Global coastal wave storminess

Coastal wave storms pose a massive threat to over 10% of the world’s population now inhabiting the low elevation coastal zone and to the trillions of $ worth of coastal zone infrastructure and developments therein. Using a ~ 40-year wave hindcast, we here present a world-first assessment of wind-wave storminess along the global coastline. Coastal regions are ranked in terms of the main storm characteristics, showing Northwestern Europe and Southwestern South America to suffer, on average, the most intense storms and the Yellow Sea coast and the South-African and Namibian coasts to be impacted by the most frequent storms. These characteristics are then combined to derive a holistic classification of the global coastlines in terms of their wave environment, showing, for example, that the open coasts of northwestern Europe are impacted by more than 10 storms per year with mean significant wave heights over 6 m. Finally, a novel metric to classify the degree of coastal wave storminess is presented, showing a general latitudinal storminess gradient. Iceland, Ireland, Scotland, Chile and Australia show the highest degree of storminess, whereas Indonesia, Papua-New Guinea, Malaysia, Cambodia and Myanmar show the lowest.


Hindcast validation
The validation focuses on the coastal wave climate.Accordingly, it has been carried out using coastal in-situ observations (from buoys and platforms) as reference.A pseudo-global in-situ dataset consisting of 281 locations was used for validation and performance evaluation, following a selection process (Figure SM1 -SM3).In-situ data was collected and provided by the Copernicus Environment Monitoring Service (CMEMS; Reference: INSITU_NWS_NRT_OBSERVATIONS_013_036), incorporating measurements from recording instruments managed by various institutions.After removing outliers and excluding buoys with anomalous values, two primary criteria were applied in the selection of the buoys for validation: - The buoy must be located at least 5 km from the coast.

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The buoy must have at least 3 years of recorded data.
Only exceptions are the buoys located in the west coast of India and the coast of Brazil, for which the record length criterion has been relaxed to provide a better coverage of the global coastlines.
Results (panel a of Figure SM1 -SM3) show correlations above 0.9 in around 90% of the in-situ locations analyzed.This indicates a very good agreement between both datasets and highlights the capability of the hindcast to reproduce the wave climate variability at global scale.
Panel b of Figure SM1 -SM3 shows the normalized Hs bias relative to in-situ data.Results show absolute biases lower than 10% at round 80% of the locations.In addition, at around 70% of in-situ locations show the hindcast product shows underestimations.Main exceptions are found in the Gulf of Mexico and Caribbean Sea, and in the southwestern coast of Australia, where a significant proportion of the locations show a positive bias (i.e., overestimation).
Panel c of Figure SM1 -SM3 shows the normalized root-mean square error in the Hs parameter between model and in-situ data.Most locations (~75%) exhibit errors below 20%.The largest errors can be found in the Mediterranean Sea and the northeastern coast of North America, where values typically range between 20% and 30%.
Since the storm definition criterion (see Methods in the main manuscript) is based on the exceedances over the 95 th percentile of Hs, a specific validation for this metric, calculated over the available buoy data period, has been conducted (Figure SM4-SM6).Results show a good agreement between the model and the buoy data for Hs95.Most locations (83%) show an underestimation of model data.This underestimation is lower than 10% of the reference value in more than 70% of the analyzed locations.Main exceptions (i.e., overestimations) are found along the western coast of the British Islands and the North Sea, with the latter showing values up to 20%.
In general, results show a good performance of the hindcast product across the world's coastlines, in comparison with observations, providing the necessary confidence to the subsequent storm analysis conducted.

Figure SM4: Validation of hindcast Hs95 against buoy data along the coasts of America. (a) Hs95 from buoy data (in m). (b) Hs95 from hindcast data (in m). (c) Relative difference (in %) in Hs95 between buoy and hindcast data relative to buoy
measurements.The plots were generated using MATLAB R2023b (https://matlab.mathworks.com).

Figure SM5: Validation of hindcast Hs95 against buoy data along the coasts of Europe. (a) Hs95 from buoy data (in m). (b) Hs95 from hindcast data (in m). (c) Relative difference (in %) in Hs95 between buoy and hindcast data relative to buoy
measurements.The plots were generated using MATLAB R2023b (https://matlab.mathworks.com).Additionally, a specific validation of the representation of tropical cyclones has been conducted.To that end, four buoys have been selected, two in the Gulf of Mexico and two in the south of Japan.We have validated the Hs provided by the wave model at the node closest to the position of these buoys, and qualitatively evaluated the representation of Hs peaks associated with tropical cyclones in the time series (Figure SM7).
The scatter plots show good agreement across the four buoy locations.The two buoys located in the Gulf of Mexico (upper two rows) indicate a slight underestimation of the most extreme values.It is however clear that storm events associated with tropical cyclones are present in the model.The study of the time series leads to the same conclusions.It is possible to observe how, except for a few exceptions, the most intense events, associated with tropical cyclones, show higher Hs values than the buoy records.
The buoys situated in the western Pacific and affected by swells generated by typhoons also show good agreement between both sources of information.Regarding the most extreme events, discrepancies exist between the two buoys.While one of them shows an underestimation, the other shows an overestimation.Nevertheless, the main conclusion to be drawn is, again, that the storm events generated by tropical cyclones are indeed represented in the hindcast with significant accuracy.

Figure SM8: Coastal bathymetry at the location of the coastal target points
The percentage of points in which annual maximum Hs would experience depth-induced breaking has been computed.To that end, the following wave breaking criterion has been used: where Hs,b is the breaking wave height and hb is the breaking depth.
As a result, less than 0.1% of the coastal points meet this relationship.

Coastal mean wave climate
A brief description of the annual mean   wave climate (1979 to 2020) along the global coastlines is presented in Figure SM9.This will be used as a basis for further analyses and classification of the coastal wave storminess.The annual mean   along the global coastlines shows an overall meridional gradient (Figure SM9a).The highest values of annual mean   are mostly observed in extratropical latitudes in both hemispheres.Relevant differences between eastern and western coastlines of the continents can also be seen, the latter displaying higher annual mean   due to the prevailing westerly winds at these latitudes and, hence, the mean eastward wave propagation 2,3 .The lowest values of annual mean   are found along the equatorial coastlines and in semi-enclosed basins, such as the Mediterranean and Red Seas, and in marginal seas, such as the Yellow Sea and South China Sea Figure SM9b shows the annual mean swell and wind sea predominance along the global coastlines.
Around half of the global coastline shows a swell dominance with a swell to wind sea ratio exceeding 0.7, estimated as the mean proportion between  0  and  0 during the whole analyzed period, which is consistent with previous studies undertaken for the deep ocean 3,4 .

Rank
Coastal

Storm independency
Figure SM24 Independence analysis between consecutive storm peaks using the Kendall's Tau correlation metric.Blue indicates that the hypothesis of events being independent cannot be rejected at 5% significance level.Yellow indicates that the hypothesis of events being independent can be rejected at 5% significance level.The plots were generated using MATLAB R2023b (https://matlab.mathworks.com).

Figure SM1
Figure SM1 Validation of hindcast Hs against buoy data along the coasts of America.(a) Correlation values.(b) Normalized bias (in %) of the Hs parameter from the hindcast product relative to buoy measurements.(c) Normalized root-mean square error (in %)of the Hs parameter from the hindcast product relative to buoy measurements.The plots were generated using MATLAB R2023b (https://matlab.mathworks.com).

Figure SM2 :
Figure SM2: Validation of hindcast Hs against buoy data along the coasts of Europe.(a) Correlation values.(b) Normalized bias (in %) of the Hs parameter from the hindcast product relative to buoy measurements.(c) Normalized root-mean square error (in %) of the Hs parameter from the hindcast product relative to buoy measurements.The plots were generated using MATLAB R2023b (https://matlab.mathworks.com).

Figure SM3 :
Figure SM3: Validation of hindcast Hs against buoy data along the coasts of Asia and Australia.(a) Correlation values.(b) Normalized bias (in %) of the Hs parameter from the hindcast product relative to buoy measurements.(c) Normalized rootmean square error (in %) of the Hs parameter from the hindcast product relative to buoy measurements.The plots were generated using MATLAB R2023b (https://matlab.mathworks.com).

Figure SM6 :
Figure SM6: Validation of hindcast Hs95 against buoy data along the coasts of Asia and Australia.(a) Hs95 from buoy data (in m).(b) Hs95 from hindcast data (in m).(c) Relative difference (in %) in Hs95 between buoy and hindcast data relative to buoymeasurements.The plots were generated using MATLAB R2023b (https://matlab.mathworks.com).

Figure SM7 :
Figure SM7: Validation of Hs against buoy data within coastal regions affected by tropical cyclones.Scatter plots show the Hs recorded by buoys versus the Hs produced by the numerical model.Black squares show theHs quantiles from 0.1 to 0.9, 0.95, 0.99, 0.999 and 0.9999, calculated over the available buoy data period.The plots were generated using MATLAB R2023b (https://matlab.mathworks.com).
. The highest values of annual mean   are found in extratropical coastlines of the SH, a consequence of the extended fetch and the sustained generation of waves caused by the intense prevailing westerly winds 2 .In particular, the southernmost part of the Chilean coast and the east coast of Tasmania show the highest annual mean   values within southern extratropical coastlines, almost reaching 4 m.The coastal annual mean   in the extratropical latitudes of the NH show the highest values (around 3 m) in the west coasts of Ireland and Scotland.The lowest values of annual mean   along the global coastlines are found in the Java and Banda Seas in Indonesia, with values between 1 and 2 m, as they are sheltered from the open Indian Ocean swell waves.

Figure SM11
Figure SM11 Seasonal global coastal annual mean number (in events/year -ev/yr) of (a) DJF wave storms, (b) JJA wave storms, (c) DJF severe wave storms, and (d) JJA severe wave storms.The color scales vary between the panels.The plots were generated using MATLAB R2023b (https://matlab.mathworks.com).

Figure SM12
Figure SM12 Seasonal global coastal annual mean number (events/year -ev/yr) of (a) SON wave storms, (b) MAM wave storms, (c) SON severe wave storms, and (d) MAM severe wave storms.The color scales vary between the panels.The plots were generated using MATLAB R2023b (https://matlab.mathworks.com).

Figure SM15
Figure SM15 Monthly percent frequency of occurrence of wave storm durations at twenty-four key locations (P1 to P24: see map).Green bars represent wave storms and purple bars represent severe wave storms.The plots were generated using MATLAB R2023b (https://matlab.mathworks.com).

Figure SM17
Figure SM17Global coastal mean annual maxima   (in m) registered in a wave storm.The plots were generated using MATLAB R2023b (https://matlab.mathworks.com).

Figure SM18
Figure SM18Global coastal mean storm-peak   (in m) for (a) wave storms and (b) severe wave storms.The plots were generated using MATLAB R2023b (https://matlab.mathworks.com).

Figure SM19
Figure SM19Global coastal mean   (in s) of (a) wave storms and (b) severe wave storms.The plots were generated using MATLAB R2023b (https://matlab.mathworks.com).

Figure SM25
Figure SM25Comparison between the storm characteristics from ERA5 and GOW2 hindcasts at the 24 key points: frequency of occurrence (upper left), mean duration (upper right), mean Hs (left bottom) and energy content (right bottom).The plots were generated using MATLAB R2023b (https://matlab.mathworks.com).