In this paper, we consider the prob

In this paper, we consider the problem of estimating a directional wave spectrum from 3-dimensional displacement data recorded by a wave buoy. We look at some of the limitations of existing methods to extend the "first five" directional moments directly obtainable from such data. With a view to providing the most detailed possible comparisons with directional spectra obtained from numerical models, we propose the use of a "diagnostic" directional spectrum, defined to be the closest possible spectrum to a given model spectrum that satisfies all measured directional moments. This method allows us to quantify the minimum error in a modelled directional spectrum consistent with a buoy record.The new method is tested on a range of artificial test cases, and applied to data obtained from a wave buoy deployment off the New Zealand coast, in conjunction with outputs from a numerical spectral wave model simulation. It is shown that the method can provide satisfactory results in a wide range of conditions. Unlike existing approaches, the proposed method can accommodate sea states with more than two directional peaks, and can assist in removing spurious spectral energy arising from existing methods for estimating directional spectra from buoy data.