The variation of polar vortex intensity is a significant factor affecting the atmospheric conditions and weather in the Northern Hemisphere (NH) and even the world. However, previous studies on the prediction of polar vortex intensity are insufficient. This paper establishes a deep learning (DL) model for multi-day and long-time intensity prediction of the polar vortex. Focusing on the winter period with the strongest polar vortex intensity, geopotential height (GPH) data of NCEP from 1948 to 2020 at 50 hPa are used to construct the dataset of polar vortex anomaly distribution images and polar vortex intensity time series. Then, we propose a new convolution neural network with long short-term memory based on Gaussian smoothing (GSCNN-LSTM) model which can not only accurately predict the variation characteristics of polar vortex intensity from day to day, but also can produce a skillful forecast for lead times of up to 20 days. Moreover, the innovative GSCNN-LSTM model has better stability and skillful correlation prediction than the traditional and some advanced spatiotemporal sequence prediction models. The accuracy of the model suggests important implications that DL methods have good applicability in forecasting the nonlinear system and vortex spatial–temporal characteristics variation in the atmosphere.
The studies of coupled partial differential equations are focus of engineering and applied mathematics. Although traditional numerical methods have been widely used, researchers are still looking for new methods to solve coupled partial differential equations. In this paper, physical information neural network (PINN) is introduced to solve one-dimensional coupled Korteweg-de Vries (cKdV) equations. Compared with the traditional neural network, the innovation of PINN is to embed the physical constraints of the equations into the network loss function. Moreover, within the acceptable relative error range, the solution can take a longer single time step than the presently available. The results revealed that PINN can solve the cKdV equations with reasonable errors only by training a small amount of data.
In this work, a new time series prediction network is proposed in the framework of CasualLSTM with physical constraints and an adjusted Fourier neural operator (FNO) for the solution of the time-dependent partial differential equation. The framework of CasualLSTM is employed to learn the time evolution of spatial features which strengthens the extrapolation capability. With the help of adjusted Fourier layers (AFLs), residual connection, and the adaptive time-marching strategy, the network can quickly converge and extrapolate without labeled data by encoding PDE constraints into loss functions. Two examples, namely, Burger’s equation and two-dimensional Navier–Stokes (N-S) equation are used to evaluate the proposed method. Numerical results show that the proposed method has a good performance in solution accuracy and extrapolability.
Polar vortex is an important weather system that affects the atmospheric circulation in the Northern Hemisphere and the climate change in the Arctic. The intensity variation of polar vortex is related to El Nino-Southern Oscillation (ENSO), Arctic Oscillation (AO) and many other climate phenomena. However, there are few researches on the prediction of polar vortex intensity change, our study analyzes and predicts the intensity variation of the Northern Hemisphere stratospheric polar vortex, and further uses convolution smoothing and depth learning methods to improve the accuracy of the prediction. The result shows that the long-short time memory network method’s prediction accuracy is not enough high. After the convolution smoothing of the time series of intensity signal, the prediction accuracy of neural network has been significantly improved. The average absolute error of the traditional long short-term memory network method is 18.29, while the average absolute error of the smoothed prediction intensity and the actual intensity is 13.77. In addition, the correlation between the predicted results and the real values is also as high as 0.9981.
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