陆地水GNSS反演的格林函数和Slepian基函数比较分析

doi:10.11947/j.AGCS.2023.20220624

摘要/Abstract

摘要： 陆地水是水资源中重要的组成部分,全球气候变暖会深远地影响陆地水分布,甚至恶化区域水资源供求关系。陆地水变化关乎人类社会发展,监测陆地水变化越来越重要。锚定在地壳上的GNSS连续观测站可直接测量地表位移的不断变化并反演水文荷载,使得GNSS技术成为研究陆地水的热点。目前GNSS反演陆地水主要有格林函数和Slepian基函数两种方法,两者在数学模型上是等价的,但实际应用上存在差异。本文在研究区域(云南地区97°E—107°E、20°N—30°N)使用相同数据,定量分析格林函数和Slepian基函数反演方法的差异,结果表明:①基于模拟数据,格林函数反演结果受GNSS测站数量和空间展布影响程度比Slepian基函数反演结果更大,而Slepian基函数反演结果受最大截断阶数的影响较大;同等情况下,格林函数反演结果总体精度比Slepian基函数反演结果更优。②基于实测的“陆态网络”和气象局的GNSS连续测站垂直时间序列数据,两种方法反演等效水高结果相关性达到0.98,Slepian基函数反演结果振幅比格林函数反演结果振幅平均大25%。③GNSS数据反演的陆地水和GRACE、GLDAS推断的陆地水相关性均大于0.65,并且与该地区月度降水数据一致性很好;GNSS反演等效水高序列波峰出现的时间比最大降雨滞后1~2个月。

关键词: GNSS, 格林函数, Slepian基函数, 陆地水储量, 等效水高

Abstract: Terrestrial water storage is an important part of water resources. Changes in terrestrial water storage are related to the development of human society. Atmospheric warming has a profound impact on the distribution of global terrestrial water storage, and even worsens the relationship between regional water supply and demand. With the construction of continuous GNSS station network in China, GNSS has become a new type of geodetic method for monitoring terrestrial water storage changes. At present, the methods for terrestrial water inversion using continuous GNSS stations are mainly divided into Green's function and Slepian basis function inversion methods, but there are few reports on the differences and applicable scenarios of those two methods. Starting from the basic principles of the two methods, this paper uses simulated data and measured GNSS data to perform inversion based on the Green's function and the Slepian basis function, respectively. Results show that: ① Based on the simulation data, the number and spatial distribution of GNSS stations are different, and the Green's function inversion results are more affected than the Slepian basis function inversion results. The overall accuracy of Green's function inversion results is better, and the Slepian basis function method is greatly affected by the maximum truncation order. ② Based on the real “land-state network” and the vertical time series data of GNSS continuous observation stations of the Meteorological Bureau, the correlation between the two methods to retrieve the equivalent water height is 0.98, and the amplitude of the Slepian basis function inversion result is 25% larger than that of the Green function inversion result on average. ③ The results of GNSS inversion and the terrestrial water phase inferred by GRACE and GLDAS are all greater than 0.65, and the monthly precipitation data are in good agreement. The peak of the equivalent water height sequence retrieved by GNSS lags behind the maximum rainfall by 1~2 months. Considered the reality in most area of China, the density GNSS stations is not enough for the application for Green's method in TWS inversion, so the Slepian method is the good choice.

Key words: GNSS, Green's function, Slepian basis function, terrestrial water storage, equivalent water height

中图分类号:

P227

陈超, 邹蓉, 曹家铭, 李瑜, 梁宏, 方智伟. 陆地水GNSS反演的格林函数和Slepian基函数比较分析[J]. 测绘学报, 2023, 52(12): 2066-2077.

CHEN Chao, ZOU Rong, CAO Jiaming, LI Yu, LIANG Hong, FANG Zhiwei. Comparative analysis of Green's functions and Slepian basis functions for GNSS inversion of terrestrial water[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(12): 2066-2077.

参考文献

[1] AMOS C B, AUDET P, HAMMOND W C, et al. Uplift and seismicity driven by groundwater depletion in central California[J]. Nature, 2014, 509(7501): 483-486.
[2] BORSA A A, AGNEW D C, CAYAN D R. Ongoing drought-induced uplift in the western United States[J]. Science, 2014, 345(6204): 1587-1590.
[3] CHEW C C, SMALL E E. Terrestrial water storage response to the 2012 drought estimated from GPS vertical position anomalies[J]. Geophysical Research Letters, 2014, 41(17): 6145-6151.
[4] GALLOWAY D L, JONES D R, INGEBRITSEN S E. Land subsidence in the United States[M]. Restown: United States Geological Survey, 1999: 1182.
[5] VAN DAM T, WAHR J, MILLY P C D, et al. Crustal displacements due to continental water loading[J]. Geophysical Research Letters, 2001, 28(4): 651-654.
[6] FARRELL W E. Deformation of the Earth by surface loads[J].Reviews of Geophysics, 1972, 10(3): 761-797.
[7] BOCK Y, MELGAR D. Physical applications of GPS geodesy: a review[J]. Reports on Progress in Physics Physical Society (Great Britain), 2016, 79(10): 106801.
[8] FU Yuning, ARGUS D F, LANDERER F W. GPS as an independent measurement to estimate terrestrial water storage variations in Washington and Oregon[J]. Journal of Geophysical Research: Solid Earth, 2015, 120(1): 552-566.
[9] ZHONG Bo, LI Xianpao, CHEN Jianli, et al. Surface mass variations from GPS and GRACE/GFO: a case study in southwest China[J]. Remote Sensing, 2020, 12(11): 1835.
[10] JIANG Zhongshan, HSU Y J, YUAN Linguo, et al. Characterizing spatiotemporal patterns of terrestrial water storage variations using GNSS vertical data in Sichuan, China[J]. Journal of Geophysical Research: Solid Earth, 2021, 126(12): e2021JB022398.
[11] 何思源, 谷延超, 范东明, 等. 利用GPS垂直位移反演云南省陆地水储量变化[J]. 测绘学报, 2018, 47(3): 332-340.DOI: 10.11947/j.AGCS.2018.20170255. HE Siyuan, GU Yanchao, FAN Dongming, et al. Seasonal variation of terrestrial water storage in Yunnan province inferred from GPS vertical observations[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(3): 332-340.DOI: 10.11947/j.AGCS.2018.20170255.
[12] 成帅, 袁林果, 姜中山, 等. 应用GPS数据和Slepian基函数反演川云渝地区陆地水储量变化[J]. 地球物理学报, 2021, 64(4): 1167-1180. CHENG Shuai, YUAN Linguo, JIANG Zhongshan, et al. Investigating terrestrial water storage change in Sichuan, Yunnan and Chongqing using Slepian basis functions[J]. Chinese Journal of Geophysics, 2021, 64(4): 1167-1180.
[13] JIANG Zhongshan, HSU Y J, YUAN Linguo, et al. Estimation of daily hydrological mass changes using continuous GNSS measurements in mainland China[J]. Journal of Hydrology, 2021, 598: 126349.
[14] HAN S C, RAZEGHI S M. GPS recovery of daily hydrologic and atmospheric mass variation: a methodology and results from the Australian continent[J]. Journal of Geophysical Research: Solid Earth, 2017, 122(11): 9328-9343.
[15] 韩建成, 陈石, 卢红艳, 等. 基于Slepian方法和地面重力观测确定时变重力场模型: 以2011—2013年华北地区数据为例[J]. 地球物理学报, 2021, 64(5): 1542-1557. HAN Jiancheng, CHEN Shi, LU Hongyan, et al. Time-variable gravity field determination using Slepian functions and terrestrial measurements: a case study in North China with data from 2011 to 2013[J]. Chinese Journal of Geophysics, 2021,64(5): 1542-1557.
[16] 沈迎春, 闫昊明, 彭鹏, 等. 质量负荷引起地表形变的格林函数和球谐函数方法对比研究[J]. 武汉大学学报(信息科学版), 2017, 42(7): 1008-1014. SHEN Yingchun, YAN Haoming, PENG Peng, et al. Comparative study of Green's function and spherical harmonic function methods on surface deformation caused by mass loading[J]. Geomatics and Information Science of Wuhan University, 2017, 42(7): 1008-1014.
[17] 孙和平. 大气重力格林函数[J]. 科学通报, 1997, 42(15): 1640-1646. SUN Heping.Green's function of atmospheric gravity[J]. Chinese Science Bulletin, 1997, 42(15): 1640-1646.
[18] WAHR J, KHAN S A, VAN DAM T, et al. The use of GPS horizontals for loading studies, with applications to northern California and southeast Greenland[J]. Journal of Geophysical Research: Solid Earth, 2013, 118(4): 1795-1806.
[19] 归庆明, 黄维彬, 张建军. 抗差泛岭估计[J]. 测绘学报, 1998, 27(3): 211-216. GUI Qingming, HUANG Weibin, ZHANG Jianjun. Robust universal ridge estimation[J]. Acta Geodaetica et Cartographic Sinica, 1998, 27(3): 211-216.
[20] TIKHONOV A N,ARSENIN V Y.Solutions of ill-posed problems[M]. Washington DC:Halsted Press,1977.
[21] LONGMAN I M. A Green's function for determining the deformation of the Earth under surface mass loads: 2. Computations and numerical results[J]. Journal of Geophysical Research, 1963, 68(2): 485-496.
[22] 王振杰, 欧吉坤. 用L-曲线法确定岭估计中的岭参数[J]. 武汉大学学报(信息科学版), 2004, 29(3): 235-238. WANG Zhenjie, OU Jikun. Determining the ridge parameter in a ridge estimation using L-curve method[J]. Geomatics and Information Science of Wuhan University, 2004, 29(3): 235-238.
[23] 胡明城. 现代大地测量学的理论及其应用[M]. 北京: 测绘出版社, 2003: 362-384. HU Mingcheng. The theory and the application of contemporary geodesy[M]. Beijing: Surveying and Mapping Press, 2003: 362-384.
[24] HOBSON E W. The theory of spherical and ellipsoidal harmonics[M].New York: Chelsea Publishing Company, 1955.
[25] BATES A P, KHALID Z, KENNEDY R A. Slepian spatial-spectral concentration problem on the sphere: analytical formulation for limited colatitude-longitude spatial region[J]. IEEE Transactions on Signal Processing, 2017, 65(6): 1527-1537.
[26] SIMONS F J, DAHLEN F A. Spherical Slepian functions and the polar gap in geodesy[J]. Geophysical Journal International, 2006, 166(3): 1039-1061.
[27] FOK H S, LIU Yongxin. An improved GPS-inferred seasonal terrestrial water storage using terrain-corrected vertical crustal displacements constrained by GRACE[J]. Remote Sensing, 2019, 11(12): 1433.
[28] ARGUS D F, FU Yuning, LANDERER F W. Seasonal variation in total water storage in California inferred from GPS observations of vertical land motion[J]. Geophysical Research Letters, 2014, 41(6): 1971-1980.