  The composition of ultra-high energy cosmic rays is still poorly known and
constitutes a very important topic in the field of high-energy astrophysics.
Detection of ultra-high energy cosmic rays is carried out via the extensive air
showers they create after interacting with the atmosphere constituents. The
secondary electrons and positrons within the showers emit a detectable electric
field in the kHz-GHz range. It is possible to use this radio signal for the
estimation of the atmospheric depth of maximal development of the showers
\xmax, with a good accuracy and a duty cycle close to $100\%$. This value of
\xmax\ is strongly correlated to the nature of the primary cosmic ray that
initiated the shower. We show in this paper the importance of using a realistic
atmospheric model in order to correct for systematic errors that can prevent a
correct and unbiased estimation of~\xmax.
