The impact of thermal expansion on nonlinear vertical variations of GNSS reference stations in Chinese mainland

The thermoelastic deformation of Global Navigation Satellite System (GNSS) monuments and foundations significantly contributes to the vertical nonlinear variations observed in the GNSS coordinate time series. A rigorous thermoelastic effect model, which takes into account the diversity of monument depths and foundation types of the reference stations, was proposed in this paper to quantify the influence of thermal expansion on the vertical displacement using 409 GNSS reference stations in Chinese mainland. The periodic characteristics of the GNSS vertical time series, GNSS Removes Environmental Loading (GREL) time series, and thermal expansion effect show a higher consistency between the GNSS Removes Environmental time series and the thermal expansion effects. The annual amplitude of thermal expansion for GNSS reference stations across Chinese mainland ranges from 0.2 mm to 1.9 mm, increasing with latitude, with a characteristic distribution of lower values in the south and higher value in the north. After applying thermal expansion corrections, 79.2% of the reference stations across Chinese mainland exhibit a decreasing trend in amplitude, with an average reduction of 0.4 mm. The average reduction in WRMS across Chinese mainland is 1.1 mm. Regional variability in the correction effects is significant: the largest corrections occur in Central China, followed by Northwest China and East China, while corrections in Southwest China, South China, and North China are comparatively smaller, and the corrections in Northeast China are negative. The thermal expansion correction demonstrates similar effectiveness across different types of foundational reference stations. A reduction in amplitude was observed in 78.5% of bedrock monument stations and 80.2% of soil monument stations, with a difference of 1.7% between the two. The average reduction in amplitude variation for different types was the same at 0.4 mm, indicating a comparable effect. Notably, the correction effect varies significantly based on the burial depth of the GNSS monuments, with the largest correction observed for the 5.5 m soil monument stations, followed by 2 m bedrock monument stations, 18 m soil monument stations, and 7.5 m soil monument stations. The correction effect for 8.5 m soil monument stations is negative.