The JJ-model of the Galactic disc is a semianalytic model based on analytic input functions for the star formation history (SFR), the IMF, the age-velocity dispersion relation (AVR), and the age-metallicty relation (AMR). In the model the vertical density profiles are derived by solving the Poisson and Jeans equations including the gravitational potential of the ISM and the dark matter halo. The comparison with observational data in order to optimize the input parameters is done in a forward procedure. After calculating the model for a chosen parameter set the stellar populations are derived based on PARSEC or MIST stellar libraries. Then an extinction model is applied, the limits and errors of the data as well as the completeness functions of the data samples are applied. The comparison is then done directly in the observational space. Therefore the density and velocity profiles shown here are profiles of the observational samples and not the intrinsic (complete) profiles of the model. For the basic model see Just & Jahreiss (MNRAS 402, 461, 2010) The most updated version is described in detail in Sysoliatina & Just (A&A 647, A39, 2021).

The four fundamental input functions of the disc model. JJ10: Just& Jahreiss 2010, RJ15: Rybizki & Just 2015, R17: Rybizki 2017.
The AMR is derived by fitting the observed metallicity distribution function (MDF) of red clump stars from APOGEE.

MDF comparison of APOGEE data with the disc model for thin (right histograms) and thick (left histograms) disc (discs are separated by the alpha-enhancement).

The identification of the observed cumulative metallicity distribution with the cumulative age distribution of the corresponding populations in the model results in the AMR for thin and thick disc.