  The reconstruction of the energy and the depth of maximum $X_{\rm max}$ of an
extensive air shower depends on the multiple scattering of fluorescence photons
in the atmosphere. In this work, we explain how atmospheric aerosols, and
especially their size, scatter the fluorescence photons during their
propagation. Using a Monte Carlo simulation for the scattering of light, the
dependence on the aerosol conditions of the multiple scattered light
contribution to the recorded signal is fully parameterised. A clear dependence
on the aerosol size is proposed for the first time. Finally, using this new
parameterisation, the effect of atmospheric aerosols on the energy and on the
$X_{\rm max}$ reconstructions is presented for a vertical extensive air shower
observed by a ground-based detector at $30~$km: for typical aerosol conditions,
multiple scattering leads to a systematic over-estimation of $5\pm1.5\%$ for
the energy and $4.0\pm 1.5~$g/cm$^2$ for the $X_{\rm max}$, where the
uncertainties refer to a variation of the aerosol size.
