We used the updated [Fe/H] abundances of 168 F-G type dwarfs and calibrated them to a third order polynomial in terms of reduced ultraviolet excess, delta(0.41) defined with ugr data in the SDSS. We estimated the M-g absolute magnitudes for the same stars via the re-reduced Hipparcos parallaxes and calibrated the absolute magnitude offsets, Delta M-g, relative to the intrinsic sequence of Hyades to a third order polynomial in terms of delta(0.41). The ranges of the calibrations are -2 < [Fe/H] <= 0.3 dex and 4 < M-g <= 6 mag. The mean of the residuals and the corresponding standard deviation for the metallicity calibration are 0 and 0.137 mag; while, for the absolute magnitude calibration they are 0 and 0.179 mag, respectively. We applied our procedures to 23,414 dwarf stars in the Galactic field with the Galactic coordinates 85 degrees <= b <= 90 degrees, 0 degrees <= l <= 360 degrees and size 78 deg(2). We estimated absolute magnitude M-g dependent vertical metallicity gradients as a function of vertical distance Z. The gradients are deep in the range of 0 < Z <= 5 kpc, while they are very small positive numbers beyond Z = 5 kpc. All dwarfs with 5 < M-g <= 6 mag are thin-disc stars and their distribution shows a mode at (g - r)(0) approximate to 0.38 mag, while the absolute magnitudes 4 < M-g <= 5 are dominated by thick disc and halo stars, i.e. the apparently bright ones (g(0) <= 18 mag) are thick-disc stars with a mode at (g - r)(0) similar to 0.38 mag, while the halo population is significant in the faint stars (g(0) > 18 mag).