(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.Comment: 29 pages, 23 figures and 1 tabl
