  Cosmic-ray particles impinging on the atmosphere induce high-energy particle
cascades in air, an Extensive Air Shower (EAS), emitting coherent radio
emission. This emission is affected by the presence of strong electric fields
during thunderstorm conditions. To reconstruct the atmospheric electric field
from the measured radio footprint of the EAS we use an analytic model for the
calculation of the radio emission, MGMR3D. In this work we make an extensive
comparison between the results of a microscopic model for radio emission,
CoREAS, to obtain an improved parametrization for MGMR3D in the presence of
atmospheric electric fields, as well as confidence intervals. The approach to
extract the electric field structure is applied successfully to an event with a
complicated radio footprint measured by LOFAR during thunderstorm conditions.
This shows that, with the improved parametrization, MGMR3D can be used to
extract the structure of the atmospheric electric field.
