Estimating trajectory uncertainties due to flow dependent errors in the atmospheric analysis

Abstract. The uncertainty of a calculated trajectory is dependent on the uncertainty in the atmospheric analysis. Using the Ensemble Transform method (originally adapted for ensemble forecasting) we sample the analysis uncertainty in order to create an ensemble of analyses where a trajectory is started from each perturbed analysis. This method, called the Ensemble analysis method (EA), is compared to the Initial spread method (IS), where the trajectory receptor point is perturbed in the horizontal and vertical direction to create a set of trajectories used to estimate the trajectory uncertainty. The deviation growth is examined for one summer and one winter month and for 15 different geographical locations. We find up to a 40% increase in trajectory deviation in the mid-latitudes using the EA method. A simple model for trajectory deviation growth speed is set up and validated. It is shown that the EA method result in a faster error growth compared to the IS method. In addition, two case studies are examined to qualitatively illustrate how the flow dependent analysis uncertainty can impact the trajectory calculations. We find a more irregular behavior for the EA trajectories compared to the IS trajectories and a significantly increased uncertainty in the trajectory origin. We conclude that by perturbing the analysis in agreement with the analysis uncertainties the error in backward trajectory calculations can be more consistently estimated.