We also show the simulation results of penetration electric field from a combined numerical model of coupled thermosphere–ionosphere–plasmasphere–electrodynamics (CTIPe) model (Millward et al., 2001; Fuller-Rowell et al., 2002) and Rice Convection Model (RCM) (Wolf, 1983; Toffoletto et al., 2003) in a storm case, as reported in Maruyama et al. (2005, 2007), and compare the empirical formula with the measured and simulated penetration electric fields. 2. Results 2.1. Observations