We present [Ci] and [Cii] observations of a linear edge region in the Taurus molecular cloud, and model this region as a cylindrically symmetric PDR exposed to a low-intensity UV radiation field. The sharp, long profile of the linear edge makes it an ideal case to test PDR models and determine cloud parameters. We compare observations of the [C i], 3P1 -> 3P0 (492 GHz), [C i] 3P2 -> 3P1 (809 GHz), and [Cii] 2P3/2 -> 2P1/2 (1900 GHz) transitions, as well as the lowest rotational transitions of 12CO and 13CO, with line intensities produced by the RATRAN radiative transfer code from the results of the Meudon PDR code. We constrain the density structure of the cloud by fitting a cylindrical density function to visual extinction data. We study the effects of variation of the FUV field, 12C/13C isotopic abundance ratio, sulfur depletion, cosmic ray ionization rate, and inclination of the filament relative to the sky-plane on the chemical network of the PDR model and resulting line emission. We also consider the role of suprathermal chemistry and density inhomogeneities. We find good agreement between the model and observations, and that the integrated line intensities can be explained by a PDR model with an external FUV field of 0.05 G0, a low ratio of 12C to 13C ~ 43, a highly depleted sulfur abundance (by a factor of at least 50), a cosmic ray ionization rate (3 - 6) x 10-17 s^-1, and without significant effects from inclination, clumping or suprathermal chemistry.
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