Catastrophic photometric redshift errors: weak-lensing survey requirements

We study the sensitivity of weak-lensing surveys to the effects of catastrophic redshift errors - cases where the true redshift is mis-estimated by a significant amount. To compute the biases in cosmological parameters, we adopt an efficient linearized analysis where the redshift errors are directly related to shifts in the weak-lensing convergence power spectra. We estimate the number N-spec of unbiased spectroscopic redshifts needed to determine the catastrophic error rate well enough that biases in cosmological parameters are below statistical errors of weak-lensing tomography. While the straightforward estimate of N-spec is similar to 106, we find that using only the photometric redshifts with z less than or similar to 2.5 leads to a drastic reduction in N-spec to similar to 30 000 while negligibly increasing statistical errors in dark-energy parameters. Therefore, the size of the spectroscopic survey needed to control catastrophic errors is similar to that previously deemed necessary to constrain the core of the z(s)-z(p) distribution. We also study the efficacy of the recent proposal to measure redshift errors by cross-correlation between the photo-z and spectroscopic samples. We find that this method requires similar to 10 per cent a priori knowledge of the bias and stochasticity of the outlier population, and is also easily confounded by lensing magnification bias. The cross-correlation method is therefore unlikely to supplant the need for a complete spectroscopic-redshift survey of the source population.