A tight-binding molecular dynamics study of the structural evolution in tetrahedral amorphous carbon networks under dynamic hydrogen saturation is presented. The incorporation of hydrogen results in higher degrees of network disorder in second-neighbour distances, and initiates orbital re-hybridization that relaxes network stress. Using the simulated structures, numerical tests are performed to verify the effectiveness of a new structural order parameter for tetrahedrally-bonded solids. It is found that the island of accessible information, within the order parameter field shows a linear dependence between the fluctuations in first-and second-nearest-neighbour distances at a preferred orientation of 36 . A comparison with similar studies on hydrogenated amorphous silicon suggests that the local network structure of tetrahedrally-bonded amorphous solids obey the same ordering rule irrespective of differences in chemical species.