We present the calibration of the [$alpha/$Fe] element in terms of ultra-violet excess for 465 dwarf stars with spectral type F0-K2. We used a single calibration, fitted to a third degree polynomial with a square of the correlation coefficient 0.74 and standard deviation 0.05 mag, for all stars due to their small colour range, $0.1<(g-r)_0leq 0.6$ mag, and high frequency in the blueward of the spectrum which minimize the guillotine effect. Our calibration provides [$alpha/$Fe] elements in the range $(-0.05, 0.35]$ dex. We applied the procedure to a high-latitude field, $85^circ leq b leq 90^circ$ with size 78 deg$^2$ and we could estimate the [$alpha/$Fe] elements of 23,414 dwarf stars which occupy a Galactic region up to a vertical distance of $z=9$ kpc. We could detect a small positive gradient, $d[alpha/{rm Fe}]/dz=+0.032 pm0.002$ dex kpc$^{-1}$, for the range $0<z<5$ kpc, while the distribution of the [$alpha/$Fe] element is flat for further $z$ distances.
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