Ali, W.H., and P.F.J. Lermusiaux, 2024b. *Dynamically Orthogonal Narrow-Angle Parabolic Equations for Stochastic
Underwater Sound Propagation. Part II: Applications.* Journal of the Acoustical Society of America 155(1), 656-672. doi:10.1121/10.0024474

The stochastic dynamically orthogonal (DO) narrow-angle parabolic equations (NAPEs) are exemplified and their properties and capabilities are described using three new 2D stochastic range-independent and range-dependent test cases with uncertain sound speed field, bathymetry, and source location. We validate results against ground-truth deterministic analytical solutions and direct Monte Carlo predictions of acoustic pressure and transmission loss fields. We verify the stochastic convergence and computational advantages of the DO-NAPEs and discuss the differences with normal mode approaches. Results show that a single DO-NAPE simulation can accurately predict stochastic range-dependent acoustic fields and their non-Gaussian probability distributions, with computational savings of several orders of magnitude when compared to direct Monte Carlo methods. With their coupling properties and their adaptation in range to the dominant uncertainties, the DO-NAPEs are shown to predict accurate statistics, from mean and variance to multiple modes and full probability distributions, and to provide excellent reconstructed realizations, from amplitudes and phases to other specific properties of complex realization fields.