Atmospheric refraction delay correction for lunar laser ranging via fusion of real-time co-located lidar and ERA5 data.

Lunar laser ranging (LLR) is a fundamental tool for investigating the Earth-Moon system and gravitational physics. To meet the millimeter-level ranging accuracy required by next-generation LLR, atmospheric refraction delay correction has become a critical bottleneck. This paper proposes a multi-source data fusion ray-tracing (MFRT) method. The primary innovation lies in dynamically integrating real-time, co-located temperature profiles from a pure rotational Raman (PRR) lidar, bias-corrected fifth-generation European Centre for Medium-Range Weather Forecasts reanalysis (ERA5) data, and the 1976 U.S. Standard Atmosphere model. This method constructs all-altitude atmospheric refractive index profiles extending from the station surface to 100 km. Consequently, it achieves real-time, co-located correction of the atmospheric refraction delay for LLR. Two independent experiments were conducted: First, the Mendes-Pavlis (MP) and Marini-Murray (MM) models were evaluated against ray-tracing benchmarks using two years of radiosonde data. The results show that the MP model outperforms the MM model. However, its correction errors can reach up to 14.7 mm locally, confirming that empirical models struggle to meet millimeter-level requirements. Second, practical ranging experiments were conducted at the TianQin (22.34∘N, 113.55∘E) station targeting the LAGEOS satellites and lunar corner cube retroreflector arrays (Apollo 15 and Luna 21). These experiments demonstrate that the MFRT method improves ranging accuracy by up to 14.7 mm compared to the MP model. Collectively, these results indicate that empirical models are subject to non-negligible localized systematic errors. In contrast, the MFRT method exhibits stable and superior correction performance in both satellite laser ranging (SLR) and LLR, marking a critical step toward achieving millimeter-level accuracy.