A statistical analysis of rogue waves in the southern North Sea

Ina Teutsch,Oliver Krueger,Jens Moeller,Ralf Weisse

doi:10.5194/nhess-20-2665-2020

Abstract

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.

Highlights

Waves that are exceptionally higher than expected for a given sea state are commonly referred to as rogue waves (BitnerGregersen and Gramstad, 2016)
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
Rogue waves refer to exceptionally high waves within a given sea state in which the state of the sea is commonly characterized by the significant wave height Hs

Summary

Introduction

Waves that are exceptionally higher than expected for a given sea state are commonly referred to as rogue waves (BitnerGregersen and Gramstad, 2016). The above definition of a rogue wave is based on a criterion developed by Haver and Andersen (2000). As rogue waves are often associated with incidents and damages to ships and offshore platforms (Haver and Andersen, 2000), these authors were primarily interested in whether or not such waves represent rare realizations of typical distributions of waves in a sea state. Based on 20 min wave samples, Haver (2000) called a wave a rogue wave when it represented an outlier in reference to the second-order model commonly used in engineering design processes. He concluded that “. . . the ratio of wave height to significant wave height that is likely to be exceeded in 1 out of 100 cases [in a second-order process] is about 2.0” (Haver, 2000)

Results

Discussion

Conclusion