  The blazar Mrk 501 is among the brightest X-ray and TeV sources in the sky,
and among the few sources whose spectral energy distributions can be
characterized by current instruments with relatively short observations
(minutes to hours). In 2013, we organized an extensive multi-instrument
campaign including Fermi-LAT, MAGIC, VERITAS, F-GAMMA, Swift, GASP-WEBT, and
other groups and instruments which provided the most detailed temporal and
energy coverage on Mrk 501 to date. This campaign included, for the first time,
observations with the Nuclear Stereoscopic Telescope Array (NuSTAR), a
satellite mission launched in 2012. NuSTAR provides unprecedented sensitivity
in the hard X-ray range 3-79 keV, which, together with very high energy (VHE;
>100 GeV) observations, is crucial to probe the highest energy electrons in Mrk
501. The campaign covered a few day long flaring activity in July 2013 which
could be studied with strictly simultaneous NuSTAR and MAGIC observations. A
large fraction of the MAGIC data during this activity was affected by hazy
atmospheric conditions, due to a sand layer from the Saharan desert. These data
would have been removed in any standard Cherenkov Telescope data analysis.
MAGIC has developed a technique to correct for adverse atmospheric conditions,
making use of information from the LIDAR facility at the MAGIC site, and
applies an event-by-event correction to recover data affected by adverse
weather conditions. This is the first time that LIDAR information has been used
to produce a physics result with Cherenkov Telescope data taken during adverse
atmospheric conditions, and hence sets a precedent for current and future
ground-based gamma-ray instruments. In this contribution we report the
observational results, focusing on the LIDAR-corrected MAGIC data and the
strictly simultaneous NuSTAR and MAGIC/VERITAS data, and discuss the scientific
implications.
