Tank experiments were performed at different water turbidities to examine relationships between the beam attenuation coefficient (c) and Weibull shape parameters derived from LiDAR waveforms measured with the Fine Structure Underwater LiDAR (FSUIL). Optical inversions were made at 532 nm, within a c range of 0.045-1.52 m-1, and based on a LiDAR system having two field-of-view (15 and 75.7 mrad) and two linear polarizations. Consistently, the Weibull scale parameter or P2 showed the strongest covariation with c and was a more accurate proxy with respect to the LiDAR attenuation coefficient.