We acknowledge the collaboration of Carl A. Friehe and Djamal Khelif at the University of California, Irvine, in planning and conducting the GOTEX experiments and in help with the analysis of the atmospheric boundary layer data. We are grateful to Allen Schanot, Henry Boynton, Lowell Genzlinger, Ed Ringleman, and the support staff at the NCAR Research Aviation Facility. We thank Bill Krabill, Bob Swift, Jim Yungel, John Sonntag, and Robbie Russell at NASA/EG&G for access to the ATM, its deployment, and initial data processing. LR is thankful to Miguel Onorato for useful comments and discussions during preliminary stages of this work. This research was supported by grants to WKM from the National Science Foundation (OCE), the Office of Naval Research (Physical Oceanography).
Bülow, T., , and G. Sommer, 2001: Hypercomplex signals-a novel extension of the analytic signal to the multidimensional case. IEEE Trans. Signal Process., 49, 2844–2852.
Cartwright, D. E., , and M. S. Longuet-Higgins, 1956: The statistical distribution of the maxima of a random function. Proc. Roy. Soc. London, 237A, 212–232.
Cavanié, A., , M. Arthan, , and R. Ezraty, 1976: A statistical relationship between individual heights and periods of storm waves. Proc. Conf. on Behavior Offshore Structures, Trondheim, Norway, Norwegian Institute of Technology, 354–360.
Huang, N., , S. R. Long, , and L. Bliven, 1981: On the importance of the significant slope in empirical wind-wave studies. J. Phys. Oceanogr., 11, 569–573.
Hwang, P. A., , and D. W. Wang, 2001: Directional distributions and mean square slopes in the equilibrium and saturation ranges of the wave spectrum. J. Phys. Oceanogr., 31, 1346–1360.
Hwang, P. A., , D. W. Wang, , E. J. Walsh, , W. B. Krabill, , and R. N. Swift, 2000a: Airborne measurements of the wavenumber spectra of ocean surface waves. Part I: Spectral slope and dimensionless spectral coefficient. J. Phys. Oceanogr., 30, 2753–2767.
Hwang, P. A., , D. W. Wang, , E. J. Walsh, , W. B. Krabill, , and R. N. Swift, 2000b: Airborne measurements of the wavenumber spectra of ocean surface waves. Part II: Directional distribution. J. Phys. Oceanogr., 30, 2768–2787.
Janssen, P. A. E. M., 2005: Nonlinear four-wave interaction and freak waves. Rogue Waves: Proc. ‘Aha Huliko’a Hawaiian Winter Workshop, Honolulu, HI, University of Hawaii at Manoa, 85–90
Krabill, W. B., , and C. F. Martin, 1987: Aircraft positioning using global positioning system carrier phase data. Navigation, 34, 1–21.
Longuet-Higgins, M. S., 1963: The effect of non-linearities on statistical distributions in the theory of sea waves. J. Fluid Mech., 17, 459–480.
Longuet-Higgins, M. S., 1975: On the joint distribution of wave periods and amplitudes of sea waves. J. Geophys. Res., 80, 2688–2694.
Longuet-Higgins, M. S., 1980: On the distribution of the heights of sea waves: Some effects of nonlinearity and finite band width. J. Geophys. Res., 85 (C3), 1519–1523.
Longuet-Higgins, M. S., 1983: On the joint distribution of wave periods and amplitudes in a random wave field. Proc. Roy. Soc. London, 389A, 241–258.
Melville, W. K., , L. Romero, , and J. M. Kleiss, 2005: Extreme waves in the Gulf of Tehuantepec. Rogue Waves: Proc. ‘Aha Huliko‘a Hawaiian Winter Workshop, Honolulu, HI, University of Hawaii at Manoa, 23–28.
Mori, N., , and P. A. E. M. Janssen, 2006: On kurtosis and occurrence probability of freak waves. J. Phys. Oceanogr., 36, 1471–1483.
Mori, N., , M. Onorato, , P. A. E. M. Janssen, , A. R. Osborne, , and M. Serio, 2007: On the extreme statistics of long-crested deep water waves: Theory and experiments. J. Geophys. Res., 112, C09011, doi:10.1029/2006JC004024.
Resio, D., , and W. Perrie, 1991: A numerical study of nonlinear energy fluxes due to wave-wave interactions. Part 1: Methodology and basic results. J. Fluid Mech., 223, 609–629.
Romero, L., , and W. K. Melville, 2010a: Airborne observations of fetch-limited waves in the Gulf of Tehuantepec. J. Phys. Oceanogr., 40, 441–465.
Romero, L., , and W. K. Melville, 2010b: Numerical modeling of fetch-limited waves in the Gulf of Tehuantepec. J. Phys. Oceanogr., 40, 466–486.
Romero, L., , and W. K. Melville, 2010c: Observations and modeling of linear and nonlinear spatio-temporal surface wave statistics. Proc. 29th Int. Conf. on Offshore Mechanics and Arctic Engineering, Shanghai, China, ASME, 1–13.
Sharma, J. N., , and R. G. Dean, 1979: Development and evaluation of procedure for simulating a random directional second order sea surface and associated wave forces. University of Delaware Ocean Engineering Rep. 20, 112 pp.
Shum, K. T., , and W. K. Melville, 1984: Estimates of the joint statistics of amplitudes and periods of ocean waves using an integral transform. J. Geophys. Res., 89 (C4), 6467–6476.
Snyder, R. L., , F. Dobson, , J. Elliott, , and R. B. Long, 1981: Array measurements of atmospheric pressure fluctuations above surface gravity waves. J. Fluid Mech., 102, 1–59.
Socquet-Juglard, H., , K. Dysthe, , K. Trulsen, , H. E. Krodgstad, , and J. D. Liu, 2005: Probability distributions of surface gravity waves during spectral changes. J. Fluid Mech., 542, 195–216.
Steenburgh, W. J., , D. M. Schultz, , and B. A. Colle, 1998: The structure and evolution of gap outflow over the Gulf of Tehuantepec, Mexico. Mon. Wea. Rev., 126, 2673–2691.
Tracy, B. A., , and D. T. Resio, 1982: Theory and calculation of the nonlinear energy transfer between sea waves in deep water. Army Engineer Waterways Experiment Station Vicksburg MS Hydraulics Lab Tech. Rep. 11, 54 pp.
van Vledder, G. P., 2006: The WRT method for the computation of non-linear four-wave interactions in discrete spectral wave models. Coastal Eng., 53, 223–242.
Walsh, E. J., , D. W. Hancock, , D. E. Hines, , R. N. Swift, , and J. F. Scott, 1985: Directional wave spectra measured with the surface contour radar. J. Phys. Oceanogr., 15, 566–592.
Xu, D., , X. Li, , L. Zhang, , N. Xu, , and H. Lu, 2004: On the distributions of wave periods, wavelengths, and amplitudes in a random wave field. J. Geophys. Res., 109, C05016, doi:10.1029/2003JC002073.
Zhu, Y. M., , F. Peyrin, , and R. Goutte, 1990: The use of a two-dimensional Hilbert transform for Wigner analysis of 2-dimensional real signals. Signal Process., 19, 205–220.
This ambiguity is often resolved in real data by additional environmental information, including the wind direction and the source of the swell.