Sea surface height inversion based on inverse modeling of multi-GNSS and multi-frequency SNR data

doi:10.11947/j. AGCS.2024.20240249.

Abstract

Abstract:

The inverse modeling utilizing signal-to-noise ratio (SNR) data enables the inversion of sea surface height (SSH) and its variations. However, the accuracy and stability of the inversion process hinge on the precision of the initial values and the temporal continuity of the SNR data. Further investigation is required into the performance of inverse modeling based on multi-mode and multi-frequency SNR data for inverting sea-level changes and its application in tidal analysis. This study introduces a dynamic correction for sea surface variations into the inversion results of the Lomb-Scargle periodogram (LSP), which is utilized for initializing parameters in the inverse modeling process. This approach yields stable and uniform high-precision SSH inversion values, which are then employed to conduct tidal harmonic analysis. Three stations with large tidal ranges, namely MAYG, BRST, and SC02, were selected for inverse modeling and inversion experiments using their one-year multi-mode and multi-frequency SNR data. Algorithm validation was conducted through comparative analysis with in-situ SSH measurements from tide gauges. The results indicate that the root-mean-square error (RMSE) of the SSH inversion via inverse modeling is 5.97 cm for MAYG, 8.78 cm for BRST, and 2.38 cm for SC02, demonstrating centimeter-level accuracy in SSH inversion. When compared with the tidal harmonic analysis results of the observed SSH, the annual and monthly fitting residuals exhibit high consistency in terms of mean square error. The mean absolute error (MAE) of the extracted tidal constituent amplitudes is better than 1 cm, and the MAE of the extracted tidal phase lags is within 3°. Both the tidal components and non-tidal water levels extracted from the tidal analysis demonstrate high consistency. Therefore, the inversion of SSH using multi-mode and multi-frequency SNR data can serve as a viable alternative to in-situ SSH measurements for tidal harmonic analysis.

Key words: GNSS-IR, sea surface height inversion, inverse modeling, LSP, SNR data

CLC Number:

P229

Lingqiu CHEN, Hongzhou CHAI, Jingyang BAO, Min WANG, Naiquan ZHENG. Sea surface height inversion based on inverse modeling of multi-GNSS and multi-frequency SNR data[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(11): 2099-2110.

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测站名	坐标	潮差/m	距海面高度/m	方位角取值	高度角取值	设备		数据间隔/s
测站名	坐标	潮差/m	距海面高度/m	方位角取值	高度角取值	接收机	天线	数据间隔/s
MAYG	12.78°S，45.26°E	4.0	6	0°~180°，330°~360°	5°~15°	TRIMBLE ALLOY	TRM59800.00	30
BRST	48.38°N，4.50°W	7.0	17	130°~330°	8°~20°	TRIMBLE ALLOY	TRM57971.00	30
SC02	48.55°N，123.01°W	3.5	5	50°~240°	5°~13°	TRIMBLE NETR9	TRM59800.80	15

GNSS	信号频率	SNR类型
GNSS	信号频率	BRST	MAYG	SC02
	L1：1 575.42 MHZ	S1C	S1C	S1
GPS	L2：1 227.60 MHZ	S2X	S2X	S2
	L5：1 176.45 MHZ	S5X	S5X	S5
GLON-ASS	G1：1602+K×9/16 MHZ	S1C，S1P	S1C，S1P	S1
GLON-ASS	G2：1246+K×7/16 MHZ	S2C，S2P	S2C，S2P	S2
	E1：1 575.42 MHZ	S1X	S1X	S1
	E5a：1 176.45 MHZ	S5X	S5X	S5
Galileo	E5b：1 207.140 MHZ	S7X	S7X	S7
Galileo	E5（E5a+E5b）：1 191.795 MHZ	S8X	S8X	S8
	E6：1 278.75 MHZ	S6X	—	—
	B1：1 561.098 MHZ	S2I	S2I	—
	B3：1 268.52 MHZ	S6I	S6I	—
BeiDou	B2：1 207.140 MHZ	S7I	S7I	—
	B1C：1 575.42 MHZ（BDS-3）	S1X	S1X	—
	B2a：1 176.45 MHZ（BDS-3）	S5X	S5X	—

GNSS	频率	SNR类型	滑动窗口SNR弧段数	RMSE/cm	相关系数
GPS	L1	GPS-S1C	2	48.30	0.843 75
	L1，L2	GPS-S1C；GPS-S2X	10	7.90	0.995 26
	L1，L2，L5	GPS-S1C；GPS-S2X；GPS-S5X	14	6.87	0.996 74
GLO GPS GLO GAL GPS	L1	GPS-S1C；GLO-S1C；GLO-S1P	7	20.18	0.968 56
GLO GPS GLO GAL GPS	L1	GPS-S1C；GLO-S1C；GLO-S1P；GAL-S1X	9	14.63	0.982 97
GPS GLO GAL BDS	L1	GPS-S1C；GLO-S1C；GLO-S1P；GA L-S1X；BDS-S2I	14	9.41	0.992 95
		GPS-S1C；GPS-S2X；GLO-S1C；GLO-S1P；GLO-S2C	；
	L1，L2	GLO-S2P；GA L-S1X；GAL-S7X；BDS-S1X；BDS-S2I；	45	3.53	0.999 14
		BDS-S6I；BDS-S7I；
	L1，L2，L5	全部	63	3.59	0.999 19

测站名	海面高度序列	分潮数	解释原始信号方差比例/（%）	中误差/cm
MAYG	验潮站实测	59	98.9	8.87
MAYG	逆建模反演	59	98.9	8.80
BRST	验潮站实测	59	98.9	16.57
BRST	逆建模反演	59	98.7	17.63
SC02	验潮站实测	59	98.0	11.55
SC02	逆建模反演	59	98.0	11.37

分潮名称	振幅/cm			迟角/（°）
分潮名称	实测	反演	差值	实测	反演	差值
M₂	104.140	101.321	2.819	26.340	27.712	-1.372
S₂	53.158	51.651	1.507	65.869	67.282	-1.413
N₂	18.720	18.548	0.172	6.941	9.068	-2.127
K₁	14.137	12.903	1.234	4.217	6.181	-1.964
K₂	14.130	14.036	0.094	61.530	63.575	-2.045
O₁	8.953	8.177	0.776	6.960	5.983	0.977
NU₂	4.172	3.900	0.272	5.612	6.449	-0.837
P₁	4.103	3.844	0.259	5.442	359.752	5.690