  We study the bias and scatter in mass measurements of galaxy clusters
resulting from fitting a spherically-symmetric Navarro, Frenk & White model to
the reduced tangential shear profile measured in weak lensing observations. The
reduced shear profiles are generated for ~10^4 cluster-sized halos formed in a
LCDM cosmological N-body simulation of a 1 Gpc/h box. In agreement with
previous studies, we find that the scatter in the weak lensing masses derived
using this fitting method has irreducible contributions from the triaxial
shapes of cluster-sized halos and uncorrelated large-scale matter projections
along the line-of-sight. Additionally, we find that correlated large-scale
structure within several virial radii of clusters contributes a smaller, but
nevertheless significant, amount to the scatter. The intrinsic scatter due to
these physical sources is ~20% for massive clusters, and can be as high as ~30%
for group-sized systems. For current, ground-based observations, however, the
total scatter should be dominated by shape noise from the background galaxies
used to measure the shear. Importantly, we find that weak lensing mass
measurements can have a small, ~5%-10%, but non-negligible amount of bias.
Given that weak lensing measurements of cluster masses are a powerful way to
calibrate cluster mass-observable relations for precision cosmological
constraints, we strongly emphasize that a robust calibration of the bias
requires detailed simulations which include more observational effects than we
consider here. Such a calibration exercise needs to be carried out for each
specific weak lensing mass estimation method, as the details of the method
determine in part the expected scatter and bias. We present an iterative method
for estimating mass M500c that can eliminate the bias for analyses of
ground-based data.
