Computational fluid dynamics (CFD) simulation of clear air turbulence (CAT) is conducted by coupling numerical weather simulation and large eddy simulation (LES). Initial and boundary conditions of the LES are defined base on Japan Meteorological Agency's Non-Hydrostatic Model (JMA-NHM) with three levels of downscaling. The target location and time of JMA-NHM are determined by 40 cases of the flight data that encountered CAT. With a goal of identifying the important turbulence indices, self-organizing map (SOM) is applied to the results of CFD simulation. The results of the SOM showed that CAT can be categorized into two types. One is CAT associated with Richardson number (Ri) and Scorer parameter (SP), which indicate atmospheric stability, and vertical wind shear (VWS), vertical gradient of horizontal wind (dVdz), energy dissipation rate (EDR) and wind direction (WD). Another is CAT cannot be detected by existing indices. Therefore, visualization of flow and turbulence index fields as well as information visualization were conducted for the latter type of CAT. In the result, we found that the unpredictable CAT is associated with the inflection point of vertical profiles concerning wind speed and direction.