Self-calibration of photometric redshift scatter from DECaLS DR8 power
  spectrum and validation with simulated catalogues
  The uncertainty in the photometric redshift estimation is one of the major
systematics in weak lensing cosmology. The self-calibration method is able to
reduce this systematics without assuming strong priors. We improve the recently
proposed self-calibration algorithm to enhance the stability and robustness
with the noisy measurement. The improved algorithm is tested on the power
spectrum measured from the simulated catalogues constructed according to DECaLS
DR8 photometric catalogue. For the fiducial analysis with 5 equal-width
redshift bins over $0<z<1$ and 6 bands over scales $100 \leqslant \ell<1000$,
we find that the improved algorithm successfully reconstructs the scatter rates
and the auto power spectrum in true redshift bins at the level of $\sim0.015$
and $\sim4.4\%$, respectively. The bias of the mean redshift is reduced by more
than 50 per cent compared to the photo-$z$ without self-calibration. The
reconstructed results of DECaLS DR8 galaxy sample are in line with the
expectations from the simulation validation, and are consistent with the
analysis on correlation functions in a companion paper. The self-calibration
code is publicly available at https://github.com/PengHui-hub/FP-NMF.
