In recent years, since the number of aircraft flights above Japan is increasing, avoiding turbulences by forecasts with high resolution of time and space is important to keep the flights safe and comfort. The present research therefore considered usability of five indices in order to predict clear air turbulence (CAT) that is difficult to be observed. Daily prediction experiments by a numerical model Cloud Resolving Storm Simulator (CReSS) are used because CReSS can simulate weather related to CAT with higher resolution in both time and space than the model used by Japan Meteorological Agency (JMA). As a result, for the CAT cases treated in the present research, turbulence kinetic energy and Richardson number are most suitable to predict CAT, horizontal temperature gradient is next suitable, and two- and three-dimensional frontogenesis functions are not appropriate. The future research should develop and improve a forecasting system of CAT by collecting more cases to investigate the best suitable indices using CReSS.