The statistical analysis described in this paper provides numbers to assess the quality of the WIS
wave directional information in comparison to the measured information using circular statistics. Sites
with large mean directional differences, low concentration statistics, and low correlations need to be
checked in regard to hindcasting problems or measurement problems. The statistics provided in this
paper verify that WIS mean wave directions are a good representation of the measured mean wave
conditions in the Gulf of Mexico during the 1990's for the sites presented in this paper. The mean wave
direction is only one parameter that describes the whole energy spectrum at each hour and is a stable
quantity to use in comparisons. The analysis described in this paper could be applied to other directional
parameters such as peak wave direction, etc. The mean wave direction and other directional parameters
are useful in many applications, but full spectra give a better description of energy-direction
characteristics. Full spectra are available for more complex applications. The statistical procedures
described in this paper could be applied to calculate statistics for only high wave heights by using a 2-m
or higher wave height threshold. It would also be interesting to calculate statistics for waves with
directions coming from the northeastern quadrant and compare these statistics with one of the other
This work was completed as part of the Wave Information Studies (WIS) as authorized by
Headquarters, U.S. Army Corps of Engineers, as part of the Coastal Field Data Collection Program at the
Engineer Research and Development Center, Waterways Experiment Station, Coastal and Hydraulics
Laboratory, Vicksburg, MS. Permission was granted by the Office of the Chief of Engineers, U.S. Army
Corps of Engineers, to publish this information. Thanks to the rest of the WIS team (Robert Jensen, Alan
Cialone, Jane Payne, and Rebecca Brooks) for the production of this hindcast. Special thanks to Ian
Morton for information about Equation 8.
Bowers, J.A., I.D. Morton and G.I. Mould, 2000: Directional statistics of the wind and waves. Applied
Ocean Research, 22, No. 1, 13-30.
Fisher, N.I., 1993: Statistical analysis of circular data. Cambridge University Press.
Hubertz, J.M., 1992 (June): User's Guide to the Wave Information Studies (WIS) Wave Model, Version
2.0. WIS Report 27(AD A254 313), U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS
Johnson, R.A. and D.W. Wichern, 1998: Applid multivariate statistical analysis. Prentice-Hall, 8.
Resio, D.T., and B.A. Tracy, 1983 (Jan): A Numerical Model for Wind-Wave Prediction in Deepwater.
WIS Report 12(AD A125 985), U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS. 
Resio, D.T., 1982: Wave Prediction in Shallow Water. Proceedings, 14th Offshore Technology
Conference, American Institute of Mining, et al., 2, 147.
Resio, D.T., 1981: The Estimation of Wind-Wave Generation in a Discrete Spectral Model. Journal of
Physical Oceanography, 2, No. 4, 510-525.