星载GNSS-R全球海浪波周期估计的经验模型构建

doi:10.11947/j.AGCS.2026.20250239

测绘学报 ›› 2026, Vol. 55 ›› Issue (4): 684-697.doi: 10.11947/j.AGCS.2026.20250239

• 大地测量学与导航 • 上一篇

星载GNSS-R全球海浪波周期估计的经验模型构建

布金伟¹^,²(), 刘淑慧¹, 徐顺双¹, 向彤粟¹, 汪秋兰¹, 籍超颖¹, 左小清¹^,²

^1.昆明理工大学国土资源工程学院，云南　昆明　650093
^2.云南省自然资源智能监测与时空大数据治理重点实验室，云南　昆明　650051

收稿日期:2025-07-01 修回日期:2026-03-17 发布日期:2026-05-11
作者简介:布金伟（1992—），男，博士，讲师，研究方向为GNSS反射遥感。　E-mail：b_jinwei@kust.edu.cn
基金资助:
国家自然科学基金(42404037);云南省“兴滇英才支持计划”青年人才项目(KKXX202521022);云南省基础研究计划(202401CF070151);昆明理工大学高层次人才平台建设项目(20230041);国家级大学生创新训练计划(202510674023)

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

Jinwei BU¹^,²(), Shuhui LIU¹, Shunshuang XU¹, Tongsu XIANG¹, Qiulan WANG¹, Chaoying JI¹, Xiaoqing ZUO¹^,²

^1.Faculty of Land Resources Engineering, Kunming University of Science and Technology, Kunming 650093, China
^2.Yunnan Key Laboratory of Intelligent Monitoring and Spatiotemporal Big Data Governance of Natural Resources, Kunming 650051, China

Received:2025-07-01 Revised:2026-03-17 Published:2026-05-11
About author:BU Jinwei (1992—), male, PhD, lecturer, majors in GNSS reflectometry remote sensing. E-mail: b_jinwei@kust.edu.cn
Supported by:
The National Natural Science Foundation of China(42404037);The Xingdian Talents Support Project of Yunnan Province(KKXX202521022);The Yunnan Fundamental Research Projects(202401CF070151);The Platform Construction Project of High-Level Talent in Kunming University of Science and Technology(20230041);The National College Students'Innovation and Entrepreneurship Training Program(202510674023)

摘要/Abstract

摘要：

波周期是海浪重要参数之一，通常由卫星高度计后向散射系数和有效波高获得。然而，由于重访周期长以及大雨期间信号衰减的问题，该方法难以满足动态变化的需求。星载GNSS-R为波周期估计提供了一种手段，但目前很少有研究关注波周期估算，复杂海洋环境缺少可靠的估算模型。因此，本文在现有散射理论的基础上，通过系统梳理星载GNSS-R观测值与海浪有效波高及波周期之间的物理数学关系，提出一种星载GNSS-R波周期估计模型构建方法。利用低风速（<10 m/s）和高风速（>10 m/s）海况条件下的星载GNSS-R数据、第五代再分析（ERA5）数据提出了波周期与有效波高和GNSS-R观测值之间的经验线性模型和幂函数模型。采用ERA5、第三代波浪模型、Jason-3和浮标波周期数据作为参考，验证所提模型估计波周期的性能。试验结果表明，归一化雷达散射截面观测值的波周期估计精度略优于前沿斜率观测值，且三参数幂函数模型稍优于线性模型和双参数幂函数模型。与现有模型相比，本文模型在均方根误差、相关系数和平均绝对百分比误差方面分别提高了16.44%、13.33%和12.65%。此外，在低风和高风条件下与不同验证数据对比均吻合良好，并且通过按比例划分验证和5折交叉验证对比分析表明，本文模型兼具良好的泛化能力与稳定的模型结构，这充分证明了该模型具有高度的可靠性。

关键词: 星载GNSS-R, 有效波高, 波周期, 幂函数模型

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

中图分类号:

P237

布金伟, 刘淑慧, 徐顺双, 向彤粟, 汪秋兰, 籍超颖, 左小清. 星载GNSS-R全球海浪波周期估计的经验模型构建[J]. 测绘学报, 2026, 55(4): 684-697.

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.

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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）

星载GNSS-R全球海浪波周期估计的经验模型构建

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

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