Addressing global challenges such as coastal hazards and climate change requires innovative tools capable of analyzing complex environmental drivers, including waves, storm surges, and cyclones, across varying scales. These tools are vital for predicting floods, assessing risks, and planning adaptive responses. BlueMath-Hub has been developed as a global collaborative initiative to provide accessible, customizable solutions for both researchers and practitioners. It aims to simplify the use of advanced statistical and numerical models, fostering creative and scalable approaches in coastal science and engineering. BlueMath, the core of this platform, is an open-source repository of Python tools accessible via a cloud-based Jupyter Hub environment. It integrates statistical methods and numerical model wrappers within a modular framework. The system includes: (a) BlueMath-Toolkit, providing tools for data mining, interpolation, and model integration; (b) BlueMath-Statistical Downscaling, focusing on extreme events and generalized models; (c) BlueMath-Hybrid Downscaling, combining statistical and numerical approaches for optimized solutions; and (d) BlueMath-Climate Services, supporting integrated applications such as compound flooding assessments. BlueMath is continuously evolving, with its tools already applied in research, publications, and training. By lowering barriers to entry and enabling collaborative workflows, BlueMath-Hub supports the development of innovative solutions to mitigate the impacts of a changing climate.

Sea turtles are key species in many coastal ecosystems worldwide, particularly coral reef and seagrass habitats. Yet, six of seven species are endangered. Their nests, which incubate in beach sand and rely on specific climatic conditions for egg viability, face significant threats from inundation, for example through wave runup. This paper examines a method to rapidly predict wave runup in low-data coral reef environments, and the implications thereof on the inundation of sea turtle nests. The study uses two metamodels, BEWARE-2 and HyCReWW, to predict wave runup at Ras Baridi, Saudi Arabia, a key nesting site of the Red Sea green turtle population. The models were used to analyze runup events and inundation durations and provide a first estimate of a safe nesting elevation. Despite data limitations, the study provides valuable insights for coastal managers to protect sea turtle nests, suggesting that a 5-year return period runup elevation could serve as a threshold for nest relocation. However, the findings also highlight the importance of more accurate hydrodynamic predictions and the need for in-situ data to validate models and improve conservation strategies.

This study presents a multivariate spatio-temporal clustering framework to characterise joint wind–wave regimes across European seas using the fifth-generation atmospheric reanalysis produced by the European Centre for Medium-Range Weather Forecasts (ERA5; 1979–2014). Seasonal and annual statistics of significant wave height, mean wave period, wind speed, and wave/wind direction were computed at 0.5° resolution. Principal component analysis was used to reduce dimensionality, retaining 30 components that captured 99% of the variance. K-means clustering was then used to identify nine coherent dynamical regimes with persistent spatio-temporal signatures. These regimes were grouped into open-ocean, transitional, and enclosed/semi-enclosed categories based on internal variability, directional spread, and geographic exposure. Open-Atlantic regimes are found to be energy-rich, exhibiting clear December–February maxima in significant wave height ((Formula presented.)), mean wave period ((Formula presented.)), and 10 m wind speed ((Formula presented.)); enclosed and semi-enclosed basins show lower amplitudes and reduced variability, while transitional shelves and the southern Mediterranean display intermediate conditions, characterised by moderate (Formula presented.) levels and seasonal rotation of wave and wind directions, reflecting a mixed influence of locally generated seas and remotely forced swell. Dispersion analysis highlights a clear Atlantic–Mediterranean partition, with transitional shelves forming a dynamical bridge between open-ocean and enclosed basins. Teleconnection analysis shows that the North Atlantic Oscillation and Arctic Oscillation dominate Atlantic regimes, while the Scandinavia, East Atlantic, and Polar/Eurasia patterns modulate variability and directional persistence in transitional and enclosed seas. The classification defines a climatological framework of European wind–wave conditions and establishes a practical basis for renewable energy assessment, engineering design, and long-term change analysis, with methods transferable to other basins.

Extreme sea level events pose significant risks to coastal regions, with non-tidal residuals (NTRs) being a primary driver in low-lying areas like the Netherlands, where shallow seas amplify their impact. This study investigates the spatial patterns of NTRs along the Dutch coast using time series clustering on historical NTR hydrographs. The design of hydraulic boundary conditions divides the Netherlands into three coastal regions. To evaluate whether this division sufficiently captures regional variability, three clustering scenarios (k = 3, k = 4, and k = 5) were explored. The analysis identified k = 5 as the optimal configuration based on the Davies-Bouldin index. This result emphasized the importance of fine-scale approaches to understanding regional spatial variations in NTR dynamics. Regional bathymetry and tide-surge interactions were explored as drivers of these spatial patterns. Southern stations near river systems and deeper waters displayed characteristics distinct from northern stations in the Wadden Sea, which are influenced by shallow tidal flats. Analysis of the M2 tidal constituent and the timing of NTR maxima relative to high tides underscored the role of tidal dynamics in shaping spatial clusters. Future research will focus on integrating spatio-temporal patterns and environmental drivers into clustering methodologies, providing deeper insights for coastal risk management and adaptation strategies.

This study explores the statistical dependence between wind speed and surge height along the Dutch coast using a large synthetic dataset. Storms were clustered based on wind direction, tidal offset, wind rotation, tidal peak, surge and wind exceedance duration, resulting in 16 clusters per wind direction and per location. Apart from wind direction, comparing clusters revealed a limited impact of clustering based on these storm characteristics on the choice of the best-fitting copula model, suggesting sub-clustering may not be necessary for accurately representing the statistical dependence between extreme wind speeds and surge heights. The BB8 copula generally provided the best fit to the data. However, the observed upper tail dependence did not decrease to zero, particularly for western to northern wind directions, indicating non-negligible dependence in joint extremes of wind speed and surge height. Therefore, applying the BB8 copula (or any other copula model without upper tail dependence) may lead to underestimation of the flood risk, when applied in probabilistic analyses. The findings from this study provide valuable insights for refining hydraulic load models for reliability assessments and design of flood defenses.

Dutch beaches are increasingly urbanized with both permanent beach pavilions and seasonal sheds and holiday houses. The effect of these buildings on long term dune development between 1999 and 2024 is studied in this paper along ~ 100 km of coast on the outer delta in the south western part of the Netherlands. A total of ~ 7000 beach buildings have been manually identified in this period based on satellite images and the time line function of Google earth desktop. The effect of the buildings is determined and analyzed at 477 cross-shore profiles with dune volumes and properties like dune toe, top and heel based on airborne lidar datasets of 1999 and 2024. On natural beaches the dune toe position is derived from profile information, whereas on urbanized beaches near buildings the dune toe is based on the location of the buildings. Yearly volume changes at the profile locations vary between -10 m³/m/y and up to 40 m³/m/y. The results indicate that smaller and standalone buildings allow for larger variations in dune volume changes and suggest that larger buildings and connected buildings impede natural dune dynamics which could impact coastal resilience in the long run.

Extreme storms over the North Sea drive coastal flood risk in the Netherlands, causing high waves and extreme sea levels. Designing flood defenses requires accurate statistical extrapolation of hydraulic load conditions with return periods of 1,000 years or more. This is a challenging task given limited observational data. This study uses a large, simulated dataset (~9,000 years) to explore the statistical dependence between extreme wind speed u and surge height s. Storms were clustered using several techniques. Self-organizing maps (SOM) effectively captured physical relationships, such as the influence of wind direction and tidal offset on storm dynamics, however variability in statistical dependence between u and s for different clusters was better represented using manual clusters. Copula models were fitted to the cluster data, with the BB8 copula outperforming others. This study illustrates the potential of machine learning to identify patterns in large datasets while emphasizing the relevance of manual clustering approaches for revealing nuanced statistical dependencies critical to flood risk assessment.

Sandy beach erosion is a pressing concern for coastal regions worldwide, driven by both natural processes and human-induced pressures. This study presents an ensemble modeling approach for predicting sandy shoreline dynamics using an equilibrium-based shoreline evolution model (EBSEM). A genetic algorithm (NSGA-II) was employed to calibrate multiple parameter sets, capturing the inherent uncertainty in model parameters. The method was tested with a publicly available dataset from Tairua Beach (New Zealand), spanning 14 years of high-resolution shoreline measurements. Results reveal a near-linear relationship between the slope and intercept parameters governing equilibrium wave energy, and demonstrate that the best-fit solution generally lies within the ensemble range. Comparisons of ensemble simulations with observed data indicate strong agreement in both calibration and validation phases, although certain extreme accretion and erosion events were underestimated. Overall, this ensemble framework provides a robust tool for medium- to long-term shoreline predictions, bringing coastal managers with stochastic/probabilistic estimates of shoreline change, which can be useful in the assessment of resilience of adaptive strategies for risk mitigation.

The causal drivers of short-term changes (days to months) in human-, wind-, and wave-driven sand transport on a sandy beach are not often considered in an integral and data-driven approach. However, improving current knowledge on (urban) sandy beach topographical change requires the incorporation of multi-scale, cross-sectional and human factors. In this research we process a time series of 21,194 hourly point clouds, obtained in a Permanent Terrestrial Laser Scanning setup. From this 3D time series we extract 5,102 short-term temporary surface dynamics, through a method called 4D objects-by-change (4D-OBCs). The causal drivers of two of these 4D-OBCs are investigated in detail. One is interpreted as an aeolian depositional surface dynamic (1), and one as a bulldozer deposit, that consecutively eroded under high wave energy conditions (2). The dynamics show clear correlation to a particular combination of wind direction and intensity (1), and wave height and wave period (2), indicating that point cloud time series derived 4D-OBCs are useful data to study causality of short-term surface dynamics of different origins. However, to study these surface dynamics systematically and derive statistical proof of causal relations we must consider multivariate correlations, as well as spatiotemporal dependence between sediment dynamics and larger scale morphological changes on the beach.

Coastal zones are highly dynamic environments shaped by various environmental forcing agents such as waves and nearshore currents operating across diverse spatio-temporal scales. For effective decision-making, coastal managers require simplified, computationally efficient models to predict future shoreline morphodynamics. Among the models developed over the years, equilibrium-based shoreline evolution models (EBSEMs) have garnered significant attention for their computational efficiency. However, their application has mainly been limited to microtidal sandy beaches when simulating shoreline orientation, necessitating further evaluation across broader coastal settings. This study investigates the applicability of EBSEMs in predicting shoreline rotational variability at two morphologically distinct sites: Narrabeen Beach, Australia, and Moncofa Beach, Spain. These sites differ in sediment size, tidal regimes, data sources, observation periods, and monitoring frequencies, providing a robust framework for model evaluation. Results demonstrate that the EBSEM successfully replicates the general trends of shoreline orientation variability on both sites, qualitatively and quantitatively. Seasonal rotation trends were accurately captured, emphasizing the model’s capability to operate across varying spatial and temporal scales. These findings further reinforced the capabilities of EBSEMs as practical tools for coastal management, particularly for predicting shoreline orientation changes under diverse environmental conditions.

Robust predictions of shoreline change are critical for sustainable coastal management. Despite advancements in shoreline models, objective benchmarking remains limited. Here we present results from ShoreShop2.0, an international collaborative benchmarking workshop, where 34 groups submitted shoreline change predictions in a blind competition. Subsets of shoreline observations at an undisclosed site (BeachX) over short (5-year) and medium (50-year) periods were withheld from modelers and used for model benchmarking. Using satellite-derived shoreline datasets for calibration and evaluation, the best performing models achieved prediction accuracies on the order of 10 m, comparable to the accuracy of the satellite shoreline data, indicating that certain beaches can be modelled nearly as well as they can be remotely observed. The outcomes from this collaborative benchmarking competition critically review the present state-of-the-art in shoreline change prediction as well as reveal model limitations, facilitate improvements, and offer insights for advancing shoreline-prediction capabilities.

Wave runup observations are important for coastal management providing data to validate predictive models of inundation frequencies and erosion rates, which are vital for assessing the vulnerability of coastal ecosystems and infrastructure. Automated algorithms to extract the instantaneous water line from video imagery struggle under dissipative conditions, where the presence of a seepage face and the lack of contrast between the sand and the swash impede proper extraction, requiring time-intensive data quality control or manual digitization. This study introduces two novel methods, based on color contrast (CC) and machine learning (ML). The CC method combines texture roughness — local entropy — with saturation. Images are first binarized using entropy values and then refined through noise reduction by binarization of the saturation channel. The ML method uses a convolutional neural network (CNN) informed by five channels: the grayscale intensity and its time gradient, the saturation channel, and the entropy and its time gradient. Both methods were validated against nine manually labeled, 80 min video time series. The CC method demonstrated strong agreement with manually digitized water lines (RMSE = 0.12 m, r=0.94 for the vertical runup time series; RMSE = 0.08 m, r=0.97 for the 2% runup exceedance (R_2%); and RMSE = 3.88 s, r=0.70 for the mean period (T_m−1,0)). The ML model compared well with the manually labeled time series (RMSE = 0.10 m, r=0.96 for the vertical runup time series; RMSE = 0.09 m, r=0.97 for R_2%; and RMSE = 3.51 s, r=0.79 for T_m−1,0). Furthermore, the computed R_2% values of both methods show a good agreement with the formula proposed by Stockdon et al. (2006) for extremely dissipative conditions, with RMSE-values lower than 0.13 m and correlations exceeding 0.70 for manual, CC, and ML estimates. While the CC method is deemed applicable for wave-by-wave analysis under similar dissipative conditions with a smooth seepage face and sufficient turbulent swash, the ML method still struggles with new, unseen data. However, it shows promise for a broader application and serves as a viable proof of concept. Together, these methods reduce the need for manual processing and enhance real-time coastal monitoring, contributing to more accurate predictive modeling of runup events and a better understanding of nearshore processes.

Robust and reliable models are needed to understand how coastlines will evolve over the coming decades, driven by both natural variability and climate change. This study evaluated how accurately five popular ‘reduced-complexity’ models replicate multi-decadal shoreline change at Narrabeen-Collaroy Beach, a sandy embayment in Sydney, Australia. Measured shoreline positions derived from approximately monthly field surveys were used for 20-year calibration and 20-year validation periods. The models performed similarly on average but with large variability between transects. The set-up of several models was modified to compensate for their sensitivity to imperfect input wave data, and further site-specific improvements were identified. Capturing interannual to decadal-scale variability in cross-shore and longshore dynamics at this site was challenging for all five models. Models appeared to aggregate key processes at this timescale into parameter values rather than representing them directly. This suggests time-varying parameters or changes to model structure may be necessary for decadal-scale simulations.

Understanding and predicting shoreline variability at various temporal and spatial scales is vital for effective, data-driven coastal management. Shoreline position, a reliable indicator of beach morphological changes, has been assessed using complex numerical models. Recently, equilibrium-based shoreline evolution models (EBSEMs) have gained traction for their efficiency in simulating shoreline orientation, including cross-shore and rotational (longshore) changes. However, existing EBSEMs for shoreline rotation have been applied predominantly to microtidal beaches, with limited validation across diverse coastal environments. This study evaluates the performance and scalability of the EBSEM proposed by Jaramillo et al. (2021) in modelling shoreline rotational variability at seven embayed beaches: Narrabeen Beach (Australia), Tairua Beach (New Zealand), Blackpool Beach (United Kingdom), Poniente Beach, Llevant Beach, Cala Millor Beach, and Moncofa Beach (Spain). These sites represent diverse environmental conditions in terms of sediment size, tidal regimes, monitoring frequency, and data types. The model was tested across full monitoring periods, elevation contours, and temporal resolutions. Results show that EBSEM performs well across contrasting beach types, effectively capturing short-term and seasonal shoreline rotation patterns. However, reduced accuracy was observed in environments with high-energy events or human interventions, such as Poniente, Llevant, and Cala Millor beaches. Sensitivity analyses highlight the importance of temporal resolution and intertidal elevation in model performance. While the EBSEM shows significant potential for broader application, further refinement is needed to better capture storm-driven and anthropogenic variability. These improvements would enhance its utility for coastal adaptation planning, hazard mitigation, and long-term shoreline management in the face of climate change.