Abstract: This paper presents a method for quantifying uncertainty in deep-sea acoustic channels based on eigenvalue distributions and probabilistic distances. By analyzing the cross-spectral density matrix of received signals, the method classifies and quantifies both model uncertainty and channel uncertainty. Model uncertainty measures the differences between the acoustics observed in sea trials and the simulated sound fields, while channel uncertainty describes the deviation between the measured deep-sea acoustic channels and an idealized completely random channel. The Jensen-Shannon divergence and Wasserstein distance are used as primary metrics, and the random matrix theory is applied to analyze the eigenvalue distributions of deep-sea channels. Simulation results demonstrate that model uncertainty and channel uncertainty exhibit different sensitivities to variations in signal-to-noise ratio. The experimental results demonstrate that the statistical analysis of frequency-domain signal eigenvalues effectively mitigates the challenges posed by insufficient experimental data sampling, while validating the applicability of the proposed method in a specified experimental area of the South China Sea. Further analysis reveals that the deep-sea acoustic channel uncertainty reaches its minimum value in the proximity of 3 km from the sound source within this marine region.