There is an offset of 0:263 on the right-hand side of Eq. (1). Several potential processes may cause the offset. First, the statistics includes 73 events, and the limited number of events may be unable to guarantee an accurate empirical formula. Second, we neglected possible changes of the background ionospheric electric field when we calculated the net increase of the ionospheric electric field, which may bring some uncertainty to the result. For example, Burke of the Air Force Research Laboratory (personal communication, 2006) has pointed out evidence for a disturbed E region dynamo in the event studied by Kelley et al. (2003). Third, the offset means that the change of the ionospheric electric field will be zero if the change of the IEF is
smaller than 2:63mVm1; this amount may represent the minimum IEF required to cause observable changes in the ionosphere. We will conduct further studies to determine the cause of the offset in the future. If we do not consider the offset, the penetration electric field in the dayside equatorial ionosphere is 9.6% of the IEF. Burke (2007) uses the Volland–Stern model to predict the penetration electric field and derives a theoretical penetration efficiency of 11.9%. The agreement between the empirical formula and the model prediction is very good.