Continuum and line modelling of discs around young stars II. Line diagnostics for GASPS from the DENT grid

Aims. We want to understand the chemistry and physics of discs on the basis of a large unbiased and statistically relevant grid of disc models. One of the main goals is to explore the diagnostic power of various gas emission lines and line ratios for deriving main disc parameters such as the gas mass. Methods. We explored the results of the DENT grid (Disk Evolution with Neat Theory) that consists of 300 000 disc models with 11 free parameters. Through a statistical analysis, we searched for correlations and trends in an effort to find tools for disc diagnostic. Results. All calculated quantities like species masses, temperatures, continuum, and line fluxes differ by several orders of magnitude across the entire parameter space. The broad distribution of these quantities as a function of input parameters shows the limitation of using a prototype T Tauri or Herbig Ae/Be disc model. The statistical analysis of the DENT grid shows that CO gas is rarely the dominant carbon reservoir in discs. Models with large inner radii (10 times the dust condensation radius) and/or shallow surface density gradients lack massive gas-phase water reservoirs. Also, 60% of the discs have gas temperatures averaged over the oxygen mass in the range between 15 and 70 K; the average gas temperatures for CO and O differ by less than a factor two. Our study of the observational diagnostics shows that the [C II] 158 mu m fine structure line flux is very sensitive to the stellar UV flux and presence of a UV excess, and that it traces the outer disc radius (R-out). In the submm, the CO low J rotational lines also trace R-out. Low [O I] 63/145 line ratios (