5.5. Correlated Velocity Structure: Mesoturbulence
In a series of papers, Levshakov, Kegel & Takahara , ,  have demonstrated a viable alternative model for the velocity distribution.
In most papers, absorption lines are modelled by Voigt profiles. The line width is the sum of the thermal broadening, turbulent broadening, and the instrumental resolution, each of which is assumed to be Gaussian. When an absorption line is more complex than a single Voigt, gas centered at other velocities is added to the model. As the signal to noise increases, we typically see that more velocity components are required to fit the absorption. Each component has its own physical parameters: central velocity, velocity dispersion (rms of thermal and turbulent broadening), ionization, column densities and elemental abundances. Prior to its use with quasars, this fitting method was developed for the ISM, where it represents gas in spatially separate clouds.
Levshakov and co-workers have proposed a different type of model, the mesoturbulent model, in which the gas velocities are correlated, and the column density per unit velocity is varied to fit the absorption line profiles. They assume that the absorption comes from a single region in space, and they calculate the distribution of the gas density down the line of sight. To simplify the calculations, in early Reverse Monte-Carlo models, they assumed that the gas temperature and density were constant along the line of sight, which is not appropriate if there are separate discrete clouds of gas with differing physical conditions.
The effects of mesoturbulence on the D/H absorbers towards Q1937-1009 , Q1009+2956  and Q1718+4807  were examined in detail using this early model. In the first paper they allowed the NHI to vary far from the observed value (NHI =7.27 x 1017 ), and consequently they found a variety of NHI , but when the NHI is held within range, the D/H is 3.3 x 10-5, exactly the same as with the usual model . For the second quasar, the D/H obtained is again similar to that obtained in the usual way. The results are the same as with the usual model in part because the H and D line widths are dominated by thermal and not turbulent motions, and for these two quasars the total NHI is not affected, because it is measured from the Lyman continuum absorption, which does not depend on velocity.
Recently they have developed a new model called MCI ,  appropriate for absorption systems which sample different densities. They now use H I and metal ions to solve for two random fields which vary independently along the line of sight: the gas density and the peculiar velocities. This model allows the temperature, ionization and density to all vary along the line of sight.
The mesoturbulent model of Levshakov et al.  and the microturbulent Voigt model give the same column densities and other parameters when one of the following conditions apply: 1) The line of sight through the absorbing gas traverses many correlation lengths. 2) If each velocity in a spectrum corresponds to gas at a unique spatial coordinate. 3) The absorbing regions are nearly homogeneous, with at most small fluctuations in density or peculiar velocities, or equivalently, thermal broadening larger than the turbulent broadening.
The Voigt model could give the wrong result when two or more regions along the line of sight, with differing physical conditions, give absorption at the same velocity. A remarkable and unexpected example of this was reported by Kirkman & Tytler  who found a Lyman limit system which comprised five main velocity components. Each component showed both C IV and O VI absorption at about the same velocity, but in each of the five components, the O VI had a larger velocity dispersion, and hence came from different gas than the C IV. While this LLS is much more complex than those in which we can see D, this type of velocity structure could be common.
All authors other than Levshakov and collaborators use standard Voigt fitting methods to determine column densities, for several reasons. The Voigt method was used, with no well known problems, for many decades to analyze absorption in the ISM, and the ISM is well modeled by discrete clouds separated in space. The Levshakov et al.  methods are more complex. In early implementations, Levshokov et al.  made assumptions which are not suitable for all absorbers. The current methods require weeks of computer time, and in many cases the two methods have given the same results.
We conclude that, when we have sufficient data, velocity structure is not a problem for the absorbers like those now used for D/H.