The separation of wind sea and swell is crucial for advancing wave dynamics research, improving wave forecasting, and optimizing the design of coastal and offshore structures. In this study, we highlight the limitations of the widely used wave age method for separating two-dimensional wind sea and swell. Specifically, under strong wind conditions, waves require extended durations to reach full development—an aspect not accounted for by the wave age method, which assumes fully developed seas and thus tends to overestimate wind sea. Furthermore, changes in wind direction and wave refraction in shallow waters can lead to misclassification. To overcome these issues, we propose a novel algorithm for directional spectral separation, grounded in wind wave growth theory and incorporating wave refraction effects. The proposed method improves separation accuracy and delivers more consistent results across a range of wave conditions.

Rogue waves are sudden and extreme occurrences, with heights that exceed twice the significant wave height of their neighboring waves. The formation of rogue waves has been attributed to several possible mechanisms such as linear superposition of random waves, dispersive focusing, and modulational instability. Recently, nonlinear Fourier transforms (NFTs), which generalize the usual Fourier transform, have been leveraged to analyze oceanic rogue waves. Next to the usual linear Fourier modes, NFTs can additionally uncover nonlinear Fourier modes in time series that are usually hidden. However, so far only individual oceanic rogue waves have been analyzed using NFTs in the literature. Moreover, the completely different types of nonlinear Fourier modes have been observed in these studies. Exploiting twelve years of field measurement data from an ocean buoy, we apply the nonlinear Fourier transform (NFT) for the nonlinear Schrödinger equation (NLSE) (referred to NLSE-NFT) to a large dataset of measured rogue waves. While the NLSE-NFT has been used to analyze rogue waves before, this is the first time that it is systematically applied to a large real-world dataset of deep-water rogue waves. We categorize the measured rogue waves into four types based on the characteristics of the largest nonlinear mode: stable, small breather, large breather and (envelope) soliton. We find that all types can occur at a single site, and investigate which conditions are dominated by a single type at the measurement site. The one and two-dimensional Benjamin-Feir indices (BFIs) are employed to examine the four types of nonlinear spectra. Furthermore, we verify on a part of the data set that for the localized types, the largest nonlinear Fourier mode can be attributed directly to the rogue wave, and investigate the relation between the height of the rogue waves and that of the dominant nonlinear Fourier mode. While the dominant nonlinear Fourier mode in general only contributes a small fraction of the rogue wave, we find that soliton modes can contribute up to half of the rogue wave. Since the NLSE does not account for directional spreading, the classification is repeated for the first quartile with the lowest directional spreading for each type. Similar results are obtained.

Hydro-meteorological risks are a growing issue for societies, economies and environments around the world. An effective, sustainable response to such risks and their future uncertainty requires a paradigm shift in our research and practical efforts. In this respect, Nature-Based Solutions (NBSs) offer the potential to achieve a more effective and flexible response to hydro-meteorological risks while also enhancing human well-being and biodiversity. The present paper describes a new methodology that incorporates stakeholders’ preferences into a multi-criteria analysis framework, as part of a tool for selecting risk mitigation measures. The methodology has been applied to Tamnava river basin in Serbia and Nangang river basin in Taiwan within the EC-funded RECONECT project. The results highlight the importance of involving stakeholders in the early stages of projects in order to achieve successful implementation of NBSs. The methodology can assist decision-makers in formulating desirable benefits and co-benefits and can enable a systematic and transparent NBSs planning process.