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.

Characterization of multimodal directional wave spectra is important for many offshore and coastal applications, such as marine forecasting, coastal hazard assessment, and design of offshore wave energy farms and coastal structures. However, the multivariate and multiscale nature of wave climate variability makes this complex problem tractable using computationally expensive numerical models. So far, the skill of statistical-downscaling model-based parametric (unimodal) wave conditions is limited in large ocean basins such as the Pacific. The recent availability of long-term directional spectral data from buoys and wave hindcast models allows for development of stochastic models that include multimodal sea-state parameters. This work introduces a statistical downscaling framework based on weather types to predict multimodal wave spectra (e.g., significant wave height, mean wave period, and mean wave direction from different storm systems, including sea and swells) from large-scale atmospheric pressure fields. For each weather type, variables of interest are modeled using the categorical distribution for the sea-state type, the Generalized Extreme Value (GEV) distribution for wave height and wave period, a multivariate Gaussian copula for the interdependence between variables, and a Markov chain model for the chronology of daily weather types. We apply the model to the southern California coast, where local seas and swells from both the Northern and Southern Hemispheres contribute to the multimodal wave spectrum. This work allows attribution of particular extreme multimodal wave events to specific atmospheric conditions, expanding knowledge of time-dependent, climate-driven offshore and coastal sea-state conditions that have a significant influence on local nearshore processes, coastal morphology, and flood hazards.

Characterization of wave climate by bulk wave parameters is insufficient for many coastal studies, including those focused on assessing coastal hazards and long-term wave climate influences on coastal evolution. This issue is particularly relevant for studies using statistical downscaling of atmospheric fields to local wave conditions, which are often multimodal in large ocean basins (e.g., Pacific Ocean). Swell may be generated in vastly different wave generation regions, yielding complex wave spectra that are inadequately represented by a single set of bulk wave parameters. Furthermore, the relationship between atmospheric systems and local wave conditions is complicated by variations in arrival time of wave groups from different parts of the basin. Here, this study addresses these two challenges by improving upon the spatiotemporal definition of the atmospheric predictor used in the statistical downscaling of local wave climate. The improved methodology separates the local wave spectrum into "wave families," defined by spectral peaks and discrete generation regions, and relates atmospheric conditions in distant regions of the ocean basin to local wave conditions by incorporating travel times computed from effective energy flux across the ocean basin. When applied to locations with multimodal wave spectra, including Southern California and Trujillo, Peru, the new methodology improves the ability of the statistical model to project significant wave height, peak period, and direction for each wave family, retaining more information from the full wave spectrum. This work is the base of statistical downscaling by weather types, which has recently been applied to coastal flooding and morphodynamic applications.

Interest in understanding long-term coastal morphodynamics has recently increased as climate change impacts become perceptible and accelerated. Multiscale, behavior-oriented and process-based models, or hybrids of the two, are typically applied with deterministic approaches which require considerable computational effort. In order to reduce the computational cost of modeling large spatial and temporal scales, input reduction and morphological acceleration techniques have been developed. Here we introduce a general framework for reducing dimensionality of wave-driver inputs to morphodynamic models. The proposed framework seeks to account for dependencies with global atmospheric circulation fields and deals simultaneously with seasonality, interannual variability, long-term trends, and autocorrelation of wave height, wave period, and wave direction. The model is also able to reproduce future wave climate time series accounting for possible changes in the global climate system. An application of long-term shoreline evolution is presented by comparing the performance of the real and the simulated wave climate using a one-line model.