Vertical and radial metallicity gradients in high latitude galactic fields with SDSS

We used the ugr magnitudes of 1437467 F-G type main-sequence stars with metal abundance $-2?[\mathrm{Fe}/\mathrm{H}]?+0.2$ dex and estimated radial and vertical metallicity gradients for high Galactic-latitude fields, $50°<b?90°$ and $0°<l?360°$, of the Milky Way Galaxy. The radial metallicity gradient $d[\mathrm{Fe}/\mathrm{H}]/\mathit{dR}=-0.042\pm 0.011$ dex kpc^?1 estimated for the stars with $1.31<z\le 1.74$ kpc is attributed to the thin-disc population. While, the radial gradients evaluated for stars at higher vertical distances are close to zero indicating that the thick disc and halo have not undergone a radial collapse phase at least at high Galactic latitudes. The vertical metallicity gradients estimated for stars with three different Galactic latitudes, $50°<b?65°,65°<b?80°$ and $80°<b?90°$ do not show a strong indication for Galactic latitude dependence of our gradients. The thin disc, $0.5<z?2$ kpc, with a vertical metallicity gradient $d\left[\mathrm{Fe}/\mathrm{H}\right]/\mathit{dz}=-0.308\pm 0.018$ dex kpc^?1, is dominant only in galactocentric distance interval $6<R?10$ kpc, while the thick disc ($2<z?5$ kpc) could be observed in the intervals $6<R?10$ and $10<R?15$ kpc with compatible vertical metallicity gradients, i.e. $d\left[\mathrm{Fe}/\mathrm{H}\right]/\mathit{dz}=-0.164\pm 0.014$ dex kpc^?1 and $d\left[\mathrm{Fe}/\mathrm{H}\right]/\mathit{dz}=-0.172\pm 0.016$ dex kpc^?1. Five vertical metallicity gradients are estimated for the halo ($z>5$ kpc) in three galactocentric distance intervals, $6<R?10,10<R?15$ and $15<R?20$ kpc. The first one corresponding to the interval $6<R?10$ kpc is equal to $d\left[\mathrm{Fe}/\mathrm{H}\right]/\mathit{dz}=-0.023\pm 0.006$ dex kpc^?1, while the others at larger galactocentric distances are close to zero. We derived synthetic vertical metallicity gradients for 2,230,167 stars and compared them with the observed ones. There is a good agreement between the two sets of vertical metallicity gradients for the thin disc, while they are different for the thick disc. For the halo, the conspicuous difference corresponds to the galactocentric distance interval $6<R?10$ kpc, while they are compatible at higher galactocentric distance intervals.