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We test the ability of the TRILEGAL and Besancon models to reproduce the CMDof SDSS data at the north Galactic pole (NGP). We show that a Hess diagramanalysis of colour-magnitude diagrams is much more powerful than luminosityfunctions (LFs) in determining the Milky Way structure. We derive abest-fitting TRILEGAL model to simulate the NGP field in the (g-r, g) CMD ofSDSS filters via Hess diagrams. For the Besancon model, we simulate the LFs andHess diagrams in all SDSS filters. We use a chi2 analysis and determine themedian of the relative deviations in the Hess diagrams to quantify the qualityof the fits by the TRILEGAL models and the Besancon model in comparison andcompare this with the Just-Jahreiss model. The input isochrones in thecolour-absolute magnitude diagrams of the thick disc and halo are tested viathe observed fiducial isochrones of globular clusters (GCs). We find that thedefault parameter set lacking a thick disc component gives the bestrepresentation of the LF in TRILEGAL. The Hess diagram reveals that ametal-poor thick disc is needed. In the Hess diagram, the median relativedeviation 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. Theisochrone analysis shows that the representation of the MS of (at leastmetal-poor) stellar populations in the SDSS system is reliable. In contrast,the RGBs fail to match the observed fiducial sequences of GCs. The Besanconmodel shows a similar median relative deviation of 26 percent in (g-r, g). Inthe u band, the deviations are larger. There are significant offsets betweenthe isochrone set used in the Besancon model and the observed fiducialisochrones. In contrast to Hess diagrams, LFs are insensitive to the detailedstructure of the Milky Way components due to the extended spatial distributionalong the line of sight.

Detailed comparison of Milky Way models based on stellar population synthesis and SDSS star counts at the north Galactic pole