Detailed comparison of Milky Way models based on stellar population
  synthesis and SDSS star counts at the north Galactic pole
  We test the ability of the TRILEGAL and Besancon models to reproduce the CMD
of SDSS data at the north Galactic pole (NGP). We show that a Hess diagram
analysis of colour-magnitude diagrams is much more powerful than luminosity
functions (LFs) in determining the Milky Way structure. We derive a
best-fitting TRILEGAL model to simulate the NGP field in the (g-r, g) CMD of
SDSS filters via Hess diagrams. For the Besancon model, we simulate the LFs and
Hess diagrams in all SDSS filters. We use a chi2 analysis and determine the
median of the relative deviations in the Hess diagrams to quantify the quality
of the fits by the TRILEGAL models and the Besancon model in comparison and
compare this with the Just-Jahreiss model. The input isochrones in the
colour-absolute magnitude diagrams of the thick disc and halo are tested via
the observed fiducial isochrones of globular clusters (GCs). We find that the
default parameter set lacking a thick disc component gives the best
representation of the LF in TRILEGAL. The Hess diagram reveals that a
metal-poor thick disc is needed. In the Hess diagram, the median relative
deviation of the TRILEGAL model and the SDSS data amounts to 25 percent,
whereas for the Just-Jahreiss model the deviation is only 5.6 percent. The
isochrone analysis shows that the representation of the MS of (at least
metal-poor) stellar populations in the SDSS system is reliable. In contrast,
the RGBs fail to match the observed fiducial sequences of GCs. The Besancon
model shows a similar median relative deviation of 26 percent in (g-r, g). In
the u band, the deviations are larger. There are significant offsets between
the isochrone set used in the Besancon model and the observed fiducial
isochrones. In contrast to Hess diagrams, LFs are insensitive to the detailed
structure of the Milky Way components due to the extended spatial distribution
along the line of sight.
