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We use N-body-spectro-photometric simulations to investigate the impact ofincompleteness and incorrect redshifts in spectroscopic surveys to photometricredshift training and calibration and the resulting effects on cosmologicalparameter estimation from weak lensing shear-shear correlations. The photometryof the simulations is modeled after the upcoming Dark Energy Survey and thespectroscopy is based on a low/intermediate resolution spectrograph withwavelength coverage of 5500{\AA} < {\lambda} < 9500{\AA}. The principalsystematic errors that such a spectroscopic follow-up encounters areincompleteness (inability to obtain spectroscopic redshifts for certaingalaxies) and wrong redshifts. Encouragingly, we find that a neuralnetwork-based approach can effectively describe the spectroscopicincompleteness in terms of the galaxies' colors, so that the spectroscopicselection can be applied to the photometric sample. Hence, we find thatspectroscopic incompleteness yields no appreciable biases to cosmology,although the statistical constraints degrade somewhat because the photometricsurvey has to be culled to match the spectroscopic selection. Unfortunately,wrong redshifts have a more severe impact: the cosmological biases areintolerable if more than a percent of the spectroscopic redshifts areincorrect. Moreover, we find that incorrect redshifts can also substantiallydegrade the accuracy of training set based photo-z estimators. The main problemis the difficulty of obtaining redshifts, either spectroscopically orphotometrically, for objects at z > 1.3. We discuss several approaches forreducing the cosmological biases, in particular finding that photo-z errorestimators can reduce biases appreciably.

Spectroscopic failures in photometric redshift calibration: cosmological biases and survey requirements