Two Methods for Data Assimilation of Wind Direction

Wind direction observations are instrumental weather records that hold promise for improving historical weather reanalyses and extending them deeper into the past. Two methods are developed for assimilating wind direction observations. The first uses a linear observation model with Gaussian additive error, and is thus amenable to use in standard EnKF and variational frameworks. The second is nonlinear and non-Gaussian, and is based on a two-step approach for sampling from the Bayesian posterior. Both methods are tested in the context of an idealized two-dimensional model of turbulent fluid dynamics. The nonlinear, non-Gaussian method assimilating only wind direction observations performs as well as an EnKF assimilating only pressure observations, whereas the first method based on the linear model provides no benefit when assimilating only wind direction observations. The method based on the linear model performs well when paired with other observations, e.g. of pressure, since it performs best when the forecast of wind direction is not far from correct.