Technical note: Automatic retrieval of wind speed and direction from in situ wave observations of a small buoy

Abstract. This study presents an automatic algorithm for estimating the wind speed and direction from wave observations. The method rests upon the decades old field-validated theory that the energy of a certain part of the wave field is directly proportional to the wind speed. The wind properties were estimated using data from a small wave buoy moored in the sheltered Finnish archipelago and in the exposed Baltic Proper (the Baltic Sea). The estimated wind speed and directions were compared to a nearby weather station (archipelago) and a high-resolution numerical hindcast (Baltic Proper). The algorithm was able to accurately estimate the wind speed (biases 0.3–0.5 m s^-1 and root-mean-square-errors 1.5–1.6 m s^-1). The wind direction was estimated from the mean wave direction of the shortest waves (1.00–1.28 Hz) and was mostly within 20° of the observed wind direction, with some of the differences clearly explained by land and coastlines tainting the measurements. As an additional measure to previously implemented algorithms, the estimated wind direction was used when determining the wind speed, which is expected to add robustness if strong swell is present. The results of the different places were obtained using slightly different equilibrium level constants, α_u, but with otherwise identical algorithm settings, which suggests that the difference is caused by a more fundamental uncertainty of the value of the experimental constant, not the details of the algorithm itself.