Abstract
The disastrous effects of numerous winter storms on the marine environment in the North Sea and the Baltic Sea during the last decade show that wind waves generated by strong winds actually represent natural hazards and require high quality wave forecast systems as warning tools to avoid losses due to the impact of rough seas. Hence, the operational wave forecast system running at the German Weather Service including a regional wave model for the North Sea and the Baltic Sea is checked extensively whether it provides reasonable wave forecasts, especially for periods of extraordinary high sea states during winter storms. For two selected extreme storm events that induced serious damage in the area of interest, comprehensive comparisons between wave measurements and wave model forecast data are accomplished. Spectral data as well as integrated parameters are considered, and the final outcome of the corresponding comparisons and statistical analysis is encouraging. Over and above the capability to provide good short-term forecast results, the regional wave model is able to predict extreme events as severe winter storms connected with extraordinary high waves already about 2 days in advance. Therefore, it represents an appropriate warning tool for offshore activities and coastal environment.
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Acknowledgements
The authors would like to thank Ocean WaveS in Lüneburg (www.oceanwaves.de) for the measured data recorded by WaMoS II at the FINO platform and for the permission to use their time series plot of the maximum wave height (Fig. 6) in this paper. Furthermore, the authors are grateful to the BSH (Bundesamt für Seeschifffahrt und Hydrographie in Hamburg, www.bsh.de) their support, and for the permission to use their photo of the damage to the FINO platform during winter storm Britta (Fig. 4) and for the wave data recorded by their Wave Rider buoy at the FINO platform.
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Appendix: Mathematical description of statistical parameters
Appendix: Mathematical description of statistical parameters
Mean of measurements and model values: | \( \overline{x} = \frac{1}{n}\sum {x_{i} } ,\quad \overline{y} = \frac{1}{n}\sum {y_{i} } \) |
Bias: | \( {\text{BIAS}} = \overline{y} - \overline{x} \) |
Root mean square error: | \( {\text{RMSE}} = \left[ {\frac{1}{n}\sum \left( {y_{i} - x_{i} } \right)^{2} } \right]^{0.5} \) |
Slope of regression line: | \( {\text{SR}} = \left[ {\frac{{\sum {y_{i}^{2} } }}{{x_{i}^{2} }}} \right] \) |
Reduction of Variance (Skill): | \( {\text{rv}} = 1 - \frac{{\sum {\left( {x_{i} - y_{i} } \right)^{2} } }}{{\sum {\left( {x_{i} - \overline{x} } \right)^{2} } }} \) |
Standard deviation: | \( {\text{STD = }}\sqrt {\frac{1}{n - 1}\sum {\left( {x_{i} - y_{i} - BIAS} \right)^{2} } } \) |
Scatter-Index: | \( {\text{SI}} = \frac{\text{STD}}{{\overline{x} }}*100 \) |
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Behrens, A., Günther, H. Operational wave prediction of extreme storms in Northern Europe. Nat Hazards 49, 387–399 (2009). https://doi.org/10.1007/s11069-008-9298-3
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DOI: https://doi.org/10.1007/s11069-008-9298-3