  The atmospheric electric fields in thunderclouds have been shown to
significantly modify the intensity and polarization patterns of the radio
footprint of cosmic-ray-induced extensive air showers. Simulations indicated a
very non-linear dependence of the signal strength in the frequency window of
30-80 MHz on the magnitude of the atmospheric electric field. In this work we
present an explanation of this dependence based on Monte-Carlo simulations,
supported by arguments based on electron dynamics in air showers and expressed
in terms of a simplified model. We show that by extending the frequency window
to lower frequencies additional sensitivity to the atmospheric electric field
is obtained.
