Besançon simulation that reproduces stars in the directions on the sky covered by BOSS. The top panel shows the original simulation; the other three panels correspond to the same stars for the BOSS spectrophotometric sample and the SEGUE MSTO and MPMS target-selection cuts. In all cases we considered stars with atmospheric parameters in the ranges of T_eff, log g, and [Fe/H] considered in this work. The plots show [Fe/H] with added noise vs. distance from the Galactic center. Red diamonds represent the resulting median [Fe/H] values (with error bars) after applying our algorithm, considering the distance values from the model. Black dots correspond to the median [Fe/H] results, but considering distances calculated from the stellar parameters and metallicity with added noise. Although uncertainties in distance estimates produce changes in the profile of [Fe/H] vs. r, it can be seen that neither the uncertainties in distance, nor the stellar parameters or the selection criteria considered in each case generate a significant gradient.