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Chemodynamical evolution of the Milky Way disk II: Variations with Galactic radius and height above the disk plane

[Abridge] In the first paper of this series (paper I) we presented a new approach for studying the chemo-odynamical evolution in disk galaxies, focusing on the Milky Way. Here we extend these results to different distances from the Galactic center, looking for variations of observables that can be related to on-going and future spectroscopic surveys. By separating the effects of kinematic heating and radial migration, we show that migration is much more important, even for the oldest and hottest stellar population. The distributions of stellar birth guiding radii and final guiding radii (signifying contamination from migration and heating, respectively) widen with increasing distance from the Galactic center. As a result, the slope in the age-metallicity relation flattens significantly at Galactic radii larger than solar. The radial metallicity and [Mg/Fe] gradients in our model show significant variations with height above the plane due to changes in the mixture of stellar ages. An inversion in the radial metallicity gradient is found from negative to weakly positive (at r<10 kpc), and from positive to negative for the [Mg/Fe] gradient, with increasing distance from the disk plane. We relate this to the combined effect of (i) the predominance of young stars close to the disk plane and old stars away from it, (ii) the more concentrated older stellar component, and (iii) the flaring of mono-age disk populations. We also investigate the effect of recycled gas flows on the mean [Fe/H] and find that in the region 4<r<12 kpc the introduced errors are less than 0.05-0.1 dex, related to the fact that inward and outward flows mostly cancel in that radial range. We show that radial migration cannot compete with the inside-out formation of the disk, exposed by the more centrally concentrated older disk populations, and consistent with recent observations.