  We present a new scheme for modeling the broad line region in active galactic
nuclei (AGNs). It involves photoionization calculations of a large number of
clouds, in several pre-determined geometries, and a comparison of the
calculated line intensities with observed emission line light curves. Fitting
several observed light curves simultaneously provides strong constraints on
model parameters such as the run of density and column density across the
nucleus, the shape of the ionizing continuum, and the radial distribution of
the emission line clouds. When applying the model to the Seyfert 1 galaxy NGC
5548, we were able to reconstruct the light curves of four ultraviolet
emission-lines, in time and in absolute flux. This has not been achieved by any
previous work. We argue that the Balmer lines light curves, and possibly also
the MgII2798 light curve, cannot be tested in this scheme because of the
limitations of present-day photoionization codes. Our fit procedure can be used
to rule out models where the particle density scales as r^{-2}, where r is the
distance from the central source. The best models are those where the density
scales as r^{-1} or r^{-1.5}. We can place a lower limit on the column density
at a distance of 1 ld, of N_{col}(r=1) >~ 10^{23} cm^{-2} and limit the
particle density to be in the range of 10^{12.5}>N(r=1)>10^{11} cm^{-3}. We
have also tested the idea that the spectral energy distribution (SED) of the
ionizing continuum is changing with continuum luminosity. None of the
variable-shape SED tried resulted in real improvement over a constant SED case
although models with harder continuum during phases of higher luminosity seem
to fit better the observed spectrum. Reddening and/or different composition
seem to play a minor role, at least to the extent tested in this work.
