Model predictions of the DLA metrics EW₂₇₉₆ (top panels) and D-index (bottom panels) as a function of logN(H I) in the two fields J1527 (left column) and J0033 (right column). The vertical dotted line denotes the DLA threshold logN(H I) = 20.3 cm⁻² whilst the horizontal dashed line denote the minimum thresholds for a system to be considered a DLA for that metric; points in the top-right corner of each panel would be considered a DLA. The hollow violins show the distribution of EW₂₇₉₆ and D-index for spaxels (with S/N ≥2 and EW₂₇₉₆ measured at > 2σ significance) within the field. The violins are arbitrarily centered at the median logN(H I) predicted by the modeling, whilst their widths are arbitrarily set for display purposes and do not represent the error in logN(H I). The pink errorbars show the median and 68^th percentile confidence interval of the literature measurements of single quasar sightlines (taken from Rao et al. 2006; Ellison 2006; Berg et al. 2017). The literature values are binned in increments of 0.5 dex in logN(H I). We note that the D-index measurements from the literature are obtained at a different spectral resolutions than the MUSE observations, and thus satisfy a different D-index threshold to be considered a DLA. These literature points are only shown to denote the dependence of D-index on logN(H I) for individual quasar sightlines. The colored symbols represent the range of models within the 32nd and 68th percentiles of the posteriors of the four free parameters $(\sigma ,{\overline{C}}_{\mathrm{frac}},N_{\mathrm{HI},\mathrm{c}},Z_{\mathrm{c}})$, and are color-coded by the covering fraction C_frac. We stress that, while the literature data are obtained from point-source quasar sightlines, our model framework is designed to reproduce the gas absorption properties on extended sources.