Data security technology is of great significance to the application of high resolution remote sensing image (HRRS) images. As an important data security technology, perceptual hash overcomes the shortcomings of cryptographic hashing that is not robust and can achieve integrity authentication of HRRS images based on perceptual content. However, the existing perceptual hash does not take into account whether the user focuses on certain types of information of the HRRS image. In this paper, we introduce the concept of subject-sensitive perceptual hash, which can be seen as a special case of conventional perceptual hash, for the integrity authentication of HRRS image. To achieve subject-sensitive perceptual hash, we propose a new deep convolutional neural network architecture, named MUM-Net, for extracting robust features of HRRS images. MUM-Net is the core of perceptual hash algorithm, and it uses focal loss as the loss function to overcome the imbalance between the positive and negative samples in the training samples. The robust features extracted by MUM-Net are further compressed and encoded to obtain the perceptual hash sequence of HRRS image. Experiments show that our algorithm has higher tamper sensitivity to subject-related malicious tampering, and the robustness is improved by about 10% compared to the existing U-net-based algorithm; compared to other deep learning-based algorithms, this algorithm achieves a better balance between robustness and tampering sensitivity, and has better overall performance.

Ocean modeling and simulation are important for understanding the dynamic processes in the geophysical system, and the simulation of tidal dynamics is of great significance for understanding the dynamic evolution of the ocean. However, there are some problems in existing simulations, including lack of specific standards to produce a desirable discrete spherical mesh for global ocean modelling. Many global ocean numerical models based on conventional longitude-latitude (LL) coordinates suffer from the “pole problem” in regions adjacent to the North Pole due to the convergence of meridians, which seriously hinders global ocean simulations. In this paper, a new longitude-latitude spherical grid coupled with rotated coordinate mapping is proposed to overcome the problem. In the design of the numerical model, for spatial approximation, the finite volume method on staggered C grid is proposed to solve the two-dimensional tidal wave equations for the global ocean. For temporal integration, the third-order Adams-Bashforth method is used to explicitly extrapolate the value on the next time interval half layer, and then the fourth-order implicit Adams-Moulton method is used to correct the water level. Finally, the constructed model is used to simulate the dynamics of two-dimensional tidal waves in the global ocean, and the co-tidal maps of two major diurnal tide and semidiurnal tide components are shown. The results demonstrate that the proposed model can support the simulation of tidal dynamics in the global ocean, especially for the Arctic Ocean.

The transport process is an important part of the research of fluid dynamics, especially when it comes to tracer advection in the atmosphere or ocean dynamics. In this paper, a series of high-order semi-Lagrangian methods for the transport process on the sphere are considered. The methods are formulated entirely in three-dimensional Cartesian coordinates, thus avoiding any apparent artificial singularities associated with surface-based coordinate systems. The underlying idea of the semi-Lagrangian method is to find the value of the field/tracer at the departure point through interpolating the values of its surrounding grid points to the departure point. The implementation of the semi-Lagrangian method is divided into the following two main procedures: finding the departure point by integrating the characteristic equation backward and then interpolate on the departure point. In the first procedure, three methods are utilized to solve the characteristic equation for the locations of departure points, including the commonly used midpoint-rule method and two explicit high-order Runge–Kutta (RK) methods. In the second one, for interpolation, four new methods are presented, including (1) linear interpolation; (2) polynomial fitting based on the least square method; (3) global radial basis function stencils (RBFs), and (4) local RBFs. For the latter two interpolation methods, we find that it is crucial to select an optimal value for the shape parameter of the basis function. A Gauss hill advection case is used to compare and contrast the methods in terms of their accuracy, and conservation properties. In addition, the proposed method is applied to standard test cases, which include solid body rotation, shear deformation of twin slotted cylinders, and the evolution of a moving vortex. It demonstrates that the proposed method could simulate all test cases with reasonable accuracy and efficiency.

In the last decade, the radial basis function-generated finite difference (RBF-FD) method has been widely used for numerical solutions of partial differential equations on smooth surfaces. In this paper, we present a comparison between two approaches for approximating spherical differential operators using the RBF-FD method based on polyharmonic splines. First, we compare common differential operators, including the surface gradient and the Laplacian operator on the sphere, employing polyharmonic splines with different degrees of augmented multivariate polynomials. Second, we examine the approximation errors for various node layouts and spatial resolutions. In most cases, the RBF-FD method with a constant along the normal direction yields more accurate results. To maintain consistency with the high-order RBF-FD spatial discretization, we employ high-order time integration methods, including two Runge–Kutta schemes and exponential Rosenbrock schemes. Finally, we apply the method to solve the spherical shallow water equations using a series of standard test cases, such as steady geostrophic flow, zonal flow over an isolated mountain, Rossby–Haurwitz wave propagation and perturbed zonal jet flow. The simulation results demonstrate that the proposed method is capable of reproducing the evolution of nonlinear dynamics successfully.