Sample variance in photometric redshift calibration: cosmological biases
  and survey requirements
  We use N-body/photometric galaxy simulations to examine the impact of sample
variance of spectroscopic redshift samples on the accuracy of photometric
redshift (photo-z) determination and calibration of photo-z errors. We estimate
the biases in the cosmological parameter constraints from weak lensing and
derive requirements on the spectroscopic follow-up for three different photo-z
algorithms chosen to broadly span the range of algorithms available. We find
that sample variance is much more relevant for the photo-z error calibration
than for photo-z training, implying that follow-up requirements are similar for
different algorithms. We demonstrate that the spectroscopic sample can be used
for training of photo-zs and error calibration without incurring additional
bias in the cosmological parameters. We provide a guide for observing proposals
for the spectroscopic follow-up to ensure that redshift calibration biases do
not dominate the cosmological parameter error budget. For example, assuming
optimistically (pessimistically) that the weak lensing shear measurements from
the Dark Energy Survey could obtain 1-sigma constraints on the dark energy
equation of state w of 0.035 (0.055), implies a follow-up requirement of 150
(40) patches of sky with a telescope such as Magellan, assuming a 1/8^2 deg
effective field of view and 400 galaxies per patch. Assuming (optimistically) a
VVDS-like spectroscopic completeness with purely random failures, this could be
accomplished with about 75 (20) nights of observation. For more realistic
assumptions regarding spectroscopic completeness, or in the presence of other
sources of systematics not considered here, further degradations to dark energy
constraints are possible. We test several approaches for reducing the
requirements. Abridged
