  We investigate the reconstruction capabilities of Dark Matter mass and
spin-independent cross-section from future ton-scale direct detection
experiments using germanium, xenon or argon as targets. Adopting realistic
values for the exposure, energy threshold and resolution of Dark Matter
experiments which will come online within 5 to 10 years, the degree of
complementarity between different targets is quantified. We investigate how the
uncertainty in the astrophysical parameters controlling the local Dark Matter
density and velocity distribution affects the reconstruction. For a 50 GeV
WIMP, astrophysical uncertainties degrade the accuracy in the mass
reconstruction by up to a factor of $\sim 4$ for xenon and germanium, compared
to the case when astrophysical quantities are fixed. However, combination of
argon, germanium and xenon data increases the constraining power by a factor of
$\sim 2$ compared to germanium or xenon alone. We show that future direct
detection experiments can achieve self-calibration of some astrophysical
parameters, and they will be able to constrain the WIMP mass with only very
weak external astrophysical constraints.
