and the observed densities of molecular (top), atomic (middle) and ionized (bottom) Hydrogen. The observational data are represented as dashed lines, with the grey areas delimited by dotted lines corresponding to 20 per cent error bands. Black solid lines display the results of the model with $n_0=1$ cm$^{-3}$, $B_0=5~\mu$G, and stellar density (\[eqRhoStar\]). A model with $n_0=0.75$ cm$^{-3}$, $B_0=4~\mu$G, $\kappa=0.5$, and $N({\rm H})=10^{22}$ cm$^{-2}$ is plotted in solid blue (see text for details). []{data-label="figObs"}](figs/Fig8.eps){width="50.00000%"}

Our single-phase model can only describe the average properties of the ISM. More precisely, it should be able to predict the density of molecular, atomic, and ionized Hydrogen as a function of the distance $z$ from the mid plane of the Galaxy, averaged over some scale larger than the typical size of the inhomogeneities.

Much observational work has been devoted to the determination of the average vertical structure of the Milky Way ISM near the solar neighbourhood. For the ionized component, we will adopt the distribution derived by @Reynolds91 $$\frac{ n_{\rm HII}(z) }{\rm cm^{-3}}
= 0.015 \,\exp\! \left(\! -\frac{z}{\rm 70~pc}  \right)
+ 0.0025\,\exp\! \left(\! -\frac{z}{\rm 900~pc} \right)$$ from pulsar dispersion measures, where the first term represents the contribution from discrete [Hii]{} regions near the Galactic plane, 