Clump integrated intensity ratio ∫I([C ii])dv/∫I([¹³C ii])dv vs. [C ii] intensity from the KOSMA-τ model for different parameters. The model parameters n, M, and χ, are coded as size, shape, and color of the respective symbols. The red horizontal line denotes the assumed elemental abundance ratio [¹²C]/[¹³C] of 67. The insert demonstrates the underlying column density ratio for the different clumps. For [¹³C ii], we sum over all hyperfine components.