Distribution of extinction and H₂O ice column densities derived from the global fits to the composite spectra. The two extinction estimates, $A_K^{\mathrm{M}\mathrm{I}\mathrm{R}}$ and A^*_K, come from our composite spectra but rely on different wavelength regimes: the mid-IR spectral shape for $A_K^{\mathrm{M}\mathrm{I}\mathrm{R}}$ and near-IR template matching for A^*_K. Objects with large solid CH₃OH column densities (N > 3 × 10¹⁷ cm⁻²; see below) are marked with open blue circles. The dashed line in the top panel indicates unity. For comparison, the solid lines in the middle and bottom panels show the empirical relation derived for the Taurus molecular cloud by Whittet et al. (2001), shifted horizontally by A_K = 2.2 mag to account for the average foreground extinction towards the CMZ.