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Improvement of the Short-Fetch Behavior in the Wave Ocean Model (WAM)

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  • 1 Royal Netherlands Meteorological Institute, De Bilt, the Netherlands
  • | 2 European Centre for Medium-Range Weather Forecasts, Reading, United Kingdom
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Abstract

The physics of wind input in the Wave Ocean Model (WAM) cycle 4 is based on scaling with the friction velocity u∗. This implies that in the case of fetch-limited wind-wave growth, universal scaling laws should follow if fetch and wave variance are scaled by means of u∗. For operational applications, such as at the European Centre for Medium-Range Weather Forecasts, the scaling of the WAM model with u∗ is well satisfied. Recently, however, it was found that this scaling is violated for very short waves at small fetches and durations, for which the model is run with very small grid spacings, a very small time step, and a large cutoff frequency. This violation of u∗ scaling, which is a serious problem for implementation on a small lake, was found to be caused by a too severe limit on the increments of the wave spectrum per time step. In this article, an alternative formulation for the limitation of spectral component growth is suggested, which does not violate u∗ scaling and, in addition, gives rise to excellent results over a large range of scaled quantities. At the same time, growth curves for wave height and peak frequency hardly depend on the time step.

Corresponding author address: Dr. Hans Hersbach, Royal Netherlands Meteorological Institute (KNMI), P.O. Box 2013730 AE Utrecht, the Netherlands.

Email: hersbach@knmi-nl

Abstract

The physics of wind input in the Wave Ocean Model (WAM) cycle 4 is based on scaling with the friction velocity u∗. This implies that in the case of fetch-limited wind-wave growth, universal scaling laws should follow if fetch and wave variance are scaled by means of u∗. For operational applications, such as at the European Centre for Medium-Range Weather Forecasts, the scaling of the WAM model with u∗ is well satisfied. Recently, however, it was found that this scaling is violated for very short waves at small fetches and durations, for which the model is run with very small grid spacings, a very small time step, and a large cutoff frequency. This violation of u∗ scaling, which is a serious problem for implementation on a small lake, was found to be caused by a too severe limit on the increments of the wave spectrum per time step. In this article, an alternative formulation for the limitation of spectral component growth is suggested, which does not violate u∗ scaling and, in addition, gives rise to excellent results over a large range of scaled quantities. At the same time, growth curves for wave height and peak frequency hardly depend on the time step.

Corresponding author address: Dr. Hans Hersbach, Royal Netherlands Meteorological Institute (KNMI), P.O. Box 2013730 AE Utrecht, the Netherlands.

Email: hersbach@knmi-nl

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