  Accurate estimations of atmospheric properties of exoplanets from
transmission spectra require understanding of degeneracies between model
parameters and observations that can resolve them. We conduct a systematic
investigation of such degeneracies using a combination of detailed atmospheric
retrievals and a range of model assumptions, focusing on H$_2$-rich
atmospheres. As a case study, we consider the well-studied hot Jupiter HD
209458 b. We perform extensive retrievals with models ranging from simple
isothermal and isobaric atmospheres to those with full pressure-temperature
profiles, inhomogeneous cloud/haze coverage, multiple molecular species, and
data in the optical-infrared wavelengths. Our study reveals four key insights.
First, we find that a combination of models with minimal assumptions and
broadband transmission spectra with current facilities allow precise estimates
of chemical abundances. In particular, high-precision optical and infrared
spectra along with models including variable cloud coverage and prominent
opacity sources, Na and K being important in optical, provide joint constraints
on cloud/haze properties and chemical abundances. Second, we show that the
degeneracy between planetary radius and its reference pressure is well
characterised and has little effect on abundance estimates, contrary to
previous claims using semi-analytic models. Third, collision induced absorption
due to H$_2$-H$_2$ and H$_2$-He interactions plays a critical role in correctly
estimating atmospheric abundances. Finally, our results highlight the
inadequacy of simplified semi-analytic models with isobaric assumptions for
reliable retrievals of transmission spectra. Transmission spectra obtained with
current facilities such as HST and VLT can provide strong constraints on
atmospheric abundances of exoplanets.
