Ocean Engineering 29 (2002) 81–98 Has wind–wave modeling reached its limit? Paul C. Liu a,* , David J. Schwab a , Robert E. Jensen b a NOAA Great Lakes Environmental Research Laboratory, Ann Arbor, MI 48105, USA b USACE Coastal and Hydraulics Laboratory, Vicksburg, MS, USA Received 29 May 2000; accepted 13 September 2000 Abstract This article uses a comparison of four different numerical wave prediction models for hind- cast wave conditions in Lake Michigan during a 10-day episode in October 1988 to illustrate that typical wave prediction models based on the concept of a wave energy spectrum may have reached a limit in the accuracy with which they can simulate realistic wave generation and growth conditions. In the hindcast study we compared the model results to observed wave height and period measurements from two deep water NOAA/NDBC weather buoys and from a nearshore Waverider buoy. Hourly wind fields interpolated from a large number of coastal and overlake observations were used to drive the models. The same numerical grid was used for all the models. The results show that while the individual model predictions deviate from the measurements by various amounts, they all tend to reflect the general trend and patterns of the wave measurements. The differences between the model results are often similar in magnitude to differences between model results and observations. Although the four models tested represent a wide range of sophistication in their treatment of wave growth dynamics, they are all based on the assumption that the sea state can be represented by a wave energy spectrum. Because there are more similarities among the model results than significant differ- ences, we believe that this assumption may be the limiting factor for substantial improvements in wave modeling.  2001 Published by Elsevier Science Ltd. Keywords: Wind waves; Wave modeling; Ocean waves; WAM model 1. Introduction Numerical modeling of wind waves developed concomitantly with the develop- ment of the computer era, spanning most of the second half of the 20th century. The * Corresponding author. Tel.: +1-734-741-2294; fax: +1-734-441-2055. E-mail address: liu@glerl.noaa.gov (P.C. Liu). 0029-8018/01/$ - see front matter  2001 Published by Elsevier Science Ltd. PII:S0029-8018(00)00074-3