  We study in detail the photometric redshift requirements needed for
tomographic weak gravitational lensing in order to measure accurately the Dark
Energy equation of state. In particular, we examine how ground-based photometry
(u,g,r,i,z,y) can be complemented by space-based near-infrared (IR) photometry
(J,H), e.g. on board the planned DUNE satellite. Using realistic photometric
redshift simulations and an artificial neural network photo-z method we
evaluate the Figure of Merit for the Dark Energy parameters $(w_0, w_a)$. We
consider a DUNE-like broad optical filter supplemented with ground-based
multi-band optical data from surveys like the Dark Energy Survey, Pan-STARRS
and LSST. We show that the Dark Energy Figure of Merit would improved by a
factor of 1.3 to 1.7 if IR filters are added on board DUNE. Furthermore we show
that with IR data catastrophic photo-z outliers can be removed effectively.
There is an interplay between the choice of filters, the magnitude limits and
the removal of outliers. We draw attention to the dependence of the results on
the galaxy formation scenarios encoded into the mock galaxies, e.g the galaxy
reddening. For example, deep u band data could be as effective as the IR. We
also find that about $10^5-10^6$ spectroscopic redshifts are needed for
calibration of the full survey.
