Assimilation of Simulated Wind Lidar Data with a Kalman Filter

The object of this paper is to present some results obtained with an extended Kalman fitter (EKF). First, a discussion is given of the way that the EKF has been implemented and tested for a global nondivergent barotropic model spectrally truncated at T21. In the present paper, the assimilation experiments focused solely on the time evolution of the forecast error covariances that are influenced by two factors: 1) their time integration performed here with the tangent linear model obtained from a linearization around the true trajectory and 2) the accuracy and distribution of the observations. Data from a simulated radiosonde network have been assimilated over a 24-h period. The results show that even though no model error has been considered, there can be a substantial forecast error growth, especially in regions where the flow is unstable and no data are available. The error growth is attributed to instability processes that are embedded within the complex flow configuration around which the nonlinear model is linearized to obtain the tangent linear model. The impact of different initial conditions for the forecast error covariance is also looked at. In an experiment where the time integration of the forecast error covariance is suppressed, the results show that error growth is suppressed, causing the analysis error variance to differ substantially from the variance field obtained with the EKF. Especially in regions where instability is present and no data are available, this “improved” optimal interpolation considers the forecast to be more accurate than it actually is. In a second set of experiments, a mini-observing system simulation experiment has been conducted for which wind data from a proposed satellite-based lidar instrument have been simulated and added to the radiosonde data of the previous experiments. Two configurations of the instrument have been considered where the satellite is set on a polar orbit, at an altitude of 400 km in the first scenario and 800 km in the second. Compared to the results obtained with the radiosonde data alone, the global data coverage leads to an improvement in the analysis, especially in the Southern Hemisphere. Data being available in the regions of instability, the assimilation is now capable of putting a stop to the unlimited error growth observed in the previous experiments. Due to a degradation of the measurement when the instrument is at an altitude of 800 km, the analysis is more accurate for the 400-km case, but the low-altitude orbit (400 km) leaves holes in the tropical belt that the data assimilation scheme is not quite able to compensate for.