The prediction of chaotic time series systems has remained a challenging problem in recent decades. A hybrid method using Hankel Alternative View Of Koopman (HAVOK) analysis and machine learning (HAVOK-ML) is developed to predict chaotic time series. HAVOK-ML simulates the time series by reconstructing a closed linear model so as to achieve the purpose of prediction. It decomposes chaotic dynamics into intermittently forced linear systems by HAVOK analysis and estimates the external intermittently forcing term using machine learning. The prediction performance evaluations confirm that the proposed method has superior forecasting skills compared with existing prediction methods.

In this paper, we proposed a high accurate and stable Legendre transform algorithm, which can reduce the potential instability for a very high order at a very small increase in the computational time. The error analysis of interpolative decomposition for Legendre transform is presented. By employing block partitioning of the Legendre-Vandermonde matrix and butterfly algorithm, a new Legendre transform algorithm with computational complexity O(Nlog²N /loglogN) in theory and O(Nlog³N) in practical application is obtained. Numerical results are provided to demonstrate the efficiency and numerical stability of the new algorithm.

In this article, we describe an implementation of single‐precision fast spherical harmonic transform (SHT) in the Yin–He global spectral model (YHGSM). The potential of single‐precision arithmetic is explored for accelerating fast SHT. In particular, we assess the impact of using single‐precision fast SHT on the meteorological skill of YHGSM. Compared to double‐precision SHT, single‐precision fast SHT against is accelerated by about 59.83%, whereas the run‐time reduction achieved 25.28% in model integration for T_L2047L137. The simulation results indicate that single‐precision fast SHT can improve computational efficiency without a noticeable impact on the forecast skill.

Complex orography is still a big challenge for all numerical weather prediction (NWP) models. Orography is an important factor that affects the NWP results. The orography in NWP mainly affects the main accuracy of the results through two aspects: orographic representation in models dynamics and orography-related parameterization schemes in the physical processes. To ensure the accuracy of NWP results, it is necessary to have a comprehensive understanding of the application of orographic data in NWP. This paper summarized the influence of orography on weather, the influence of orographic representation on prediction accuracy, and the parametrization of orography-related drag in NWP models. Finally, this paper elaborates the problems of the application of orographic data in NWP and looks forward to future directions in this field, hoping to improve the performance of NWP in complex orographic areas and provide a reference for better application in NWP.

In recent years, the study of numerical weather prediction (NWP) in complex orographic areas has attracted a great deal of attention. Complex orography plays an important role in the occurrence and development of extreme rainfall events. In this study, the Yin–He Global Spectrum Model (YHGSM) was used, and the wave number truncation method was employed to decompose the orographic data to different resolutions. The obtained orographic data with different resolutions were used to simulate the extreme rainfall in Zhengzhou, Henan Province, China, to discuss the degree of influence and mechanism of the different orographic resolutions on the extreme rainfall. The results show that the simulation results of the YHGSM with high-resolution orography are better than those of the low-resolution orography in terms of the rainfall intensity and range. When the rainfall intensity is higher, the results of the low-resolution orography simulated the rainfall range of big heavy rainfall better. The orography mainly affected the rainfall by affecting the velocity of the updraft, but it had a limited influence on the maximum height that the updraft could reach. A strong updraft is one of the key factors leading to extreme rainfall in Henan Province. When the orographic resolution changes, the sensitivity of the vertical velocity of the updraft to the orographic resolution is the greatest, the sensitivity of the upper-air divergence and low-level vorticity to the orographic resolution is lower than that of the vertical velocity. In conclusion, the high-resolution orography is helpful in improving the model’s prediction of extreme rainfall, and when predicting extreme rainfall in complex orographic areas, forecasters may need to artificially increase rainfall based on model results.