  We examine the projected ability to reconstruct the mass, scattering, and
annihilation cross section of dark matter in the new generation of large
underground detectors, XENON-1T, SuperCDMS, and DarkSide-G2, in combination
with diffuse gamma radiation from expected 15 years of data from Fermi-LAT
observation of 46 local spiral dwarf galaxies and projected CTA sensitivity to
a signal from the Galactic Center. To this end we consider several benchmark
points spanning a wide range of WIMP mass, different annihilation final states,
and large enough event rates to warrant detection in one or more experiments.
As previously shown, below some 100 GeV only direct detection experiments will
in principle be able to reconstruct the WIMP mass well. This may, in case a
signal at Fermi-LAT is also detected, additionally help restricting \sigma v
and the allowed decay branching rates. In the intermediate range between some
100 GeV and up a few hundred GeV, direct and indirect detection experiments can
be used in complementarity to ameliorate the respective determinations, which
in individual experiments can at best be rather poor, thus making the WIMP
reconstruction in this mass range very challenging. At large WIMP mass, ~1 TeV,
CTA will have the ability to reconstruct mass, annihilation cross section, and
the allowed decay branching rates to very good precision for the $\tau^+\tau^-$
or purely leptonic final state, good for the $W^+W^-$ case, and rather poor for
$b\bar{b}$. A substantial improvement can potentially be achieved by reducing
the systematic uncertainties, increasing exposure, or by an additional
measurement at Fermi-LAT that would help reconstruct the annihilation cross
section and the allowed branching fractions to different final states.
