Researchers from the Xinjiang Astronomical Observatory of the Chinese Academy of Sciences have developed a hybrid deep learning model that can accurately predict atmospheric delay, a key source of error in astronomical observations and geodetic measurements.

The results were published in Research in Astronomy and Astrophysics.

Electromagnetic waves slow down when passing through the Earth's atmosphere due to variations in air density and water vapor content, resulting in what is known as "tropospheric delay." This delay is considered a major source of error in Very Long Baseline Interferometry (VLBI) and Global Navigation Satellite System (GNSS) positioning. Acting like an "invisible lens," it causes signals to bend slightly and lag in the atmosphere, thereby affecting measurement accuracy. Accurately modeling and forecasting this delay has become an important challenge in the fields of astronomical observation and geodetic measurement.

Using multi-year GNSS and meteorological data obtained from the NanShan 26-meter Radio Telescope, the researchers led by LI Mingshuai developed the deep learning model combining a Gated Recurrent Unit (GRU) and a Long Short-Term Memory (LSTM) network. This model is an important branch of artificial intelligence and can automatically learn the patterns of atmospheric delay variations from large volumes of data. It achieves high-precision short-term forecasting of the Zenith Tropospheric Delay (ZTD).

Through spectral analysis of long-term GNSS observations at the NanShan station, the researchers identified distinct annual and semi-annual cycles in ZTD variation, with greater delays in summer and lesser delays in winter. These variations were closely correlated with temperature and water vapor content; the warmer and more humid the atmosphere, the greater the signal delay.

To address the limitations of traditional empirical models that struggle to capture complex nonlinear behaviors, the researchers adopted a deep learning architecture in which the GRU extracts short-term dynamic features while the LSTM captures long-term trends. By combining the two, the "hybrid neural network" effectively models both short-term fluctuations and seasonal regularities in atmospheric delay. 

Results show that the model achieves a prediction error of only about 8 millimeters and a correlation coefficient of 96%, significantly outperforming conventional statistical and single-network approaches.

High-precision forecasts of tropospheric delay can substantially improve atmospheric phase calibration for VLBI observations, enhance radio source positioning and baseline solutions, and provide more accurate meteorological support for millimeter-wave astronomy. Moreover, the results have broad applications in precipitable water vapor retrieval and weather forecasting. 

This study demonstrates the potential of artificial intelligence in atmospheric calibration for radio telescopes and lays a technical foundation for high-frequency operations of the Qitai 110-meter Telescope and future multi-station interferometric observations.