In this paper, the Chebyshev spectral method is used to solve the normal mode and parabolic equation models of underwater acoustic propagation, and the results of the Chebyshev spectral method and the traditional finite difference method are compared for an ideal fluid waveguide with a constant sound velocity and an ideal fluid waveguide with a deep-sea Munk speed profile. The research shows that, compared with the finite difference method, the Chebyshev spectral method has the advantages of a high computational accuracy and short computational time in underwater acoustic propagation.

Solving an acoustic wave equation using a parabolic approximation is a popular approach for many existing ocean acoustic models. Commonly used parabolic equation (PE) model programs, such as the range-dependent acoustic model (RAM), are discretized by the finite difference method (FDM). Considering the idea and theory of the wide-angle rational approximation, a discrete PE model using the Chebyshev spectral method (CSM) is derived, and the code is developed. This method is currently suitable only for range-independent waveguides. Taking three ideal fluid waveguides as examples, the correctness of using the CSM discrete PE model in solving the underwater acoustic propagation problem is verified. The test results show that compared with the RAM, the method proposed in this paper can achieve higher accuracy in computational underwater acoustics and requires fewer discrete grid points. After optimization, this method is more advantageous than the FDM in terms of speed. Thus, the CSM provides high-precision reference standards for benchmark examples of the range-independent PE model.

The accuracy and efficiency of sound field calculations highly concern issues of hydroacoustics. Recently, one-dimensional spectral methods have shown high-precision characteristics when solving the sound field but can solve only simplified models of underwater acoustic propagation, thus their application range is small. Therefore, it is necessary to directly calculate the two-dimensional Helmholtz equation of ocean acoustic propagation. Here, we use the Chebyshev–Galerkin and Chebyshev collocation methods to solve the two-dimensional Helmholtz model equation. Then, the Chebyshev collocation method is used to model ocean acoustic propagation because, unlike the Galerkin method, the collocation method does not need stringent boundary conditions. Compared with the mature Kraken program, the Chebyshev collocation method exhibits a higher numerical accuracy. However, the shortcoming of the collocation method is that the computational efficiency cannot satisfy the requirements of real-time applications due to the large number of calculations. Then, we implemented the parallel code of the collocation method, which could effectively improve calculation effectiveness.

The accurate calculation of the sound field is one of the most concerning issues in hydroacoustics. The one-dimensional spectral method has been used to correctly solve simplified underwater acoustic propagation models, but it is difficult to solve actual ocean acoustic fields using this model due to its application conditions and approximation error. Therefore, it is necessary to develop a direct solution method for the two-dimensional Helmholtz equation of ocean acoustic propagation without using simplified models. Here, two commonly used spectral methods, Chebyshev–Galerkin and Chebyshev–collocation, are used to correctly solve the two-dimensional Helmholtz model equation. Since Chebyshev–collocation does not require harsh boundary conditions for the equation, it is then used to solve ocean acoustic propagation. The numerical calculation results are compared with analytical solutions to verify the correctness of the method. Compared with the mature Kraken program, the Chebyshev–collocation method exhibits higher numerical calculation accuracy. Therefore, the Chebyshev–collocation method can be used to directly solve the representative two-dimensional ocean acoustic propagation equation. Because there are no model constraints, the Chebyshev–collocation method has a wide range of applications and provides results with high accuracy, which is of great significance in the calculation of realistic ocean sound fields.

The upper troposphere and the lower stratosphere (UTLS) are the transition areas between the troposphere and stratosphere. Water vapor, cirrus clouds and aerosols in this area have a strong modulation effect on solar short-wave radiation and earth long-wave radiation. Changes in the content and distribution of aerosols in this level will have a radiant forcing impact on the climate. This article uses the observation data of MPL lidar (micropulse lidar) at SACOL station (Semi-arid Climate and Environment Observation Station of Lanzhou University, 34.946°N, 104.93°E) and ERA-Interim reanalysis data from June to December 2011 to study the changes of stratospheric aerosol over SACOL station after Nabro volcano eruption on June 12, 2011. The result indicates that after the Nabro volcanic eruption, there is an aerosol layer with significantly enhanced scattering ratio over the SACOL station, and the depolarization ratio of particles in the aerosol layer is relatively small, mainly spherical particles; by analyzing the backward trajectory of the stronger aerosol layer, it can be determined that the special aerosol layer was caused by the Nabro volcanic eruption.