We present radiative transfer models of the circumstellar environment of classical T Tauri stars, concentrating on the formation of the H-alpha emission. The wide variety of line profiles seen in observations are indicative of both inflow and outflow, and we therefore employ a circumstellar structure that includes both magnetospheric accretion and a disc wind. We perform systematic investigations of the model parameters for the wind and the magnetosphere to search for possible geometrical and physical conditions which lead to the types of profiles seen in observations. We find that the hybrid models can reproduce the wide range of profile types seen in observations, and that the most common profile types observed occupy a large volume of parameter space. Conversely, the most infrequently observed profile morphologies require a very specific set of models parameters. We find our model profiles are consistent with the canonical value of the mass-loss rate to mass-accretion rate ratio (mu=0.1) found in earlier magneto-hydrodynamic calculations and observations, but the models with 0.05<mu<0.2 are still in accord with observed H-alpha profiles. We investigate the wind contribution to the line profile as a function of model parameters, and examine the reliability of H-alpha as a mass accretion diagnostic. Finally, we examine the H-alpha spectroscopic classification used by Reipurth et. al, and discuss the basic physical conditions that are required to reproduce the profiles in each classified type.
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