Joint along-track and cross-track crossover adjustment of SWOT/KaRIn altimetry data

doi:10.11947/j.AGCS.2026.20260122

Abstract

Abstract:

This study proposes a joint along-track and cross-track crossover adjustment method for SWOT/KaRIn altimetry data to enhance the quality of sea surface heights (SSHs). The approach employs a hybrid polynomial model to correct time-dependent errors along-track and a linear model to compensate for geographically correlated errors across-track. Validation was conducted in the sea region around Japan (130°E—145°E, 27°N—43°N) using scientific-phase Level 2 Ka-band Radar Interferometer low-rate SSH products (L2_LR_SSH) from cycle 003. Four adjustment schemes were tested: along-track Fourier model, along-track hybrid polynomial model, along-track hybrid polynomial model+cross-track Fourier model, and along-track hybrid polynomial model+cross-track linear model. Results indicate that, for along-track-only adjustment, along-track hybrid polynomial model yields higher accuracy in reducing crossover discrepancies compared to along-track Fourier model. Incorporating cross-track adjustment, along-track hybrid polynomial model+cross-track linear model achieves the lowest standard deviation (STD) of crossover discrepancies, measuring 4.27 cm along-track and 3.62 cm cross-track. To assess generalizability, external crossover adjustments were performed between SWOT and reference missions (Sentinel-6A and Jason-3). Along-track hybrid polynomial model+cross-track linear model consistently delivers optimal accuracy post-adjustment, with unequal weighting proving superior to equal weighting. These findings demonstrate that joint along-track and cross-track crossover adjustment significantly improves SWOT SSH data quality, providing a robust dataset for marine gravity field research.

Key words: crossover adjustment, sea surface height, SWOT altimetry satellite, crossover discrepancies, along-track and cross-track

CLC Number:

P228

Xin Liu, Shaoshuai Ya, Xin Fan, Yongjun Jia, Xiaotao Chang, Guangbin Zhu, Jinyun Guo. Joint along-track and cross-track crossover adjustment of SWOT/KaRIn altimetry data[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(7): 1199-1211.

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References 44

[1]	孙和平. 对我国重力学未来发展的几点思考[J]. 中国科学院院刊, 2024, 39(5): 881-890.
	Sun Heping. Some reflections on developing trend of gravimetry in China[J]. Bulletin of Chinese Academy of Sciences, 2024, 39(5): 881-890.
[2]	孙中苗, 管斌, 翟振和, 等. 海洋卫星测高及其反演全球海洋重力场和海底地形模型研究进展[J]. 测绘学报, 2022, 51(6): 923-934. DOI: . doi: 10.11947/j.AGCS.2022.20220069
	Sun Zhongmiao, Guan Bin, Zhai Zhenhe, et al. Research progress of ocean satellite altimetry and its recovery of global marine gravity field and seafloor topography model[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(6): 923-934. DOI: . doi: 10.11947/j.AGCS.2022.20220069
[3]	Zhu Chengcheng, Guo Jinyun, Ya Shaoshuai, et al. Moving geoid gradient method for high-precision and high-resolution gravity recovery from SWOT wide-swath data[J]. IEEE Transactions on Geoscience and Remote Sensing, 2025, 63: 4205613
[4]	Li Zhen, Guo Jinyun, Zhu Chengcheng, et al. The SDUST2022GRA global marine gravity anomalies recovered from radar and laser altimeter data: contribution of ICESat-2 laser altimetry[J]. Earth System Science Data, 2024, 16(9): 4119-4135.
[5]	胡敏章, 李建成, 邢乐林. 由垂直重力梯度异常反演全球海底地形模型[J]. 测绘学报, 2014, 43(6): 558-565, 574.
	Hu Minzhang, Li Jiancheng, Xing Lelin. Global bathymetry model predicted from vertical gravity gradient anomalies[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(6): 558-565, 574.
[6]	Wan Xiaoyun, Ran Jiangjun. An alternative method to improve gravity field models by incorporating GOCE gradient data[J]. Earth Sciences Research Journal, 2018, 22(3): 187-193.
[7]	Yu Daocheng, Hwang C, Andersen O B, et al. Gravity recovery from SWOT altimetry using geoid height and geoid gradient[J]. Remote Sensing of Environment, 2021, 265: 112650.
[8]	Yuan Jiajia, Guo Jinyun, Zhu Chengcheng, et al. High-resolution sea level change around China seas revealed through multi-satellite altimeter data[J]. International Journal of Applied Earth Observation and Geoinformation, 2021, 102: 102433.
[9]	Yan Weishuang, Liu Xin, Li Zhen, et al. Performance of marine gravity anomalies extracted from SWOT KaRIn data of science phase in the Gulf of Mexico[J]. Scientific Reports, 2025, 15(1): 38385.
[10]	Zhang Shengjun, Chen Xu, Zhou Runsheng, et al. NSOAS24: a new global marine gravity model derived from multi-satellite sea surface slopes[J]. Geoscientific Model Development, 2025, 18(4): 1221-1239.
[11]	押少帅, 刘新, 周瑞宸, 等. 基于科学阶段SWOT/KaRIn测高数据反演高精度的垂直重力异常梯度模型[J]. 测绘学报, 2025, 54(9): 1583-1595. DOI: . doi: 10.11947/j.AGCS.2025.20240520
	Ya Shaoshuai, Liu Xin, Zhou Ruichen, et al. High accuracy vertical gradient of gravity anomaly model determined from SWOT/KaRIn altimetry data during scientific phase[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(9): 1583-1595. DOI: . doi: 10.11947/j.AGCS.2025.20240520
[12]	李真, 郭金运, 孙中苗, 等. 基于ICESat-2多波束激光测高数据的全球海洋重力异常反演分析[J]. 测绘学报, 2024, 53(2): 252-262. DOI: . doi: 10.11947/j.AGCS.2024.20230207
	Li Zhen, Guo Jinyun, Sun Zhongmiao, et al. Global marine gravity anomalies recovered from multi-beam laser altimeter data of ICESat-2[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(2): 252-262. DOI: . doi: 10.11947/j.AGCS.2024.20230207
[13]	Miao Xiangying, Wang Jing, Mao Peng, et al. Cross-track error correction and evaluation of the Tiangong-2 interferometric imaging radar altimeter[J]. IEEE Geoscience and Remote Sensing Letters, 2022, 19: 1505505.
[14]	Dibarbour G, Anandon C, Briol F, et al. Blending 2D topography images from SWOT into the altimeter constellation with the Level-3 multi-mission DUACS system[PP/OL]. EGUsphere (2024-05-27) [2026-02-03]. https://doi.org/10.5194/egusphere-2024-1501.
[15]	Wan Jianhua, Sun Qinting, Liu Shanwei, et al. Sea-level change over the China sea and its vicinity derived from 25-year T/P series altimeter data[J]. Journal of the Indian Society of Remote Sensing, 2018, 46(12): 1939-1947.
[16]	胡建国, 章传银, 常晓涛. 近海多卫星测高数据联合处理的方法及应用[J]. 测绘通报, 2004(1): 1-4.
	Hu Jianguo, Zhang Chuanyin, Chang Xiaotao. Methods of multi-satellite altimetry data processing and its application[J]. Bulletin of Surveying and Mapping, 2004(1): 1-4.
[17]	金涛勇, 李建成, 邢乐林, 等. 多源卫星测高数据基准的统一研究[J]. 大地测量与地球动力学, 2008, 28(3): 92-95, 99.
	Jin Taoyong, Li Jiancheng, Xing Lelin, et al. Research on datum unification of multi-satellite altimetric data[J]. Journal of Geodesy and Geodynamics, 2008, 28(3): 92-95, 99.
[18]	Wagner C A. Radial variations of a satellite orbit due to gravitational errors: implications for satellite altimetry[J]. Journal of Geophysical Research: Solid Earth, 1985, 90(B4): 3027-3036.
[19]	Rummel R. Principle of satellite altimetry and elimination of radial orbit errors[M]//RUMMEL R, SANSO'F. Satellite altimetry in geodesy and oceanography. Berlin: Springer, 1993: 190-241.
[20]	黄谟涛, 王瑞, 翟国君, 等. 多代卫星测高数据联合平差及重力场反演[J]. 武汉大学学报(信息科学版), 2007, 32(11): 988-993.
	Huang Motao, Wang Rui, Zhai Guojun, et al. Integrated data processing for multi-satellite missions and recovery of marine gravity field[J]. Geomatics and Information Science of Wuhan University, 2007, 32(11): 988-993.
[21]	黄谟涛, 翟国君, 欧阳永忠, 等. 海洋磁力测量误差补偿技术研究[J]. 武汉大学学报(信息科学版), 2006, 31(7): 603-606.
	Huang Motao, Zhai Guojun, Ouyang Yongzhong, et al. On error compensation in marine magnetic survey[J]. Geomatics and Information Science of Wuhan University, 2006, 31(7): 603-606.
[22]	刘传勇, 暴景阳, 黄谟涛, 等. 验后平差方法在Geosat/GM卫星测高数据处理中的应用[J]. 海洋测绘, 2008, 28(1): 5-8.
	Liu Chuanyong, Bao Jingyang, Huang Motao, et al. The application of posteriori compensation theory of error in altimeter data set from Geosat/GM crossover adjustment[J]. Hydrographic Surveying and Charting, 2008, 28(1): 5-8.
[23]	Deng X, Featherstone W E. A coastal retracking system for satellite radar altimeter waveforms: application to ERS-2 around Australia[J]. Journal of Geophysical Research: Oceans, 2006, 111(C6): C06012.
[24]	张胜军, 李建成, 王立伟, 等. GM测高数据反演中国近海及邻域精细重力场[J]. 海洋学报(中文版), 2014, 36(11): 85-89.
	Zhang Shengjun, Li Jiancheng, Wang Liwei, et al. Refined marine gravity field of the China's seas and its adjacent area derived from GM altimeter data[J]. Haiyang Xuebao, 2014, 36(11): 85-89.
[25]	Zwally H, Schutz B, Abdalati W, et al. ICESat's laser measurements of polar ice, atmosphere, ocean, and land[J]. Journal of Geodynamics, 2002, 34(3/4): 405-445.
[26]	Rudenko S, Dettmering D, Zeitlhöfler J, et al. Radial orbit errors of contemporary altimetry satellite orbits[J]. Surveys in Geophysics, 2023, 44(3): 705-737.
[27]	Tai Changkou, Fu L L. On crossover adjustment in satellite altimetry and its oceanographic implications[J]. Journal of Geophysical Research: Oceans, 1986, 91(C2): 2549-2554.
[28]	Fan Xin, Guo Jinyun, Zhang Huiying, et al. A two-step method of crossover adjustment for satellite altimeter data[J]. Advances in Space Research, 2025, 75(1): 219-232.
[29]	Van Gysen H, Coleman R. On the satellite altimeter crossover problem[J]. Journal of Geodesy, 1997, 71(2): 83-96.
[30]	Fu L L, Pavelsky T, Cretaux J F, et al. The surface water and ocean topography mission: a breakthrough in radar remote sensing of the ocean and land surface water[J]. Geophysical Research Letters, 2024, 51(4): e2023GL107652.
[31]	于道成. 多源卫星测高数据反演南海最佳重力场[J]. 测绘学报, 2025, 54(10): 1908. DOI: . doi: 10.11947/j.AGCS.2025.20240037
	Yu Daocheng. Optimal gravity field recovery in the South China Sea from multiple altimeter missions[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(10): 1908. DOI: . doi: 10.11947/j.AGCS.2025.20240037
[32]	Li Zhen, Guo Jinyun, Hwang Cheinway, et al. Tailored method for optimizing deflection of the vertical model using multidirectional geoid gradients from SWOT/KaRIn observations[J]. Geophysical Journal International, 2026, 244(2): ggaf484.
[33]	Zhu Chengcheng, Li Zhen, GUO Jinyun, et al. The calculation and analysis of along-track and cross-track crossover SSHs discrepancies from wide-swath altimetry data[PP/OL]. Research Square (2024-08-15) [2026-02-03]. https://doi.org/10.21203/rs.3.rs-4766084/v1.
[34]	Guo Hengyang, Wan Xiaoyun, Zhang Keyan, et al. An improved latitude difference method for SWOT accuracy evaluation using crossover discrepancies[J]. IEEE Transactions on Geoscience and Remote Sensing, 2025, 63: 4203912.
[35]	Ishii M, Kimoto M, Sakamoto K, et al. Steric sea level changes estimated from historical ocean subsurface temperature and salinity analyses[J]. Journal of Oceanography, 2006, 62(2): 155-170.
[36]	Surface Water Ocean Topography Mission. SWOT product description L2_LR_SSH_20220902 Rev A[R/OL]. 2023. https://archive.podaac.earthdata.nasa.gov/podaac-ops-cumulus-docs/web-misc/swot_mission_docs/pdd/D-56407_SWOT_Product_Description_L2_LR_SSH_20220902_RevA.pdf.
[37]	Peng Fukai, Deng Xiaoli. Validation of Sentinel-3A SAR mode sea level anomalies around the Australian coastal region[J]. Remote Sensing of Environment, 2020, 237: 111548.
[38]	祝程程, 李真, 郭金运, 等. 基于限定区域的纬度做差法解算宽刈幅测高数据交叉点位置[J]. 测绘学报, 2026, 55(4): 673-683. DOI: . doi: 10.11947/j.AGCS.2026.20250341
	Zhu Chengcheng, Li Zhen, Guo Jinyun, et al. Improved latitude difference method for calculating cross over point position from wide-swath measurement data[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(4): 673-683. DOI: . doi: 10.11947/j.AGCS.2026.20250341
[39]	魏巧云. 交叉点位置确定方法研究及相关数据处理[D]. 开封: 河南大学, 2017: 15-17.
	Wei Qiaoyun. Research on crossover points location determination method and related data processing[D]. Kaifeng: Henan University, 2017: 15-17.
[40]	Yuan Jiajia, Guo Jinyun, Niu Yupeng, et al. Mean sea surface model over the Sea of Japan determined from multi-satellite altimeter data and tide gauge records[J]. Remote Sensing, 2020, 12(24): 4168.
[41]	Gaultier L, Ubelmann C, Fu L L. The challenge of using future SWOT data for oceanic field reconstruction[J]. Journal of Atmospheric and Oceanic Technology, 2016, 33(1): 119-126.
[42]	Dibarboure G, Labroue S, Ablain M, et al. Empirical cross-calibration of coherent SWOT errors using external references and the altimetry constellation[J]. IEEE Transactions on Geoscience and Remote Sensing, 2011, 50(6): 2325-2344.
[43]	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.
[44]	Jiang Maofei, Xu Ke, Wang Jiaming. Evaluation of Sentinel-6 altimetry data over ocean[J]. Remote Sensing, 2022, 15(1): 12.

测高卫星	轨道高度/km	轨道倾角/（°）	发布机构	测高任务	重复周期/d	观测时间	周期
Sentinel-6A	1 336	66	ESA	ERM	10	2023-08-26—2023-09-24	103～105
Jason-3	1 336	66	ESA	ERM	10	2023-08-28—2023-09-26	350～351
SWOT	890	77.6	NASA	ERM	21	2023-08-31—2023-09-21	003

交叉点个数	模型形式	k取值	模型参数个数
1	平均分配交叉点不符值	0	0
2～3	只选用误差模型线性部分	0	2
4～5	线性方程与一级傅里叶级数结合	1	4
6～8	线性方程与二级傅里叶级数结合	2	6
>8	线性方程与三级傅里叶级数结合	3	8

统计量	平差前	沿轨傅里叶模型	沿轨混合多项式模型	沿轨混合多项式模型+跨轨傅里叶模型	沿轨混合多项式模型+跨轨线性模型
Max	86.93	82.26	72.29	81.64	62.33
Min	－55.54	－53.31	－53.35	－55.75	－51.38
Mean	－1.15	－0.04	0.05	0.07	0.02
STD	8.47	6.32	6.08	6.57	4.27
RMS	8.55	6.32	6.08	6.57	4.27

范围绝对值/cm	平差前		沿轨傅里叶模型		沿轨混合多项式模型		沿轨混合多项式模型+跨轨傅里叶模型		沿轨混合多项式模型+跨轨线性模型
范围绝对值/cm	数量	百分比/（%）	数量	百分比/（%）	数量	百分比/（%）	数量	百分比/（%）	数量	百分比/（%）
<5	7 7312	55.73	99 756	71.91	10 0872	72.72	98 482	70.99	116 853	84.23
[5，10）	37 153	36.78	24 548	17.69	24 432	17.61	25 207	18.17	17 110	12.33
[10，20）	18 732	13.50	11 364	8.19	10 792	7.78	12 499	9.01	4 330	3.12
[20，30）	4448	3.21	2699	1.94	2384	1.72	2132	1.53	331	0.24
≥30	1072	0.77	350	0.25	237	0.17	397	0.28	93	0.06

统计量	平差前	沿轨傅里叶模型	沿轨混合多项式模型	沿轨混合多项式模型+跨轨傅里叶模型	沿轨混合多项式模型+跨轨线性模型
Max	46.78	39.05	36.34	38.24	26.83
Min	－36.91	－33.72	－33.64	－40.64	－29.57
Mean	－0.98	－0.23	0.07	0.17	0.11
STD	8.20	6.34	6.13	6.35	3.62
RMS	8.26	6.35	6.13	6.35	3.62