where DEyðionoÞ and DEyðIEFÞ are the net increases of
the ionospheric and interplanetary electric fields,
respectively, and measured in mVm1. 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.