In this study, global satellite data were analyzed to determine trends in oceanic wind speed and significant wave height over the 33-year period from 1985 to 2018. The analysis uses an extensive database obtained from 31 satellite missions comprising three types of instruments—altimeters, radiometers, and scatterometers. The analysis shows small increases in mean wind speed and significant wave height over this period, with larger increases in extreme conditions (90th percentiles). The largest increases occur in the Southern Ocean. Confidence in the results is strengthened because the wind speed trends are confirmed by all three satellite systems. An extensive set of sensitivity analyses confirms that both the mean and 90th percentile trends are robust, with only small impacts caused by satellite calibration and sampling patterns.

This dataset consists of 33 years (1985 to 2018), of global significant wave height and wind speed obtained from 13 altimeters, namely: GEOSAT , ERS-1 , TOPEX , ERS-2 , GFO , JASON-1 , ENVISAT , JASON-2 , CRYOSAT-2 , HY-2A , SARAL , JASON-3 and SENTINEL-3A . The altimeter data have been calibrated and validated against National Oceanographic Data Center (NODC) buoy data. Differences between altimeter and buoy data as a function of time are investigated for long-term stability. A cross validation between altimeters is also carried out in order to check the stability and consistency of the calibrations developed. Quantile-quantile comparisons between altimeter and buoy data as well as between altimeters are undertaken to test consistency of probability distributions and extreme value performance. The data were binned into 1° by 1° bins globally, to provide convenient access for users to download only the regions of interest. All data are quality controlled. This globally calibrated and cross-validated dataset provides a single point of storage for all altimeter missions in a consistent format.

Linear instability of two-dimensional wave fields and its concurrent evolution in time is here investigated by means of the Alber equation for narrow-banded random surface waves in deep water subject to inhomogeneous disturbances. The probability of freak waves in the context of these simulations is also discussed. The instability is first studied for the symmetric Lorentz spectrum, and continued for the realistic asymmetric Joint North Sea Wave Project (JONSWAP) spectrum of ocean waves with variable directional spreading and steepness. It is found that instability depends on the directional spreading and parameters α and γ of the JONSWAP spectrum, where α and γ are the energy scale and the peak enhancement factor, respectively. Both influence the mean steepness of waves with such a spectrum, although in different ways. Specifically, if the instability stops as a result of the directional spreading, increase of the steepness by increasing α or γ can reactivate it. A criterion for the instability is suggested as a dimensionless 'width parameter', Π. For the unstable conditions, long-time evolution is simulated by integrating the Alber equation numerically. Recurrent evolution is obtained, which is a stochastic counterpart of the Fermi-Pasta-Ulam recurrence obtained for the cubic Schrödinger equation. This recurrence enables us to study the probability of freak waves, and the results are compared to the values given by the Rayleigh distribution. Moreover, it is found that stability-instability transition, the most unstable mode, recurrence duration and freak wave probability depend solely on the dimensionless 'width parameter', Π .