﻿ 地表温度变化对GNSS连续运行基准站垂向形变影响研究
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 大地测量与地球动力学  2020, Vol. 40 Issue (11): 1170-1174  DOI: 10.14075/j.jgg.2020.11.013

### 引用本文

WANG Haitao, NIE Jianliang, TIAN Jie, et al. Research on Influence of Surface Temperature Change on Vertical Deformation of GNSS Continuously Operating Reference Station[J]. Journal of Geodesy and Geodynamics, 2020, 40(11): 1170-1174.

### Foundation support

National Natural Science Foundation of China, No. 41774004, 41604001, 41904040; Scientific Program of Shaanxi Bureau of Surveying, Mapping and Geoinformation, No.2020-4;Project for High Level Innovative Talent of Science and Technology, MNR, No.12110600000018003926.

### 第一作者简介

WANG Haitao, assistant engineer, majors in geodetic data processing and impact of environmental load changes, E-mail:1280181825@qq.com.

### 文章历史

1. 国家自然资源部大地测量数据处理中心，西安市友谊东路344号，710054

1 温度变化对垂向形变影响的物理模型

 $\Delta d = \alpha \cdot h \cdot \left[ {T\left( t \right) - \bar T} \right]$ (1)

 $\frac{{\partial T}}{{\partial t}} = k\frac{{{\partial ^2}T}}{{\partial {z^2}}}$ (2)

 $\left\{ \begin{array}{l} T = \bar T + \sum\limits_{i = 1}^N {{A_i}{\rm{cos}}({\omega _i}t - {\varphi _i})} , z = 0\\ {\rm{ }}T = \bar T, z \to \infty \end{array} \right.$ (3)

 $\Delta h\left( t \right) = \frac{{1 + \nu }}{{1 - \nu }}\alpha \sum\limits_{i = 1}^N {{A_i}} \sqrt {\frac{k}{{{\omega _i}}}} {\rm{cos}}({\omega _i}t - \frac{{\rm{ \mathsf{ π} }}}{4} - {\varphi _i})$ (4)

2 温度变化对GNSS连续运行基准站垂向形变的影响 2.1 数据整理

 图 1 气象站与GNSS连续运行基准站分布 Fig. 1 Distribution of meteorological stations and GNSS continuously operating reference stations

 图 2 GNSS基准站地表温度变化时间序列 Fig. 2 Time series of surface temperature of GNSS reference stations
2.2 温度变化对GNSS基准站垂向形变影响的计算与分析

 $\begin{array}{l} y = {a_0} + {A_{周年}}{\rm{cos}}({\omega _{周年}}t + {\varphi _{周年}}) + \\ \;\;\;\;\;\;\;{A_{半周年}}{\rm{cos}}({\omega _{半周年}}t + {\varphi _{半周年}}) \end{array}$ (5)

 图 3 温度变化对XJDS站垂向形变的影响 Fig. 3 Influence of temperature change on vertical deformation of XJDS station

 图 4 大气负荷和温度变化对GNSS基准站的影响 Fig. 4 Effect of atmospheric load and temperature change on GNSS reference stations

23个测站垂向时间序列在移除大气负荷影响后RMS值减小，平均减小量约为0.75 mm，占比约12%，结果见表 2(单位mm)。TASH、XJKC和XJWU测站分别移除温度和大气负荷影响后RMS值小幅增大，从图 5可以看出，基准站垂向时间序列呈现发散无序形态，周期性变化不明显，可能导致移除温度和大气负荷影响后RMS增大。TASH测站存在异常，可能与该测站受到当地复杂环境因素影响有关[6]

 图 5 TASH、XJKC和XJWU测站垂向位置时间序列 Fig. 5 Vertical position time series of TASH, XJKC and XJWU stations

3 结语

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Research on Influence of Surface Temperature Change on Vertical Deformation of GNSS Continuously Operating Reference Station
WANG Haitao1     NIE Jianliang1     TIAN Jie1     LIU Xiaoyun1     GUO Xinwei1     JIN Xinyang1
1. Geodetic Data Processing Centre, MNR, 334 East-Youyi Road, Xi'an 710054, China
Abstract: We use measured surface temperature data to calculate the vertical deformation effect of temperature change on pillar and bedrock of GNSS reference station. Combining with the atmospheric load change, the influence of temperature change on vertical deformation of reference station is comprehensive analyzed. We use Xinjiang GNSS continuously operating reference station data as an example, the results show that the annual impact of temperature change on Xinjiang GNSS continuously operating reference station is 1.4 － 2.1 mm, and the half-annual amplitude is 0.01 － 0.33 mm. The annual amplitude accounts for the majority. When the vertical time series change minus the effect of temperature change, the average RMS value is reduced by 0.55 mm, and the accuracy is improved by about 9%. The effect of temperature change and atmospheric load on the vertical deformation is basically same, showing an increase in the first half of the year and a decrease in second half. At the same time, when the two effects are deducted, the accuracy is improved by about 13%. The research in this paper shows that the changes in temperature and atmospheric load are very important factors for the periodic displacement of reference station.
Key words: temperature change; GNSS reference station; vertical deformation; atmospheric load