The spectral wave model WAVEWATCH III is extended from the windsea and swell band to lower frequencies, in order to represent free waves in the infragravity (IG) wave band. This extension is based on an empirical source of IG energy, which is defined along shorelines from the signi cant wave height and a mean period. The empirical proportionality factor is is found to reproduce accurately the variations of free IG wave energy in coastal areas, where it was calibrated, and also has a good skill at global scales. In the open ocean, the model is particularly verified for frequencies in the range 5 to 14 mHz for which ocean bottom records are sensitive to the IG signal. The model captures between 30 and 80% of the variance in IG wave heights, depending on location, and reproduces the mean IG energies within 50%. Where the model reproduces best the IG variability, it can be used to fill in the gaps between recording stations, providing a first view of the global IG wave field. Our first application is the estimation of the surface gravity wave contribution to the surface elevation spectra that will be measured by the Surface Water Ocean Topography (SWOT) satellite mission. The actual contribution of IG waves on measured along-track wavenumber spectra varies with the cross-track averaging method. Typically, the strongest IG signal is expected to occur for wavelengths between 2 and 10 km. For a given region, the spectral level at 10 km wavelength are not very sensitive to the local depth in the range 200 to 5000 m. At this wavelength, and on the east side of allmid-latitude ocean basins, the median spectral density associated to free IG waves is of the order of 0.4 cm 2/(cycle/km), equal to the expected quasi-geostrophic signature of surface currents. IG spectra rise above 4 times this level for 16% of the time. Even at 20 km wavelength, spectral levels above 1 cm 2/(cycle/km) are likely to occur more that 10% of the time for some oceanic regions.