We numerically investigated possibility of a data assimilation methodology for reproduction of Clear Air Turbulence (CAT) observed by LIDAR. The three-dimensional vortices induced by the shear layer instability were predicted by combining pseudo Lidar observation and the 6th-order accuracy numerical simulation based on the Euler equations by using the data assimilation. The assimilation performance was verified in identical-twin experiments; the true state and the observation data were generated artificially. We considered three methods for pseudo observation to verify the sensitivity of observed variables to prediction accuracy: observing only horizontal velocity, horizontal and vertical velocity components on the flight path, and wind speeds projected on the LIDAR’s line of sight. The results of the identical-twin experiments indicated that observing u and vertical wind components reduced the forecast error, and the data assimilation was able to restore the information of these two essential wind components from a wind speed data observed by LIDAR when its line of sight was inclined in the z-direction.