InWaveSR: Topography-aware super-resolution network for internal solitary waves

The effective utilization of observational data is frequently hindered by insufficient resolution. To address this problem, we present a new spatio-temporal super-resolution (STSR) model, called InWaveSR. It is built on a deep learning framework with physical restrictions and can efficiently generate high-resolution data from low-resolution input, especially for data featuring internal solitary waves (ISWs). To increase generality and interpretation, the model InWaveSR uses the non-hydrostatic primitive equations with eddy viscosity and diffusivity as the constraint, ensuring that the output results are physically consistent. In addition, the proposed model incorporates an HF-ResBlock component that combines the attention mechanism and the Fast Fourier Transform (FFT) method to improve the performance of the model in capturing high-frequency characteristics. Simultaneously, in order to enhance the adaptability of the model to complicated bottom topography, an edge sampling and numerical pre-processing method are carried out to optimize the training process. In evaluations, the proposed InWaveSR achieved a peak signal-to-noise ratio (PSNR) of $37.8$dB, demonstrating superiority over traditional interpolation and previous neural network methods. This highlights its effectiveness and reliability in reconstructing high-resolution ISW structures with physically consistent dynamics.