Retrieval of Significant Wave Height in Coastal Seas of China from GaoFen-3 Satellites Based on Deep Learning

Highlights

What are the main findings?

• A deep learning-based significant wave height (SWH) retrieval method in China’s coastal seas from Gaofen-3 Quad-Polarization Stripmap (QPS) mode was developed, achieving an RMSE of 0.33 m and a bias of −0.13 m. The SWH retrieval results from along-track SAR images exhibit good continuity.
• Based on the polarization ratio model, the SWH retrieval method was extend to Fine Stripmap (FS) and Ultra Fine Stripmap (UFS). Evaluation results demonstrate that the SWH retrieved from both FS and UFS data is encouraging, with RMSEs of 0.44 m and 0.39 m, respectively.

What are the implications of the main findings?

• Different from the conventional single-mode retrieval framework, this study introduced a multi-polarization, multi-observation, high-precision SWH retrieval method, enriching SAR SWH retrieval with more encouraging results.
• The method proposed in this study enables the retrieval of SWH in coastal areas, which can provide data support for human activities and climate studies.

Abstract

The acquisition of significant wave height (SWH) in coastal seas is significantly important to human activities. The Gaofen-3 (GF-3) satellites, comprising GF-3, GF-3B and GF-3C, are independently developed operational SAR of China, capable of providing high-precision, high-resolution, multi-polarization coastal ocean wave observations. In order to obtain SWH in coastal seas, the retrieval of SWH using Quad-Polarization Stripmap (QPS) mode data from GF-3 satellites based on the deep learning method is implemented in this study. Furthermore, to obtain more SWH data, the polarization ratio model was applied to the Fine Stripmap (FS) mode data and Ultra Fine Stripmap (UFS) mode data to extend the model application. Comparisons with ECMWF Reanalysis v5 (ERA5) wave heights show that the QPS mode SWH retrieval achieves a root mean square error (RMSE) of 0.33 m. For the FS mode, the RMSE is 0.44 m (vs. ERA5) and 0.52 m (vs. altimeter). For the UFS mode, the RMSE is 0.39 m (vs. ERA5). Evaluation results indicate the feasibility of the proposed method for coastal SWH retrieval.

1. Introduction

Coastal seas represent the most intensive zone of human–ocean interaction and serve as a critical gateway for deep ocean exploration. Acquiring wave height data in these regions is vital for scientific research, nearshore constructions and navigation. Synthetic Aperture Radar (SAR), an active remote sensing sensor, captures high-resolution microwave images via synthetic aperture technology. Owing to its day-and-night, all-weather operational capabilities, SAR is one of the tools for wave information acquisition [1].

The imaging mechanism of SAR is a nonlinear and complex process [2]. Currently, three main approaches exist for retrieving significant wave height (SWH) from SAR images: theoretical, empirical, and machine learning methods. The retrieval process of theoretical methods typically begins by retrieving ocean wave spectra from the SAR images, after which the wave height is integrated from the ocean wave spectra. Representative algorithms include the Max Planck Institute (MPI) algorithm [3], semi-parametric algorithm (SPRA) [4], partition rescaling and shift algorithm (PARSA) [5], and parameterized first-guess spectrum method (PFSM) [6]. Their retrieval accuracy is affected by prior information quality, and complex computational procedures limit operational applications. Consequently, theoretical methods have not been widely adopted.

To avoid the complex computation of ocean wave spectra and directly establish the relationship between SAR images and SWH, empirical SWH retrieval methods have become a preferred alternative. Schulz-Stellenfleth et al. [7] proposed an empirical algorithm named CWAVE_ERS based on ERS SAR, pioneering the use of orthogonal decomposition to extract SAR image parameters. These parameters were then used to establish a functional relationship with wave height for subsequent retrieval. Building on the CWAVE_ERS framework, Stopa [8] and Li [9] extended the empirical SAR wave height retrieval algorithm to Sentinel-1 and Envisat satellites, respectively. Pleskachevsky [10] developed the XWAVE_C empirical algorithm for SWH retrieval from X-band SAR data, with results demonstrating good retrieval accuracy. Wang et al. [11] proposed an empirical SWH retrieval algorithm using quad-polarimetric data from GF-3 satellite, employing six SAR image-related parameters to achieve SWH retrieval. Comparisons with reference data showed favorable results, and the algorithm exhibited promising application potential for other GF-3 imaging modes.

In recent years, with the continuous growth of SAR ocean observations and advances in data analysis methods, machine learning-based SAR wave height retrieval has gradually emerged as a new research field. Some researchers have adopted simple machine learning model structures, which offer fast computation but relatively large errors. For example, Leng et al. [12] proposed a GF-3 wave height retrieval method based on the XGBoost model, demonstrating that XGBoost outperformed both the Convolutional Neural Network (CNN) and Support Vector Regression models, achieving an RMSE of 0.34 m. Gao et al. [13] developed an Envisat–ASAR wave height retrieval method based on a Support Vector Machine (SVM), with RMSEs of 0.34 m and 0.48 m when compared to reanalysis wave height data and in situ data, respectively. Gao et al. [14] presented a Multilayer Perceptron (MLP) method for SWH retrieval from Sentinel-1A SAR data; comparisons with wave heights from the European Centre for Medium-Range Weather Forecasts (ECMWF) and Jason-3 yielded RMSEs of 0.47 m and 0.54 m, respectively.

Other researchers have utilized deep learning model structures, which can extract more underlying patterns hidden in data. While these models have lower computational speed, they yield relatively more accurate retrieval results. Wang [15] proposed an SWH retrieval model based on a residual convolutional neural network using GF-3 wave mode data. Assessment results based on altimeter observation data showed an RMSE of 0.32 m. Yan [16] also conducted research on GF-3 wave mode SWH retrieval using a dual-branch neural network combining a Backpropagation Neural Network (BPNN) and a CNN; comparisons with altimeter and buoy observation data indicated good retrieval accuracy. Quach et al. [17] researched Sentinel-1 SAR SWH retrieval based on a dual-branch neural network model, reporting an RMSE of 0.3 m when assessed with altimeter data. Wu et al. [18] studied Sentinel-1 SAR SWH retrieval in the Arctic region using a BPNN, achieving an RMSE of 0.6 m against Surface Waves Investigation and Monitoring (SWIM) data. Xue et al. [19] proposed a Sentinel-1 SAR SWH retrieval method based on a CNN model, with an RMSE of 0.32 m when compared to in situ measurements.

Wave mode is one of GF-3 satellites’ means of acquiring ocean wave information. Using wave mode data for wave height retrieval has the following limitations: Wave mode observations are predominantly distributed in deep ocean regions, resulting in insufficient capability for obtaining wave information in coastal areas. Moreover, although wave mode provides quad-polarimetric images with abundant wave information, the spatial coverage is limited to 5 km × 5 km, which is comparable to the footprint spacing of adjacent altimeter nadir points [20], and the spatial distribution of wave mode observations is relatively sparse, with large distances between adjacent observations.

Moreover, in shallow coastal waters (typically defined as areas where water depth is less than half the wavelength), wave propagation dynamics differ from those in deep waters, and the SAR backscatter signal is also affected by seafloor topography [21], which may introduce error into the retrieved results. Sea surface wind is a key factor influencing the variation in sea surface micro-scale waves and one of the main drivers of ocean wave height changes. Therefore, sea surface wind is adopted as an input parameter for coastal SWH retrieval in this study.

To obtain coastal SWH, this study conducted research on the retrieval of SWH in coastal seas of China based on Quad-Polarimetric Stripmap (QPS) mode data from GF-3 satellites (representing GF-3, GF-3B, and GF-3C). GF-3B and GF-3C are the follow-up operational satellites of the GF-3 mission, optimized based on GF-3 technology. Based on QPS mode data of GF-3 satellites, this study established a dual-branch SWH retrieval model composed of residual blocks and a BPNN, and compared the retrieval results with ECMWF Reanalysis v5 (ERA5) wave heights. To expand SWH data availability, the retrieval model was further extended to Fine Stripmap (FS) and Ultra Fine Stripmap (UFS) modes based on the Polarization Ratio (PR) model, enabling SWH retrieval from GF-3 satellites’ FS and UFS modes. The FS and UFS mode-retrieved SWH were compared with both ERA5 wave height and altimeter SWH to validate the generalization capability of the proposed retrieval method. Section 2 of this paper introduces the data and methods used in this study, Section 3 presents the SWH retrieval results, Section 4 is a discussion about this study, and Section 5 provides conclusions of this study.

2. Data and Methods

2.1. Data

The data utilized in this study consist of the following: GF-3 SAR images, altimeter wave height, and ERA5 sea surface wind speed and wave height.

2.1.1. GF-3 SAR Images

The GF-3 SAR images used in this study include QPS, FS and UFS imaging modes. The QPS mode is a quad-polarimetric mode (HH, HV, VH, VV) with two subtypes: QPSI and QPSII. QPSI has an azimuth resolution of 8 m and a range resolution of 6~9 m, with a swath of 20~35 km. In contrast, QPSII offers an azimuth resolution of 25 m and a range resolution of 15~27 m, covering a swath of 35~50 km [22]. Both subtypes can capture ocean wave information in coastal areas. This study utilized Level-1A QPS mode HH and VV polarized data acquired from January 2022 to April 2025 over coastal and adjacent seas of China. Compared with single polarization, dual-polarization (HH and VV) retrieval has the advantage of providing more sea surface scattering information, which enhances the accuracy and robustness of retrieval results. A total of 1467 images from January 2022 to December 2024 were used for training and tuning the retrieval model, while 75 images from January to April 2025 were reserved for accuracy assessment. The spatial distribution of QPS mode data used in this study are shown in Figure 1.

The FS mode is a dual-polarization imaging mode (HH, HV or VV, VH) with two subtypes: FSI and FSII. FSI has an azimuth resolution of 5 m and a range resolution of 4~6 m, with a swath exceeding 50 km. FSII provides an azimuth resolution of 10 m and a range resolution of 8~12 m, covering a swath of 95~110 km. The UFS mode is a single-polarization (HH) imaging mode that has an azimuth resolution of 3 m and a range resolution of 2.5–5 m. The imaging swath of UFS mode is 30 km [22]. A total of 874 Level-1A FS mode images and 554 Level-1A UFS mode images from January to April 2025 were used for model application extension. The spatial distribution of the FS and UFS mode data utilized in this study are shown in Figure 2.

A summary of the incidence angle, imaging swath and polarization for the FS, QPS and UFS observation modes used in this study is presented in

Table 1. The parameters of QPS, FS and UFS data used in this study.

Mode	Incidence (Degree)	Imaging Swath (km)	Polarization
FS	19~51	50~110	HH, HV/VV, VH
QPS	19~50	20~50	HH, HV, VH, VV
UFS	21~50	30	HH

below.

It can be seen from Table 1 that the incidence of the three modes falls almost within the same range, and the imaging swath of the FS mode is significantly larger than that of the other two modes. The QPS mode provides quad-polarimetric data and encompasses the polarization modes of both FS and UFS. Therefore, it is feasible to develop an SWH retrieval method based on QPS mode data, which can then be extended and applied to the FS and UFS modes.

2.1.2. Altimeter Wave Height Data

To accurately evaluate the retrieval results of SAR-derived SWH, altimeter wave height data from nine satellites between January and April 2025 were used as references for assessing the FS and UFS mode retrieval outcomes. These altimeter data were obtained from the global near-real-time Level 3 wave height product provided by the Copernicus Marine Environment Monitoring Service (CMEMS). The altimeter measurements in this product were uniformly normalized to Sentinel-6A and calibrated against in situ buoy observations, with high data quality ensured through a rigorous screening process.

2.1.3. ERA5 Reanalysis Data

ERA5 reanalysis data, the fifth-generation atmospheric reanalysis dataset from ECMWF, integrate extensive historical observations into an advanced modeling and data assimilation system to provide hourly estimates of atmospheric parameters. This study employed both ERA5 sea surface wind speed data and ERA5 wave height data. The wind speed served as input to the retrieval model, with a spatial resolution of 0.25° and a temporal resolution of 1 h. The ERA5 wave height, which had a spatial resolution of 0.5° and a temporal resolution of 1 h, were used as references during model training and validation process.

Due to the insufficient number of matched samples between QPS data and altimeter measurements for training a deep learning model, ERA5 wave height data were selected as the reference dataset for model training, benefiting from their high temporal resolution. Existing studies have demonstrated good agreement between ERA5 wave height data and buoy observations from the National Data Buoy Center (NDBC) [23]. ERA5 wave height has also been successfully used as reference data in several previous studies, yielding good results [24]. In order to evaluate the accuracy of ERA5 wave height in coastal areas, an assessment of the ERA5 wave height for the coastal seas of China from January to May 2025 was implemented based on altimeter data described in Section 2.1.2. The evaluation results indicate that ERA5 wave height in this region exhibits good accuracy, as shown in Figure 3.

2.2. Methods

The methods employed in this study comprise SAR image preprocessing, training dataset generation, retrieval model construction, and retrieval results validation.

2.2.1. SAR Image Preprocessing

For the quantitative application of SAR images in SWH retrieval, radiometric correction of SAR Level-1A data is essential. Radiometric correction was performed using the method described in Equation (1):

$${\sigma }_{dB}^0=10{log}_{10}\left(P^I\times {\left({\displaystyle \frac{QV}{m}}\right)}^2\right)-K_{dB}$$

(1)

Here, $QV$ (Quality Value) represents the pre-quantification image parameter, and $K_{dB}$ denotes the calibration constant. Both are provided in the auxiliary data files of the SAR L1A product. ${\sigma }_{dB}^0$ refers to the radiometrically corrected backscattering coefficient. $P^I=I^2+Q^2$, where $I$ and $Q$ are the value of real and imaginary channels of the Level-1A images, respectively, and $m$ is a constant with a value of 32,767. A case of a radiometrically corrected QPS image at VV polarization is illustrated in Figure 4. This image was acquired at 21:45:55 UTC on 27 October 2024, and the incidence angle ranges from 35.37° to 37.11°.

Secondly, denoising was applied to the radiometrically corrected SAR images. The mean filtering with a 10 × 10 window size was employed to reduce speckle noise in this study.

2.2.2. Training Dataset Generation

After radiometric correction and mean filtering, QPS mode images were segmented into 256 × 256-pixel sub-images with a step size of 256 pixels. Based on these sub-images, further filtering was conducted, including heterogeneity calculation and land–sea discrimination.

The quality of sub-images affects SWH retrieval accuracy. Heterogeneity index ${\mathsf{\xi }}_{\mathrm{H}}$ [25] was applied here to assess the homogeneity of each SAR sub-image and filter out heterogeneous samples like heavy rainfall, oil spills and artificial features. The formulas for calculating ${\mathsf{\xi }}_{\mathrm{H}}$ are as follows:

$${\mathsf{\xi }}_{\mathrm{H}} ={\left(\sum _{\mathrm{k}}\stackrel{\mathrm{-}}{\mathrm{mean}}\left({\widehat{\mathsf{\Phi }}}_{\mathrm{k}}\right)\right)}^{-1}\sum _{\mathrm{k}}{\displaystyle \frac{\stackrel{\mathrm{-}}{\mathrm{var}}\left({\widehat{\mathsf{\Phi }}}_{\mathrm{k}}\right)}{\stackrel{\mathrm{-}}{\mathrm{mean}}\left({\widehat{\mathsf{\Phi }}}_{\mathrm{k}}\right)}}$$

(2)

$$\stackrel{\mathrm{-}}{\mathrm{var}}\left({\widehat{\mathsf{\Phi }}}_{\mathrm{k}}\right)={\displaystyle \frac{1}{\mathrm{N}}}\sum _{\mathrm{j}=1}^{\mathrm{N}}{\left({\widehat{\mathsf{\Phi }}}_{\mathrm{k}}^{\mathrm{j}}\right)}^2-\mathrm{mean}{\left({\widehat{\mathsf{\Phi }}}_{\mathrm{k}}\right)}^2$$

(3)

Here, ${\widehat{\mathsf{\Phi }}}_{\mathrm{k}}$ denotes the power spectral density of SAR sub-images. In this study, only SAR sub-images satisfying ${\mathsf{\xi }}_{\mathrm{H}}\le$ 1.05 were used as input data. Additionally, 1 km spatial resolution elevation data provided by the National Oceanic and Atmospheric Administration (NOAA) were employed to determine whether a SAR sub-image contained land areas. If a sub-image was found to cover land, it was discarded from the training dataset.

Next, spatial-temporal matching was performed between SAR sub-images and ERA5 data, including both ERA5 wind speed and wave height. Since the temporal resolution of the ERA5 data was 1 h, the temporal matching window was set to 30 min. To obtain a sufficient number of training data for the retrieval model, two-dimensional spatial interpolation was adopted as spatial matching. The center latitude and longitude of each SAR sub-image were taken as the interpolation point, and the wind speed or wave height at that location were interpolated using the four surrounding ERA5 grid points. This interpolation-based spatial matching method was also applied in the evaluation of test results. The two-dimensional spatial interpolation method based on ERA5 grid data is illustrated in Figure 5.

Based on the methods mentioned above, the input data of the SWH retrieval model were ultimately obtained. In this study, the training data fed into the retrieval model consisted of two-dimensional (2D) and one-dimensional (1D) data. The 2D input with a size of 256 × 256 × 2 included HH-polarized and VV-polarized SAR sub-images. The 1D inputs included the mean backscattering coefficients (${\sigma }_{HH}^0$,${ \sigma }_{VV}^0$), the variances (${cvar}_{HH}$, ${cvar}_{VV}$), and the central incidence angle of the SAR sub-images, and the interpolated ERA5 wind speed at the center of SAR sub-images. The formulas for calculating the mean backscattering coefficients and variances are provided below.

$${\sigma }_{pp}^0={\displaystyle \frac{1}{n^2}}\sum _{i=1}^n\sum _{j=1}^n{\sigma }_{ij}^0$$

(4)

$${cvar}_{pp}={\displaystyle \frac{1}{n^2}}\sum _{i=1}^n\sum _{j=1}^n{\left({\sigma }_{ij}^0-{\sigma }_{pp}^0\right)}^2$$

(5)

Here, $n$ denotes the side length of the SAR sub-image, which was 256 in this study; $i$ and $j$ represent the row and column indices within the sub-image, respectively; and $p$ indicates the polarization channel. The training dataset for the retrieval model contained 274,594 samples in total, 80% of which were used for model training and the remaining 20% for validation during the training process. The histograms of SWH and incidence angle for the training data are presented in Figure 6.

2.2.3. Retrieval Model Construction

To establish the relationship between SAR backscattering signals and SWH while fully leveraging the spatial information of ocean waves, this study proposes a dual-branch retrieval model that integrates both SAR backscattering information and spatial feature information of ocean waves. The architecture of the proposed retrieval model is illustrated in Figure 7.

As shown in Figure 7, the proposed dual-branch SAR SWH retrieval model consists of two distinct branches: one composed of five Residual Blocks, and the other consisting of a six-layer Fully Connected (FC) neural network. The outputs of these two branches are concatenated and then passed through two additional FC layers to produce the final estimated SWH.

The Residual Block, a fundamental component of residual networks, is a type of CNN originally proposed by He et al. [26]. Given the relatively limited dataset used in this study, Residual Blocks with a simple structure were adopted. Each Residual Block in the retrieval model contains two convolutional layers with 3 × 3 kernels, Rectified Linear Unit (ReLU) activation functions, a max pooling layer, and a batch normalization layer. A skip connection is implemented using a 1 × 1 convolutional layer. The other branch of the retrieval model employs a six-layer FC network, which performs non-linear transformations through weighted connections and activation functions. As the depth increases, the number of neurons first increases and then decreases, enabling the network to capture increasingly complex non-linear features.

2.2.4. Retrieval Results Validation

The accuracy of the retrieved SWH in this study was evaluated by comparison with two reference datasets: ERA5 wave height data and altimeter wave height data.

For the ERA5-based evaluation, the two-dimensional spatial interpolation method detailed in Section 2.2.2 was applied. Specifically, the retrieved SWH data were partitioned into successive 5 × 5 square grids, with the central latitude and longitude of each grid designated as the interpolation point. The interpolated reference wave height at this point was then compared with the mean wave height of the corresponding grid.

For the altimeter-based evaluation, the following procedure was adopted: The mean value of the retrieved SWH within a 5 × 5 square grid centered on the altimeter footprint was calculated for comparison. The validation methodology for altimeters is illustrated in Figure 8.

Furthermore, the bias, RMSE, correlation coefficient (R), and scatter index (SI) were employed in this study to evaluate the accuracy of the retrieved SWH. The formulas for these indexes are provided below.

$$bias={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left(x_i-y_i\right)$$

(6)

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{\left(x_i-y_i\right)}^2}$$

(7)

$$R={\displaystyle \frac{{\sum }_{i=1}^n[{(x}_i-\overline{x})(y_i-\overline{y})]}{\sqrt{{\sum }_{i=1}^n{\left(x_i-\overline{x}\right)}^2{\sum }_{i=1}^n{\left(y_i-\overline{y}\right)}^2}}}$$

(8)

$$SI={\displaystyle \frac{\sqrt{\frac{1}{n}{\sum }_{i=1}^n{\left[\left(x_i-\overline{x}\right)-\left(y_i-\overline{y}\right)\right]}^2}}{\overline{y}}}$$

(9)

Here, $x_i$ and $y_i$ represent the $i$-th retrieved SWH and the reference wave height, respectively, while $\overline{x}$ and $\overline{y}$ denote the mean values of the retrieved SWH and the reference wave height, respectively. $n$ indicates the number of validation data points.

3. Results

Based on the training data and neural network described in Section 2.2.2 and Section 2.2.3, the SWH retrieval model was developed through training process. The retrieval accuracy of the model was subsequently evaluated using test data from January to April 2025 of the QPS, FS and UFS modes. The detailed validation procedure is described below.

3.1. The Evaluation of QPS Mode-Retrieved SWH

GF-3 satellites acquire spatially continuous SAR images along their flight orbit. To evaluate the retrieval model’s performance on continuous SAR images, this study performed SWH retrieval using a single orbit of QPS images and validated the accuracy of the along-track results. The along-track QPS images were acquired on 17 January 2025 from the orbit “GF3_MYC_QPSI_044438”. Due to the lack of spatial–temporally matched altimeter data, ERA5 wave heights were used as the reference for validating the QPS mode SWH retrievals. The retrieved SWH and corresponding evaluation for “GF3_MYC_QPSI_044438” are presented in Figure 9. The black dots in Figure 9a represent the matched points between the QPS-retrieved SWH and the ERA5 reference data, where the ERA5 wave heights were derived using the spatial interpolation method detailed in Section 2.2.2. It should be noted that the two distinct gaps within the black dots in Figure 9a occur because at least one of the four surrounding ERA5 grid points near the interpolation location is an invalid value (i.e., a land point). Figure 9b displays the comparison of wave heights at these matched points.

As shown in Figure 9a, the SWH retrieved by the proposed model from continuous SAR images exhibits good spatial continuity. Figure 9b indicates that the trend of the retrieved SWH is generally consistent with that of the ERA5 wave heights as latitude increases, with the retrieved values distributed relatively symmetrically around the ERA5 reference. Only a very small number of points show significant deviations from the ERA5 data. However, at lower wave heights (28°N–30°N), the retrieved SWH values are mostly higher than those of ERA5, indicating a slight overestimation by the proposed model under low-wave-height conditions. Furthermore, the RMSE of these matched points was calculated to be 0.3 m.

To comprehensively evaluate the QPS mode SWH retrievals, this study conducted an accuracy validation using all QPS mode images acquired over China’s coastal seas from January to April 2025. The validation results are presented in Figure 10.

As shown in Figure 10, the comparison between QPS-retrieved SWH and ERA5 wave heights is generally distributed along both sides of the diagonal, with an RMSE of 0.33 m and a bias of −0.13 m. For wave heights below 1 m, most retrieved values are overestimated relative to the reference. This indicates that the retrieval model tends to overestimate low wave heights, which may be attributed to the relatively limited training data under low-wave-height conditions.

3.2. The Evaluation of FS Mode- and UFS Mode-Retrieved SWH

Although QPS mode observations provide quad-polarimetric wave information, their spatial coverage is relatively limited. FS and UFS are alternative acquisition modes of GF-3 satellites that can obtain wave information in coastal waters. In order to obtain more SWH data, the retrieval model proposed in this study was extended for application to FS mode and UFS mode images. The SAR SWH retrieval model employed in this study requires both HH and VV polarized images. However, the FS mode provides only HH or VV polarized data and the UFS mode provides only HH polarized data. To address this limitation, a PR model was applied to generate the complementary polarization channel. The observed image and the calculated complementary polarization image were then jointly input into the model to produce SWH estimates for the FS and UFS modes.

Following the empirical PR model originally proposed by Mouche [27], Zhang et al. [28] developed a PR model suitable for GF-3 QPS mode observations based on 3170 images. This PR model was adopted in this study to generate the complementary polarization channel image and construct the input dataset for the FS and UFS modes. The PR model is defined as follows:

$$PR={\displaystyle \frac{{\sigma }_{VV}^0}{{\sigma }_{HH}^0}}=0.649\times e^{0.0268\theta }-0.14$$

(10)

Here, ${\sigma }_{VV}^0$ and ${\sigma }_{HH}^0$ represent the radiometrically corrected linear backscattering coefficients, and $\theta$ denotes the incidence angle in degrees. The PR model used in this study is a function of the incidence angle, and there is a significant overlap in the incidence angle ranges among the FS, UFS, and QPS modes mentioned above. Therefore, it is reasonable to generate the complementary polarization data for both the FS and UFS modes. Figure 11 shows the results of observed FS mode and UFS mode images and their corresponding calculated images using the PR model. The FS mode image was taken by GF-3 at 10:02:59 UTC on 24 February 2025, with a mean incidence angle of 34.85° and a center longitude and latitude of 121.22°E and 21.37°N, respectively. The UFS mode image was taken by GF-3C at 22:08:44 UTC on 28 March 2025, with a mean incidence angle of 34.63° and a center longitude and latitude of 118.05°E and 22.03°N, respectively.

Since the retrieval process of the FS mode utilizes a calculated HH or VV polarized image, this paper evaluated the continuity of FS mode retrieval results following the same approach as for the QPS mode. The retrieval results from the orbit “GF3_MYC_FSII_044257” acquired on 5 January 2025 are presented in Figure 12a, where the black circles represent the nadir footprints of the Chinese–French Oceanography Satellite (CFOSAT) SWIM spectrometer. The footprints are interrupted approximately between 31°N and 32°N because the corresponding data in the original file are flagged as 1, which indicates invalid values. The comparison method between the retrieval SWH and the SWIM wave heights is described in Section 2.2.4, and the results are illustrated in Figure 12b. The time interval between the two sets of observations is within 30 min, yielding a total of 102 matched points between the retrievals of “GF3_MYC_FSII_044257” and the SWIM nadir wave heights.

As illustrated in Figure 12a, the retrieval results maintain good continuity across different images. In Figure 12b, the retrieved SWHs generally exhibit a consistent trend with the altimeter wave height. However, within the latitude range of 32°N–33°N, the retrieved SWHs are slightly higher than those from SWIM—consistent with the conclusion drawn for the QPS mode, indicating that the retrieval model proposed in this study tends to overestimate low-wave-height values. Furthermore, the RMSE of these matched points is calculated as 0.26 m.

This study conducted an evaluation of the FS mode SWH retrieval based on a total of 874 FS images between January and April 2025. The accuracy of the FS mode-retrieved SWH was validated against two reference datasets: ERA5 wave height data and altimeter wave height data. The evaluation results are presented in Figure 13.

As shown in Figure 13, the comparison results between FS mode-retrieved SWH and ERA5 wave height are symmetrically distributed along both sides of the diagonal, with an RMSE of 0.44 m, while the RMSE against altimeter wave height is 0.52 m. Since our retrieval model was trained using ERA5 wave heights as the reference, this may explain the higher accuracy observed when validated against ERA5 data. In contrast, the FS mode retrieval accuracy is slightly lower than that of the QPS mode, which is associated with the use of the simulated complementary polarization channel image as model input. Despite this minor accuracy trade-off, this work achieves a broader spatial coverage of SWH retrievals. The comparison results demonstrate that the FS mode-retrieved SWH values are acceptable, confirming the suitability of our retrieval model for FS data.

Additionally, to validate the UFS mode retrieval accuracy, two along-track retrieval results are presented from the orbits “GF3C_SYC_UFS_015523” acquired on 18 March 2025 and “GF3C_MH1_UFS_015084” acquired on 16 February 2025, both of which have matched altimeter data. The retrieval results are shown in Figure 14a, where the black circles represent the footprints of the satellite with ARgos and ALtiKa (SARAL) altimeters. Detailed comparisons between SARAL wave heights and the retrieved SWH values are provided in Figure 14b and Figure 14c, respectively.

As illustrated in Figure 14, there is good consistency between the UFS mode-retrieved SWHs and the SARAL wave heights, with the maximum deviation within 0.5 m. Under both high-wave-height conditions (orbit: GF3C_SYC_UFS_015523) and low-wave-height conditions (orbit: GF3C_MH1_UFS_015084), the retrieved results are consistently lower than those from SARAL. However, the retrieval results for high wave heights exhibit greater fluctuations, indicating relatively larger errors in high-wave-height retrievals.

To comprehensively evaluate the retrieval accuracy of the UFS mode, this study conducted an evaluation of the retrieved SWH from 554 scenes of the UFS mode based on ERA5 wave height. The evaluation results are shown in Figure 15.

As can be seen from Figure 15, the comparative results are relatively symmetrically distributed on both sides of the diagonal, with an RMSE of 0.39 m. The retrieval accuracy is superior to that of the FS mode but inferior to that of the QPS mode. Consistent with previous findings, the evaluation results indicate that the model still tends to overestimate low wave heights. Overall, the proposed retrieval method demonstrates good suitability for UFS mode data.

4. Discussion

This paper develops a method for retrieving SAR SWH in nearshore coastal waters using observational data from the GF-3 series of satellites. Compared to existing SAR wave height retrieval methods, the improvement of this paper lies in achieving wave height retrieval for multiple SAR observation modes using a model, while maintaining accuracy consistent with other approaches. However, there are also some deviations in the paper that require discussion and represent areas for future improvement.

This study employs a two-dimensional spatial interpolation method to address the problem of insufficient model training data. However, the need for interpolation between ERA5 grid points could be a source of error in the retrievals. As a result, there is a deviation between the interpolated results and the actual wave heights. In the future, with the availability of more QPS mode observations from GF-3 satellites, an increasing number of SAR images will directly match ERA5 grid points. This will reduce errors associated with spatial interpolation and further improve the accuracy of SAR-derived SWH, which represents a key direction for future refinement of this work.

5. Conclusions

A study of SWH retrieval in coastal seas of China using GF-3 satellites QPS mode observations from January 2022 to April 2025 is implemented based on a dual-branch deep learning model. The model is composed of a residual neural network and an FC network. QPS mode data from January 2022 to December 2024 were used for training the retrieval model, while data from January to April 2025 served as the test data. The retrieval results from the test data were compared with ERA5 wave height data. Furthermore, to acquire more wave height data, FS mode and UFS mode observations were also used for SWH retrieval based on the PR model, following a comparative analysis of their observational conditions. Retrieval results for the UFS and FS modes were validated against both ERA5 wave heights and altimeter wave heights. The main conclusions of this study are as follows:

SWH retrieved from along-track QPS mode SAR images exhibit good continuity. When validated against ERA5 wave heights, the QPS mode retrieval results yield an RMSE of 0.33 m and a bias of −0.13 m. Evaluation indicates that the model tends to overestimate low wave heights, which may be associated with the distribution of wave height data used for model training.

SWH retrieved from along-track FS mode and UFS mode images also maintain good continuity. For the FS mode retrieval results, the RMSE of the evaluation based on ERA5 wave height is 0.44 m, with a bias of −0.02 m, and the RMSE of the evaluation based on altimeter wave height is 0.52 m, with a bias of 0.05 m. For the UFS mode retrieval results, the RMSE is 0.39 m when compared with ERA5 wave height. Evaluation results for both modes confirm that the proposed retrieval model tends to overestimate low wave heights. This may be attributed to the limited availability of training data for low-sea-state conditions. Another possible reason is that when the wave height is low, the local wind speed is also relatively low, resulting in a smoother sea surface., which leads to a lack of backscatter signals received by the SAR, making it impossible to accurately capture wave information. However, these results still demonstrate that SWH retrieved from FS mode and UFS mode data are encouraging, verifying the suitability of the retrieval model for FS and UFS mode observations.

SAR provides observations of high spatial resolution, reaching up to the meter level, yet the capacity for continuous long-term monitoring is limited by instrumental constraints. In contrast, ERA5 wave height data has high temporal resolution but sparse spatial grids, which is insufficient for providing detailed wave height information. This study combines the advantages of both datasets by collocating SAR observations with ERA5 data and applying deep learning techniques to map ERA5 wave heights onto SAR images, which generates high-spatial-resolution SAR SWH products. These SWH products can be used in wave height climate studies, providing a reference for wave height changes and prediction. By integrating the spatial details of SAR with the temporal continuity of ERA5, the generated dataset enables more comprehensive investigations into regional wave dynamics and long-term trends. It is hoped that with further work this approach could refine wave height analysis accuracy and support more robust predictive forecasting for oceanographic applications.