Assimilation of wave data into the wave model WAM using an impulse response function method

A new method for the assimilation of wave data into a third-generation wave model is presented, Deviations between observed and modeled wave spectra are used to derive corrections of the wind field which drives the wave model, The wave field can then be subsequently corrected by a new integration of the wave model with the improved wind field, A basic difficulty of such dynamically consistent wave data assimilations schemes which correct both wind and wave data is the nonsynchronous and nonlocal nature of the wind field corrections: errors observed in the wave spectrum at a given measurement time and location can be produced by errors in the wind field at much earlier times and far distant locations, Formally, these problems can be rigorously resolved by the adjoint modeling method, However, in practice, the adjoint technique requires an order of magnitude more computer time than the integration of the wave model itself, Here an alternative method is developed, The linearized wave model equation which relates small wind to wave spectrum changes is inverted, The central assumption of the inversion is that the wind impact functions representing the impulse response (Green's) function of the wave evolution can be approximated by a S-function, Physically, this implies that the wind field perturbations responsible for observed perturbations in the wave spectrum can be regarded as strongly localized in space and time for any given component of the spectrum, To obtain stable estimates, the corrections for different wave components are averaged over wavenumber clusters representing different wave systems, For cases in which the linear approximation is inadequate, the method can be applied iteratively, Tests of the concept and application of the method for a number of synthetic wind field cases are encouraging,