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 c
osmological 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
In Lima et al. 2008 we presented a new method for estimating the redshift distribution, N(z), of a photometric galaxy sample, using photometric observables and weighted sampling from a spectroscopic subsample of the data. In this paper, we extend thi
s method and explore various applications of it, using both simulations of and real data from the SDSS. In addition to estimating the redshift distribution for an entire sample, the weighting method enables accurate estimates of the redshift probability distribution, p(z), for each galaxy in a photometric sample. Use of p(z) in cosmological analyses can substantially reduce biases associated with traditional photometric redshifts, in which a single redshift estimate is associated with each galaxy. The weighting procedure also naturally indicates which galaxies in the photometric sample are expected to have accurate redshift estimates, namely those that lie in regions of photometric-observable space that are well sampled by the spectroscopic subsample. In addition to providing a method that has some advantages over standard photo-z estimates, the weights method can also be used in conjunction with photo-z estimates, e.g., by providing improved estimation of N(z) via deconvolution of N(photo-z) and improved estimates of photo-z scatter and bias. We present a publicly available p(z) catalog for ~78 million SDSS DR7 galaxies.
