Examples of N₂H⁺ spectra from the MHD model where the ratio of optical depths derived from noiseless and noisy spectra ranges from ~0.1 (frame a) to ~10 (frame j). The black histograms show the observed spectra that contain 3% relative noise. The fits to noiseless and noisy spectra are plotted with dashed red and dotted cyan lines, respectively. The T_ex and τ estimates from the fits are listed in the frames in the same colours.