  Calibrating the redshift distributions of photometric galaxy samples is
essential in weak lensing studies. The self-calibration method combines angular
auto- and cross-correlations between galaxies in multiple photometric redshift
(photo-$z$) bins to reconstruct the scattering rates matrix between redshift
bins. In this paper, we test a recently proposed self-calibration algorithm
using the DECaLS Data Release 9 and investigate to what extent the scattering
rates are determined. We first mitigate the spurious angular correlations due
to imaging systematics by a machine learning based method. We then improve the
algorithm for $\chi^2$ minimization and error estimation. Finally, we solve for
the scattering matrices, carry out a series of consistency tests and find
reasonable agreements: (1) finer photo-$z$ bins return a high-resolution
scattering matrix, and it is broadly consistent with the low-resolution matrix
from wider bins; (2) the scattering matrix from the Northern Galactic Cap is
almost identical to that from Southern Galactic Cap; (3) the scattering
matrices are in reasonable agreement with those constructed from the power
spectrum and the weighted spectroscopic subsample. We also evaluate the impact
of cosmic magnification. Although it changes little the diagonal elements of
the scattering matrix, it affects the off-diagonals significantly. The
scattering matrix also shows some dependence on scale cut of input
correlations, which may be related to a known numerical degeneracy between
certain scattering pairs. This work demonstrates the feasibility of the
self-calibration method in real data and provides a practical alternative to
calibrate the redshift distributions of photometric samples.
