The Gulf of Tehuantepec is well known for having strong offshore winds, which occur predominantly during the winter months, when significant atmospheric pressure differences develop between the Gulf of Mexico and the Pacific Ocean, forcing winds through a mountain gap at the head of the gulf. During the Gulf of Tehuantepec Experiment (GOTEX), conducted in February 2004, we made surface-wave measurements using a scanning LIDAR (Airborne Topographic Mapper, ATM) on the NSF/NCAR C-130 aircraft during fetch-limited conditions with winds speeds ranging from 10 to 20 m/s. We present direct comparisons between the observed evolution of the wave field and numerical simulations using a recently proposed parameterization of the wave energy dissipation in deep water. In particular, we compare the observed and computed evolution of the directional spectra for fetch-limited conditions under strong wind forcing. All model simulations were carried out with exact computations of the nonlinear energy transfer due to four-wave resonant interactions and two empirical wind input functions. The agreement of the integral parameters between the observations and the simulations is within the typical scatter of field observations. The model spectrum can maintain power-law behaviors within the tail of the one dimensional spectra, consistent with the observations. The comparison between the observations and the numerical simulations highlights some of the issues associated with the source term balance within the tail of the spectrum. The possible reasons for differences between the measurements and the simulations are discussed.