  Outflows promote the escape of Lyman-$\alpha$ (Ly$\alpha$) photons from dusty
interstellar media. The process of radiative transfer through interstellar
outflows is often modelled by a spherically symmetric, geometrically thin shell
of gas that scatters photons emitted by a central Ly$\alpha$ source. Despite
its simplified geometry, this `shell model' has been surprisingly successful at
reproducing observed Ly$\alpha$ line shapes. In this paper we perform automated
line fitting on a set of noisy simulated shell model spectra, in order to
determine whether degeneracies exist between the different shell model
parameters. While there are some significant degeneracies, we find that most
parameters are accurately recovered, especially the HI column density ($N_{\rm
HI}$) and outflow velocity ($v_{\rm exp}$). This work represents an important
first step in determining how the shell model parameters relate to the actual
physical properties of Ly$\alpha$ sources. To aid further exploration of the
parameter space, we have made our simulated model spectra available through an
interactive online tool.
