  We consider the bias introduced by a spatially-varying multiplicative shear
bias (m-bias) on tomographic cosmic shear angular power spectra. To compute the
bias in the power spectra, we estimate the mode-coupling matrix associated with
an m-bias map using a computationally-efficient pseudo-Cl method. This allows
us to consider the effect of the m-bias to high l. We then conduct a Fisher
matrix analysis to forecast resulting biases in cosmological parameters. For a
Euclid-like survey with a spatially-varying m-bias, with zero mean and rms of
0.01, we find that parameter biases reach a maximum of ~10% of the expected
statistical error, if multipoles up to l_max = 5000 are included. We conclude
that the effect of the spatially-varying m-bias may be a sub-dominant but
potentially non-negligible contribution to the error budget in forthcoming weak
lensing surveys. We also investigate the dependence of parameter biases on the
amplitude and angular scale of spatial variations of the m-bias field, and
conclude that requirements should be placed on the rms of spatial variations of
the m-bias, in addition to any requirement on the mean value. We find that, for
a Euclid-like survey, biases generally exceed ~30% of the statistical error for
m-bias rms 0.02 - 0.03 and can exceed the statistical error for rms ~0.04 -
0.05. This allows requirements to be set on the permissible amplitude of
spatial variations of the m-bias that will arise due to systematics in
forthcoming weak lensing measurements.
