Assimilation of buoy and satellite data in wave forecasts with integral control variables

The quality of numerical wave forecasts can be improved significantly by assimilating wave observations prior to the forecast. In the present study a technique for such assimilation is developed that exploits (a) the efficiency of a limited number of integral control variables, and (b) the effectiveness of variational (model-consistent) assimilation. The formal procedure is independent of the type of control variables and of the wave model (moreover, no adjoint wave model is required). In the present study, integral control variables are chosen to represent large-scale errors in the driving wind fields and uncertainties in the wave model. The assimilation technique is validated with observations of the ERS-1 satellite altimeter and two waverider buoys in two consecutive storms in the Norwegian Sea. The assimilation of the observations reduced the errors in the forecasted significant wave height at the buoy locations typically from 25% to 12%. For low-frequency waves the effect of the assimilation is similarly significant at one buoy location but marginal at the other buoy location.