Validation and Improvement of the Pan-STARRS Photometric Calibration
  with the Stellar Color Regression Method
  As one of the best ground-based photometric dataset, Pan-STARRS1 (PS1) has
been widely used as the reference to calibrate other surveys. In this work, we
present an independent validation and re-calibration of the PS1 photometry
using spectroscopic data from the LAMOST DR7 and photometric data from the
corrected Gaia EDR3 with the Stellar Color Regression (SCR) method. Using per
band typically a total of 1.5 million LAMOST-PS1-Gaia stars as standards, we
show that the PS1 photometric calibration precisions in the $grizy$ filters are
around $4\sim 5$ mmag when averaged over $20'$ regions. However, significant
large- and small-scale spatial variation of magnitude offset, up to over 1 per
cent, probably caused by the calibration errors in the PS1, are found for all
the $grizy$ filters. The calibration errors in different filters are
un-correlated, and are slightly larger for the $g$ and $y$ filters. We also
detect moderate magnitude-dependent errors (0.005, 0.005, 0.005, 0.004, 0.003
mag per magnitude in the 14 -- 17 magnitude range for the $grizy$ filters,
respectively) in the PS1 photometry by comparing with the Gaia EDR3 and other
catalogs. The errors are likely caused by the systematic uncertainties in the
PSF magnitudes. We provide two-dimensional maps to correct for such magnitude
offsets in the LAMOST footprint at different spatial resolutions from $20'$ to
$160'$. The results demonstrate the power of the SCR method in improving the
calibration precision of wide-field surveys when combined with the LAMOST
spectroscopy and Gaia photometry.
