  Context. We are operating an elastic LIDAR for the monitoring of atmospheric
conditions during regular observations of the MAGIC Telescopes. Aims. We
present and evaluate methods to convert aerosol extinction profiles, obtained
with the LIDAR, into corrections of the reconstructed gamma-ray event energy
and Instrument Response Functions of Imaging Atmospheric Cherenkov Telescopes.
Methods. We assess the performance of these correction schemes with almost
seven years of Crab Nebula data taken by the MAGIC Telescopes under various
zenith angles and different aerosol extinction scenarios of Cherenkov light.
Results. The methods enable the reconstruction of data taken under non-optimal
atmospheric conditions with aerosol transmissions down to around 0.65 with
systematic uncertainties comparable to those for data taken under optimal
conditions. For the first time, the correction of data affected by clouds has
been included in the assessment. The data can also be corrected when the
transmission is lower than 0.65, but the results are less accurate and suffer
from larger systematics.
