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

The study addresses how non-linear interactions between astronomical tides and meteorologically driven non-tidal residuals (surges and other components) affect extreme sea levels, and how neglecting this interaction biases coastal flood risk assessments. Although tide-surge interaction (TSI) has been documented for decades and shown to shift surge maxima away from high tide, a robust global quantification and transferable understanding have been lacking due to site-specific studies, limitations of numerical models, and short study durations. The purpose is to develop and apply a statistical framework using global tide-gauge records to quantify TSI effects on extremes, assess their temporal changes, compare their magnitude to sea-level rise (SLR) projections, and evaluate implications for global coastal exposure and flood costs.

Prior studies on tide-surge interaction are largely local, focusing on estuaries, bays, and continental shelves (e.g., southern North Sea, UK, English Channel, Taiwan Strait), with findings dependent on local bathymetry, geometry, and event characteristics. Numerical model experiments have separated tide, surge, and interaction contributions but are often limited by bathymetric resolution, event-based scope, and short durations. Methodological issues in harmonic analysis can bias surge estimates, motivating use of skew surge metrics. Some work suggested independence of the largest skew surges from the tide, but the independence does not hold for skew surges or NTR associated with the highest total water levels. A generalized, global quantification of TSI and its implications has remained missing.

Data: High-frequency tide-gauge records from the GESLA-2 database were used and quality controlled. Records were interpolated to hourly resolution. Three subsets were defined: S (≥18 years, end ≥2010; 621 stations), M (≥30 years, end ≥2010; 362 stations), and L (≥60 years, end ≥2010; 102 stations). High-water peaks were extracted and extremes identified using a peaks-over-threshold approach selecting on average the largest 3 values per year, with 36 h declustering to ensure event independence. Tsunami-affected events (within 24 h of known tsunamis) were removed. Separation and dependence: For each year, tidal constituents (67) were estimated using the T_Tide harmonic analysis, and total water level was decomposed into tide and non-tidal residual (NTR). At observed peak high waters, pairs of tide and NTR values were extracted. Dependence was quantified using Kendall’s rank correlation τ (−1 to 1, with negative values indicating stronger disagreement consistent with TSI) for each site and subset. Temporal changes in τ were assessed for set L using 30-year moving averages, with trends and correlations to PSMSL mean sea level computed (significance at 90–95% levels, accounting for serial correlation). Copula framework and extreme synthesis: To quantify TSI effects, copula theory was applied to construct joint distributions of tide and NTR using Frank, Gaussian, or t-copulas, with nonparametric kernel marginals. For each site, 10,000 synthetic joint events (~3300 years) were generated (set MA), selecting the best copula by RMSE between empirical and parametric copulas and reproducing observed τ (RMSE ~0.017). Two setups were run: descriptive (sa) using observed τa at each site and prognostic (sp) with τp = 0 (independence). Percentiles (10th–90th; 99th for extreme) of total water level were computed for each setup, and TSI was defined as sp − sa, representing the reduction (negative values) or increase due to interaction. Regression-based global extrapolation: A multiple regression relating TSI to τ was derived: TSI ≈ a + bτ + cτ^2 + dτ^3, with coefficients varying by percentile (10th–99th). Observed τ from set S were spatially interpolated (natural kriging) to >12,000 GTSR coastal model locations to estimate percentile-based TSI globally (TSIe) via the regression. Impact assessment: Using the DIVA framework, 100-year return water levels from GTSR (baseline) were adjusted by TSI via Eq. (1) and compared in terms of two exposure indicators (population and flood costs in the 1-in-100-year floodplain) for present-day (2020). Regional and global changes were quantified. SLR comparison: Probabilistic regional SLR projections compatible with +1.5 °C and +2.0 °C warming by 2100 (Jackson & Jevrejeva 2016) were compared to site-specific TSI magnitudes to estimate the year when SLR exceeds TSI. Projections (relative to 1986–2005) were spline-interpolated to annual values; GIA corrections (ICE-6G) included. Validation: Comparisons with published TSI estimates for the UK, English Channel, and Taiwan Strait showed similar magnitudes. A German Bight numerical model (tide-only, surge-only, total) for 75 events (1970–2013) yielded event-varying TSI (~10–85 cm, mean ~30 cm) at Cuxhaven; the statistical method captured average effects (~3 cm) but not event-to-event spread. Bias in GTSR 99th-percentile levels relative to observations improved after TSI adjustment (mean difference ~−12.7 cm to ~4.9 cm; to ~1.9 cm excluding sites with τ ≥ −0.35).

• Spatial hotspots: Strongest TSI-induced reductions in extreme sea levels occur along the US East Coast and Gulf of Mexico, the UK North Sea coast, and parts of southern Japan.
• US East Coast: Average TSI at the 99th percentile ≈ −28 cm (largest effects in the Mid-Atlantic Bight, average ~−38 cm); maximum −61 cm at Sandy Hook (NY); minimum −14 cm at Bar Harbor (ME). Gulf of Mexico average ≈ −27 cm (−45 cm at Pensacola, FL; −36 cm at St. Petersburg, FL). US West Coast: smaller effects, average ≈ −10 cm; tides account for ~85% of extreme levels.
• UK North Sea: Very strong effects, average ≈ −48 cm; −37 cm at North Shields, −66 cm at Cromer, −55 cm at Dover. English Channel/Brittany: ~−42 cm at Dunkerque, ~−28 cm at Saint-Malo, +18 cm at Le Conquet (smaller reduction or slight increase reported at some sites).
• Southern Japan: Average ≈ −22 cm (71% tidal contribution); specific sites such as Nagoya −50 cm (75% tidal), Uno −42 cm (76% tidal), Matsuyama −39 cm (89% tidal). After excluding bay-influenced outliers, average ≈ −20 cm.
• Proxy relationships: At ~75% of stations, tides contribute >50% of extreme levels. TSI reduction is strongest when tides contribute ~60–70% of the extreme level; TSI approaches zero or positive when tidal contribution <20%. Correlation between tidal contribution and TSI magnitude is weak (~0.15), whereas Kendall’s τ is a strong predictor (correlation ≈ −0.83) of TSI magnitude.
• Dependence finding: NTR and skew surge associated with the highest total water levels are dependent on the tide; contrary to assumptions of independence at the largest skew surges when considered in isolation.
• Temporal changes: Many long records show significant increases in |τ| since ~1950 (reported as 2–4% per year at many sites), implying growing damping of extremes due to TSI and potentially reducing required defence heights; no consistent correlation between τ trends and mean sea level trends was found.
• SLR comparison: At 90% of stations, extreme sea levels are overestimated if TSI is neglected. On average, TSI magnitudes are comparable to SLR expected by 2050 under +1.5 °C warming (and by ~2040 for +2.0 °C) at many sites; at some hotspots, TSI equals or exceeds SLR projected by 2100.
• Impact assessment: Accounting for TSI reduces exposure: globally, population affected by 1-in-100-year floods decreases by ~8% and flood costs by ~16%. Regionally: US coast −17% people, −13% costs; southern Japan −22% people, −15% costs; UK North Sea coast −5% people, −7% costs.
• Validation consistency: Statistical TSI estimates align with literature values (e.g., Immingham–Cromer ~53–66 cm; Dunkerque ~28–42 cm vs 51–74 cm modelled; Taiwan Strait ~25–27 cm). Adjusting GTSR with TSI reduces bias in 99th-percentile levels notably.

The analysis shows that non-linear tide–NTR interaction systematically modulates extreme sea levels, typically reducing extremes relative to a linear superposition assumption. This modulation is strongest where tides contribute roughly two-thirds of the total water level, and it varies by location due to local bathymetry, geometry, and dynamics. Because many global impact and hazard assessments combine tide and surge independently, they often overestimate extreme levels and associated risks; incorporating TSI via the proposed statistical method yields more realistic extremes and substantially lowers estimated exposure and costs. The dependence between tide and NTR (and skew surge) at the highest observed total water levels challenges common assumptions of independence and suggests the tide modulates extremes even for rare events. Temporal increases in the strength of interaction (|τ|) at many sites imply that TSI could partially offset increasing flood risk from SLR and changing storm/tidal characteristics, although drivers of these τ changes are not yet fully understood. The method offers a computationally efficient alternative to fully coupled high-resolution models for global studies, improving existing reanalyses (e.g., GTSR) when adjusted for TSI, while highlighting the need to consider TSI in design allowances and adaptation planning.

The study introduces a global, observationally grounded statistical framework to quantify tide–surge (tide–NTR) interaction and its impact on extreme sea levels. It identifies global hotspots (US East/Gulf coasts, UK North Sea, southern Japan), demonstrates that neglecting TSI can lead to overestimation of extremes by up to ~70 cm (~30%), and shows that TSI magnitudes can rival SLR projections this century at many sites. Incorporating TSI reduces estimated populations and assets exposed to 1-in-100-year flooding at regional and global scales. The dependence between tide and NTR at the highest total water levels indicates that extremes are modulated by tidal phase. Future work should develop process-based understanding of TSI variability and trends, capture event-to-event variability beyond mean effects, integrate wave setup and other processes, and embed TSI-aware extremes into global risk and adaptation assessments.

• The statistical model captures average TSI effects but not the event-to-event spread; at some locations (e.g., very shallow German Bight), the highest NTRs occur across all tidal phases, yielding weak dependence and potential misestimation.
• Sites influenced by seiches or harbor oscillations (e.g., Baltic Sea, certain tropical locations) can exhibit positive TSI or reversed responses; such dynamics may bias τ and TSI estimates since they are implicitly included in marginals.
• Input records, especially shorter ones (≥18 years), may not contain the most extreme storms or spring tides, potentially biasing dependence estimates.
• The adjustment of GTSR using TSI does not account for processes absent from GTSR (e.g., regional wave setup), limiting direct comparability to observations.
• Copula-based synthesis assumes stationarity within analyzed periods and relies on accurate τ estimation; regression extrapolation assumes the τ–TSI relationship holds spatially when interpolated to ungauged locations.
• Reported temporal trends in τ lack a clear process-based attribution; correlations with mean sea level are generally insignificant or mixed.