Non-linear interaction modulates global extreme sea levels, coastal flood exposure, and impacts

Coastal regions worldwide face the recurring threat of extreme sea levels resulting from storm surges and high astronomical tides, leading to significant flooding and economic losses. Accurate prediction of these extremes is crucial for effective coastal protection strategies. Tide gauge measurements capture the combined effects of astronomical tides, meteorological surges, and mean sea level. However, for over 60 years, research has documented non-linear interactions between tidal and non-tidal sea level components, with the highest observed surges often occurring around mid-tide or low-tide, rather than at high tide. While previous studies highlighted the importance of tide-surge interaction (TSI), a comprehensive global quantification remained lacking. Several factors contributed to this gap: most TSI research was localized, early studies focused on specific geographic features like estuaries and bays, numerical model experiments had limitations in accuracy and scope, and a universally applicable explanation for the physical drivers of TSI was absent. Methodological limitations also introduced analysis artifacts, leading some studies to utilize skew surge instead of the non-tidal residual (NTR) for analysis. This study addresses these shortcomings by introducing a novel statistical method for global TSI estimation, examining temporal changes in TSI, and assessing TSI’s impact on coastal flood exposure.

Existing literature extensively documents local instances of tide-surge interaction (TSI). Early research focused on estuaries and bays, revealing the non-linear interplay between tidal and non-tidal components of sea level. Subsequent studies expanded to broader continental shelves, identifying regional variations and drivers. However, these studies often lacked global applicability due to their focus on specific locations and events. Numerical modeling efforts attempted to separate the contributions of tide, surge, and TSI, but were often limited by model resolution and the inability to accurately reproduce complex tidal and surge dynamics influenced by bathymetric features. Methodological inconsistencies also complicated the analysis, with some studies employing skew surge (the difference between observed and predicted maximum sea levels) as a proxy, leading to potential biases. Existing methods also did not provide a generalized global estimation of TSI influence.

This study utilizes a novel statistical method to assess the global impact of tide-surge interaction (TSI) on extreme sea levels. The researchers employed data from the GESLA-2 (Global Extreme Sea Level Analysis) database, encompassing 621 tide gauge stations with high temporal resolution. The methodology involves several key steps: 1. **Data Handling:** The GESLA-2 dataset underwent quality checks to remove spurious outliers and datum shifts. Three subsets of data (M, S, L) were created based on record length (≥30 years, ≥18 years, ≥60 years respectively), enabling analyses with varying temporal resolutions. High-water peaks were extracted using a peak-over-threshold (POT) method to identify extreme events, applying a declustering scheme to ensure independence. Tsunami events were removed to avoid biases. 2. **Statistical Dependence:** Kendall's rank correlation (τ) was used to measure the ordinal association between tide and NTR (non-tidal residual) at peak high waters. This measure quantifies the nonlinear interaction. Temporal changes in τ were calculated using moving averages across 30-year windows. 3. **TSI Estimates:** Copula theory was applied to model the dependence structure between tide and NTR, creating 10,000 artificial events to increase the data sample. Different copula models (Frank, Gaussian, t-Copula) were compared, selecting the best fit based on Root Mean Square Error (RMSE). Two copula setups were used: one incorporating observed τ and the other assuming independence (τ=0). Differences in extreme sea level percentiles between these setups quantified TSI effects. 4. **Regression Analysis:** A multiple regression model was developed to relate TSI effects to τ, enabling the interpolation of TSI to locations beyond the original tide gauge stations. 5. **Impact Assessment:** The Dynamic and Interactive Vulnerability Assessment (DIVA) modeling framework was used to estimate the impact of TSI on coastal flood costs and affected populations, comparing results with and without TSI correction using the derived regression model. 6. **Sea Level Rise (SLR) Comparison:** Probabilistic SLR projections were used to compare the magnitude of TSI effects to projected SLR increases by the end of the century. 7. **Validation:** The results were validated against previously published TSI values from various locations, confirming consistency and order of magnitude.

The study's key findings include: 1. **Spatial Variation of TSI:** The largest TSI influences on extreme sea levels (99th percentile) were found along the US East Coast and Gulf of Mexico, the UK North Sea coastline, and parts of the southern Japanese coast. The magnitude of TSI effects varied significantly depending on the region. For example, along the US East Coast, the average TSI effect was -28cm, reaching a maximum of 61cm at Sandy Hook, NY and a minimum of -14cm in Bar Harbour, ME. These findings highlight the importance of considering regional variations when assessing TSI impact. 2. **A Simple Proxy for Non-Linearity:** Analysis revealed a significant correlation between the tidal contribution to extreme sea levels and the magnitude of TSI effects (τ). While regions dominated by tidal contributions showed the strongest negative TSI effects, suggesting that large TSI effects are often found in regions where the tidal contribution accounts for nearly two thirds of the total water level. However, this is not a simple relationship and other factors influence the effect, highlighting the need for a more robust method using τ instead of the tidal contribution alone. 3. **Temporal Changes in TSI:** Significant positive trends in τ (indicating an increased effect of non-linear interaction) were observed over the past 60 years at many stations. This suggests that the damping effect of TSI on extreme sea levels has increased over time, potentially partially offsetting the increasing flood risk from sea level rise and other factors. However, a clear process-based explanation for this change remains elusive, needing further research. 4. **TSI vs. Sea Level Rise:** In 90% of stations, the overestimation of extreme sea levels when ignoring TSI was comparable to or exceeded SLR projections by the year 2100 at certain locations. This highlights the significant impact TSI can have on overall flood risk estimations and coastal planning. 5. **Impact on Coastal Flood Assessments:** Incorporating TSI into coastal impact assessments significantly reduces estimates of both population affected and flood costs. Globally, integrating TSI reduces estimates of the affected population by 8% and flood costs by 16%. The regions where TSI has a strong impact (US East Coast, UK, Japan) showed the largest reductions in these estimates. 6. **Validation:** The study’s findings are consistent with previous research using different methodologies and datasets, strengthening the reliability of the novel method. Comparison with prior studies confirm the findings of similar order. However, one exception was noted at the Cuxhaven station, where the statistically based TSI was significantly smaller than the numerically derived results. This discrepancy likely reflects the limitations of the new model in capturing the full range of variability in TSI.

This study provides a novel statistical method to estimate the global impact of tide-surge interaction (TSI) on extreme sea levels. The findings demonstrate that ignoring TSI leads to significant overestimation of extreme sea levels, an error comparable to or exceeding projected sea-level rise by 2100 in some areas. The temporal changes in TSI identified suggest a potential counteracting effect on increased flood risk, but further research is needed to understand the underlying mechanisms. The incorporation of TSI into coastal impact assessments substantially reduces estimates of affected populations and flood costs. The limitations of the method, particularly in capturing the full event-to-event variability in TSI at certain sites (e.g., Cuxhaven), emphasize the need for continued research and improvements to the approach. The potential influence of seiches in certain regions also necessitates further study. Despite these limitations, the study's findings highlight the urgent need to integrate TSI into global sea level and coastal risk assessments for more accurate predictions and effective adaptation strategies.

This research introduces a novel statistical method for estimating the global impact of tide-surge interaction (TSI) on extreme sea levels, demonstrating that ignoring TSI significantly overestimates extreme sea levels in many locations. The study reveals considerable spatial and temporal variability in TSI, with regions like the US East Coast, UK, and Japan exhibiting the strongest effects. Incorporating TSI into coastal impact assessments drastically reduces projected population affected and flood costs. The methodology provides a valuable tool for future research and coastal planning, though further investigation is needed to fully understand the mechanisms driving TSI changes and to refine the method's accuracy, particularly in regions where additional factors (like seiches) influence water levels.

The study acknowledges several limitations. First, the accuracy of the TSI estimates is affected by the data availability and the quality of the tide gauge records. The temporal resolution and length of the available data may not fully capture the variability in extreme events. Second, the model's ability to capture the full range of TSI variability at individual sites, particularly in shallow areas influenced by standing oscillations (seiches), could be improved. Lastly, the study primarily focused on the interaction between tides and surges, potentially overlooking other factors influencing extreme sea levels. More extensive and higher-resolution data combined with more sophisticated model development would help overcome these issues and to gain a deeper understanding of the complexities of the tide-surge interactions.