We investigate how damped Lyman alpha absorbers (DLAs) at z similar to 2 - 3, detected in large optical spectroscopic surveys of quasars, trace the population of star-forming galaxies. Building on previous results, we construct a model based on observed and physically motivated scaling relations in order to reproduce the bivariate distributions of metallicity, Z, and H column density, N-HI. Furthermore, the observed impact parameters fOr galaxies associated tti DLAs are in agreement with the model predictions. The model strongly favours a metallieity gradient, which scales with the luminosity of the host galaxy, with a value of gamma* = -0.019 +/- 0,008 dex kpc(-1) for L* galaxies that gets steeper for fainter galaxies. We find that DLAs trace galaxies over a wide range of galaxy luminosities, however, the bulk of the DLA cross-section arises in galaxies with L similar to 0.1 L* at z similar to 2.5 consistent with numerical simulations.