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We perform Lyman-$\alpha$ (Ly$\alpha$) Monte-Carlo radiative transfercalculations on a suite of $2500$ models of multiphase, outflowing media, whichare characterized by $14$ parameters. We focus on the Ly$\alpha$ spectraemerging from these media, and investigate which properties are dominant inshaping the emerging Ly$\alpha$ profile. Multiphase models give rise to a widevariety of emerging spectra, including single, double and triple peakedspectra. We find that the dominant parameters in shaping the spectra include(i) the cloud covering factor, $f_c$, in agreement with earlier studies, and(ii) the temperature and number density of residual HI in the hot ionizedmedium. We attempt to reproduce spectra emerging from multiphase models with`shell models' which are commonly used to fit observed Ly$\alpha$ spectra, andinvestigate the connection between shell-model parameters and the physicalparameters of the clumpy media. In shell models, the neutral hydrogen contentof the shell is one of the key parameters controlling Ly$\alpha$ radiativetransfer. Because Ly$\alpha$ spectra emerging from multi-phase media dependmuch less on the neutral hydrogen content of the clumps, the shell modelparameters such as HI column density (but also shell velocity and dust content)are generally not well matched to the associated physical parameters of clumpymedia.

Ly$\alpha$ Spectra from Multiphase Outflows, and their Connection to Shell Models