Enhancing Significant Wave Height Retrieval with FY-3E GNSS-R Data: A Comparative Analysis of Deep Learning Models

Abstract

Significant Wave Height (SWH) is a crucial parameter in oceanographic research, essential for understanding various marine and atmospheric processes. Traditional methods for obtaining SWH, such as ship-based and buoy measurements, face limitations like limited spatial coverage and high operational costs. With the advancement of Global Navigation Satellite Systems reflectometry (GNSS-R) technology, a new method for retrieving SWH has emerged, demonstrating promising results. This study utilizes Radio occultation sounder (GNOS) data from the FY-3E satellite and incorporates the latest Vision Transformer (ViT) technology to investigate GNSS-R-based SWH retrieval. We designed and evaluated various deep learning models, including ANN-Wave, CNN-Wave, Hybrid-Wave, Trans-Wave, and ViT-Wave. Through comparative training using ERA5 data, the ViT-Wave model was identified as the optimal retrieval model. The ViT-Wave model achieved a Root Mean Square Error (RMSE) accuracy of 0.4052 m and Mean Absolute Error (MAE) accuracy of 0.2700 m, significantly outperforming both traditional methods and newer deep learning approaches utilizing Cyclone Global Navigation Satellite Systems (CYGNSS) data. These results underscore the potential of integrating GNSS-R technology with advanced deep-learning models to enhance SWH retrieval accuracy and reliability in oceanographic research.

1. Introduction

The retrieval of Significant Wave Height (SWH) is crucial in meteorology and oceanography as it serves as a fundamental parameter for assessing ocean wave conditions. Accurate SWH measurements are Vital for understanding the sea state, which directly influences marine navigation, offshore operations, and coastal management. Utilizing remote sensing techniques to retrieve SWH allows for high-resolution, wide-coverage wave data collection, essential for improving weather forecasts, monitoring marine environments, and studying climate change impacts. Moreover, SWH data play a significant role in validating and calibrating wave models, which are integral to predicting extreme weather events and managing coastal risks [1,2,3,4,5]. Traditional methods for retrieving SWH, such as using altimeter satellites, buoys, and ship-based observations, face several challenges, including computational complexity, data acquisition difficulties, and platform-specific limitations. Conventionally, the primary methodology for measuring Significant Wave Height (SWH) utilizes altimeter satellites, including TOPEX/Poseidon, Jason-1, Jason-2, and Sentinel-3. While these satellites provide extensive global coverage, their data collection is subject to temporal and spatial discontinuities, which stem from their specific orbital configurations. The advent of GNSS-R technology introduces a novel observational approach for SWH measurement, potentially mitigating some of the limitations faced by traditional altimetric methods [6,7,8]. Buoys, although highly accurate and capable of providing real-time data, are limited by geographic distribution and are susceptible to damage from severe weather, necessitating regular maintenance, which is costly and logistically challenging [9,10]. Ship-based observations, while valuable for direct measurements, are infrequent, geographically constrained, and costly, often restricted to specific routes or missions. In the context of Voluntary Observing Ship (VOS) data, the quality of data can be suboptimal, which may stem from the inherent limitations and challenges of the data collection process itself [11,12]. Furthermore, the calibration and validation of SWH data require continuous efforts and integration of various datasets, adding to the overall complexity and resource requirements [9,10].

GNSS-Reflectometry (GNSS-R) is an innovative remote sensing technique that leverages reflected signals from Global Navigation Satellite Systems (GNSS) to extract various environmental parameters, including surface wind speeds, ice extent, soil moisture, and SWH [13,14,15,16,17,18,19]. By processing Delay-Doppler Maps (DDMs) to correlate surface roughness with wave height, GNSS-R offers a compelling alternative to traditional SWH retrieval methods. Compared to traditional methods, GNSS-R has several advantages in SWH retrieval. It overcomes the limitations of buoys, which are restricted by geographic distribution and susceptibility to severe weather damage, and ship-based observations, which are infrequent and geographically constrained. Additionally, GNSS-R data collection is less affected by adverse weather conditions and does not require complex and resource-intensive data processing algorithms [13]. The spaceborne GNSS-R research commenced with the TechDemoSat-1 (TDS-1) mission, launched by the UK Space Agency (UKSA), which carried the SGR-ReSI payload to demonstrate GNSS-R’s feasibility for environmental monitoring [7]. This pioneering mission paved the way for subsequent advancements, notably the Cyclone Global Navigation Satellite System (CYGNSS), launched by NASA in December 2016. Comprising eight microsatellites, CYGNSS provides frequent and comprehensive measurements. Initially scheduled to terminate on 30 September 2023, the mission has been extended due to its excellent operational performance and high-quality data products. The extension of CYGNSS’s mission underscores the significant potential and broad applicability of GNSS-R technology. This technique not only enhances our ability to monitor and understand oceanic and atmospheric conditions but also promises a robust future for environmental remote sensing [19]. By integrating GNSS-R capabilities with advanced machine learning models, researchers can achieve unprecedented accuracy in SWH retrieval, contributing significantly to marine navigation, weather forecasting, and climate research. The continued operation of CYGNSS beyond its planned termination date highlights its importance and efficacy in environmental monitoring, affirming the broad and meaningful impact of GNSS-R technology.

Studies by Ruf et al. [20] have demonstrated strong correlations between CYGNSS-derived oceanographic parameters measurements and buoy data, validating the approach for SWH retrieval. Additionally, Clarizia et al. [21] have significantly improved noise reduction in DDMs, enhancing the precision of SWH measurements. In addition to these data analysis methods, machine learning techniques have also been widely applied to SWH retrieval. These techniques have notably enhanced the capabilities of CYGNSS in retrieving various environmental parameters. For instance, neural networks have been applied to retrieve sea surface wind speeds with high accuracy. Methods developed by Stopa and Cheung [7] and Quach et al. [22] utilize large datasets of co-located buoy and satellite data to train models that accurately retrieve wind speeds based on GNSS-R signal characteristics. Neural networks trained on extensive datasets of the co-located buoy and satellite data have modeled the relationship between reflected signal characteristics and SWH with high precision. For example, Morris et al. [23] and Gleason et al. [24] used neural networks to retrieve SWH from CYGNSS data, demonstrating significant improvements in accuracy. Furthermore, deep learning approaches, such as those explored by Li et al. [25], have shown promise in extracting SWH from GNSS-R data, leveraging the ability of deep neural networks to handle complex and non-linear relationships. Recent studies, such as those by Patanè et al., have proposed the use of LSTM-based estimation models [26], while Bu et al. combined ERA5 data with CNN networks for SWH retrieval research [27].

Despite these advancements, there are still limitations in using machine learning for SWH retrieval compared to wind speed retrieval. It has been noted in several studies that the models employed for SWH often exhibit less sophistication and the datasets used are relatively sparse [25,28]. Research on SWH retrieval lags behind that of wind speed, where more advanced models like transformers have been applied. For instance, the use of hybrid transformer networks and ConvLSTM models in wind speed forecasting has shown significant improvements in accuracy and prediction horizons [29,30]. In contrast, SWH models tend to rely on older, simpler architectures, which may not capture the complex dynamics as effectively. Overall, the integration of advanced machine learning techniques with GNSS-R data from CYGNSS not only improves the accuracy and precision of SWH retrievals but also broadens the scope of applications, making it a crucial tool for contemporary remote sensing. However, the field still faces challenges, particularly in the sophistication of models used for SWH retrieval compared to wind speed retrieval.

In China, the current approach to SWH retrieval predominantly utilizes data from the CFOSAT (China France Oceanography Satellite). Launched in 2018, CFOSAT employs GNSS-R to monitor ocean surface wind speeds and SWH [31,32]. However, its single-satellite design limits both data coverage and temporal resolution. With the launch of the FY-3E series satellites in 2021, equipped with GNOS (GNSS Occultation Sounder) payloads capable of GNSS-R data collection, China’s spaceborne GNSS-R technology has seen rapid development. Comparatively, CYGNSS, composed of eight microsatellites, offers high-frequency data that are particularly useful for monitoring extreme weather conditions. CYGNSS processes DDMs from reflected GPS signals to maintain data quality under adverse weather, while FY-3E’s GNOS leverages multi-frequency DDMs to improve measurement accuracy and reduce noise [20,21,33]. The GNOS sensor on FY-3E also demonstrates superior capabilities in monitoring polar ice changes and high-latitude ocean environments, complementing the strengths of CYGNSS [14,34,35,36,37,38,39,40]. Despite significant progress in sea surface wind speed retrieval [41,42,43], comprehensive research on SWH retrieval using FY-3E data has yet to be conducted. Developing this capability would significantly enhance the utility and accuracy of FY-3E products. By focusing on SWH retrieval, FY-3E can provide more reliable data, crucial for applications such as marine navigation, weather forecasting, and climate research [44,45,46]. This research would not only improve the precision of FY-3E’s measurements but also extend its applicability, thereby solidifying its role in global oceanographic monitoring [37,47,48].

Given the challenges in machine learning-based GNSS-R retrieval methods, this study focuses on using FY-3E GNOS payload data with ERA5 as the reference data for SWH retrieval. The contributions of this paper are as follows:

• Application of FY-3E GNOS Data in SWH Retrieval: This study is the first to utilize FY-3E GNOS payload data for SWH retrieval, achieving promising accuracy.
• Proposal of the ViT-Wave Model: Combining the latest transformer models with ViT models tailored for the task, we propose a specialized model, ViT-Wave, for SWH retrieval.
• Global Ocean Analysis: The global ocean analysis demonstrates that the model significantly improves the retrieval accuracy of high wave heights and enhances the overall precision distribution across different sea states.

The structure of this paper is as follows: Section 2 introduces the data encountered in the experiment. Section 3 describes the experimental methods and models. Section 4 details the experimental process. Section 5 provides a summary and discussion of the experimental results. Section 6 concludes the paper with final remarks. By advancing the application of neural network models and integrating state-of-the-art transformer techniques, this research aims to significantly improve the accuracy and reliability of SWH retrieval using FY-3E GNOS data, contributing to the broader field of oceanographic monitoring and analysis.

2. Date Description

2.1. FY-3E Data

The FY-3E satellite is equipped with the GNOS payload, which enables the reception of GNSS-R signals, thereby facilitating research in SWH retrieval. Unlike CYGNSS, which can only receive GPS signals, FY-3E can simultaneously receive reflected signals from GPS, BeiDou, and Galileo satellites. This capability provides FY-3E with a broader observational range. Specifically, FY-3E’s observation coverage extends from 67°N to 67°S, compared to CYGNSS’s coverage from 34°N to 34°S. This wider observational range allows FY-3E to monitor a more extensive area, including high-latitude regions. Moreover, the effective scattering area for DDM data also differs between the two systems. FY-3E features an effective scattering area of 9 × 20 bins, while CYGNSS has an area of 17 × 11 bins. These distinctions enhance the observational capabilities of FY-3E, providing more detailed and accurate measurements. Currently, the FY-3E observation system consists of a single satellite. Plans are underway to expand this system with additional satellites, which, once operational, will facilitate multiple observations of the same location within a single day. This expanded capability mirrors the technological approach utilized by the CYGNSS satellite system, which boasts a revisit cycle of less than seven hours as detailed in the CYGNSS handbook [49]. The accompanying Figure 1 provides a schematic representation of the FY-3E satellite’s observation points over a single day. For this study, data from one month (August 2023 to September 2023) were selected.

In the experimental analysis, a total of thirty-two essential data parameters were utilized. The variables sp_lat and sp_lon denote the geographic coordinates of the specular reflection points. An additional twenty-nine variables comprehensively characterize various attributes of the DDM, all of which are detailed in

Table 1. Variables utilized in the experiment.

Variables
sp_lat	sp_lon	Ddm_brcs_factor	Ddm_effective_area	Ddm_doppler_refer
Ddm_kurtosis	Ddm_noise_m	Ddm_noise_raw	Ddm_noise_source	Ddm_peak_column
Ddm_peak_delay	Ddm_peak_doppler	Ddm_peak_power_ratio	Ddm_peak_raw	Ddm_peak_row
Ddm_peak_snr	Ddm_power_factor	Ddm_quality_flag	Ddm_range_refer	Ddm_skewness
Ddm_sp_column	Ddm_sp_delay	Ddm_sp_dles	Ddm_sp_doppler	Ddm_sp_les
Ddm_sp_nbrcs	Ddm_sp_normalized_snr	Ddm_sp_raw	Ddm_sp_reflectivity	Ddm_sp_row
Ddm_sp_snr

. Notably, Ddm_effective_area is presented as a two-dimensional array measuring 9 × 20, while Sp_delay_doppler_flag is utilized as a quality assessment metric. Comprehensive descriptions of each variable are provided in Appendix A.

2.2. ERA5 SWH

ERA5 is a fifth-generation reanalysis dataset produced by the European Centre for Medium-Range Weather Forecasts (ECMWF). It provides comprehensive and high-resolution climate and weather data, including SWH, on a global scale. ERA5 offers detailed temporal and spatial resolution, with hourly data on a 0.25° × 0.25° grid. This fine resolution allows for precise monitoring and analysis of wave conditions across different regions and time periods. The dataset spans several decades, enabling long-term studies and trend analysis in wave dynamics and climate change.

In numerous research studies, ERA5 SWH data have been utilized as training labels for machine learning models due to its high accuracy and consistency, which make it an ideal reference dataset [50,51]. In prior initiatives to incorporate buoy data for machine learning applications, we gathered measurements from 255 buoys, ranging from ID 41001 to 46279. Regrettably, only 90 datapoints from the same month were successfully matched, an amount deemed insufficient for machine learning analysis. Consequently, we adopted ERA5 as the training label, a method commonly utilized in SWH retrieval research, as corroborated by multiple studies in the domain. Our experiments effectively matched nearly 100,000 data points with ERA5, facilitating thorough experimental analysis. Should adequate buoy data become available, we aim to conduct additional experiments to further validate and refine our models. Compared to other datasets, the integration of satellite observations, buoy measurements, and numerical weather prediction models in ERA5 provides a robust and reliable source of SWH data [52]. In this experiment, ERA5 SWH data corresponding to the same time period as the FY-3E observations were used for reference and validation.

3. Methodology

This study introduces five distinct neural network models tailored for SWH retrieval: the ANN-Wave model, based on ANN; the CNN-Wave model, utilizing CNN; the hybrid-Wave model, integrating both ANN and CNN architectures; the Trans-Wave model, built on the transformer framework; the ViT-Wave model, leveraging the ViT architecture. Each model comprises different network layers and weights, as indicated in

Table 2. Weights for Each Layer in the Models.

Layer	ANN-Wave	CNN-Wave	Hybrid-Wave	Trans-Wave	ViT-Wave
Convolutional Layers
Conv2d	-	[128, 1, 5, 5]	[128, 1, 5, 5]	-	-
Conv2d	-	[32, 128, 4, 4]	[32, 128, 4, 4]	-	-
Conv2d	-	[1, 32, 2, 2]	[1, 32, 2, 2]	-	-
Transformer Layers
Embedding	-	-	-	[20, 64]	[4 * 4, 64]
TransformerEncoder	-	-	-	[64, 8, 3, 256]	[64, 8, 3, 256]
Linear Layer
Linear	[31, 1000]	[12, 1000]	[43, 1000]	[(9 * 64) + 31, 1000]	[(45 * 64) + 31, 1000]
SWH Retrieval Layers	Weight Dimensions
Linear	[1000, 2000]
Linear	[2000, 1500]
Linear	[1500, 500]
Linear	[500, 200]
Linear	[200, 100]
Linear	[100, 10]
Linear	[10, 1]

. The models are structured into several parts: the first part consists of convolutional layers that employ CNN methods to extract features from the DDM; the second part includes transformer layers that analyze DDM features using transformer techniques; the third part consists of linear layers that process the features derived from various methods in a unified manner; the final part, also composed of linear layers, outputs the model’s final SWH retrieval results.

In the following sections, each model will be introduced and discussed in detail, highlighting their unique structures and the methodologies employed for SWH retrieval.

3.1. ANN-Wave

The ANN-Wave model is predominantly based on an Artificial Neural Network (ANN) architecture. The primary inputs to this model consist of spatial-temporal auxiliary information, including the latitude and longitude of the specular point (SP), one-dimensional feature data from DDMs, and quality control labels. In total, the model utilizes 31 one-dimensional features, as detailed in Appendix A, variables numbered 2–32. The network architecture is illustrated in Figure 2. The input features are concatenated and fed into the linear network structure. Initially, Batch Normalization (BatchNorm) is applied to normalize the inputs, which helps in accelerating the training process and improving the stability of the network. Following this, a Rectified Linear Unit (ReLU) activation function is employed to introduce non-linearity into the model, enabling it to learn complex patterns in the data. Subsequently, Dropout is utilized to prevent overfitting by randomly setting a fraction of the input units to zero during training, thereby promoting model generalization. The linear network consists of a total of eight layers, each incorporating BatchNorm, ReLU, and Dropout. The final layer is a fully connected layer that outputs the retrieved SWH.

3.2. CNN-Wave

The CNN-Wave model is primarily based on a Convolutional Neural Network (CNN) architecture, designed to process two-dimensional feature data from DDMs. The primary input feature for this model corresponds to the variable listed as number 1 in Appendix A. The network architecture is illustrated in Figure 3. Initially, the model employs convolutional layers with kernel sizes of 5, 4, and 2, respectively. These varying kernel sizes enable the extraction of features at different scales, capturing both broad and fine-grained information from the input DDM data. Each convolutional layer is followed by a ReLU activation function, which introduces non-linearity and aids in learning complex patterns within the data. After the convolutional layers, the extracted features are flattened and fed into a series of linear network layers. This transformation converts the two-dimensional feature maps into a one-dimensional vector, suitable for further processing by the fully connected layers. The final layer of the CNN-Wave model is a fully connected layer that outputs the retrieved SWH. This architecture ensures that the CNN-Wave model effectively leverages the spatial structure of the DDM data to accurately predict SWH.

3.3. Hybrid-Wave

The Hybrid-Wave model integrates both ANN and CNN, utilizing all 32 variables listed in Appendix A as inputs. The network architecture is illustrated in Figure 4. In this model, the two-dimensional DDM data are initially fed into a convolutional network, which extracts relevant features through a series of convolutional layers. These features are then flattened to form a one-dimensional vector. Simultaneously, the one-dimensional linear features are processed. The extracted features from the Conv network are concatenated with the one-dimensional linear features. This combined feature vector is then fed into a series of linear network layers. The final layer of the Hybrid-Wave model is a fully connected layer that outputs the retrieved SWH. This architecture leverages the strengths of both ANN and CNN, effectively capturing and processing the diverse input features to enhance the prediction accuracy of SWH.

3.4. Trans-Wave

The Trans-Wave model, as depicted in Figure 5, is predicated on the transformer architecture, uniquely tailored for analyzing the DDM features for SWH retrieval. This model simplistically preprocesses the DDM data before directly inputting them into the Transformer alongside auxiliary one-dimensional features, thus forming a comprehensive set of inputs. The transformer layers, consisting of an embedding layer and a TransformerEncoder layer, transform the raw input into a dense 64-dimensional representation suitable for processing by the transformer encoder. Configured with 64-dimensional inputs, eight attention heads, three encoder layers, and a feedforward dimension of 256, the encoder adeptly captures complex dependencies among features. Post-processing, the outputs are concatenated with additional auxiliary features and routed through a linear layer, concluding with a series of SWH retrieval layers. These layers comprise multiple linear layers enhanced with BatchNorm, ReLU, and Dropout, leading to the final SWH prediction. This architecture allows the Trans-Wave model to effectively utilize both the spatial-temporal structure of the input data and the sequential characteristics of the DDM features.

3.5. ViT-Wave

The ViT-Wave model, illustrated in Figure 6, utilizes the Vision Transformer (ViT) architecture to handle image-like input data from DDMs. Differing from the Trans-Wave model, it begins by segmenting the DDM into several small patches to enhance feature learning. The primary inputs include these DDM patches and auxiliary one-dimensional features. The ViT-Wave model’s embedding layer maps each patch into a 64-dimensional space, preparing it for the VisionTransformerEncoder. This encoder, with identical configuration settings as the Trans-Wave model, processes the embedded patches, meticulously capturing the relationships across the input field. Its self-attention mechanism focuses on relevant features while ignoring irrelevant ones, enhancing the model’s precision in predicting SWH. Following this, the outputs are concatenated with auxiliary features and passed through a linear layer. The final SWH retrieval layers, similar to those in the Trans-Wave model, consist of multiple linear stages equipped with BatchNorm, ReLU, and Dropout, ultimately delivering the SWH prediction. This model’s structure effectively leverages the spatial structure of the DDM data and the power of self-attention to achieve high accuracy in SWH retrieval.

4. Experiment

In this study, the experiment was conducted using the OpenI computing platform, which efficiently supported the needs of our neural network models. This platform is tailored for various scientific and engineering applications, ensuring adequate computational resources for the project.

4.1. Data Preprocessing

The data preprocessing stage involved meticulous steps to ensure the completeness and reliability of the dataset utilized in subsequent analyses. The process began with a thorough data cleaning operation, where outliers and missing values, such as NaN, were identified and removed. Common outliers included data points that exceeded typical geographic coordinates (latitude and longitude) and unusual fill values such as −9999 and infinity (inf). Moreover, entries associated with these outliers and missing values, including corresponding data points and labels, were systematically eliminated to prevent any distortion of results and degradation of model performance. Following this, temporal and spatial matching of the data was conducted to ensure alignment between different datasets. Specifically, the observed variables from FY-3E were interpolated onto a 0.25° × 0.25° grid. Temporally, the data were interpolated to the nearest hour using the nearest-neighbor method, ensuring consistency with the spatial and temporal resolution of the ERA5 data.

After the cleaning and matching processes, the resulting dataset comprised 390,261 entries. A significant portion of this data, 87.92%, corresponded to SWH ranging from 0 to 4 m. Entries with SWH between 4 and 8 m accounted for 47,148 records, representing 11.87% of the total dataset. Only 824 entries, or 0.21%, had SWH values exceeding 8 m. Thus, the vast majority of SWH measurements were below 8 m, making up 99.79% of the data. The maximum observed SWH was 14.80 m, while the minimum was 0.03 m. This distribution shown in Figure 7, highlights that extreme SWH values are relatively rare within the dataset.

4.2. Experimental Procedure

The experimental process commenced with the random shuffling of data, followed by its division into training, validation, and test sets in a 7:2:1 ratio. The training set was utilized to train the model, the validation set to verify the results of each training iteration, and the test set to evaluate the final performance of the model. To ensure reproducibility and robustness, five different random seeds were selected, and each of the five models was trained and evaluated five times under the same experimental configuration.

In the model training phase, the loss function used was Mean Squared Error Loss (MSELoss). To prevent overfitting, a regularization parameter was introduced. The total loss during training included both the prediction loss and an L2 regularization term:

$$\mathrm{total}\_\mathrm{loss}=\mathrm{loss}+\lambda \sum \mathrm{L2}\_\mathrm{reg}$$

(1)

where $\lambda$ is the regularization parameter, and $\mathrm{L2}\_\mathrm{reg}$ is the sum of the L2 norms of the model parameters. This regularization helps in mitigating overfitting by penalizing large weights in the model. Additional key parameters set during the experiment included the optimizer and learning rate. The Adam optimizer was chosen with a learning rate of 0.0005 to balance the speed and stability of convergence. The number of epochs was set to 500, providing ample iterations for the model to learn from the data. Data loaders were configured with a batch size of 512, ensuring efficient data handling and processing.

The training process involved several steps. To begin with, the dataset was randomly shuffled and divided into training, validation, and test sets. Throughout each epoch of model training, the model’s parameters were updated using the training set, and the loss was calculated for each batch. This loss, combined with the L2 regularization term, was used to adjust the model parameters via backpropagation. Subsequently, the model’s performance was evaluated using the validation set, and the validation loss was recorded after each epoch. This step ensured that the model’s learning was appropriately generalized and not overfitted to the training data. Finally, after the last epoch, the model’s performance was assessed using the test set, and the test loss was recorded to evaluate the model’s prediction accuracy on unseen data. As is shown in

Table 3. Average Train and Validation Loss with Standard Deviations.

Model	Train Loss ± Std	Validation Loss ± Std
ANN-Wave	0.2135 ± 0.0146	0.2177 ± 0.0044
CNN-Wave	1.1400 ± 0.0191	1.9116 ± 0.6267
Hybrid-Wave	0.2065 ± 0.0165	0.1938 ± 0.0109
Trans-Wave	0.2034 ± 0.0148	0.1955 ± 0.0086
ViT-Wave	0.1816 ± 0.0040	0.1735 ± 0.0042

, after five rounds of training, the ViT-Wave model demonstrates the most superior performance across all metrics. Specifically, the ViT-Wave model achieved the lowest average training loss and validation loss, with the smallest standard deviations. This indicates that the ViT-Wave model not only converges quickly during training but also maintains high stability and consistency, highlighting its comprehensive superiority. In contrast, the CNN-Wave model with single input exhibits the poorest performance, characterized by the highest training and validation losses, along with significant error variability. Moreover, Hybrid-Wave and Trans-Wave models achieve moderate training and validation losses with relatively small standard deviations, indicating stable performance. Overall, the experimental results clearly delineate the performance differences among the models. The ViT-Wave model stands out as the best-performing model with significant advantages.

4.3. Evaluation Metrics

To comprehensively evaluate the performance of each neural network model in retrieving SWH, several key metrics were selected as evaluation standards. These metrics offer unique insights into different aspects of model accuracy and reliability. The selected evaluation metrics include Root Mean Square Error (RMSE), Bias, Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and the Coefficient of Determination (R²). The specific formulas and meanings of each metric are detailed below:

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{(y_i-{\widehat{y}}_i)}^2}$$

(2)

$$\mathrm{MAE}={\displaystyle \frac{1}{n}}\sum _{i=1}^n|y_i-{\widehat{y}}_i|$$

(3)

$$\mathrm{Bias}={\displaystyle \frac{1}{n}}\sum _{i=1}^n(y_i-{\widehat{y}}_i)$$

(4)

$$\mathrm{MAPE}={\displaystyle \frac{100\%}{n}}\sum _{i=1}^n\left|{\displaystyle \frac{y_i-{\widehat{y}}_i}{y_i}}\right|$$

(5)

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^n{(y_i-{\widehat{y}}_i)}^2}{{\sum }_{i=1}^n{(y_i-\overline{y})}^2}}$$

(6)

Parameters

-

$y_i$: Observed SWH value (ERA5 data)

-

${\widehat{y}}_i$: Predicted SWH value (model output)

-

n: Number of observations

-

$\overline{y}$: Mean of observed SWH values

-

$\overline{\widehat{y}}$: Mean of predicted SWH values

These metrics collectively provide a robust framework for evaluating the performance of the neural network models, ensuring that various aspects of prediction accuracy and reliability are comprehensively assessed in the context of SWH retrieval using ERA5 data as the reference.

5. Result

Upon completing the experimental tests, we evaluated the finalized models using the test dataset. The performance of these models was assessed based on several predetermined evaluation metrics: RMSE, MAE, BIAS, MAPE, and R². The test results are summarized in

Table 4. Evaluation accuracy of all models.

	RMSE	MAE	Bias	MAPE	R2
ANN-Wave	0.4546	0.3048	0.0040	18.6814	0.8889
CNN-Wave	1.2337	0.9447	0.2715	74.6440	0.1819
Hybrid-Wave	0.4225	0.2799	0.0144	17.7126	0.9040
Trans-Wave	0.4344	0.2931	−0.0012	23.2238	0.8986
SNR [28]	0.534	0.421	-	21.52	-
NCDW LES [28]	0.503	0.390	-	20.02	-
ANN [25]	0.59	-	-	-	-
BT [25]	0.48	-	-	-	-
DCNN [27]	0.422	-	-	-	0.89
ViT-Wave	0.4052	0.2700	−0.0015	18.0200	0.9117

. Overall, it can be seen that the Vit-Wave model has achieved the best comprehensive effect. In addition to these evaluations, we conducted comparative studies with other models that utilize CYGNSS data for SWH retrieval. When compared with traditional data statistical analysis methods such as SNR [28] and NCDW LES [28], the ViT-Wave model exhibited improved performance in terms of RMSE and MAE. These improvements highlight the advantages of leveraging advanced neural network architectures over conventional statistical methods. Furthermore, the ViT-Wave model outperformed several other machine learning models, including ANN [25], BT [25], and DCNN [27]. The enhancements in retrieval accuracy with the ViT-Wave model underscore its potential for more accurate and reliable SWH retrievals compared to these existing methods.

To better illustrate the performance improvements of the ViT-Wave model,

Table 5. Percentage Improvement of ViT-Wave Model Over Other Models.

	RMSE	MAE	Bias	MAPE	R2
ANN-Wave	10.85%	11.45%	137.50%	3.54%	2.57%
CNN-Wave	67.15%	71.42%	100.55%	75.86%	401.10%
Hybrid-Wave	4.10%	3.53%	110.42%	−1.74%	0.83%
Trans-Wave	6.72%	7.88%	−20.00%	28.28%	1.46%
SNR [28]	24.07%	35.87%	-	16.26%	-
NCDW LES [28]	19.43%	30.77%	-	10.00%	-
ANN [25]	31.36%	-	-	-	-
BT [25]	15.62%	-	-	-	-
DCNN [27]	4.00%	-	-	-	2.44%
ViT-Wave	-	-	-	-	-

presents the percentage enhancements of key parameters when compared to other models.

Scatter density plots were generated for each model to comprehensively evaluate their performance as shown in Figure 8. In these plots, the black solid line represents the ideal $y=x$ line, indicating perfect agreement between the observed and retrieved values. Additionally, a red dashed line depicts the linear fit of the data, with the corresponding regression equation displayed in the bottom right corner of each plot. The scatter density plots reveal that the ViT-Wave model demonstrates the most favorable distribution of data points around the ideal $y=x$ line, indicating a high degree of accuracy in its retrievals. The linear regression equation for the ViT-Wave model, $y=0.88x+0.32$, underscores the model’s superior fitting performance. This close alignment with the ideal line suggests that the ViT-Wave model effectively captures the underlying relationship between the observed and retrieved SWH values, resulting in minimal deviations and high fidelity in its predictions.

In comparison, other models show varying degrees of dispersion around the y = x line, reflecting differences in retrieval accuracy and consistency. The scatter density plots reveal that models such as the CNN-Wave and Trans-Wave have more scattered points, indicating higher retrieval errors and less reliable performance. The fitting equations for these models also exhibit greater deviations from the ideal line, further highlighting their comparative inferiority. Overall, the scatter density analysis reinforces the earlier findings from the quantitative metrics, solidifying the ViT-Wave model’s status as the most robust and accurate model for SWH retrieval among those evaluated. Its superior performance across both quantitative metrics and visual scatter plots underscores its potential for practical applications in wave height prediction and oceanographic research.

We also conducted a segmented error analysis based on the range of SWH values. The SWH data were divided into five segments: 0–2 m, 2–4 m, 4–6 m, 6–8 m, and >8 m. The blue column represents the ANN-Wave model; the orange column represents the CNN-Wave model; the blue column represents the ANN-Wave model; the gray column represents the Hybrid-Wave model; the red column represents the Tans-Wave model; the green column represents the ViT-Wave model. The errors for each model within these segments were calculated and presented in the form of bar charts (see Figure 9, Figure 10 and Figure 11).

From these bar charts, it is evident that the ViT-Wave model consistently demonstrates the lowest errors across the SWH range of 0–8 m, indicating its superior performance in this range. Notably, the error range of 0–4 m is where all models perform best across all metrics, which may be related to the data distribution, as shown in Figure 7. This suggests that the ViT-Wave model is highly effective in accurately retrieving SWH values, particularly within the common range encountered in oceanographic observations. Interestingly, for SWH values greater than 8 m, the Trans-Wave model shows the smallest errors, outperforming other models in this higher SWH segment. This indicates that while the ViT-Wave model excels in general SWH conditions, the Trans-Wave model has a notable advantage in extreme wave conditions, where its architecture might better capture the complex features associated with higher wave heights. The segmented error analysis highlights the strengths of both the ViT-Wave and Trans-Wave models, each excelling in different SWH ranges and collectively offering robust solutions for a wide spectrum of wave height retrieval scenarios.

To better understand the global distribution of SWH across the ocean surface, we utilized reference points based on ERA5 SWH data along with their corresponding latitudes and longitudes. Upon evaluating the test dataset, it was observed that 95% of the SWH values were concentrated in the 0–5 m range. To enhance the visibility of the overall SWH distribution, a customized color bar was employed, as shown in Figure 12, where darker colors indicate lower SWH values and lighter colors indicate higher SWH values. From Figure 12 and Figure 13, it can be seen that most of the colors are consistent, indicating that the ViT-Wave model’s retrieval results are close to the ERA5 SWH. However, in the central part of the Southern Hemisphere, the color in Figure 13 is darker than in Figure 12, indicating that the ViT-Wave model underestimates the SWH compared to the ERA5 data. This suggests that the ViT-Wave model requires further optimization in high-value ranges.

From Figure 12, which represents the ERA5 data, it is evident that SWH values tend to be higher in high-latitude regions, particularly in the Southern Hemisphere. This observation cannot be made using CYGNSS data due to their limited coverage between 33°N and 33°S latitude, highlighting the advantage of FY-3E data. Overall, the ViT-Wave model shows a distribution that closely resembles the ERA5 reference, indicating its superior performance in capturing the global SWH distribution.

To evaluate the error distribution of the ViT-Wave model across the global ocean surface, we generated residual and rmse 3° × 3° grid distribution maps (see Figure 14 and Figure 15). These maps visually represent the differences between the ViT-Wave model predictions and the ERA5 reference data. In these maps, negative biases (indicating model underestimation) are shown in red, with darker shades representing larger discrepancies. Conversely, positive biases (indicating overestimation) are shown in blue, with darker shades indicating greater deviations. Regions where the model predictions match the ERA5 data are displayed in white. From Figure 14 and Figure 15, it is evident that the ViT-Wave model tends to underestimate SWH values overall. The biases are more pronounced in high-latitude regions compared to areas near the equator, suggesting that the model’s performance is less accurate in these regions. This indicates a need for further refinement and optimization of the ViT-Wave model to improve its accuracy, particularly in high-latitude areas. Future research should focus on addressing these discrepancies to enhance the model’s reliability and performance in various oceanographic conditions.

6. Discussion

Among the evaluated models, as shown in Table 4, the ViT-Wave model demonstrated superior performance across all five metrics. The ViT-Wave model achieved an RMSE of 0.4052 m, indicating the lowest overall error distribution among the models assessed. This suggests its high efficacy in capturing data variability and minimizing retrieval errors, particularly in handling outliers effectively. Furthermore, its MAE of 0.27 m reflects the model’s ability to maintain low absolute errors, underscoring its robustness in providing accurate retrievals with minimal deviations from observed values, indicating overall good performance even without considering extreme values. The model’s near-zero bias, recorded at −0.0015 m, suggests that the ViT-Wave’s retrievals are almost unbiased, with negligible systematic errors, thereby enhancing its reliability for practical applications and indicating a slight tendency of the model to underestimate. The MAPE was 18.02%, showcasing its efficiency in minimizing percentage errors relative to observed values, a crucial metric for assessing performance where relative error measurements are important. However, the Hybrid-Wave model’s slightly lower MAPE of 17.71% suggests it may be more effective in applications requiring precise percentage error reduction, possibly due to less influence from extreme values. The R² value of 0.9117 indicates a high level of correlation between the retrieved and observed values, showing that the model explains a substantial proportion of the variance in the observed data, which further validates its effectiveness.

The superior performance of the ViT-Wave model can largely be attributed to the unique capabilities of its architecture. The ViT segments the input images into patches, a method that enables the model to capture detailed features within each segment effectively. This patch-based processing approach allows the ViT-Wave model to learn fine-grained details and spatial hierarchies in the data, which are crucial for accurately predicting SWH. By focusing on local and global patterns simultaneously, the model can better understand and integrate various data relationships, enhancing its precision and effectiveness in SWH retrieval. This capability is advantageous for SWH retrieval, where the complexity of ocean surface dynamics requires models to discern subtle features and patterns that significantly impact prediction accuracy. The ViT-Wave’s ability to handle non-linearities and dependencies in data more efficiently than conventional models suggests that its method of slicing the image data into manageable pieces before processing contributes significantly to its lower RMSE and MAE.

Furthermore, the slight underperformance in minimizing MAPE compared to the Hybrid-Wave model might be addressed by exploring hybrid architectures. Combining the detailed feature extraction capabilities of the Vision Transformer with the robustness against outliers of other models could lead to a more balanced approach, enhancing performance across all metrics. Moreover, the analysis indicates that while the ViT-Wave model demonstrates high effectiveness across many metrics, there is room for improvement, especially in regions with high latitude and extreme wave conditions. Investigating the training data diversity and distribution might reveal the need for more representative samples from these challenging conditions.

Future research could also explore modifications to the ViT architecture to further optimize its processing capabilities for SWH data. By enhancing the model’s ability to handle outliers and extreme values, and possibly integrating more diverse training scenarios, the overall accuracy and reliability of SWH retrievals can be significantly improved. This exploration into the causes of discrepancies and potential mitigation strategies will be crucial for advancing the model’s practical applications in oceanographic research.

7. Conclusions

This research capitalizes on GNSS-R data from the FY-3E satellite and introduces the Vision Transformer model to advance the field of SWH retrieval. The model has achieved the lowest recorded RMSE of 0.4 m, which underscores its superior accuracy over traditional methods. This high level of precision highlights the model’s capability to effectively harness advanced machine learning techniques for the retrieval of complex environmental data through GNSS-R data. However, the ViT-Wave model needs more matching and more accurate data such as buoy data and altimeter data to improve its retrieval accuracy. While the ViT-Wave model excels in providing enhanced spatial and temporal resolution and broad global coverage, it faces challenges in high wave conditions and at high latitudes it is notably reduced, suggesting areas where further model optimization is necessary. Despite these challenges, the integration of cutting-edge technology with satellite observations marks a significant step forward in the domain.

In general, the model has good retrieval effects in 0–8 m and low- and mid-latitude regions, and needs further optimization when used in areas above 8 m and high-latitude regions. For optimal use, the ViT-Wave model is suitable for environments with moderate to high wave conditions and where extensive area coverage is needed, such as in global marine environmental monitoring and climate studies. It should be used with caution in extreme sea conditions and areas that require real-time data processing because the model calculation data are missing under such conditions and the accuracy will be reduced. This foundation sets the stage for future enhancements and wider applications of the technology in oceanographic monitoring.