Bayesian based estimation of turbulent flow fields from lidar observations in a conventionally neutral atmospheric boundary layer

In this paper, we consider the reconstruction of 3D turbulent flow fields from a time series of lidar data in a conventionally neutral atmospheric boundary layer (CNBL). For the reconstruction we use the maximum a posteriori estimate of the flow field. This corresponds to an optimization problem, with a cost function that has two contributions; a first term originating from the prior belief on the probability of having a certain turbulent flow field without any observations. Flow field fluctuations are assumed normally distributed and thus statistically fully determined by the mean and two-point covariance of the velocity field. The second term, is related to the likelyhood of the observations, influenced by model and measurement uncertainties. The two-point covariance is computed and found to be significantly altered by the Coriolis force, breaking up longer streamwise velocity streaks and veering spanwise structures by ∼ 45° with respect to the mean flow direction. For the reconstruction, we consider two different scanning modes, a plan position indicator (PPI) mode and a trajectory which is based on a Lissajous curve. For the PPI scanning mode we find that the mean squared error of the reconstructed velocity field is around 10% of the background variance in the scanning plane, and quickly increases outside this region. The Lissajous curve on the other hand attains an average error of 40% over the scanning region, which spans almost the whole BL height.