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Wide-field imaging surveys such as the Dark Energy Survey (DES) rely oncoarse measurements of spectral energy distributions in a few filters toestimate the redshift distribution of source galaxies. In this regime, samplevariance, shot noise, and selection effects limit the attainable accuracy ofredshift calibration and thus of cosmological constraints. We present a newmethod to combine wide-field, few-filter measurements with catalogs from deepfields with additional filters and sufficiently low photometric noise to breakdegeneracies in photometric redshifts. The multi-band deep field is used as anintermediary between wide-field observations and accurate redshifts, greatlyreducing sample variance, shot noise, and selection effects. Our implementationof the method uses self-organizing maps to group galaxies into phenotypes basedon their observed fluxes, and is tested using a mock DES catalog created fromN-body simulations. It yields a typical uncertainty on the mean redshift ineach of five tomographic bins for an idealized simulation of the DES Year 3weak-lensing tomographic analysis of $\sigma_{\Delta z} = 0.007$, which is a60% improvement compared to the Year 1 analysis. Although the implementation ofthe method is tailored to DES, its formalism can be applied to other largephotometric surveys with a similar observing strategy.

Phenotypic redshifts with self-organizing maps: A novel method to characterize redshift distributions of source galaxies for weak lensing