  Photometric redshifts are a key ingredient in the analysis and interpretation
of large-scale structure (LSS) surveys. The accuracy and precision of these
redshift estimates are directly linked to the constraining power of photometric
surveys. It is hence necessary to define precision and accuracy requirements
for the redshift calibration \revision{to not} infer biased results in the
final analysis. For weak gravitational lensing of the LSS, the photometry
culminates in the estimation of the source redshift distribution (SRD) in each
of the tomographic bins used in the analysis. The focus has been on shifts of
the mean of the SRDs and how well the calibration must be able to recover
those. Since the estimated SRDs are usually given as a normalized histogram
with corresponding errors, it would be advantageous to propagate these
uncertainties accordingly to see whether the requirements of the given survey
are indeed fulfilled. Here we propose the use of functional derivatives to
calculate the sensitivity of the final observables, e.g. the lensing angular
power spectrum, with respect to the SRD at a specific redshift. This allows the
propagation of arbitrarily shaped small perturbations to the SRD, without
having to run the whole analysis pipeline for each realization again. We apply
our method to an EUCLID survey and demonstrate it with SRDs of the KV450 data
set, recovering previous results. Lastly, we note that the moments of the SRD
of order larger than two will probably not be relevant when propagating
redshift uncertainties in cosmic shear analysis.
