The sea surface height (SSH) is a key parameter in marine research and contributes significantly to the development of high-precision ocean gravity fields and the detection of changes in the dynamic environment of the ocean (Li et al. 2020; Li et al. 2014; Zhang et al. 2021). SSH can be categorized into nearshore and oceanic types, each requiring different monitoring strategies due to their distinct geographic characteristics (Antony et al. 2002). Satellite altimetry can monitor SSH with high precision; however, near-shore sea surface altimetry is limited by the spatiotemporal resolution of altimetry satellite orbits (Archer et al. 2020). Obtaining high-precision nearshore SSH changes is indispensable for constructing a global ocean height field (Jiang et al. 2022; Zheng et al. 2012; Zheng et al. 2006).
Traditional methods for monitoring nearshore SSH typically involve water level gauges, tide gauges, and radar water level meters. These methods offer the advantages of low cost, easy operation, and high accuracy (Vignudelli et al. 2019). However, limitations exist, such as low automated monitoring of water level gauges requiring significant labor and resources (Ansari et al. 2020). Moreover, the accuracy of tide and radar water level meters is affected by sea environment conditions, including lower temperatures, mud, and sand (Guerova and Simeonov 2022). Therefore, exploring cost-effective, accurate alternatives is imperative. Many researchers utilize Global Navigation Satellite System (GNSS) reflection signals to observe SSH changes due to continuous GNSS development. Numerous studies exist (Song et al. 2020; Zhang et al. 2021; Zhu et al. 2023). In 2000, Anderson used traditional geodetic GNSS receivers to establish an interferometric model from signal-to-noise ratio (SNR) observations. The SSH was measured by GNSS signals reflecting back to the interferometric direct signal after reflecting the sea level (Anderson 2000). In 2013, Larson et al. introduced GNSS interferometry reflectometry (GNSS-IR), which led to the development of classical GNSS-IR water level inversion theories and the extensive use of geophysical parameter monitoring, such as sea surface altimetry, snow depth, soil moisture, and permafrost (Hoffman et al. 2023; Larson et al. 2013).
The GNSS-IR technique leverages the multipath interference effect in GNSS positioning to invert the height of mirror-like regions (Hu et al. 2021). The GNSS-IR sea surface altimetry technique can infer the SSH from the interference characteristics of the SNR data in the receiver observation file (Larson et al. 2017). Using GNSS-IR technology, all-weather, low-cost, high temporal resolution, long-term continuous SSH monitoring can be realized, and the monitoring results are automatically fixed in a stable frame. This approach has wide applications in various fields, including marine surveying, scientific research, safety monitoring, and weather forecasting (Chen et al. 2023; Holden and Larson 2021; Larson et al. 2013). However, shore-based GNSS-IR technology mainly contains two error sources, namely, sea level dynamic error and atmospheric delay effect error, which greatly affect the accuracy of GNSS-IR inversion results (Gholamrezaee et al. 2023; Wang et al. 2022). In 2013, Larson et al. reported that sea surface undulations caused sea level dynamic in inversion results and proposed a correction algorithm, verifying that strategies effectively inverted SSH (Larson et al. 2013). In 2014, Löfgren et al. used five GNSS stations for SSH inversion and proposed empirical tidal wave coefficient-based error correction improvements (Löfgren et al. 2014). In 2017, Larson et al. proposed a SSH fitting method without empirical tidal wave coefficients based on a tidal wave analytical model, further improving the correction algorithm for height errors (Larson et al. 2017). The atmospheric delay error mainly comprises two parts: the tropospheric refraction error and the ionospheric refraction error. In 2016, Santamria et al. used a refraction correction formula to correct the elevation angle deviation caused by atmospheric refraction, significantly improving the accuracy of inversion measurements (Santamaría-Gómez and Watson 2017). In 2017, Williams et al. used the VMF1 mapping function model and the GPT2w tropospheric delay model to correct the tropospheric delay error, yielding more accurate tidal amplitudes (Williams and Nievinski 2017). These studies showed that GNSS-IR can serve as an independent monitoring method for inverting high-precision SSH geophysical parameter information.
Deep learning is a powerful machine learning method that can process complex data and extract sophisticated features. This approach has enabled numerous preliminary studies in the field of GNSS-IR (Siemuri et al. 2022; Wang et al. 2021). These investigations have been widely applied to sea surface altimetry (Zheng et al. 2023), soil moisture (Li et al. 2022; Pan et al. 2020), and snow depth (Altuntas et al. 2022; Zhan et al. 2022) measurements. Moreover, deep learning algorithms can optimize GNSS-IR parameters, enhancing model performance. In 2023, Wang et al. proposed an improved residual multimodal deep learning method for sea surface altimetry using time-delayed Dopplergrams, which outperformed traditional GNSS-R altimetry by 35.21% (Wang et al. 2023). In 2021, Zhang et al. inverted SSH using support vector machine (SVR) and convolutional neural network (CNN). The results showed that this strategy effectively inverts the SSH with an accuracy of up to 0.71 m (Zhang et al. 2022). In 2023, Jin et al. proposed the F-ResNet SSH inversion method for sea surface altimetry. Using the fractional order Fourier transform to filter delay doppler map (DDM) data, the results were comparable to those of Jason-3 sea surface altimetry data, which showed accuracies up to 1.17 m, 15.2% higher than those of other traditional learning algorithms (Xing et al. 2023). All the above studies applied deep learning algorithms to satellite-based GNSS-R sea surface altimetry data, aiming to increase its precision. However, fewer studies have applied deep learning algorithms to shore-based GNSS-IR sea surface altimetry. Therefore, how to reasonably and effectively apply deep learning algorithms to GNSS-IR sea surface altimetry data is currently a popular research topic.
Unlike prior research, this study combines LSTM algorithm and GNSS-IR to construct a new deep learning composite atmospheric delay correction inversion model (DCCIM) for GNSS-IR inversion. The DCCIM processing process is described as follows: first, traditional GNSS-IR is used to invert SSH; second, GNSS-IR atmospheric delay errors are determined from tide station observations; third, LSTM is used to model the errors and driving data, followed by correction of unobserved periods; fourth, DCCIM is applied to invert SSH, and the results are compared with those of traditional GNSS-IR to calculate accuracy improvements.