﻿ 大气负荷效应对浙江地区的影响分析
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 大地测量与地球动力学  2020, Vol. 40 Issue (6): 591-595  DOI: 10.14075/j.jgg.2020.06.009

引用本文

LIU Yu, LI Aiqin, YU Zhiqiang, et al. Analysis of the Impact of Atmospheric Load Effect on Zhejiang Province[J]. Journal of Geodesy and Geodynamics, 2020, 40(6): 591-595.

Foundation support

National Natural Science Foundation of China, No. 41674024;Basic Research Program of Chinese Academy of Surveying and Mapping, No. 7771806.

Corresponding author

ZHANG Chuanyin, PhD, researcher, majors in satellite altimetry application technology and crustal deformation analysis, E-mail: zhangchy@casm.ac.cn.

About the first author

LIU Yu, postgraduate, majors in geodetic data processing, E-mail: 1845137433@qq.com.

文章历史

1. 山东科技大学测绘科学与工程学院，青岛市前湾港路579号，266000;
2. 中国测绘科学研究院，北京市莲花池西路28号，100830;
3. 浙江省测绘科学技术研究院，杭州市文二西路，310000

1 理论方法 1.1 负荷形变理论和公式

 $\begin{array}{l} {h_w}\left( {\varphi , \lambda } \right) = R\sum\limits_{n = 1}^N {\sum\limits_{m = 0}^n {\left[ {\Delta C_{nm}^q\cos m\lambda } \right.} } + \\ \left. {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \Delta S_{nm}^q\sin m\lambda } \right]{{\bar P}_{nm}}\left( {\sin \lambda } \right) \end{array}$ (1)

 $\begin{array}{l} {\kern 1pt} {\kern 1pt} {\kern 1pt}{\kern 1pt} {\kern 1pt} {\kern 1pt}{\kern 1pt} {\kern 1pt} {\kern 1pt}{\kern 1pt} {\kern 1pt} {\kern 1pt}\Delta r\left( {\varphi , \lambda } \right) = 3\frac{{{\rho _w}}}{{{\rho _e}}}\frac{{GM}}{{\gamma R}}\sum\limits_{n = 1}^N {{{h'}_{2n + 1}}} \cdot \\ \sum\limits_{m = 0}^n {\left( {\Delta C_{nm}^q\cos m\lambda + {\kern 1pt} \Delta S_{nm}^q\sin m\lambda } \right)} {{\bar P}_{nm}}\left( {\sin \varphi } \right) \end{array}$ (2)

 $\begin{array}{l} {g_t}\left( {\varphi , \lambda } \right) = - 3\frac{{{\rho _w}}}{{{\rho _e}}}\sum\limits_{n = 1}^N {\frac{{n + 2{{h'}_n} - \left( {n + 1} \right){{k'}_n}}}{{2n + 1}}} \cdot \\ {\kern 1pt} {\kern 1pt} {\kern 1pt}{\kern 1pt} {\kern 1pt} {\kern 1pt}{\kern 1pt} {\kern 1pt} {\kern 1pt}\sum\limits_{m = 0}^n {\left( {\Delta C_{nm}^q\cos m\lambda + {\kern 1pt} \Delta S_{nm}^q\sin m\lambda } \right)} {{\bar P}_{nm}}\left( {\sin \varphi } \right) \end{array}$ (3)

 $\begin{array}{l} {\kern 1pt} {\kern 1pt} {\kern 1pt}{\kern 1pt} {\kern 1pt} {\kern 1pt}\zeta \left( {\theta , \lambda } \right) = 3\frac{{GM}}{{\gamma {R^2}}}\frac{{{\rho _w}}}{{{\rho _e}}}\sum\limits_{n = 1}^N {\frac{{1 + 2{{k'}_n} - {{h'}_n}}}{{2n + 1}}} \cdot \\ \sum\limits_{m = 0}^n {\left( {\Delta C_{nm}\cos m\lambda + {\kern 1pt} \Delta S_{nm}^{}\sin m\lambda } \right)} \frac{{\partial {{\bar P}_{nm}}\left( {\cos \theta } \right)}}{{\partial \theta }} \end{array}$ (4)
 $\begin{array}{l} {\kern 1pt} {\kern 1pt} {\kern 1pt}{\kern 1pt} {\kern 1pt} {\kern 1pt}n\left( {\theta , \lambda } \right) = 3\frac{{GM}}{{\gamma {R^2}\sin \theta }}\frac{{{\rho _w}}}{{{\rho _e}}}\sum\limits_{n = 1}^N {\frac{{1 + 2{{k'}_n} - {{h'}_n}}}{{2n + 1}}} \cdot \\ \sum\limits_{m = 0}^n {\left( {\Delta C_{nm}^{}\cos m\lambda + {\kern 1pt} \Delta S_{nm}^{}\sin m\lambda } \right)} {{\bar P}_{nm}}\left( {\cos \theta } \right) \end{array}$ (5)

 $\begin{array}{l} {\kern 1pt} {\kern 1pt} {\kern 1pt}{\kern 1pt} {\kern 1pt} {\kern 1pt}e\left( {\theta , \lambda } \right) = 3\frac{{GM}}{{\gamma {R^{}}\sin \theta }}\frac{{{\rho _w}}}{{{\rho _e}}}\sum\limits_{n = 1}^N {\frac{{{{l'}_n}}}{{2n + 1}}} \cdot \\ \sum\limits_{m = 0}^n {m\left( {\Delta C_{nm}^{}\cos m\lambda - {\kern 1pt} \Delta S_{nm}^{}\sin m\lambda } \right)} {{\bar P}_{nm}}\left( {\cos \theta } \right)\\ \end{array}$ (6)
 $\begin{array}{l} {\kern 1pt} {\kern 1pt} {\kern 1pt}{\kern 1pt} {\kern 1pt} {\kern 1pt}n\left( {\theta , \lambda } \right) = 3\frac{{GM}}{{\gamma {R^{}}\sin \theta }}\frac{{{\rho _w}}}{{{\rho _e}}}\sum\limits_{n = 1}^N {\frac{{{{l'}_n}}}{{2n + 1}}} \cdot \\ \sum\limits_{m = 0}^n {m\left( {\Delta C_{nm}^{}\cos m\lambda + {\kern 1pt} \Delta S_{nm}^{}\sin m\lambda } \right)} {{\bar P}_{nm}}\left( {\cos \theta } \right) \end{array}$ (7)

 $\Delta \Theta \left( {\varphi , \lambda } \right) = G{\rho _w}\int {\int_S^{} {\frac{{{h_w}\left( {\varphi ', \lambda '} \right)}}{L}} } G\left( \psi \right){\rm{d}}S$ (8)

1.2 移去-恢复法

 $\begin{array}{l} {\kern 1pt} {\kern 1pt} {\kern 1pt}{\kern 1pt} {\kern 1pt} {\kern 1pt}\Delta \Theta \left( {\varphi , \lambda } \right)\left| {_{{S_0}}} \right. = G{\rho _w}\int {\int_S^{} {\frac{{{h_w}\left( {\varphi ', \lambda '} \right)}}{L}} } G\left( \psi \right){\rm{d}}S + \\ \int {\int_{{S_0}}^{} {\left[ {\Delta {h_w}\left( {\varphi ', \lambda '} \right) - \Delta {h_{wM}}\left( {\varphi ', \lambda '} \right)} \right]} } G\left( {{\psi _0}} \right){\rm{d}}S + {\varepsilon _M} \end{array}$ (9)

 $\begin{array}{l} \Delta \Theta \left( {\varphi , \lambda } \right)\left| {_{{S_0}}} \right. = \Delta {\Theta _M}\left( {\varphi , \lambda } \right)\left| {_{{S_0}}} \right. + \\ \int {\int_{{S_0}}^{} {{\rm{d}}{h_w}\left( {\varphi ', \lambda '} \right)G\left( {{\psi _0}} \right){\rm{d}}S + {\varepsilon _M}} } \end{array}$ (10)

1) 将全球大气压变化数据模型扣除基准值，构建全球等效水高变化格网数字模型，利用球谐函数对其进行计算，得到全球等效水高规格化球谐系数模型。

2) 将各气象站数据扣除基准值后，利用全球等效水高规格化球谐系数模型计算等效水高模型值。从区域等效水高变化格网中移去等效水高模型值，得到区域剩余等效水高格网模型，再采用克里金插值法将站点残差等效水高格网化，利用负荷格林函数积分法确定大气压引起的区域剩余负荷地壳形变场及重力场变化格网的时间序列。

3) 将区域剩余负荷影响格网与全球负荷影响模型值格网相加，得到区域高精度非潮汐负荷影响格网数字模型，包括各种类型的大气负荷形变场与重力场变化格网的数字模型，得到大气负荷的间接影响。

2 数据获取及处理 2.1 研究范围

 图 1 气象站分布 Fig. 1 Meteorological station distribution
2.2 数据采集与预处理

1) 全球大气压模型。从欧洲中期天气预报中心下载2015-01~2017-12分辨率为0.25°的全球大气压月变化格网模型[11]，将数据扣除基准之后按照1 hPa=10.2 mm的换算关系将大气压数据转换为等效水高。根据式(1)进行球谐展开，得到等效水高球谐系数，根据研究区内气象站点坐标求得每月等效水高作为模型值。

2) 气象站资料。从国家气象信息中心下载浙江丽水、温州地区周边98个气象站的中国地面气候资料月值数据，将其扣除基准之后转化为等效水高，再扣除第1)步中求得的模型值，得到残差等效水高，并利用克里金插值法生成2015-01~2017-12大气压变化格网时间序列。

3 大气负荷形变场计算与分析 3.1 大气负荷对地壳形变影响

 图 2 2015年大气负荷引起的垂直形变的变化 Fig. 2 Change of vertical deformation caused by atmospheric load in 2015

 图 3 2015年大气负荷引起的水平形变的变化 Fig. 3 Changes of horizontal deformation caused by atmospheric load in 2015

 图 4 2015年大气负荷引起的垂线偏差变化 Fig. 4 Variation of vertical deviationcaused byatmosphericloadin 2015
3.2 大气负荷对地面重力影响

 图 5 2015年大气负荷引起的浙江区域地面重力变化 Fig. 5 Thechange ofregional gravityin Zhejiang cansed byatmosphericloadin 2015
3.3 数据统计与分析

 图 6 CORS站处大气负荷对各种形变的影响 Fig. 6 Effect of CORS outgoing atmospheric load on various deformations
4 结语

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Analysis of the Impact of Atmospheric Load Effect on Zhejiang Province
LIU Yu1,2     LI Aiqin3     YU Zhiqiang3     JI Yuanming3     ZHANG Chuanyin2
1. College of Geodesy and Geomatics, Shandong University of Science and Technology, 579 Qianwangang Road, Qingdao 266000, China;
2. Chinese Academy of Surveying and Mapping, 28 West-Lianhuachi Road, Beijing 100830, China;
3. Zhejiang Institute of Surveying and Mapping Science and Technology, West-Wen'er Road, Hangzhou 310000, China
Abstract: In this paper, based on the global atmospheric model and the data of Zhejiang regional meteorological station, the load deformation field and the change of gravity field caused by atmospheric pressure are calculated by the method of removing and restoring according to the load theory. The results show that the vertical deformation caused by atmospheric load in Zhejiang province reaches 12.1 mm, and the ground gravity change caused by atmospheric load exceeds 12 μGal. The influence of vertical deviation is small, and the atmospheric load has obvious annual periodicity and seasonality.
Key words: atmospheric load; Green's function; spherical harmonic function; removal recovery method; crustal deformation