Construction of an empirical model for estimating the global wave period of spaceborne GNSS-R

doi:10.11947/j.AGCS.2026.20250239

Abstract

Abstract:

Wave period is one of the important parameters of ocean waves, usually obtained by backscatter coefficient and significant wave height (SWH) using satellite altimeters. However, due to the long revisit period and signal attenuation during heavy rain, this method is difficult to meet the needs of dynamic changes. Spaceborne global navigation satellite system reflectometry (GNSS-R) provides a new method for wave period estimation, but currently there is little research on wave period estimation, and there is a lack of reliable estimation models in complex marine environments. Therefore, on the basis of existing scattering theory, this article proposes a method for constructing a wave period estimation model for spaceborne GNSS-R by systematically sorting out the physical and mathematical relationship between the spaceborne GNSS-R observables and the wave parameters (SWH and wave period). Using spaceborne GNSS-R data and ERA5 data under low wind speed (<10 m/s) and high wind speed (>10 m/s) sea conditions, empirical linear models and power function models were proposed for the relationship between wave period, SWH, and GNSS-R observables. And using ERA5, WW3, Jason-3, and buoy wave period data as references, verify the performance of the proposed model in estimating wave periods. The experimental results show that the wave period estimation accuracy of normalized bistatic radar cross-section (NBRCS) observable is slightly better than leading edge slope (LES) observable, and the three parameters power function model is slightly better than the linear model and the two parameters power function model. Compared with existing models, the proposed model can improve root-mean-square error (RMSE), correlation coefficient (CC), and mean absolute percentage error (MAPE) by up to 16.44%, 13.33%, and 12.65%, respectively. Furthermore, it shows good agreement with different validation datasets under both low and high wind speed conditions. Comparative analysis between proportional division validation and 5-fold cross validation shows that the model proposed in this article has both good generalization ability and stable model structure, which fully demonstrates the high reliability of the model.

Key words: spaceborne GNSS-R, significant wave height, wave period, power function model

CLC Number:

P237

Jinwei BU, Shuhui LIU, Shunshuang XU, Tongsu XIANG, Qiulan WANG, Chaoying JI, Xiaoqing ZUO. Construction of an empirical model for estimating the global wave period of spaceborne GNSS-R[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(4): 684-697.

Figures/Tables 15

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Tab. 1

Tab. 2

Tab. 3

Tab. 4

Tab. 5

Fig. 8

Tab. 6

Fig. 9

References 32

[1]	BU J W, YU K, PARK H, et al. Estimation of swell height using spaceborne GNSS-R data from eight CYGNSS satellites[J]. Remote Sensing, 2022, 14(18): 4634.
[2]	WANG Q, BU J, NI J, et al. Ocean swell height estimation from spaceborne GNSS-R data using hybrid deep learning model[J]. GPS Solutions, 2024, 28(4): 187.
[3]	HW ANG P A, TEAGUE W J, JACOBS G A, et al. A statistical comparison of wind speed, wave height, and wave period derived from satellite altimeters and ocean buoys in the Gulf of Mexico region[J]. Journal of Geophysical Research: Oceans, 1998, 103(C5): 10451-10468.
[4]	GOMMENGINGER C, SROKOSZ M, CHALLENOR P, et al. Measuring ocean wave period with satellite altimeters: a simple empirical model[J]. Geophysical Research Letters, 2003, 30(22): 2150.
[5]	WANG J, AOUF L, BADULIN S. Retrieval of wave period from altimetry: deep learning accounting for random wave field dynamics[J]. Remote Sensing of Environment, 2021(265): 112629.
[6]	ZHAO D, LI S, SONG C. The comparison of altimeter retrieval algorithms of the wind speed and the wave period[J]. Acta Oceanologica Sinica, 2012(31): 1-9.
[7]	MACKAY E, RETZLER C, CHALLENOR P, et al. A parametric model for ocean wave period from Ku band altimeter data[J]. Journal of Geophysical Research: Oceans, 2008, 113(C3): C03029.
[8]	KSHATRIYA J, SARKAR A, KUMAR R. Determination of ocean wave period from altimeter data using wave-age concept[J]. Marine Geodesy, 2005, 28(1): 71-79.
[9]	QUARTLY G, GUYMER T, SROKOSZ M. The effects of rain on Topex radar altimeter data[J]. Journal of Atmospheric and Oceanic Technology, 1996, 13(6): 1209-1229.
[10]	BU J, LI H, YU K, et al. Machine learning methods for earth observation and remote sensing using spaceborne GNSS reflectometry: current status, challenges, and future prospects[J]. IEEE Geoscience and Remote Sensing Magazine, 2025(6): 62-66.
[11]	CARDELLACH E, LI W, RIUS A, et al. First precise spaceborne sea surface altimetry with GNSS reflected signals[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2020(13): 102-112.
[12]	LI W, CARDELLACH E, FABRA F, et al. Assessment of spaceborne GNSS-R ocean altimetry performance using CYGNSS mission raw data[J]. IEEE Transactions on Geoscience and Remote Sensing, 2020, 58(1): 238-250.
[13]	LI M, HOU Y, SONG X, et al. Self-attention-guided multi-indicator retrieval for ocean surface wind field with multimodal data augmentation and fusion[J]. IEEE Transactions on Geoscience and Remote Sensing, 2024, 62: 4108822
[14]	BU J W, YU K G, ZUO X, et al. GloWS-Net: a deep learning framework for retrieving global sea surface wind speed using spaceborne GNSS-R data[J]. Remote Sensing, 2023, 15(3): 590.
[15]	YAN Q, HUANG W. Spaceborne GNSS-R sea ice detection using delay-doppler maps: first results from the U. K. TechDemoSat-1 mission[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2016, 9(10): 4795-4801.
[16]	BU J W, YU K G. Sea surface rainfall detection and intensity retrieval based on GNSS-reflectometry data from the CYGNSS mission[J]. IEEE Transactions on Geoscience and Remote Sensing, 2022(60): 5802015.
[17]	BU J W, YU K G, NI J, et al. Machine learning-based methods for sea surface rainfall detection from CYGNSS delay-doppler maps[J]. GPS Solutions, 2022, 26(4): 132.
[18]	BU J W, YU K G. Significant wave height retrieval method based on spaceborne GNSS reflectometry[J]. IEEE Geoscience and Remote Sensing Letters, 2022(19): 1503705.
[19]	BU J W, WANG Q L, NI J. Estimating sea surface swell height using a hybrid model combining CNN, ConvLSTM, and FCN based on spaceborne GNSS-R data from the CYGNSS mission[J]. GPS Solutions, 2024, 28(3): 133.
[20]	REINKING J, ROGGENBUCK O, EVEN-TZUR G. Sea state observation using ground-based GNSS-SNR data[Z]. EGU General Assembly 2020. 2020: EGU2020-2709.
[21]	WANG X, HE X, SHI J, et al. Estimating sea level, wind direction, significant wave height, and wave peak period using a geodetic GNSS receiver[J]. Remote Sensing of Environment, 2022, 279: 113135.
[22]	MAHESHWARI M, CHAKRABORTY A, KUMAR A, et al. Investigation of the relationship of CYGNSS observables with ocean wave parameters[C]//Proceedings of 2021 IEEE International India Geoscience and Remote Sensing Symposium. Ahmedabad: IEEE, 2021.
[23]	HUANG F, GARRISON J L, LEIDNER S M, et al. A forward model for data assimilation of GNSS ocean reflectometry delay-Doppler maps[J]. IEEE Transactions on Geoscience and Remote Sensing, 2021, 59(3): 2643-2656.
[24]	ZAVOROTNY V U, VORONOVICH A G. Scattering of GPS signals from the ocean with wind remote sensing application[J]. IEEE Transactions on Geoscience and Remote Sensing, 2000, 38(2): 951-964.
[25]	CHEN-ZHANG D D, RUF C S, ARDHUIN F, et al. GNSS-R nonlocal sea state dependencies: model and empirical verification[J]. Journal of Geophysical Research: Oceans, 2016, 121(11): 8379-8394.
[26]	GLEASON S, RUF C S, CLARIZIA M P, et al. Calibration and unwrapping of the normalized scattering cross section for the cyclone global navigation satellite system[J]. IEEE Transactions on Geoscience and Remote Sensing, 2016, 54(5): 2495-2509.
[27]	SARKAR A, KUMAR R, MOHAN M. Estimation of ocean wave periods by spaceborne altimeters[J]. Oceanographic Literature Review, 1998, 7(45): 1116.
[28]	QIU T, ZHENG Q, WANG X, et al. Retrieving ocean surface wind speeds in real time on spaceborne GNSS-R receivers: algorithm and validation[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2024(17): 2201-2212.
[29]	LIU X Y, BU J W, ZUO X Q, et al. Performance validation of sea surface wind speed retrieval algorithms and products from the Chinese Tianmu-1 constellation GNSS-R: first results on comparison with other wind speed products[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2025(18): 5189-5203.
[30]	布金伟. 星载GNSS-R技术反演海面降雨强度及风速和浪高方法研究[J]. 测绘学报, 2023, 52(9): 1616. DOI: . doi: 10.11947/j.AGCS.2023.20220709
	BU Jinwei. Study on retrieving sea surface rainfall intensity, wind speed and wave height using spaceborne GNSS-R technology[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(9): 1616. DOI: . doi: 10.11947/j.AGCS.2023.20220709
[31]	布金伟, 余科根, 汪秋兰, 等. 融合星载GNSS-R数据和多变量参数全球海洋有效波高深度学习反演法[J]. 测绘学报, 2024, 53(7): 1321-1335. DOI: . doi: 10.11947/j.AGCS.2024.20230050
	BU Jinwei, YU Kegen, WANG Qiulan, et al. Deep learning retrieval method for global ocean significant wave height by integrating spaceborne GNSS-R data and multivariable parameters[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(7): 1321-1335. DOI: . doi: 10.11947/j.AGCS.2024.20230050
[32]	BALASUBRAMANIAM R, RUF C. Characterization of rain impact on L-band GNSS-R ocean surface measurements[J]. Remote Sensing of Environment, 2020, 239: 111607.

GNSS-R观测值	精度指标	低风速（<10 m/s）		高风速（10~25 m/s）
GNSS-R观测值	精度指标	双参数幂函数	三参数幂函数	线性模型	三参数幂函数
NBRCS	RMSE/s	1.35	1.32	1.23	1.23
	Bias/s	0.03	－0.01	0.03	－0.01
	CC	0.62	0.64	0.59	0.60
	MAPE/（%）	12.36	11.87	10.73	10.68
LES	RMSE/s	1.37	1.35	1.25	1.24
	Bias/s	0.03	0.00	0.03	－0.01
	CC	0.60	0.62	0.58	0.58
	MAPE/（%）	12.57	12.17	10.85	10.76

GNSS-R观测值	精度指标	低风速（<10 m/s）		高风速（10~25 m/s）
GNSS-R观测值	精度指标	双参数幂函数	三参数幂函数	线性模型	三参数幂函数
NBRCS	RMSE/s	1.25	1.20	1.10	1.08
	Bias/s	0.04	－0.03	0.03	－0.02
	CC	0.70	0.72	0.74	0.75
	MAPE/（%）	12.50	12.0	10.80	10.50
LES	RMSE/s	1.28	1.22	1.12	1.10
	Bias/s	0.04	0.02	0.03	－0.03
	CC	0.68	0.70	0.72	0.73
	MAPE/（%）	13.00	12.50	11.20	10.90

GNSS-R观测值	精度指标	低风速（<10 m/s）		高风速（10~25 m/s）
GNSS-R观测值	精度指标	双参数幂函数	三参数幂函数	线性模型	三参数幂函数
NBRCS	RMSE/s	1.45	1.42	1.43	1.41
	Bias/s	0.04	－0.02	0.05	－0.02
	CC	0.58	0.60	0.55	0.56
	MAPE/（%）	13.50	13.01	13.80	13.52
LES	RMSE/s	1.48	1.45	1.45	1.46
	Bias/s	0.04	0.01	0.07	－0.04
	CC	0.56	0.57	0.54	0.53
	MAPE/（%）	14.01	12.53	14.21	13.10

模型	精度指标	正常海洋条件（风速<15 m/s）		气旋海洋条件（风速≥15 m/s）
模型	精度指标	NBRCS观测值	LES观测值	NBRCS观测值	LES观测值
文献[22]中的模型	RMSE/s	1.19	1.52	1.51	1.53
	Bias/s	－0.04	0.42	－0.57	－0.57
	CC	0.72	0.60	0.55	0.55
	MAPE/（%）	11.19	13.75	14.01	14.13
本文模型	RMSE/s	1.09	1.27	1.33	1.38
	Bias/s	0.03	0.13	0.23	0.43
	CC	0.72	0.68	0.59	0.58
	MAPE/（%）	11.01	12.01	13.86	13.91

GNSS-R观测值	精度指标	按比例划分验证		5折交叉验证
GNSS-R观测值	精度指标	双参数幂函数（线性）模型	三参数幂函数	双参数幂函数（线性）模型	三参数幂函数
NBRCS	RMSE/s	1.13（0.93）	1.11（0.92）	1.18（0.96）	1.15（0.96）
	Bias/s	－0.05（－0.05）	0.00（0.00）	－0.04（－0.06）	0.01（－0.02）
	CC	0.75（0.71）	0.76（0.72）	0.73（0.68）	0.75（0.68）
	MAPE/（%）	10.38（8.32）	10.25（8.35）	10.98（8.75）	10.69（8.75）
LES	RMSE/s	1.22（1.03）	1.21（1.03）	1.27（1.08）	1.25（1.08）
	Bias/s	－0.05（－0.05）	0.00（0.00）	－0.04（－0.06）	0.01（－0.02）
	CC	0.71（0.63）	0.72（0.63）	0.68（0.58）	0.69（0.57）
	MAPE/（%）	11.18（9.29）	11.21（9.37）	11.85（9.79）	11.76（9.88）