Abstract. A new wave data set from the southern North Sea covering the period 2011–2016 and composed of wave buoy and radar measurements sampling the sea surface height at frequencies between 1.28 and 4 Hz was quality controlled and scanned for the presence of rogue waves. Here, rogue waves refer to waves whose height exceeds twice the significant wave height. Rogue wave frequencies were analyzed and compared to Rayleigh and Forristall distributions, and spatial, seasonal, and long-term variability was assessed. Rogue wave frequency appeared to be relatively constant over the course of the year and uncorrelated among the different measurement sites. While data from buoys basically correspond with expectations from the Forristall distribution, radar measurement showed some deviations in the upper tail pointing towards higher rogue wave frequencies. The amount of data available in the upper tail is, however, still too limited to allow a robust assessment. Some indications were found that the distribution of waves in samples with and without rogue waves was different in a statistical sense. However, differences were small and deemed not to be relevant as attempts to use them as a criterion for rogue wave detection were not successful in Monte Carlo experiments based on the available data.

Abstract. The shallow waters off the coast of Norderney in the southern North Sea are characterised by a higher frequency of rogue wave occurrences than expected according to second-order theory. The role of nonlinear processes for the generation of rogue waves at this location is currently unclear. Within the framework of the Korteweg–de Vries (KdV) equation, we investigated the discrete soliton spectra of measured time series at Norderney to determine differences between time series with and without rogue waves. For this purpose, we applied a nonlinear Fourier transform for the Korteweg–de Vries equation with vanishing boundary conditions (vKdV-NLFT). For each time series containing a rogue wave, we were able to identify at least one soliton in the discrete nonlinear vKdV-NLFT spectrum that contributed to the occurrence of the rogue wave in that time series. The amplitudes of these solitons were generally found to be smaller than the crest height of the corresponding rogue wave and interaction with the continuous wave spectrum is needed to fully explain the observed rogue wave. Time series with and without rogue waves showed different characteristic soliton spectra. In most of the spectra calculated from rogue wave time series, most of the solitons clustered around similar heights, while the largest soliton was outstanding with an amplitude significantly larger than all other solitons. The presence of a clearly outstanding soliton in the spectrum was found to be an indicator pointing towards enhanced probability for detecting a rogue wave in the time series. Similarly, when the discrete spectrum appears as a cluster of solitons without the presence of a clearly outstanding soliton, the presence of a rogue wave in the observed time series is unlikely. Under the hypothesis that the KdV describes the evolution of the sea state around the measurement site well, these results suggest that solitons and nonlinear processes substantially contribute to the enhanced occurrence of rogue waves off Norderney.

Abstract. The shallow waters off the coast of Norderney in the southern North Sea are characterised by a higher frequency of rogue wave occurrences than expected. Here, rogue waves refer to waves exceeding twice the significant wave height. The role of nonlinear processes in the generation of rogue waves at this location is currently unclear. Within the framework of the Korteweg–de Vries (KdV) equation, we investigated the discrete soliton spectra of measured time series at Norderney to determine differences between time series with and without rogue waves. For this purpose, we applied a nonlinear Fourier transform (NLFT) based on the Korteweg–de Vries equation with vanishing boundary conditions (vKdV-NLFT). At measurement sites where the propagation of waves can be described by the KdV equation, the solitons in the discrete nonlinear vKdV-NLFT spectrum correspond to physical solitons. We do not know whether this is the case at the considered measurement site. In this paper, we use the nonlinear spectrum to classify rogue wave and non-rogue wave time series. More specifically, we investigate if the discrete nonlinear spectra of measured time series with visible rogue waves differ from those without rogue waves. Whether or not the discrete part of the nonlinear spectrum corresponds to solitons with respect to the conditions at the measurement site is not relevant in this case, as we are not concerned with how these spectra change during propagation. For each time series containing a rogue wave, we were able to identify at least one soliton in the nonlinear spectrum that contributed to the occurrence of the rogue wave in that time series. The amplitudes of these solitons were found to be smaller than the crest height of the corresponding rogue wave, and interaction with the continuous wave spectrum is needed to fully explain the observed rogue wave. Time series with and without rogue waves showed different characteristic soliton spectra. In most of the spectra calculated from rogue wave time series, most of the solitons clustered around similar heights, but the largest soliton was outstanding, with an amplitude significantly larger than all other solitons. The presence of a clearly outstanding soliton in the spectrum was found to be an indicator pointing towards the enhanced probability of the occurrence of a rogue wave in the time series. Similarly, when the discrete spectrum appears as a cluster of solitons without the presence of a clearly outstanding soliton, the presence of a rogue wave in the observed time series is unlikely. These results suggest that soliton-like and nonlinear processes substantially contribute to the enhanced occurrence of rogue waves off Norderney.

Abstract. A new wave dataset from the southern North Sea covering the period 2011–2016 and composed of wave buoy and radar measurements sampling the sea surface height at frequencies between 1.28–4 Hz was quality controlled and scanned for the presence of rogue waves. Here rogue waves refer to waves whose height exceeds twice the significant wave height. Rogue wave frequencies were analysed, compared to Rayleigh and Forristall distributions, and spatial, seasonal and long-term variability was assessed. Rogue wave frequency appeared to be relatively constant over the course of the year and uncorrelated among the different measurement sites. While data from buoys basically correspond with expectations from the Forristall distribution, radar measurement showed some deviations in the upper tail pointing towards higher rogue wave frequencies. Number of data available in the upper tail is, however, still limited to allow a robust assessment. Some indications were found that the distribution of waves in samples with and without rogue waves were different in a statistical sense. However, differences were small and deemed not to be relevant as attempts to use them as a criterion for rogue wave detection were not successful in Monte Carlo experiments based on the available data.

The role of the modulational instability for rogue wave generation in the ocean is still under debate. We investigated a continuous data set, consisting of buoy and radar wave elevation data of different frequency resolutions, from eight measurement stations in the southern North Sea. For periods with rogue waves, we evaluated the presence of conditions for the modulational instability to work, that is, a narrow-banded wave spectrum in both, frequency and angular direction. We found rogue waves exceeding twice the significant wave height indeed to occur at slightly lower frequency bandwidths than usual. For rogue waves that are defined only by high crests, this was, however, not the case. The results were dependent on the measurement frequency. The directional spreading of the buoy spectra yielded no information on the presence of a rogue wave. In general, all spectra estimated from the data set were found to be broad in frequency and angular direction, while the Benjamin–Feir index yielded no indication on a high nonlinearity of the sea states. These are unfavorable conditions for the evolution of a rogue wave through modulational instability. We conclude that the modulational instability did not play a substantial role in the formation of the rogue waves identified in our data set from the southern North Sea.