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tokens: given by We define z ph to be where the scattering optical depth s 1 (where subscript s denotes scattering) and set f cor / f cor,0 1. Near the photosphere, magnetic pressure begins to play a major role in hydrostatic equilibrium (e.g. Blaes, Hirose Krolik 2007 ), and near the effective photosphere, the gas temperature begins to diverge from the radiation temperature, so we acknowledge that the assumptions underlying our scheme do not reflect the detailed physics in this region. But since our goal is only to calculate spectra, for optical depths s 1, the accuracy of this scheme is not important. We can assess the validity of this scheme in the region s 1 by comparing the flux from spectral calculations with the intended flux given by equation ( 9 ), or, equivalently, by comparing the corresponding Eddington ratios. In Section 3.1 , we make this comparison for each set of scaling parameters we use and find that they generally agree to within 10percent. More importantly, we find that normalizing the spectra at different radii so that their corresponding Eddington ratios match has a negligible impact on the observed spectrum when contrasted with the discrepancies between spectral calculations with and without bulk velocities. In other words, because the potential error is significantly less than the effect we are measuring, our scaling scheme is adequate. These are the appropriate equations for scaling data to a different set of fundamental shearing box simulation parameters, in particular, z , x v y and . If we substitute in equation ( 9 ) for , we can alternatively regard F as a fundamental parameter instead of . Shearing box scalings in terms of F are given in Appendix C . This substitution is useful in order to scale to a different set of fundamental accretion disc parameters, since it is straightforward to express F in terms of accretion disc radius, mass and accretion rate. The scalings for z , x v y and F for both Newtonian and Kerr discs, allowing for a non-zero stress inner boundary condition, are given in Appendix D . The final scalings for , T g , v and v s in terms of fundamental accretion disc parameters are given in Appendix E . We only use Kerr scalings for our spectral calculations, but the Newtonian scalings are potentially useful for the purpose of comparing with other works in which Newtonian parameters are used and also for developing physical intuition. 2.3 Dependence of turbulent Comptonization on radius To characterize the contribution of turbulent Comptonization, we must model spectra at multiple radii. Our choice of radii is guided by the scaling of the ratio of bulk to thermal electron energies. We estimate this effect for a disc with no spin and a stress-free inner boundary condition with the Newtonian scalings in Appendix E . The bulk velocity scaling is The photosphere thermal velocity scaling is The scaling for the ratio of bulk velocity to thermal velocity at the photosphere is We also calculate the scaling for