**1. Introduction**

Tropical cyclones, also popularly known as hurricanes or typhoons, are among the most spectacular and deadly geophysical phenomena. Not only the intense winds associated with the storms can create enormous waves, the ocean wave field generated by tropical cyclones are extremely complex with a combination of swell and wind sea due to the spatially inhomogeneous and directionally varying wind fields, and the directional distribution of the wind sea component is often skewed due to the rapid variation in the wind direction. Thus, the tropical cyclone-generated wave fields are of interest not only operationally for predicting potentially hazardous conditions for ship navigation and coastal regions, but also scientifically for understanding wind–wave-ocean interaction physics.

There have been considerable efforts made to understand the characteristics of tropical cyclone-generated surface waves through both measurements and numerical modeling. Several third generation wave models such as WAVEWATCH III [1], the Wave Model (WAM) [2], Simulating Waves Nearshore (SWAN) [3], University of Miami Wave Model (UMWM) [4], etc., have been used to study surface wave responses during hurricanes. The third generation wave models, as well as its predecessors (the first and second generation wave models), are all spectra models. Which means that the model solves the evolution of the surface wave energy spectral instead of the physical form of the surface wave itself, and thus it is also known as non-phase resolving wave model. Although phase resolving wave models have been actively developed during the past two decades, the spectral models are still the only approach capable of solving the temporal and spatial variations in the

oceanic surface gravity wave fields. Thus, it will be the focus of this chapter. The readers interested in phase resolving wave modeling can read the chapter on "High-Resolution Numerical Simulation of Surface Wave Development under the Action of Wind" by Dr. Dmitry Chalikov. In this chapter, we will review the progress on the development of the third generation models, their applications to tropical cyclone wave forecasts, the improvements made to the input and dissipation source function in the model, and the challenges we face in advancing the wave forecast skills.

Since tropical cyclones are driven by enthalpy fluxes from the sea and limited mostly by surface drag, being able to accurately estimate the momentum and heat flux under these extreme wind conditions is critical for tropical cyclone predictions. During the past three decades, more and more scientific evidence has suggested that the air-sea fluxes is closely coupled to the sea state in the ocean [5–9]. With the continuous improvements in surface wave forecasts under tropical cyclone conditions, fully coupled atmosphere-wave-ocean model is suggested for accurate hurricane predictions as well as corresponding ocean responses [10–13]. However, the outcome from the coupled models are mixed, which we will discuss in more details at the end of the chapter.
