(Abridged) We investigate the observational characteristics of BLR geometries in which the BLR clouds bridge the gap, both in distance and scale height, between the outer accretion disc and the hot dust, forming an effective surface of a bowl. The gas dynamics are dominated by gravity, and we include the effects of transverse Doppler shift, gravitational redshift and scale-height dependent macro-turbulence. Our simple model reproduces many of the phenomena observed in broad emission-line variability studies, including (i) the absence of response in the core of the optical recombination lines on short timescales, (ii) the enhanced red-wing response on short timescales, (iii) differences between the measured delays for the HILs and LILs, and (iv) identifies turbulence as a means of producing Lorentzian profiles (esp. for LILs) in low inclination systems, and for suppressing significant continuum--emission-line delays between the line wings and line core (esp. in LILs). A key motivation of this work was to reveal the physical underpinnings of the reported measurements of SMBH masses and their uncertainties. We find that SMBH masses derived from measurements of the fwhm of the mean and rms profiles show the closest correspondence between the emission lines in a single object, even though the emission line fwhm is a more biased mass indicator with respect to inclination. The predicted large discrepancies in the SMBH mass estimates between emission lines at low inclination, as derived using the line dispersion, we suggest may be used as a means of identifying near face-on systems. Our general results do not depend on specific choices in the simplifying assumptions, but are in fact generic properties of BLR geometries with axial symmetry that span a substantial range in radially-increasing scale height supported by turbulence, which then merge into the inner dusty TOR.
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