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.