Wave steepness is presented as an extension and a valuable add-on to the conventional set of sea state parameters retrieved from satellite altimetry data. Following physical model based on recent advances of weak turbulence theory wave steepness is estimated from directly measured spatial gradient of wave height. In this way the method works with altimetry trajectories rather than with point-wise data. Moreover, in contrast to widely used parametric models this approach provides us with instantaneous values of wave steepness and period. Relevance of single-track estimates of wave steepness (period) is shown for wave climate studies and confirmed by a simple probabilistic model. The approach is verified via comparison against buoy and satellite data including crossover points for standard 1 second data of Ku-band altimeters. High quality of the physical model and robustness of the parametric ones are examined in terms of global wave statistics. Prospects and relevance of both approaches in the ocean wave climate studies are discussed. KEYWORDS: Wave turbulence; satellite altimetry; wave steepness; parametric and physical models of wave period.