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Weak gravitational lensing surveys using photometric redshifts can have theircosmological constraints severely degraded by errors in the photo-z scale. Weexplore the cosmological degradation vs the size of the spectroscopic surveyrequired to calibrate the photo-z probability distribution. Previous work hasassumed a simple Gaussian distribution of photo-z errors; here we describe amethod for constraining an arbitrary parametric photo-z error model. As anexample we allow the photo-z probability distribution to be the sum of $N_g$Gaussians. To limit cosmological degradation to a fixed level, photo-z modelswith multiple Gaussians require up to 5 times larger calibration sample thanone would estimate from assuming a single-Gaussian model. This degradationsaturates at $N_g\approx 4$. Assuming a single Gaussian when the photo-zdistribution has multiple parameters underestimates cosmological parameteruncertainties by up to 35%. The size of required calibration sample alsodepends upon the shape of the fiducial distribution, even when the RMS photo-zerror is held fixed. The required calibration sample size varies up to a factorof 40 among the fiducial models studied, but this is reduced to a factor of afew if the photo-z parameters are forced to be slowly varying with redshift.Finally we show that the size of the required calibration sample can besubstantially reduced by optimizing its redshift distribution. We hope thisstudy will help stimulate work on better understanding of photo-z errors.

Size of spectroscopic calibration samples for cosmic shear photometric redshifts