# Climate mode interactions amplify coastal flood risks and their seasonal predictability

Julien Boucharel, Rafael Almar, Fei-Fei Jin, Sen Zhao, Malte Stuecker, Boris Dewitte

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Julien Boucharel, Rafael Almar, Fei-Fei Jin, Sen Zhao, Malte Stuecker, et al. Climate mode interactions amplify coastal flood risks and their seasonal predictability. Nature Geoscience, 2026, 10.1038/s41561-025-01903-0. ird-05493112

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# Climate mode interactions amplify coastal flood risks and their seasonal predictability

Received: 22 April 2025

Accepted: 11 December 2025

Published online: 20 January 2026

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Julien Boucharel Ⓓ1,2you, Rafael Almar Ⓓ1you, Fei-Fei Jin Ⓓ2,3you, Sen Zhao Ⓓ2, Malte F. Stuecker Ⓓ3,4 and Boris Dewitte$^{5,6,7}$

Extreme coastal flooding often arises when large-scale climate patterns and local ocean-atmosphere variability combine to magnify water levels beyond what communities can withstand. Understanding and anticipating these interactions is essential for protecting vulnerable coastlines. Here we aim to determine how two major modes of climate variability—the El Niño/Southern Oscillation and the North Atlantic Oscillation—individually and jointly influence extreme coastal water levels worldwide. Using global observational and reanalysis datasets spanning 1958–2023, we analyse their separate effects and diagnose potential nonlinear interactions through statistical and process-based methods. We show that specific, seasonally aligned phases of these two climate modes interact nonlinearly, producing coastal water levels far higher than expected from either mode alone. These combinations enhance storm activity and wave conditions from the eastern seaboard of North America to western Europe and the Mediterranean. We further show that incorporating these nonlinear interactions into a conceptual climate model enables skilful seasonal predictions of coastal flooding hazards several months in advance, demonstrating the feasibility of reliable early-warning systems for coastal risk reduction.

Approximately 10% of the world's population lives in coastal areas less than 10 m above sea level<fnref n="1" />, and sea-level rise is already affecting coastal communities. Superimposed on this global trend²⁻⁴, internal climate variability causes pronounced interannual and decadal variations in regional sea level and coastal water level (CWL)⁵⁻⁷ mainly via dynamic or steric effects and freshwater fluxes⁸,⁹. Climate variability also modulates the CWL through atmospheric synoptic variability, particularly via extra-tropical and tropical storms¹⁰,¹¹, which generate surges from wind set-up and surface pressure effects, as well as wave run-up, which can cause flooding¹²⁻¹⁵. Wave effects are the largest contributors to CWL interannual variability¹⁶⁻²⁰ and can reach several metres under storm tracks, causing devastating damage to coastal infrastructures.

The El Niño/Southern Oscillation (ENSO) is the primary driver of global climate variability and plays a central role in modifying climate and weather patterns over the tropics/subtropics²¹. ENSO causes inter-annual variations in the zonal distribution of heat in the upper ocean across the tropical Pacific, resulting in sea-level anomalies of more than 30 cm locally. ENSO also influences weather patterns, particularly tropical²² and extra-tropical²³ storms, as well as subsequent surface wave activity and coastal hazards such as flooding and erosion²⁴⁻³⁰. A recent study¹¹ showed that ENSO increases the frequency of tropical and extra-tropical storms and, depending on its phase and type, for example, eastern Pacific (EP) El Niño with sea surface temperature (SST) anomalies in the eastern Pacific or central Pacific (CP) El Niño

<footnote n="1">¹LEGOS, Université de Toulouse III, CNRS/IRD/UPS/CNES, Toulouse, France. ²Department of Atmospheric Sciences, University of Hawai'i at Mānoa, Honolulu, HI, USA. ³International Pacific Research Center, University of Hawai'i at Mānoa, Honolulu, HI, USA. ⁴Department of Oceanography, University of Hawai'i at Mānoa, Honolulu, HI, USA. ⁵CECI, Université de Toulouse III, CERFACS/CNRS, Toulouse, France. ⁶Centro de Estudios Avanzados en Zonas Áridas (CEAZA), Coquimbo, Chile. ⁷Center for Ecology and Sustainable Management of Oceanic Islands (ESMOI), Departamento de Biología Marina, Facultad de Ciencias del Mar, Universidad Católica del Norte, Coquimbo, Chile.✉e-mail: julien.boucharel@ird.fr; rafael.almar@ird.fr; jff@hawaii.edu</footnote>
<figure><img src="image_3.png" /><figcaption>**Fig. 1 | Individual and compounded influence of climate modes on coastal risks.** Composites (h month⁻¹) of flooding risk interannual anomalies for different phases of climate modes during the period 1958–2023. a,b, Positive phases of the EP (E+) (a) and CP (C+) (b) ENSO modes. c,d, Positive (c) and negative (d) phases of the NAO and for different combinations of climate-mode phases. e, The combination of E+ and NAO+ (E+/NAO+). f, C+ and NAO+ (C+/NAO+). g, E+/NAO–. h, C+/NAO–. The flooding risk is calculated as when the monthly aggregated interannual anomalies of the hourly total CWL reach a third</figcaption></figure>

of the maximum local coastal elevation (Methods). Green dots indicate where the composite anomalies are statistically significant at the 95% confidence interval using a two-sample Student's t-test. The upper left panel shows the regression patterns of the interannual SST and 10 m wind anomalies on the EP El Niño mode, CP El Niño mode and NAO indices, respectively. The arrows in each map indicate the composites for surface winds, visualizing anomalies in pressure systems. The coloured boxes delineate the regions of interest detailed in the study.

with anomalies largest near the dateline³¹, alternates coastal hazards between the western and eastern Pacific and even at high latitudes via atmospheric teleconnections²³,³².

Similarly, the North Atlantic Oscillation (NAO) is the dominant pattern of variability in the Atlantic Ocean affecting the atmospheric circulation³³,³⁴. It is characterized by the pressure difference between the Icelandic low and the Azores high. The NAO influences sea level on seasonal to interannual timescales through changes in heat exchange, atmospheric pressure fields and wind patterns³⁵. Positive NAO phases (NAO+) correspond to a stronger Icelandic low and Azores high, shifting the storm track northwards, while negative phases (NAO–) weaken westerlies and shift the storm track southwards. This impacts wave activity and CWL in the North Atlantic³⁶, with remote effects even reaching the tropics⁷,³⁷. Both ENSO and NAO exert strong influences on the interannual variability of extreme CWL that modulates coastal risks in the Northern Hemisphere. They influence variability in mean sea level, storm surges and tides, enabling the seasonal to interannual predictability of extreme sea levels³⁸, modulating coastal flooding probabilities³⁹, even at decadal scales⁴⁰,⁴¹. While many studies have analysed their effects separately, these events often do not occur in isolation⁴², and their collective effect, which can amplify impacts⁴³, has rarely been discussed. Recent studies show an increase in winter precipitation over the southeastern United States associated with El Niño and the NAO–⁴⁴, while the combination of El Niño and NAO+ leads to enhanced warming in the Eurasian steppe⁴⁵. While recent advances in seasonal climate prediction have resulted from accounting for interactions between ENSO and other climate modes⁴⁶, the combined effect of ENSO and NAO on coastal risk remains unexplored.

In this Article, we use observational and reanalysis datasets to evaluate how extreme CWL and associated potential flooding risks are modulated by different environmental conditions corresponding to different phases of ENSO, NAO and their co-occurrence. We subsequently assess aggregated risk to the population by accounting

for the severity, frequency and duration of these background climate conditions. Finally, we demonstrate that coastal risks are influenced by compounded effects of multiple seasonally modulated climate modes, notably ENSO and NAO. In addition, nonlinear interactions of the primary CWL hydrodynamic drivers—particularly waves and sea level–play a key role. As such, they contain intrinsic low-frequency memory and can be reliably predicted with long lead times by the extended recharge oscillator (XRO) model⁴⁶.

## Individual influence of ENSO and NAO on flooding risk

We assess how different phases of ENSO and NAO individually influence potential flooding risk along the world's coastlines. Following ref. 15, we define flooding risk as periods in hours per month when the monthly cumulated hourly CWL exceeds one-third of the maximum coastal elevation within the first kilometre inland (Extended Data Fig. 1; see Methods for coastal topography extraction). CWL represents the combined effect of sea level (including storm surge), tides and the parameterized wave run-up (Methods) over 1958–2023. This risk metric successfully reproduces major historical flood events (Extended Data Fig. 2) – including the 1964 Christmas flood on the US West Coast, the 1962 Ash Wednesday storm on the US East Coast, Cyclone Xynthia in Europe (2010) and the 2010 Alexandria flood in the Mediterranean—all of which caused fatalities, mass evacuations, infrastructure damage and multi-billion-euro losses⁴⁷,⁴⁸. Figure 1a–d presents the composite of flooding risk interannual anomalies for different phases of climate modes, defined as periods when the relevant index exceeds one standard deviation while other indices remain near neutral (Methods). EP El Niño events elevate flooding risk along the eastern Pacific coast, while reducing it in the western Pacific and Maritime Continent (see Supplementary Fig. 1 for a global perspective), highlighting the classic ENSO dipole pattern across the tropical Pacific (Fig. 1a). Along the US West Coast, EP El Niño events bring about 25 additional hours per month
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**Fig. 2 | Coastal risk matrix: severity versus frequency.** a–d, Composite of potential coastal flooding risk positive anomalies for different individual or co-occurring phases of climate modes, shown as a function of their respective return period averaged for the US West Coast (a), US East Coast (b), western Europe (c) and the Mediterranean (d). Insets rank the aggregated risk of each individual or co-occurring climate-mode phase (from highest to lowest), computed as the product of risk intensity (cumulative anomalies) with event frequency and duration (Methods). Shading from green to red represents risk levels calculated

as the product of potential flooding risk and frequency (as a percentage of the maximum across phases), from low (green) to very high (red). Bars along the y axis indicate the standard deviation of intensity across events for each climate-mode phase centred around the potential coastal flooding risk positive anomalies composite (sample size in number of climate events: 18 for C+, 6 for E+, 12 for C–, 13 for E–, 41 for NAO+, 27 for NAO–, 15 for C+/NAO+, 4 for C+/NAO–, 8 for E+/NAO+, 5 for E+/NAO–).

of potential flooding compared with climatology (Extended Data Fig. 3), representing a 35% chance that flooding risk exceeds the 95th percentile (Extended Data Fig. 4).

Conversely, La Niña conditions increase risk only in the western Pacific and Maritime Continent (Supplementary Fig. 2a,b), extending into the Indian Ocean for EP La Niña, and decrease risk almost everywhere else. This arises from the atmospheric response to the EP El Niño SST anomaly pattern (Fig. 1 top left), with increased SST anomalies in the eastern Pacific and weaker trade winds, providing a sea-level background state more conducive to extreme CWL in the eastern Pacific during El Niño and in the western Pacific during La Niña events. El Niño events are also characterized by an intensified Aleutian low, leading to enhanced west-northwest winds in the mid-latitudes, generating waves along the eastern Pacific coastlines and increasing wave run-up. A similar, although not as pronounced, picture is seen for CP El Niño (Fig. 1b).

The largest impacts of the NAO on extreme CWL and flooding risk occur in the tropical and North Atlantic regions with positive anomalies in northern Europe and Scandinavia during positive phases (Fig. 1c) and in the Mediterranean Sea and West Africa during negative phases (Fig. 1d), both associated with a 15–20% chance that flooding risk exceeds the 95th percentile (Extended Data Fig. 4). In particular, NAO– leads to a 27% increased risk compared with climatology (Extended Data Fig. 3) along the Mediterranean coast. This meridional shift reflects the NAO-driven displacement of the mid-latitude storm track and the associated changes in wave generation across the North Atlantic.

## Nonlinear amplification of flooding risk

We next assess the impact of compounding climate modes on flooding potential. Figure 1e–h shows composites of flooding risk anomalies

for different combinations of co-occurring ENSO and NAO phases. For example, Fig. 1e shows the anomalous risk when EP El Niño events coincide with NAO+ (that is, when both climate indices are greater than one standard deviation). The combination of either EP or CP El Niño with NAO+ (Fig. 1e,f) tends to exacerbate flooding risk in the North Atlantic, reaching 7% and 11% of the seasonal amplitude along western Europe (Extended Data Fig. 3), respectively. Interestingly, the co-occurrence of either type of El Niño with NAO+ results in an amplification exceeding the sum of their individual effects, highlighting nonlinear amplification. Extended Data Fig. 5a–d illustrates the compounding influence of different climate-mode phases and their significance relative to simple additive effects. The co-occurrence of CP (and EP to some extent) El Niño and NAO+ increases the risks along the US West Coast by 15% compared with the sum of their individual effects. Notably, co-occurrence of CP El Niño with a positive/negative NAO has opposite effects in the eastern Atlantic, enhancing flooding potential in northern Europe/southern Europe and the Mediterranean by 10%. Coastal risks along the US East Coast increase during both types of El Niño event by 20% compared with their sum, independent of NAO phase, further emphasizing a nonlinear amplification, significant at the 90% confidence level in the Euro–Atlantic region (Extended Data Fig. 5e–h). Supplementary Fig. 2 shows little change due to La Niña conditions in the Atlantic compared with just the prevailing NAO state.

## A coastal risk matrix: severity versus frequency

The co-occurrence of ENSO and NAO is associated with more severe flooding compared with the influence of either climate mode alone or their combined additive effects. While severity is important, risk also depends on how frequently extreme conditions occur. Managers often
<figure><img src="image_5.png" /><figcaption>**Fig. 3 | ENSO and NAO atmospheric teleconnections.** Composite of monthly averaged interannual eddy kinetic energy (EKE) anomalies of the 14-day high-pass filtered winds at the 200 hPa (shading) and 850 hPa (plain/dashed blue contours for positive/negative EKE every 2 m² s⁻²) pressure levels for different phases of the climate modes: **a**, **E+**, **b**, **C+**, **c**, **NAO+**, **d**, **NAO-**, **e**, **E+/NAO+**, **f**, **C+/NAO+**, **g**, **E+/NAO-**, **h**, **C+/NAO-**. Black dots indicate where the composite</figcaption></figure>

anomalies of EKE at either the 200 or 850 hPa pressure level are statistically significant at the 95% confidence interval using a two-sample Student's t-test. The thick magenta lines delineate the corresponding approximate position of the jet streams calculated as the position of maximum EKE anomalies at the 200 hPa level and smoothed using a 15°-window Savitzky-Golay filter.

represent this with a risk matrix, plotting frequency against intensity to classify threats. Figure 2 shows the assessment of risk severity versus frequency for different individual and co-occurring climate phases averaged in four key regions in the Northern Hemisphere, chosen for their high population density and economic influence (see boxes in Fig. 1e). To compute frequency, we classified each climate-mode phase into distinct events defined by consecutive months of occurrence, then estimated their frequency as the return period in years (Methods). The scatter plot shows composite positive flooding risk anomalies for each combination of climate event phases as a function of return period. Background shading from green to red indicates approximate risk level, expressed as a percentage of the maximum across phases. Overall, the different phases of each climate mode tend to be more frequent (346 months combined, representing 117 events) than their combination (84 months and 32 events) but are associated with limited intensity, except for relatively rare but strong EP El Niño events. The inset in the upper right corner of each panel illustrates aggregated risks associated with each combination of climate-mode phases, calculated as the product of their intensity, frequency and average duration (Supplementary Fig. 3). Globally, CP La Niña represents the highest risk due to its long duration, followed by NAO+ owing to its high frequency (Supplementary Fig. 4). The remaining individual modes and their combinations reach fairly similar risk levels, as compensation between frequency, intensity, duration and differing regions of impact smooths out differences in the global average. We therefore focus on specific regions to highlight emerging differences across the Northern Hemisphere. The combination of EP El Niño with NAO+ increases risk along the US West and East coasts (Fig. 2a,b), reaching or surpassing the levels of EP and CP El Niño alone, although via different mechanisms: EP Niño/NAO+ raises risk mainly through greater intensity, EP El

Niño through both high intensity and longer duration, and CP El Niño through higher frequency. Meanwhile, CP El Niño, when paired with NAO+, intensifies flood hazards in western Europe (Fig. 2c), while its pairing with NAO-shifts increased risk to the Mediterranean (Fig. 2d), with aggregated risk levels surpassing those of highly frequent NAO-conditions. Extended Data Fig. 6 shows the relative contributions of the different components of the CWL monthly mean and maximum averaged over the period when the coastal flooding risk anomalies are greater than one standard deviation (Methods). Overall, the largest episodes of severe risks are due to high tides (~70%) and waves (~30%), revealing another compounding effect when peak storm conditions coincide with high tides.

## Seasonal synchronization of ENSO-NAO teleconnections

Next we investigate how the NAO state can lead to enhanced ENSO teleconnections in the Atlantic. Figure 3 presents composites of monthly mean interannual eddy kinetic energy (EKE) anomalies derived from 14-day high-pass filtered winds at 200 hPa (shading) and 850 hPa (blue contours) for individual and co-occurring phases of the climate modes. This allows us to diagnose the corresponding jet-stream and storminess activity (Methods), respectively¹¹. The high-level atmospheric circulation associated with El Niño events (Fig. 3a,b) shows an intensified, southward-shifted jet stream in the Pacific, with EP events showing greater eastward extension over North America. Similarly, low-level atmospheric circulation associated with NAO conditions shows the dipole over the North Atlantic, with increased low pressure and storminess in high/mid-latitudes for its positive/negative phase (Fig. 3c,d). Indeed, the combination of El Niño events with NAO+ leads to an eastward extension of the jet streams into the Atlantic and European
<figure><img src="image_6.png" /><figcaption>**Fig. 4** | Coastal flood risk seasonal predictions from the XRO. **a**, Global forecast horizon of extreme CWL and associated coastal risk, defined as the maximum lead time at which the forecast skill (based on the ACC) remains above 0.5. **b,d,f,g**, Summarized predictive skills of the XRO model in different regions on the basis of the ACC (thick blue lines for averaged score over the entire period and dotted-dashed black lines for co-occurring (that is, compound) El Niño/NAO events) and the root mean square (RMS) error (thick orange line) metrics computed on</figcaption></figure>

the corresponding ensemble of out-of-sample forecasts (thin red lines) shown in **c,e,g,i**, which are initialized each month over the period 1993–2022 with actual observations (thick blue lines) and running for 7 months. **b–i**, Spatially cumulated (over all coastal points of the corresponding regions) risk over the US West Coast (**b,c**), the US East Coast (**d,e**), western Europe (**f,g**) and the Mediterranean (**h,i**). Thick dashed blue and orange lines on panels **b,d,f** and **h** show the ACC and RMS error, respectively, for the persistence forecasts.
continent, with both CP and EP types causing the jet stream to mean-
der and reach northern Europe (Fig. 3e,f). This generates strong wave
activity towards western Europe, increasing coastal risks. By contrast,
NAO- is associated with a straight jet stream extending east into South-
ern Europe and the Mediterranean Sea (for C+/NAO-), coinciding with
low-pressure anomalies and increased storminess, leading to higher
coastal risks in this region.

El Niño events tend to follow a similar pattern, develop-
ing during the boreal summer and peaking in winter⁴⁹⁻⁵¹. This
results in seasonal modulation of ENSO-driven coastal waves¹¹ and
impacts³⁷, exacerbated in winter when storm activity is strongest
(Extended Data Fig. 7a,c,d). By contrast, the NAO displays a second
peak in variance in summer, albeit weaker than its winter peak, high-
lighting a semi-annual variance distribution (Extended Data Fig. 7a,e).
This leads to a more predictable seasonal sequence of ENSO/NAO
teleconnections (Extended Data Fig. 7g–j). In particular, EP El Niño
events trigger a consistent NAO phase reversal, shifting from posi-
tive to negative throughout their cycle (Extended Data Fig. 7k–m and
Supplementary Figs. 5k–t and 6)⁵²⁻⁵⁷, highlighting a possible anticipa-
tion of co-occurring climate modes and compounding effects on the
storm tracks and extreme CWL.

Reliable predictions of coastal risks

The approach we use to define coastal risks—counting hourly CWL
events exceeding a topographic threshold within a month—captures
cumulative impacts reflecting the nonlinear nature of the climate–haz-
ard teleconnection (Methods). This highlights the nonlinear influence
of sea-level anomalies (SLA) and waves on flood potential, while tides
primarily modulate impacts. Extended Data Fig. 8 illustrates nonlinear
relationships between coastal hazard time series and CWL contribu-
tors. Nonlinearity arises from both the topographical threshold and
climate-mode interactions, particularly ENSO and NAO in the Northern
Hemisphere. We then use a modified XRO model⁴⁶ to assess coastal
risk predictability. The XRO is an ENSO conceptual model represent-
ing equatorial Pacific coupled dynamics; by incorporating multiple
climate-mode interactions, it improves the seasonal climate forecast
skill. In this study, we expand it to include the seasonal ENSO–NAO
interactions and flooding risk time series as state vectors (Methods).
Figure 4a shows the global forecast horizon, defined as the maximum
lead time with the anomaly correlation coefficient (ACC) > 0.5. Strong
seasonal synchronization of ENSO with other tropical basin climate
modes, such as the Atlantic Niño⁵⁸ and the Indian Ocean Dipole⁵⁹, allows
skilful forecasting at lead times over 6 months within the tropical band
and over 12 months in the Indo-Pacific. The lower panels summarize
XRO predictive skill with ACC and root mean square error metrics for
forecasts initialized monthly over 1993–2023. Skill is high along the
US West Coast, dominated by ENSO’s influence on the CWL (Fig. 4b,c).
NAO predictability alone is limited to 1–2 months due to chaotic atmos-
pheric variability, constraining North Atlantic forecasts. Co-occurrence
with strong ENSO extends predictability to nearly a year, particularly in
western Europe (back dashed line in Fig. 4f), valuable since ENSO–NAO
episodes often produce stronger impacts than NAO alone. Improved
Euro–Atlantic predictions at lead times up to 5 months (Fig. 4d–i) arise
from seasonal ENSO–NAO interactions, ENSO initial conditions and
the contribution of coastal risk state vectors, encapsulating nonlin-
ear large-scale climate and CWL interactions (Supplementary Figs. 7
and 8). Supplementary Figs. 9–11 assess contributions of CWL com-
ponents to predictability by fixing each at climatology. SLA, driven
by ENSO’s recharge–discharge cycle, dominates tropical CWL and
long-lead skill; fixing SLA reduces skill along the US West Coast but
increases it along the East Coast due to wave effects, while tides
remain critical at higher latitudes, with skill in western Europe drop-
ping when tides are fixed. These results highlight how climate-mode
interactions shape coastal drivers and risks, supporting reliable
seasonal forecasts.

This study presents a globally consistent coastal risk metric grounded in observational and reanalysis datasets spanning six decades. By incorporating all key components of total CWL, and integrating inland topography, we establish a robust measure of coastal flooding intensity and demonstrate its skill in reconstructing historical events, highlighting its value for risk management. This metric captures nonlinear, compounding effects of co-occurring climate modes—specifically ENSO and NAO phases—revealing amplified flood impacts in major population centres. Beyond capturing present-day hazards, the framework exhibits strong predictive skill. By coupling the XRO model with coastal risk time series, we demonstrate the ability to forecast coastal flood risks up to 12 months ahead in the Pacific and 5 months in the Euro–Atlantic. Skill arises because the metric integrates nonlinear impacts of CWL contributors, each nonlinearly modulated by large-scale climate forcing. Skill is particularly strong in tropical bands, where XRO-represented modes interact through Walker circulation alterations, but weakens at higher latitudes and in enclosed seas due to chaotic atmospheric variability and small-scale complexity. Extended lead times are valuable given the rarity but high impact of phase-aligned climate modes, whose seasonal synchronization enhances predictability beyond considering each mode alone (Fig. 4 and Supplementary Fig. 12). These results underscore the metric’s potential as a globally applicable tool for early-warning systems.

Future iterations could integrate river discharge and precipitation, key drivers of coastal inundation that compound CWL⁶⁰. Compound flooding arises when storm surges coincide with heavy rainfall; treating them independently may underestimate risk, requiring fully coupled modelling. Similarly, integrating dynamic coastal morphology and nearshore bathymetry, enabled by upcoming remote sensing missions and improved wave modelling⁶¹, will enhance understanding of wave-driven local hazards⁶².

While this study focused on the ENSO-NAO system in the Northern Hemisphere, future work should consider broader climate oscillations that may amplify or dampen coastal risks⁶³. Examining ENSO-Southern Annular Mode co-occurrence could reveal how high-latitude variability modulates Southern Hemisphere jet streams⁶⁴ and long-period swells affecting distant tropical coasts⁷. Including such variability in the XRO framework may improve representation of nonlinear tropical-extra-tropical interactions driving storms. As climate change alters the frequency, intensity and teleconnections of major climate modes, adaptive frameworks such as this will be essential to capture the evolving nature and predictability of compounding coastal risks.

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maries, source data, extended data, supplementary information,
acknowledgements, peer review information; details of author contri-
butions and competing interests; and statements of data and code avail-
ability are available at https://doi.org/10.1038/s41561-025-01903-0.

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# Methods

## Total CWL and its components

In this study, we express the CWL at the coast as such:

$$ \text{CWL} = \text{SLA} + \text{Waverunup} + \text{Tide}, \quad (1) $$

where SLA represents regional mean sea-level anomalies (m) and combines contributions from sterodynamic sea-level changes<sup>65</sup>, manometric sea-level changes (due to land ice mass loss and terrestrial water storage changes) as observed by satellite altimetry, and storm surges.

For the satellite altimetry era (1993–2023), we used the daily altimetry-based sea-level time-series anomalies (combining only sterodynamic and manometric sea-level changes with reference to the ellipsoid–WGS84/GRS80), extracted at the closest points to the coast from the gridded daily maps produced by the SSALTO/DUACS multi-mission<sup>66</sup> and distributed by the Copernicus Marine Environment Monitoring Service<sup>67</sup>. To account for storm surge effects that are not included in SSALTO/DUACS, the MOG2D-G barotropic model<sup>68</sup> forced by European Centre for Medium-Range Weather Forecasts Reanalysis v5 (ERA5) surface winds and atmospheric pressure<sup>69</sup> was run with 6-hourly outputs. MOG2D-G storm surge outputs are daily. More specifically, MOG2D-G is used to generate high-frequency sea-level corrections associated with pressure and wind forcing, providing a barotropic estimate of atmospheric surge that is routinely applied to all major satellite altimetry missions (for example, Jason, Sentinel-3 and SWOT). The model is forced at 6-hourly resolution on an -20 km global grid, which is the state-of-the-art configuration used operationally by CNES (Centre National d'Etudes Spatiales) and partner agencies (see https://www.aviso.altimetry.fr/en/data/products/auxiliary-products/dynamic-atmospheric-correction.html). Despite its moderate spatial resolution, MOG2D-G has been extensively validated and shown to perform well against tide-gauge and altimetric observations, capturing global-scale surge and high-frequency sea-level variability with skill comparable to or higher than more complex models<sup>66,68,70–80</sup>. For example, ref. 81 demonstrated that a higher-resolution (1/12°) baroclinic model forced at hourly intervals reproduced global storm surges with accuracy approaching—but generally lower than—that of the product derived from MOG2D-G, particularly for variability at periods shorter than 6 h, confirming that MOG2D-G remains a benchmark for global high-frequency atmospheric corrections and surge estimates.

Results from the recent period, presented in the Supplementary Information, show that coastal risks are dominated by wave run-up and tides, while regional SLA and storm surge largely act as a more slowly varying background for extreme CWL (Extended Data Fig. 6). This finding is consistent with a growing body of literature demonstrating that, at global scales, waves and tides generally outweigh atmospheric surge in controlling coastal water-level variability and flood occurrence. Waves—through set-up and run-up—are often the primary driver of inundation along the open-ocean coastlines that compose most of the global dataset<sup>8,82</sup>. Tidal levels and tidal residuals also account for a substantial fraction of observed historical flooding<sup>83,84</sup>. Although storm surge can be a dominant contributor locally, particularly during landfalling tropical cyclones or extra-tropical storms over wide continental shelves, multiple global assessments show that its contribution is generally subdominant compared with waves and tides, in both its mean effect and its long-term variance<sup>85–87</sup>. Together, these results support our interpretation that the dominant controls on global coastal risk reflect the combined nonlinear influence of wave run-up and tidal variability superimposed on low-frequency SLA and surge variations.

However, the 30-year altimetric record is too short for robust statistics and particularly for assessing out-of-sample predictive skill of the XRO, motivating the extension of the dataset back in time.

Before the altimetric period, no daily global reanalyses of SLA exist, and only a limited number of monthly products are available. We therefore used the monthly ORA-S5 ocean reanalysis (1958–2014)<sup>67,88</sup>,

which is forced by ERA5<sup>69</sup> and thus consistent with the MOG2D-G forcing and wave data (see below). Given that SLA contributes primarily as a background state rather than the dominant driver of extreme CWL, the use of monthly outputs does not compromise the analysis of coastal hazard extremes (Supplementary Figs. 13–16 compare results presented in this study over the entire period with the most recent altimetric period).

To build a continuous long-term dataset of SLA + surge over 1958–2023, we combined these products as follows: (1) 1958–1992: ORA-S5 monthly SLA (which includes regional sea-level anomalies and storm surges); (2) 1993–2014: blended product obtained by averaging monthly SLA from ORA-S5 and monthly SLA + surge from altimetry-based datasets to ensure continuity; (3) 2015–2023: monthly SLA + surge derived from the altimetry-based records. This approach provides a consistent and extended CWL dataset suitable for assessing long-term variability and predictability of coastal hazards.

Wave data (significant wave height $H_s$ and peak wave period $T_p$) were extracted from the ERA5 by the European Centre for Medium-Range Weather Forecasts model<sup>69</sup> at 0.25° × 0.25° and 6-hourly temporal resolution between 1958 and 2023.

Astronomical tidal elevations (Tide (m) in equation (1)) for the 1958–2023 period were obtained at the closest points to the coast from the global tide model FES at an hourly resolution<sup>78</sup>.

Wave run-up ($R$ (m)), the maximum vertical reach of wave uprush on the beach, was computed from the classic Stockdon parameterization<sup>89</sup>. Here the Stockdon parameterization was used in two forms, depending on the ratio between the coastal slope and incident waves as described by the Iribarren number $\xi$ (ref. 90):

at coasts with $\xi < 0.3$:

$$ R = 0.043 \sqrt{H_s \times L_o}, \quad (2) $$

at coasts with $\xi > 0.3$:

$$ R = 1.1 \left( 0.35\beta \sqrt{H_s L_o} + 0.5[H_s L_p (0.5625\beta^2 + 0.004)]^{1/2} \right) \quad (3) $$

$$ \text{With } L_p = \frac{g \times T_p^2}{2\pi} $$

where $R$ is a function of deep-water significant wave height $H_s$, wavelength ($L_o$), and sub-aerial coastal slope ($\beta$), and $T_p$ is the peak period. See ref. 15 for more details about this calculation. The automated computation procedures used in this study ensure that equation (2) is used on natural beaches with milder slopes, while equation (3) is used at steep profiles, such as, for example, when coastal defence structures are present. All the components feeding into equation (1) are ultimately interpolated to an hourly resolution.

All global-scale datasets used in this study—including wave reanalyses (for example, ERA5), tide models (for example, FES2014), surge model (MOG2D-G), mean sea-level reconstructions, hydrological input—inherit the resolution and forcing limitations typical of global reanalysis systems. Consequently, while suitable for representing large-scale variability, these models and products do not fully resolve the most intense and localized storm events associated (for example, landfalling tropical cyclones). These extreme events are known to be underestimated in global products due to the ~20 km grid spacing and forcing. Our resulting global CWL metric should therefore be interpreted as a conservative estimate for the most intense episodes.

## Method to compute coastal flooding risks

Using the datasets described above, the individual contributions to CWL were calculated on an hourly basis from 1958 to 2023. Coastal flooding
risks were identified when the hourly CWL exceeded one-third of the maximum coastal elevation within the first kilometre inland (compare explanatory schematic diagram in Extended Data Fig. 1 and next section; see also the Supplementary Information and Extended Data Fig. 2 for an assessment of the sensitivity to the choice of coastal elevation threshold). To summarize the event-level information over time, the number of hours with potential overtopping events was tallied at each calculation point for each month.

## Global Digital Surface Model and coastal topography extraction

We used the AW3D30 Global Digital Surface Model, a freely available dataset from the ALOS World 3D project that provides 30-m (1 arcsec) resolution derived from satellite data collected between 2006 and 2011<sup>15,91,92</sup>. It is based on optical stereo photogrammetry and uses the ITRF97 coordinate system with the EGM96 geoid model for elevation. The data are limited to latitudes between 60°N and 60°S and exclude high latitudes due to data quality issues. In this study, the AW3D30 dataset was used to extract maximum coastal elevations and slopes along the global coastline. For the analysis, coastal profiles were extracted at 0.05° intervals, with regional profiles constructed every -0.5° by averaging ten adjacent profiles. This method captured large-scale regional coastal features but excluded small islands and local variations. An automated detection process calculated coastal slopes and elevations by identifying the maximum elevation within 1 km landward of the shoreline. It was previously demonstrated that the AW3D30 dataset had the lowest error (-1.5-2.0 m) in estimating maximum coastal elevations<sup>15</sup>.

## Climate-mode indices

The EP and CP El Niño modes are two uncorrelated and independent ENSO indices, calculated as the first two rotated principal components of the empirical orthogonal function decomposition of SST interannual anomalies<sup>93</sup> and accounting for the variability of the two different types of ENSO, respectively, the extreme warm events in the eastern Pacific (EP El Niño) and moderate warm events in the central Pacific (CP El Niño). The monthly NAO index is measured as the difference in atmospheric pressure at the surface sea level between the subpolar low pressure in Iceland and the subtropical high pressure in the Azores and is extracted from the NOAA data portal<sup>94</sup>.

## Distinct and co-occurring phases of climate modes

We identify and process specific periods on the basis of threshold values of standardized indices for the EP El Niño mode, the CP El Niño mode and the NAO. The procedure involves filtering periods when these indices exceed or fall below a specified threshold, defined as $K \times \text{std}$ (index), where $K=1$ is a scaling factor, and std is the standard deviation of the index. The steps are as follows:

**Threshold filtering:** extract periods in which each index (EP El Niño mode, CP El Niño mode and NAO) is greater than $K \times \text{std}$ (positive climate-mode phase) or less than $-K \times \text{std}$ (negative phase).

**Intersecting conditions:** identify periods that simultaneously satisfy positive or negative thresholds across multiple indices. For example, E+/NAO+ represents periods when both EP El Niño mode and NAO indices are above the threshold. Similar intersections are computed for different combinations of EP El Niño mode, CP El Niño mode and NAO indices.

**Exclusive periods:** we identify exclusive periods for each index by removing overlaps with the intersections of other indices.

**Final outputs:** the entire process allows for the analysis of the distinct and overlapping influences of these climate modes, isolating periods of interaction or exclusivity to better understand their impact on climatic and environmental conditions.

## Frequency of climate-mode phases

To assess the frequency of climate-mode phases, we first identified distinct events by grouping consecutive months satisfying the preceding classification. Each uninterrupted sequence was counted as a single event. The length of each event was defined by the number of consecutive months above or below the threshold, and events separated by at least two neutral months were considered independent. The frequency of occurrence was then quantified as the return period (in years), computed as the total number of years in the record divided by the total number of detected events. This event-based classification was subsequently used to compare the severity of coastal flooding risk anomalies across individual and co-occurring phases of ENSO and NAO (Fig. 2).

## Other climate data

Oceanic (SST) and atmospheric (surface winds, sea-level pressure) variables all come from monthly ERA5 outputs<sup>69</sup> over the period 1958-2023.

## Component contributions to extreme CWLs

To quantify the relative contributions of tides, waves and SLA to flooding risk induced by extreme CWLs, we first identify months when flooding risk exceeds one standard deviation. For each region and climate phase, we compute the mean and maximum CWL over these months. The contribution of each component to either the monthly mean or the monthly maximum of CWL is then expressed as a percentage of the total CWL:

$$ \% \text{Component} = \frac{\text{Component (Tide, SLA, or Wave)}}{\text{Total CWL}} \times 100 \quad (4) $$

The resulting percentages allow a clear assessment of the relative influence of each CWL driver during periods of elevated coastal risk.

## Characterization of extra-tropical storminess and jet-stream activity

Winter storms are driven primarily by mid-latitude jet streams, which are narrow, zonally variable flows of strong winds in the mid-troposphere between 850 and 200 hPa. These jet streams are influenced by atmospheric Rossby waves on timescales of 1-2 weeks<sup>95</sup>. To analyse near-surface storminess and jet-stream activity affecting oceanic surface waves, we use EKE derived from 14-day high-pass filtered winds at 850 and 200 hPa pressure levels respectively:

$$ \text{EKE} = \frac{1}{2} [U_*^2 + V_*^2] \quad (5) $$

with $U_*$ and $V_*$ being, respectively, the 14-day high-pass filtered daily zonal and meridional components of the winds at the 850 and 200 hPa levels.

## Anomaly calculation

All variables were linearly detrended, and their monthly climatology was removed to isolate interannual variability. The resulting anomalous extreme CWL time series were then spatially smoothed with a 200-km Gaussian filter to reduce small-scale influences, such as localized embayments.

## XRO model for coastal risk prediction

To explore the predictability of coastal risk, we use a modified version of a recently developed XRO<sup>46</sup>, which consists of a recharge oscillator (RO) model for ENSO<sup>96,97</sup> coupled to seasonally modulated stochastic-deterministic models for other climate modes<sup>98-100</sup>. In our modified XRO formulation, we explicitly introduce the NAO mode and coastal risk as additional state vectors, thereby enabling two-way interactions between ENSO, NAO and coastal risks:
$$ \frac{d}{dt} \begin{pmatrix} \mathbf{X}_{\text{ENSO}} \\ \mathbf{X}_{\text{M}} \end{pmatrix} = \mathbf{L} \begin{pmatrix} \mathbf{X}_{\text{ENSO}} \\ \mathbf{X}_{\text{M}} \end{pmatrix} + \begin{pmatrix} \mathbf{N}_{\text{ENSO}} \\ \mathbf{N}_{\text{M}} \end{pmatrix} + \boldsymbol{\xi}, \quad (6) $$

where $\mathbf{X}_{\text{ENSO}} = [T_{\text{ENSO}}, h]$ is state vector of ENSO, $T_{\text{ENSO}}$ and $h$ represent SST anomalies averaged over the Niño3.4 region (170° W–120° W; 5° S–5° N) and thermocline depth anomalies averaged over the equatorial Pacific [120° E–80° W; 5° S–5° N] respectively; $\mathbf{X}_{\text{M}} = [T_{\text{NPMM}}, T_{\text{SPMM}}, T_{\text{IOB}}, T_{\text{IOD}}, T_{\text{SIOD}}, T_{\text{TNA}}, T_{\text{ATL3}}, T_{\text{SASD}}, I_{\text{NAO}}, I_{\text{R}}]$ are state vectors of the other climate modes and coastal risk, representing SST indices of the other climate modes, namely, the North Pacific Meridional Mode (NPMM¹⁰¹), South Pacific Meridional Mode (SPMM¹⁰²), Indian Ocean Basin (IOB¹⁰³) mode, Indian Ocean Dipole (IOD¹⁰⁴), Southern Indian Ocean Dipole (SIOD¹⁰⁵), Tropical Northern Atlantic (TNA¹⁰⁶), Atlantic Niño¹⁰⁷ and South Atlantic Subtropical Dipole¹⁰⁸, the monthly mean NAO index ($I_{\text{NAO}}$), and the monthly extreme CWL index ($I_{\text{R}}$) either at each along-shore location or averaged in the region of interest. The governing dynamics contain linear (L) and nonlinear (N) operator terms:

$$ \mathbf{L} = \begin{pmatrix} \mathbf{L}_{\text{ENSO}} & \mathbf{C}_1 \\ \mathbf{C}_2 & \mathbf{L}_{\text{M}} \end{pmatrix}, \quad (7) $$

$$ \mathbf{N}_{\text{ENSO}} = [b_1 T_{\text{ENSO}}^2 + b_2 T_{\text{ENSO}} h, 0], \quad (8) $$

$$ \mathbf{N}_{\text{M}} = [0, 0, 0, b_3 T_{\text{IOD}}^2, 0, 0, 0, 0, 0], \quad (9) $$

where $\mathbf{L}_{\text{ENSO}}$ represents the ENSO recharge-discharge dynamics, $\mathbf{L}_{\text{M}}$ are the stochastic-deterministic (Hasselmann-type) dynamics of the other climate modes, $\mathbf{C}_1$ represents the effect of ENSO on the climate modes and $\mathbf{C}_2$ their feedback on ENSO. To implement nonlinear dynamics associated with ENSO asymmetry, quadratic nonlinearities are incorporated into the SSTA equation of ENSO. A local quadratic nonlinearity is also incorporated in the SSTA equation for the IOD following the recent insights that IOD asymmetry is dominated by local nonlinear processes. Nonlinear operators are only for ENSO and IOD, following ref. 46, while those for the other modes are set to zero because of their weak asymmetry and skewness.

Last, $\boldsymbol{\xi}$ represents stochastic forcing due to weather and other high-frequency noise such as the Madden-Julian Oscillation and westerly wind bursts. Since we employ a deterministic forecast in this study, the noise term is omitted.

We explicitly incorporate seasonality into linear and nonlinear operators following ref. 46 by estimating parameters as follows:

$$ \mathbf{L} = \mathbf{L}_0 + \sum_{j=1}^{2} (\mathbf{L}_j^c \cos j\omega t + \mathbf{L}_j^s \sin j\omega t), \quad (10) $$

$$ \text{and } \mathbf{N} = \mathbf{N}_0 + \sum_{j=1}^{2} (\mathbf{N}_j^c \cos j\omega t + \mathbf{N}_j^s \sin j\omega t), $$

where $\omega = 2\pi/(12 \text{ months})$. The subscripts 0, 1 and 2 denote the mean, annual cycle and semi-annual cycle components, respectively. Operator parameters are estimated by multivariate linear regression using the XRO.fit_matrix procedure in the XRO model code¹⁰⁹.

To generate out-of-sample forecasts of coastal risk, we trained the model (equation (6)) on the 1958–1992 period to obtain a robust XRO parameter fit for each along-shore location or region average. With the fitted XRO parameters, we then conducted deterministic retrospective 21-month forecasts for the 1993–2023 period by integrating equation (6) forwards from the observed initial state values, with the noise term omitted. These forecasts are generated following the XRO. reforecast procedure of the XRO model code¹⁰⁹. We verified that the coupling of the original XRO and risk time series did not affect the ENSO predictive skill, suggesting that the feedback of risk to ENSO is minimal.

## Nonlinear climate influence on coastal risks

The coastal risk metric described above is an hourly exceedance indicator $e$ that can be mathematically described using the Heaviside step function $H(\cdot)$

$$ e(t) = H(\text{CWL}(t) - h_c) \text{ with } H(x) = \begin{cases} 1 & x > 0 \\ 0 & x \le 0 \end{cases}, \quad (11) $$

where the threshold $h_c$ is set as a fraction of the local maximum coastal elevation within the first 1 km. The monthly risk metric (hours per month potentially flooded) that we include in the XRO model (see above) $I_R$ is obtained by summing hourly exceedances over each month $m$:

$$ I_R(m) = \sum_{t \in m} e(t) = \sum_{t \in m} H(\text{CWL}(t) - h_c) \quad (12) $$

Because $H(\cdot)$ is a discontinuous (threshold) operator, the mapping CWL($t$) $\mapsto I_R(m)$ ($m$) is inherently nonlinear: small changes in CWL($t$) near $h_c$ can produce discrete jumps in $I_R$, while changes far from $h_c$ have negligible effect. This nonlinearity amplifies the imprint of strong compound forcing (for example, combinations of SLA, waves, tides) and climate variability and filters weak perturbations.

Because $I_R$ is a nonlinear transform of the CWL components, coupling it to the XRO allows the model operators L and N to capture interactions across climate-mode timescales that are translated into discrete hazard events, thereby improving forecast skill relative to models that treat only CWL components.

## Persistence analysis

To quantify the persistence of coastal hazard risks, we compute the lagged autocorrelation of the observed risk time series. Specifically, for each region, we compute the Pearson correlation coefficient between the time series and its lagged counterpart for lags ranging from 1 to 13 time steps.

## Data availability

The SSALTO/DUACS altimeter products were produced and distributed by the Copernicus Marine Environment Monitoring Service (http://marine.copernicus.eu/). Dynamical atmospheric corrections were produced by the Collecte Localisation Satellites Space Oceanography Division using the MOG2D model from Laboratoire d'Etudes en Géophysique et Océanographie Spatiales (LEGOS) and distributed by AVISO (Archiving, Validation and Interpretation of Satellite Oceano-graphic data), with support from Centre National d'Etudes Spatiales (CNES) (http://www.aviso.altimetry.fr/). FES2016 tidal data are produced by LEGOS. ERA5 data were produced by the European Centre for Medium-Range Weather Forecasts and are available through Copernicus data centre (https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-pressure-levels?tab=overview). Coastal topographical product AW3D30 is also freely available. Coastal DEM is distributed by Climate Central under a non-commercial license. Relevant data are available on request from the authors. The coastal risk dataset¹¹⁰ that supports the findings of this study is openly available in DataSuds repository (IRD, France) at https://dataverse.ird.fr/dataset.xhtml?persistentId=doi:10.23708/OUZPH4. Data reuse is granted under CC-BY license.

## Code availability

The XRO model code is publicly available at https://github.com/senclimate/XRO.

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## Acknowledgements

F.-F.J., S.Z., M.F.S. and J.B. were supported by the NOAA Climate Program Office's Modeling, Analysis, Predictions, and Projections (MAPP) Program Grant (NA23OAR4310602). R.A. is supported by the French ANR through the project GLOBCOASTS (ANR-22-ASTR-0013 GLOBCOASTS). B.D. acknowledges support from ANID (Concurso de Fortalecimiento al Desarrollo Científico de Centros Regionales 2020-R20F0008-CEAZA, Fondecyt Regular N°1231174). This is IPRC publication 1820 and SOEST contribution 12054.

## Author contributions

J.B. and R.A. designed and conceptualized the study. J.B. conducted the analysis and wrote the initial version of the manuscript. S.Z. conducted the XRO coastal risk forecasts. J.B., R.A., F.-F.J., S.Z., M.F.S. and B.D. discussed the results and contributed to writing the manuscript.

## Competing interests

The authors declare no competing interests.

## Additional information

**Extended data** is available for this paper at
https://doi.org/10.1038/s41561-025-01903-0.

**Supplementary information** The online version contains supplementary material available at https://doi.org/10.1038/s41561-025-01903-0.

**Correspondence and requests for materials** should be addressed to Julien Boucharel, Rafael Almar or Fei-Fei Jin.

**Peer review information** *Nature Geoscience* thanks Ioana Colfescu and Thomas Rackow and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Aliénor Lavergne and James Super, in collaboration with the *Nature Geoscience* team.

**Reprints and permissions information** is available at
www.nature.com/reprints.
<figure><img src="image_7.png" /><figcaption>**Extended Data Fig. 1** | **Methodology of extraction of coastal flood risk time series.** (a) Schematic of the methodology used to identify coastal flooding risks explained in (b): when the anomalous extreme CWL, calculated as when the monthly aggregated interannual anomalies of the hourly total coastal water level</figcaption></figure>

(the sum of SLA composed of the dynamic, steric and surge components, tide and wave-induced water level (Runup)) reach one-third (33%) of the maximum coastal elevation within the first kilometer shown in (c). Panels adapted with permission from: a, ref. 111, HAL; c, ref. 15, Springer Nature Limited.
**Extended Data Fig. 2** | Coastal flood risk time series with different coastal elevation thresholds. Observed interannual anomalies (in blue and above one standard deviation in black) of extreme coastal water levels reaching different maximum elevation thresholds: (a) 33%, (b) 50%, (c) 66%, and (d) 75%, averaged along the U.S. West Coast. (e), (f), (g), and (h) show the same for the U.S. East

Coast. (i), (j), (k), and (l) show the same for Western Europe. (m), (n), (o), and (p) show the same for the Mediterranean Sea. Notable extreme events, as reported in the press or scientific literature, are highlighted and described to the right of the panels for each region.

<figure><img src="image_8.png" /></figure>

**Christmas Flood of 1964:** This catastrophic event affected Northern California, Oregon, and Washington between December 18, 1964, and January 7, 1965. It was considered a 100-year flood, causing extensive damage and loss of life. Source Wikipedia

**El Niño Winter of 2015–2016:** One of the strongest El Niño events in the past 145 years led to extreme oceanographic conditions, resulting in significant coastal flooding and erosion along the U.S. West Coast. Source Bamard et al 2017

**Ash Wednesday Storm of 1962:** This devastating no'easter struck in March 1962, causing extensive coastal flooding from North Carolina to New York. In Norfolk, Virginia, tides reached 8.2 feet, flooding thousands of cars and damaging numerous homes. The storm also led to significant beach erosion and property damage along the New Jersey shoreline. Source Wikipedia

**October 1991,** the U.S. East Coast experienced a significant meteorological event known as the "Perfect Storm" or the "Halloween No'easter." This powerful storm resulted from the rare convergence of a no'easter and the remnants of Hurricane Grace, leading to devastating impacts along the coast. Source nps.gov

**Winter Storms of 2013–2014:** A series of severe Atlantic storms during the winter of 2013–2014 led to significant coastal flooding across parts of England and Wales
Source Sibley et al 2015

In 2010, the Mediterranean region experienced several significant coastal flooding events, primarily due to intense storms and heavy rainfall. Notable incidents include:
**Cyclone Xynthia (February 2010):** This powerful windstorm affected Mediterranean coastal areas.

Source: en.wikipedia.org

**Liguria Flash Flood (October 2010):** On October 4, 2010, a severe storm struck Italy's Ligурian coast, exacerbated by the Alpine-Apennine mountain range and unusually high sea temperatures. The event led to significant flash flooding, causing property damage and disrupting local communities. Source Faccini et al 2021

**Nile Delta Storm Surge (December 2010):** In December 2010, a powerful storm impacted Egypt's Nile Delta, generating surges up to 1.0 meter and wave heights reaching 7.5 meters offshore Alexandria. The event posed significant risks to coastal zones. Source Ismail et al 2012
<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /><figcaption>**Extended Data Fig. 3** | Coastal flood risks climatology. (a) Annual mean and (b) seasonal amplitude (maximum minus minimum of the monthly mean climatology) in (hours/month) of coastal risks calculated as when the monthly aggregated interannual anomalies of the hourly total coastal water level reach a third of the maximum coastal elevation.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Extended Data Fig. 4** | Coastal flood risks exceedance probability. Probability (in %) of the coastal risk (Extreme CWL (ECWL) exceeding the 33% threshold of maximum coastal elevation) anomalies exceeding the 95th percentile during (a),</figcaption></figure>

(b) positive phases of the EP (E+) and CP (C+) ENSO modes respectively; (c), (d) positive and negative phases of the NAO and for different combination of climate mode phases: (e) E + /NAO +, (f) C + /NAO +, (g) E + /NAO-, (h) C + /NAO-.
a. C+/NAO+ increased
compared to (C+) + (NAO+)

<figure><img src="image_12.png" /></figure>

c. E+/NAO+ increased
compared to (E+) + (NAO+)

<figure><img src="image_13.png" /></figure>

e. Significant Multiplicative
effects of C+/NAO+

<figure><img src="image_14.png" /></figure>

g. Significant Multiplicative
effects of E+/NAO+

<figure><img src="image_15.png" /></figure>

Extended Data Fig. 5 | Additive versus multiplicative effects of climate modes phases on coastal flood risks. Compounding influence of the different phases of ENSO and NAO: Percentage of changes in anomalous extreme CWL conditions during co-occurring phases of climate modes relative to the sum of anomalous extreme CWL conditions during the corresponding individual climate phases (C+ and NAO+ (**a**), C+ and NAO- (**b**), E+ and NAO+ (**c**) and E+ and NAO- (**d**)). Green,

b. C+/NAO- increased
compared to (C+) + (NAO-)

<figure><img src="image_16.png" /></figure>

d. E+/NAO- increased
compared to (E+) + (NAO-)

<figure><img src="image_17.png" /></figure>

f. Significant Multiplicative
effects of C+/NAO-

<figure><img src="image_18.png" /></figure>

h. Significant Multiplicative
effects of E+/NAO-

<figure><img src="image_19.png" /></figure>

blue, yellow and red dots show the location where the compounded (that is, multiplicative) effects of climate modes (C+ and NAO+ (**e**), C+ and NAO- (**f**), E+ and NAO+ (**g**) and E+ and NAO- (**h**) are significant compared to their additive effects at the 50%, 70%, 90% and 95% confidence level respectively based on a Student's t-test.
<figure><img src="image_20.png" /></figure>
<figure><img src="image_21.png" /></figure>

**Extended Data Fig. 7** | Annual Variability of climate mode phases and coastal flood risks. (a) Monthly standardized variance of climate modes indices (the blue left y-axis corresponds to the EP and CP ENSO modes variance and the orange right y-axis corresponds to the NAO variance). (b) Monthly variance of extreme CWL calculated as when the monthly aggregated interannual anomalies of the hourly total coastal water level reach 33% of the maximum coastal elevation accumulated over different regions (US west coast in blue, US east coast in orange, western Europe in green and the Mediterranean Sea in purple). Monthly occurrence of different co-occurring phases of climate modes

(c) E+, (d) C+, (e) NAO+, (f) NAO-, (g) E+/NAO+, (h) C+/NAO+, (i) E-/NAO-, (j) C+/NAO-. (k.) Scatter plots of the EP ENSO index versus the NAO index. The month of occurrence is shown in color when both the EP ENSO and NAO indices are simultaneously greater than one standard deviation, and when the EP ENSO index (E index) is greater while the NAO index is less than one standard deviation. (l.) Same as (k.) but for the CP ENSO (C) and NAO indices. (m.) Time evolution of the E and NAO indices during different EP El Niño events (thin blue and orange lines respectively) and during the composite of these events (thick lines). (n.) Same as (m.) but during CP El Niño events.
<figure><img src="image_22.png" /></figure>

**Extended Data Fig. 8** | Nonlinear relationships between coastal flood risks and coastal water level contributors. Nonlinear relationships between the extreme coastal water level interannual anomalies (reaching at least one-third of the maximum coastal elevation) and its contributor's interannual anomalies along the US west coast: wave (a) and SLA (b) monthly mean and tide monthly

maximum (c), (d), (e) and (f) are the same as (a), (b) and (c) but along the western European coasts. (g), (h) and (i) are the same as (a), (b) and (c) but along the US east coast. (j), (k) and (l) are the same as (a), (b) and (c) but along the Mediterranean coast. The red lines show the best-fit third-order nonlinear curve.