In this paper, a new methodology is proposed for the computation of Background Errors in wave data assimilation systems. Background errors define the spatial influence of an observation in the model domain. Since at present the directional wave spectrum is the fundamental variable of both state-of-the-art numerical models and most modern instrumentation, this is at the core of the proposed methodology. The advantage of the spectral approach is that the wave spectrum contains detailed information of the different wave systems and physical processes at work (e.g., wind-sea or swells). These systems have different origins and may be driven by different mechanisms, having therefore different spatial structures, length scales, and sensitivity to local wind conditions. The presented method enables making consistent and specific corrections to each component of the spectrum, in time and space. The innovations presented here require an integral look at the data assimilation algorithm for which a suitable scheme is also proposed. Examples of computed background errors are presented for shelf and oceanic basins showing the spatial structures of the different wave systems active in these areas.