An idealized model is used to simulate radio occultation bending angles and residual ionospheric errors. The test results of the proposed simulation method agree with those of previous studies that use end-to-end simulation tools. Also, a new residual ionospheric error model proposed by Healy and Culverwell (2015) is verified in this letter by characterizing the key parameter, κ. A simple model, κ(a) = A − B × (a − 20)/60, is used to estimate the values of κ, where A and B are constants that indicate the magnitude and variation of the values of κ, respectively, and a represents the impact height. When the modelled values of κ are applied in performing ionospheric corrections, the residual ionospheric errors decrease from approximately 5 × 10−8 rad to 1 × 10−9 rad at a latitude of 40°N during the daytime and at a solar activity level of F10.7 = 210. Though the proposed model does not assess other error terms, such as those associated with asymmetry and noise, it will likely prove to be an effective tool for describing idealized residual ionospheric errors in radio occultation, and the features of the κ values identified in this study may be helpful in improving ionospheric correction methods.

Gravity waves (GWs) are important for the vertical coupling of the Martian atmosphere. The middle atmosphere is the key region where GWs propagate to the upper thermosphere and generate momentum and energy exchange, but the knowledge of middle-atmosphere GWs is incomplete, due to the lack of observations with the kilometer-scale resolution. We have analyzed the climatology of GW activity in the middle and upper atmosphere of Mars using 20–180 km temperature profiles measured by the Atmospheric Chemistry Suite instrument on board the Trace Gas Orbiter. The results show that the amplitudes of GWs extracted in this study are generally less than 15% and that the centers of the strongest GW activity vary significantly with the seasons. Second, the strongest GW activity in the mesosphere indicates the strong dissipation effects of the mesopause, and the mid-atmospheric GWs show a seasonal pattern that is stronger in the winter hemisphere. During the global dust event of MY34, the enhancement of GWs in the middle atmosphere is most pronounced at low and middle latitudes where the dust storms are active. It is possible that changes in the temperature structure of the middle atmosphere adjust the atmospheric circulation and thus improve the propagation of GWs. Furthermore, GW activity is stronger on the dayside than on the nightside, and there is no significant correlation between amplitudes and background temperature. This suggests a limited role of convective instability in limiting the growth of GWs in the middle atmosphere, with nonlinear damping competing with that of molecular diffusion at different harmonics.

This paper is the first to integrate the two scientific paradigms of the negative feedback dynamics mechanism of El Niño–Southern Oscillation (ENSO) and deep learning methods, and systematically studies the prediction method of key regional variables of ENSO. This paper mainly performed two activities: first, two physics-informed neural network methods are proposed to solve the ordinary differential equations (ODEs) of ENSO negative feedback theory, including classical physics-informed neural networks (PINNs) and variant-physics-informed Long Short-Term Memory (PILSTM) neural networks, and the novel defined physics-informed neural network loss function weights are optimized and balanced. Second, only 780 natural month-scale small datasets in the Coupled Model Intercomparison Project Phase 6 (CMIP6) model are used to improve the accuracy of correlative skills, and solve the problem of obvious decline in medium- and long-term correlative skills in the current air–ocean coupled dynamic prediction model. The results show that the research paradigms of the two physics-informed neural networks are an effective and complementary method in dealing with medium- and long-term prediction problems. Moreover, the PILSTM model based on recharge–discharge oscillator theory performed the best, and were better than the traditional delayed oscillator theory numerical operator method and the recharge–discharge oscillator theory numerical operator method. Meanwhile, the proposed method solved the delay problem in the recharge–discharge oscillator theory, indicating that the physics-informed neural networks learned the negative feedback dynamics mechanism of ENSO well, and effectively complemented the existing ENSO oscillator theory through the features learned from the training data, which help us to further comprehend the complex mechanism of ENSO events.

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