathit{Bias}(\%)=100\times \left(\frac{\overline{y}}{\overline{x}}-1\right)$$ 5

In the aforementioned formulas, x_i denotes the i-th observed value, representing the actual storm surge water level recorded by tide gauges, which reflects the true environmental conditions. y_i represents the i-th predicted value, derived from the model simulations based on predictor variables such as wind speed and atmospheric pressure. x̄ and ȳ denote the mean values of the observed and predicted series, respectively, which are used to compute the standardized Pearson correlation coefficient (r_xy), measuring the strength and direction of the linear relationship between the two datasets. n is the total number of samples. The root mean square error (RMSE) and mean absolute error (MAE) quantify the overall magnitude of prediction deviations. The mean bias (Bias) represents the average systematic deviation between the predicted and observed values, while the mean bias percent (Bias%) expresses this bias as a relative percentage compared to the mean observed value, indicating whether the model systematically overestimates or underestimates the true water levels.

To further validate the reconstructed dataset, this study compares its performance against current three available storm surge datasets (Table 1), focusing on their predictive accuracy and suitability for the coastal China region. The comparative datasets include:

Table 1.

Summary of Datasets Used for Validation.

Dataset	Predictors	Method Used	Coverage
ERA20_ml	ERA-20C (1.125°)	Multiple Linear Regression; Random Forest	1900–2010
20CR_ml	20-CR (1.0°)	Multiple Linear Regression; Random Forest	1900–2010
GTSM	ERA5 (0.1°,0.25°,0.5°,1°)	Hydrodynamic Equations Modelling	1979–2010
Ours	ERA5 (0.25°)	LSTM; CNN-LSTM; ConvLSTM; Informer	1970–2020

GTSMv3_surge^8,33: Based on the third version of the Global Tide and Storm Surge Model (GTSMv3.0), this dataset utilizes a depth-averaged hydrodynamic approach to dynamically simulate tides and storm surges. It covers the period from 1950 to 2017 with a high temporal resolution (10-minute simulation interval), making it particularly suitable for hydrodynamic studies. (https://cds.climate.copernicus.eu).

20 CR_ml^25,26,41: This dataset provides reconstructions of daily maximum storm surges at individual tide gauge stations, employing multiple linear regression and random forest methods. It spans an extended period from 1836 to 2015. (10.6084/m9.figshare.12971075).

ERA20C_ml²⁶: Similarly applying multiple linear regression and random forest methods, this dataset reconstructs daily maximum storm surges, covering the period from 1900 to 2010. (https://gssr.info/).

These global products were chosen as benchmarks because they represent the most widely used and publicly accessible data sources available to international researchers for studying coastal water levels and storm surges in this region. To ensure comparability, all datasets were processed to derive daily maximum storm surge values using an identical extraction and aggregation procedure. For GTSMv3_surge, the model grid point nearest to each tide gauge station (based on station latitude and longitude) was selected to represent the corresponding observation site. In contrast, both ERA20C_ml and 20CR_ml reconstructions were evaluated at exactly the same tide gauge locations as in this study, since all three datasets are derived from the GESLA-3 observational archive. Comparisons were restricted to the overlapping testing periods defined for each station to ensure a fair and consistent evaluation.

Validation of daily maximum storm surge

Model accuracy was evaluated using the RMSE by comparing predictions with observational data. The results indicate that the Informer model demonstrated superior performance at 19 out of the 23 stations, while the LSTM model achieved the highest performance at the remaining four tide gauges (Lianyungang, Pinghu, Wenzhou, Shijiusuo) (See Supplementary Table S1).

Overall, the model exhibits excellent performance, as illustrated in Fig. 3. Across all stations, the average Pearson correlation coefficient (R) is 0.81, with a root-mean-square error (RMSE) of 12 cm. Notably, 87% of stations achieve R > 0.7, 65% exceed R > 0.8, and the maximum correlation coefficient reaches 0.91. Specific stations, including Zhapo, Dinghai, Shanwei, and Xiamen, exhibit particularly outstanding performance, with correlation coefficients exceeding 0.89.

Fig. 3.

Distribution of statistical indicators of coastal stations in China (best model): (a) Pearson correlation coefficient (0–1, black high, white low); (b) RMSE (0–40 cm, white lower and black higher); (c) MAE (0–40 cm, white lower and black higher). The left figure shows the total, and the right figure shows ≥95%.

Consistent with findings by Tadesse and Wahl (2021), stations at higher latitudes north of the Yangtze River Estuary (e.g., Zhapo, Dinghai, Lianyungang) generally exhibit superior performance compared to those at lower latitudes in the south. This performance disparity is likely attributable to more pronounced variations in wind speed and atmospheric pressure at higher latitudes, enabling the model to more accurately capture storm surge dynamics in these regions. Nevertheless, several southern stations, such as Haikou and Hong Kong, also achieve high correlation coefficients and low RMSE values, underscoring the model’s robust generalization capability.

Figure 4 specifically illustrates the predictive performance comparison for daily maximum storm surges at Xiamen in 1978. All four deep learning models effectively reproduce the temporal trends of observed storm surges, though differences emerge in their response to extreme values and overall fit accuracy. The Informer model outperforms the others, with its predicted sequence closely aligning with observations, achieving a correlation coefficient (R) of 0.91, a RMSE of 8.85 cm, and a mean absolute error (MAE) of 6.90 cm. In comparison, ConvLSTM, CNN-LSTM, and LSTM models attain correlation coefficients around 0.89, with slightly higher RMSE and MAE values than Informer. Scatter plots further confirm that the Informer model exhibits the highest correlation between predicted and observed values, with the most concentrated data point distribution and a superior capability to simulate extreme storm surge events.

Fig. 4.

Comparison of predicted and observed storm surges at Xiamen station in 1978 using four deep learning models (Informer/ConvLSTM/CNN-LSTM/LSTM).

To rigorously assess the predictive efficacy of the optimized model, we present representative results for four key tide gauge stations (Xiamen, Zhapo, Hongkong, and Kanmen), each exemplifying its performance over a selected year. As illustrated in Fig. 5, the evaluation for each station is structured across three panels: (1) the left panel features a time series comparison of observed and predicted monthly daily maximum storm surge heights, supplemented with annual performance metrics—including the correlation coefficient (R), root-mean-square error (RMSE), and mean absolute error (MAE)—offering both a visual and quantitative evaluation of the capacity to capture temporal variability; (2) the middle panel displays a scatter plot encompassing all test samples, providing an overview of the overall alignment between observed and predicted values and reflecting generalization capability; and (3) the right panel presents a Q-Q plot, which evaluates the distributional concordance between predictions and observations, thereby highlighting potential systematic biases or deviations. Collectively, elevated R values coupled with reduced RMSE and MAE values indicate enhanced predictive accuracy. This multidimensional metric analysis enables a comprehensive evaluation of the predictive capability inherent to the framework across different stations and temporal scales, laying a robust foundation for its application in historical storm surge reconstruction and future warning systems.

Fig. 5.

Model performance at four representative stations: (a) Xiamen, (b) Zhapo, (c) Hong Kong, (d) Kanmen. For each station, the left panel shows the time series of observed and predicted daily maximum storm surge, the middle panel presents the scatter plot of observations versus predictions with evaluation metrics (R, RMSE, MAE), and the right panel displays the quantile-quantile (Q-Q) plot.

Validation of extreme storm surge

This study validates the capability of the proposed framework to simulate extreme storm surge events. Using the 95th percentile of observed storm surge series at each station as a threshold, extreme events were selected for comparative analysis, as depicted in Fig. 3. The results indicate an average correlation coefficient of 0.68 for extreme events, with 52% of stations exceeding 0.7, primarily distributed in the Yangtze River Estuary and areas to the north (such as Lusi, Laohutan, Daishan), the southeastern coast (such as Haimen, Wenzhou, Kanmen, Xiamen, Macau), and regions near the Pearl River Estuary (such as Hong Kong, Shanwei, Zhapo). Stations like Kanmen, Hong Kong, Zhapo, Xiamen, and Wenzhou achieved the highest correlation coefficients for extreme values, all exceeding 0.8. The majority of stations (65.2%) exhibited RMSE values below 20 cm for extreme events, indicating relatively small prediction errors for extreme storm surges at most locations. Overall, the framework achieved high reconstruction accuracy across all major tide gauge stations along China’s coastline, demonstrating particularly strong simulation capabilities for extreme events in high-latitude regions (such as Laohutan, Dalian) and certain typical stations (such as Hong Kong, Zhapo).

This study further focuses on the predictive performance for extreme storm surge events, specifically visualized and evaluated through scatter plots and typhoon-related extreme event figures. Figure 6 presents scatter plots of storm surges over 95th percentile at each station, detailing the correspondence between predicted and observed values under extreme conditions. Evidently, most stations show strong linear correlations between predicted and observed extreme storm surge values, with correlation coefficients (R) generally exceeding 0.7. Some stations (such as Zhapo, Hong Kong, Kanmen) achieved correlation coefficients above 0.8, demonstrating the framework’s high prediction accuracy even in high-value regions. Meanwhile, error metrics such as RMSE and MAE remained at relatively low levels, further validating the framework’s reliability and generalization capability for extreme storm surge events. Notably, although some stations exhibited slight underestimation in extremely high-value intervals, the overall fitting performance still surpasses traditional methods, providing strong support for extreme event risk assessment.

Fig. 6.

Scatter plot of the model performance verification using the test set (thresholds ≥95%).

Figure 7 concentrates on typhoon-induced extreme storm surge events, selecting several representative typhoon processes (e.g., “Fitow” in 2013, “Chan-hom” in 2015, among others). Through a comparative analysis of observed and simulated time series, coupled with pertinent evaluation metrics, this study systematically examines the framework’s simulation efficacy under typhoon influences. The findings reveal that the framework effectively captures the rapid escalation and extreme responses of storm surges during typhoon passages, with peak timing aligning closely with observations and demonstrating satisfactory performance in both correlation coefficients and error metrics. For certain typhoon events, deviations in extreme peak values are noted, potentially attributable to the limited availability of extreme samples or uncertainties in input meteorological data. Overall, the framework exhibits robust adaptability and stability in simulating typhoon-driven extreme storm surge events, thereby providing a scientific foundation for typhoon disaster warning and coastal disaster prevention and mitigation strategies.

Fig. 7.

Comparison of Observed and Simulated Storm Surge Heights During Representative Typhoon Events.

Comparison with other datasets

To further validate the reconstruction performance of the proposed deep learning method, this study conducted a comprehensive comparative analysis between the model results and observational data from major tide gauge stations along coastal China, as well as three other existing storm surge reconstruction products. To quantify the performance of various reconstruction products, this paper compared the performance of Informer, GTSMv3_surge, 20CR_ml, and ERA20C_ml at major tide gauge stations along coastal China. Table 2 summarizes statistical indicators, such as Pearson correlation coefficient (R), root mean square error (RMSE), and mean absolute error (MAE) for all samples and extreme storm surge (≥95th percentile) samples across different products. The results clearly demonstrate that the Informer model outperforms the other three products in both overall and extreme event correlation and error metrics, exhibiting higher reconstruction accuracy and superior capability in capturing extreme events.

Table 2.

The average indicators of the four products along the coast of China include ≥95%.

Products	Pearson’s correlation (95%)	RMSE (95%)	MAE (95%)
ERA20_ml	0.31 (0.18)	17.19 (36.72)	12.09 (32.51)
20CR_ml	0.36 (0.33)	16.21 (32.62)	11.53 (29.08)
GTSM	0.66 (0.65)	14.27 (18.45)	10.64 (15.38)
Ours	0.85 (0.71)	8.90 (16.39)	6.93 (13.58)

Figure 8 shows the time series of observed and simulated daily maximum storm surge heights at 4 tide gauge stations along coastal China over a one-year period. For each station, a year with relatively high typhoon intensity during 1979–2010 was selected and annotated in the figure. During these years, typhoon passages clearly caused significant fluctuations in storm surge heights. Figure 8 demonstrates that the optimal model (selected from our comparison of CNN-LSTM, LSTM, ConvLSTM, and Informer) generally fits well with observed values, achieving the highest R (range 0.89 to 0.93), lowest RMSE (range 5.50 to 8.85 cm), and lowest MAE (range 4.39 to 6.90 cm). GTSMv3_surge ranks second after the optimal model, showing the second-best performance. The remaining two products have R values mostly below 0.5.

Fig. 8.

Comparison of the daily maximum surge time series (one-year period) provided by the four products and the four tide level observation stations. Different colors represent different datasets.

Tidal harmonic analysis

In this study, to obtain daily maximum total water level sequences, a step-by-step superposition method was adopted. First, the UTide package was used to perform tidal harmonic analysis on historical observed tide level data from each station, extracting major astronomical tide components and reconstructing high-precision astronomical tide sequences. The UTide package can effectively process data with irregular time intervals, ensuring the accuracy and reliability of astronomical tide reconstruction. Taking the Hong Kong station as an example, as shown in Fig. 9, the astronomical tide heights reconstructed by UTide for 2018 match well with the astronomical tide heights separated from GESLA-3, with a correlation coefficient (R) reaching 0.99 and a root mean square error (RMSE) of only 2.3 cm, indicating extremely high extraction precision of astronomical tide components. Subsequently, the daily maximum storm surge sequences predicted by the deep learning model were superimposed with the astronomical tide values at corresponding moments on a daily basis. Specifically, for each day, the maximum values of astronomical tide and storm surge were taken separately, and the sum of the two yielded the maximum total water level for that day. This method not only fully reflects the combined effect of astronomical tides and storm surges but also realistically reproduces the occurrence process of extreme water level events. Through this superposition approach of “astronomical tide + storm surge,” the daily maximum water level sequences for major tide gauge stations along China’s coast from 1970 to 2020 were ultimately obtained. Comparison results between model-reconstructed daily maximum water level sequences and observational data demonstrate that this method can accurately capture extreme high water level events, providing a solid data foundation and scientific basis for subsequent extreme event analysis, risk assessment, and coastal disaster prevention and mitigation decision-making.

Fig. 9.

Tidal Simulation. The Utide tide simulation effect at the Hongkong site showcases the time series of predicted and observed tide heights in January 2020.

Validation of reconstructed total water levels (TWL)

To complement the storm-surge validation, we further evaluated the reconstructed total water level (TWL) series by comparing the combined product (tide + surge) with observed water levels at representative tide gauges. Figure 10a–d illustrate the temporal variations, scatter plots, and quantile–quantile (Q–Q) relationships for four stations (Xiamen, Zhapo, Hong Kong, and Kanmen) over one representative year. The reconstructed TWL shows strong agreement with observations, with correlation coefficients (R) ranging from 0.91 to 0.96, RMSE between 10.8 cm and 24.4 cm, and MAE between 8.7 cm and 19.5 cm. The Q–Q plots confirm that the model effectively captures both the central distribution and upper-tail extremes of observed Water levels.

Fig. 10.

Validation of reconstructed TWL at four representative stations (Xiamen, Zhapo, Hong Kong, and Kanmen), including time series, scatter, and Q-Q plots.

Overall, the reconstructed TWL exhibits strong agreement with observations, with a mean correlation coefficient (R) of 0.90, a root mean square error (RMSE) of 21.4 cm, a mean absolute error (MAE) of 17.5 cm, and a mean bias of 14.9 cm, corresponding to an average overestimation of approximately 14.8%. These results demonstrate the high consistency and reliability of the reconstructed TWL dataset. The specific verification results of each site can be found in Supplementary Material S6.

Figure 11 summarizes the evaluation of extreme TWL values ( ≥95th percentile) across nine representative tide gauges. Overall, RMSE values for these extremes are typically below 25 cm, and MAE values are comparable to or slightly lower than those from the full-sample evaluation. Stations such as Zhapo, Hong Kong, and Lusi show particularly consistent results with small amplitude errors for high-water events.

Fig. 11.

Evaluation of ≥95th-percentile TWL extremes across nine representative stations.

Although some sites exhibit relatively weak linear correlations due to the limited number of extreme events, the absolute magnitude errors (RMSE and MAE) remain stable or even reduced. This reflects the statistical sensitivity of correlation to small sample sizes and slight phase mismatches, rather than systematic model bias. Consequently, the reconstructed TWL product maintains reliable accuracy in reproducing both the daily variability and the magnitude of extreme coastal water levels that are most critical for coastal risk assessment.

Event-based verification of TWL exceedances To further evaluate the dataset’s utility for hazard assessment, we conducted an event-based verification focusing on Total Water Level (TWL) exceedances using the 95th percentile threshold. Based on the contingency table of Hits (H), Misses (M), and False Alarms (FA), two categorical metrics were computed.First, the Probability of Detection (POD) measures the ratio of correctly predicted extreme events to the total number of observed extreme events:

$$\mathit{POD}=\frac{H}{H+M}$$ 6

Second, the Equitable Threat Score (ETS) measures the skill of the forecast relative to random chance:

$$\mathit{ETS}=\frac{H-H_{\mathit{random}}}{H+M+\mathit{FA}-H_{\mathit{random}}}$$ 7

where the random hits component (Hrandom) is defined as:

$$H_{\mathit{random}}=\frac{(H+M)(H+\mathit{FA})}{N}$$ 8

and N represents the total number of samples.

The station-specific results are provided in Supplementary Table S7. Across all 23 stations, the reconstruction demonstrates high sensitivity to extreme events, achieving an average POD of 0.85. This indicates that the model successfully captures approximately 85% of the significant high-water events defined by the threshold. Furthermore, the average ETS is 0.36, a value that signifies meaningful predictive skill for rare events, substantially exceeding what would be expected from random chance (ETS = 0). Notably, stations prone to frequent typhoon impacts, such as Hong Kong and Beihai, exhibited particularly strong performance with ETS values exceeding 0.45. While a few stations (e.g., Keelung, Pinghu) showed lower skill scores likely due to local topographic complexities or observational noise, the overall results reinforce the dataset’s reliability for regional extreme sea-level analysis.

Author contributions

Conceptualization: J.F.; Data curation: J.F., J.H., W.B.; Formal analysis: J.F., J.H.; Methodology: J.F.; Project administration: J.F.; Resources: All authors, Y.Z.; Software: J.H.; Supervision: J.F.; Visualization: J.H., W.B.; Writing-original draft: J.H.; Writing-review & editing: All authors.

Data availability

All datasets generated and analyzed during this study are publicly available in the Figshare repository⁴⁰.

Code availability

All source code for data processing, model training is included in the Figshare repository⁴⁰. The code is implemented in Python and includes detailed documentation, installation instructions, and example usage scripts.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41597-026-06593-w.