The Inversion of Three-Dimensional Ocean Temperature and Salinity Fields for the Assimilation of Satellite Observations

Abstract

The lack of dimensionality of ocean observations makes it difficult to utilize multi-scale data assimilation to correct model errors with limited observations. Since satellite observations can provide high-resolution and time-continuous sea surface information, this study utilizes sea surface temperature (SST), sea surface salinity (SSS), and sea surface height (SSH) anomalies to invert the vertical temperature and salinity fields and thus realize multi-scale data assimilation in the three-dimensional space. We propose a temperature and salinity inversion network (TSI-Net) for reconstructing the mapping of the sea surface’s spatial distribution features to vertical structural features to obtain pseudo-observed fields. In this study, measured satellite remote-sensing data and temperature and salinity profiles are used to correct the model errors in the waters around the China Sea. The sensitivity analysis shows that the multi-component inversion can better fit the temperature field relationship, with a correlation coefficient of about 0.87. The results of the assimilation experiments show that the analytical field obtained by assimilating the pseudo-observed field is more consistent with the target field in terms of the spatial distribution characteristics.

1. Introduction

For most of the oceans and remote sea areas, underwater observation data are very sparse and spatially unevenly distributed. At the same time, the information on certain marine elements obtained from conventional observations does not match the model variables for forecasting, which causes certain difficulties in the practical application of marine data assimilation algorithms [1,2]. With the increase of the number of ocean observation stations and the development of satellite remote-sensing technology. In fact, the lack of observations in the time and space dimensions limits the performance of assimilation methods, and suitable parameterization schemes are needed to deal with physical processes at different scales in scale conversion and model forecasting [3,4,5].

With the rapid development of satellite remote-sensing technology, satellite observations have the advantages of high resolution and wide coverage, which are of high value for numerical forecasting [6]. However, direct assimilation cannot effectively correct the background error, and the traditional method of assimilating sea surface observation data needs to fit the mapping relationship with temperature and salinity variables, and then vertically project them into the temperature and salinity, so the corresponding inversion technique becomes an indispensable part of assimilation research [7,8]. The average feature accuracy of the model is improved [9]. Li et al. proposed an assimilation method based on the mutual constraints of the altimeter and sea surface temperature (SST) in the framework of 3DVar, and they demonstrated that the assimilation of satellite remote-sensing data can effectively improve the prediction of the ocean temperature and salinity [10]. He et al. established a numerical prediction model of the sea surface’s high and 3D temperature and salinity currents based on the POMgcs ocean model and the multigrid 3D variational assimilation method, which effectively reduced the sea surface prediction error [11,12]. The most widely used system in the current operationalization is the U.S. Navy’s MODAS system, in which the module for obtaining the three-dimensional ocean temperature and salinity fields is a statistical model based on linear regression [13].

Traditional empirical analysis methods usually need to introduce the temperature and salt balance operator to ensure the vertical correlation of the error field of the temperature and salt background field, and they can only analyze the linear relationship between the sea surface parameters and the underwater temperature and salt field, while there are limitations in dealing with nonlinear problems [14,15]. With the deep development of artificial intelligence methods in various fields, training models using historical observation data can better predict and invert the 3D temperature and salt fields [16,17,18]. For example, Han et al. reconstructed the sub-surface temperature field of the Pacific Ocean using Convolutional Neural Networks (CNNs) based on satellite observations, including the sea surface temperature, sea surface salinity and sea surface height [19]. Shao et al. utilized satellite data combined with multivariate empirical orthogonal functions, complete ensemble empirical modal decomposition, and multilayer perceptron to predict and invert the three-dimensional temperature and salinity fields [20]. Su et al. used the support vector machine (SVM) method to well invert the sea subsurface temperature anomaly (SSTA), sea surface salinity anomaly (SSSA), and sea surface height anomaly (SSHA) from satellite measurements to obtain the SSTA for the shallow depths of 1000 m in the Indian Ocean [15].

In conclusion, deep learning has higher inversion accuracy and efficiency compared to statistical methods due to its strong multivariate spatial extraction capability, data-driven obtaining of temperature and salt constraints, and simultaneous learning of nonlinear relationships over multiple iterations [21,22]. In this study, to address the problem of the missing dimensions of the ocean subsurface as well as deep observations, the sea surface observations are inverted into vertical temperature and salt fields by multi-factor inversion for multi-scale assimilation, which effectively corrects the background error.

This study can be directly applied to the marine environmental protection system and business to provide multi-factor, multi-temporal and spatial-scale marine environmental information products and scientific bases for the national defense and security of marine environmental services, and to improve the marine environmental independent protection capability.

2. Methods

Deep-learning networks have been widely used in oceanography due to the strong feature extraction capability. At present, it is difficult to obtain ocean observation data and the data sources are scarce, which has an impact on the performance of assimilation [14,23,24]. The characteristics of satellite observation data in a large range can effectively expand ocean observation data, but satellite observation can only obtain ocean surface information, and it is difficult to provide deep ocean information for assimilation algorithms [25]. Therefore, in order to solve the problem of the lack of mapping relationship between the sea surface state field and vertical temperature and salinity fields in multi-scale data assimilation, it is difficult to effectively assimilate satellite observation data. In this study, a deep learning-based ocean temperature and salinity inversion network (TSI-Net) is proposed.

2.1. TSI-Net

TSI-Net adopts the structure of an Encoder–Decoder to realize the end-to-end inversion of three-dimensional ocean temperature and salinity information. The design of this network refers to the design of U-Net’s jump connection and fuses the original information with the information after feature extraction [26,27]. The information loss caused by the convolution process and pooling process is reduced to the maximum extent, and the inversion ability of the network is improved. The model structure of TSI-Net is shown in Figure 1.

As shown in Figure 1, TSI-Net is a full convolutional network with an Encoder–Decoder structure, using a setup of four down-samples and four up-samples. The left half of the figure is the encoded part of TSI-Net, the right half is the decoded part, C is the number of channels of input data (1< C <3), and C’ is the number of vertical layers of the labeled dataset. Each coding unit in the coding part includes two convolutional layers and one down-sampling layer. The ReLU function is used as the activation function to realize nonlinear conversion, and batch-normal layers are added to standardize the data. The maximum pooled layer is adopted for down sampling, which can retain the local feature invariance, which is conducive to capturing the multi-scale mapping relationship between the multi-scale and vertical structures of the sea surface.

In the decoding process, the input data are continuously encoded and extracted, and with each passing encoding unit, the input information will obtain a larger number of channels and a smaller data size, resulting in a change in the size of the dataset, as shown in Figure 1. Using this approach, the model will gradually obtain a relatively larger sensory field, strengthening the model’s ability to extract information from the surrounding pixels. In the decoding part, each decoding unit contains 2 convolutional layers and an up-sampling layer, where the up sampling uses the inverse convolution to realize the reduction of the original information. Meanwhile, in the decoding unit, jump connections are used to realize the constant fusion of the original information in the encoding stage with the information after complex information extraction in the decoding stage, so that as much original information as possible can be retained, which helps the network to reduce the problem of information loss brought about by the calculation of the convolutional and pooling layers. The network contains an input layer and an output layer. The input layer is used to process the multi-factor satellite observation data and input them into the network for feature extraction, and the output layer is used to control the output of the network to be the ocean satellite data in multiple depth layers.

2.2. Training Method

The target area for the inversion is within 13–30° N and 105.5–130.5° E. In order to facilitate the subsequent assimilation experiments, the spatial resolution of all the data in the experiments is 0.25 × 0.25°. Where the inversion element is the sea surface temperature, the surface ocean salinity data will be regarded as the sea surface salinity and sea surface height anomaly data. Considering the actual topographic factors of the South China Sea, 1000 m is set as the maximum depth of the inversion, and the temperature and salinity information in the deeper layers of the reanalyzed data will be used as the labeling information in the model training process. The preprocessed data contain data from 2006 to 2010, where the data from 2006 to 2009 are used in the training process of the model, and the data from 2010 are used in the testing and evaluation process of the model, and MSE is used as the loss function of the model in the training process.

$$MSEloss\left(x,y\right)=\frac{1}{n}\sum _{i=1}^n{\left(x_i-y_i\right)}^2$$

(1)

Due to the high resolution of the satellite observations, the data size is large, but the capacity of the computer memory or the graphics card memory is limited and not all the information can be input into the model at the same time. Therefore, it is necessary to divide the training data into different batches and input them into the model in batches, using the mini-batch size technique for training. At the same time, the input data will be input in a disrupted manner to strengthen the robustness of the network. The network is optimized using the Adam optimizer with a learning rate of 0.001, and the parameters of Adam are set to ${\alpha }_1$ = 0.9 and ${\alpha }_2$ = 0.999. A total of 2000 iterations are used to train the network and the early-stopping technique is used to prevent overfitting [28].

2.3. Integration of Pseudo-Observation Cost Functions

Due to the high spatial resolution of satellite observations and the multi-scale features extracted by TSI-Net through multiple convolutions, we integrate pseudo-observations into the framework of the multi-grid 3D variational method to diffuse the observation news in the 3D space, and we evaluate the enhancement of the pseudo-observations compared with the temperature and salt profiles on this basis. The basic idea of this method is to solve the variational assimilation equation using different scale grids, i.e., to achieve the effect of multi-scale information correction by gradually smoothing the approximation of the assimilation equation and then gradually correcting the assimilation results [7,29,30].

As shown in Figure 2, the rate of change of each assimilation grid layer is 0.5, using the error-smoothing effect of the coarse grid on the fine grid, so that the observation of new information is preferentially diffused on large scales, and then error correction is carried out on smaller scales, with the spatial extensibility being preserved in the multi-scale grids. The incremental form of the cost function for the integration of the pseudo-observations is as follows:

$$J^{\left(n\right)}\left({\epsilon }^{\left(n\right)}\right)=\frac{1}{2}{\epsilon }^{{\left(n\right)}^T}{\epsilon }^{\left(n\right)}+\frac{1}{2}{\left(H^{\left(n\right)}{\epsilon }^{\left(n\right)}-Y^{\left(n\right)}\right)}^T{O}^{{\left(n\right)}^{-1}}\left(H^{\left(n\right)}{\epsilon }^{\left(n\right)}-Y^{\left(n\right)}\right)\left(n=\mathrm{1,2},\dots ,N\right)$$

(2)

where $Y^{\left(n\right)}$ is the observation innovation matching the background field at the nth scale, $B^{\left(n\right)}$ and $O^{\left(n\right)}$ are the background field error and observation error covariance matrix at the corresponding scale, respectively, and $H^{\left(n\right)}$ is the observation operator at this scale. The background field of any grid is interpolated by the analysis field of the coarser grid.

$$X_b^{\left(1\right)}=X^{mod}$$

(3)

$$X_b^{\left(n\right)}=I_{\left(n\right)}^{\left(n-1\right)}{X}_b^{\left(n\right)}$$

(4)

where $I_{\left(n\right)}^{\left(n-1\right)}$ denotes an interpolation operator that represents the $n$ vector $n-1$ vector grid. The corresponding observation innovation is expressed as follows:

$$Y^{\left(1\right)}=Y^{obs}-H^{\left(1\right)}{X}^{mod}$$

(5)

$$Y^{\left(n\right)}=Y^{obs}-H^{\left(n\right)}{X}_b^{\left(n\right)}$$

(6)

The final analysis results are expressed as the superposition of the background field and the analysis increment s in each grid.

$$X_a=X_b+{\Sigma }_{n=1}^N{\epsilon }^{\left(n\right)}$$

(7)

From Equations (2)–(7), it can be seen that the smoothing process can be reasonably constrained for each multi-scale assimilation by integrating the pseudo-observed terms.

3. Sensitivity Analysis of Multi-Factor Inversion

The deep learning-based ocean temperature/salinity inversion task consists of two different components, the satellite L4-level observation products for the model input and the Euro-center reanalysis data for the labeling and assessment. The satellite L4 observation products for the model input include the SST, SSS and SLA, and the different data sources and preprocessing methods will be presented separately as the different data have different spatial resolutions.

3.1. Data Sources and Experimental Schemes

The SLA data are derived from Copernicus Climate Change Service (C3S) global ocean satellite observations, with a temporal resolution of daily averaging. It integrates high-resolution absolute dynamic topography (ADT) and SLA from multiple satellites.

C3S also provides the Group for High Resolution Sea Surface Temperature Multi-product Ensemble (GMPE). The spatial and temporal resolution of this product is the same as that of the satellite altimetry data. The dataset is derived from SST analyses by OSTIA, ESA and HadISST, and it is fused with observations from AVHRR, with a spatial resolution of 0.25 × 0.25°, which are cropped and directly used as SST input to the model.

The SSS data are derived from the global SSS and sea surface density (SSD) datasets provided by the Copernicus program, with a spatial resolution of 0.125 × 0.125° and a temporal resolution of daily averaging. These data fuse the SSS from multiple satellites, such as the Soil Moisture Active and Passive Acquisition Program (SMAP) from NASA satellites in the United States and the Soil Moisture Ocean Salinity (SMOS) satellite from ESA, with in situ salinity measurement information. To match the intended spatial resolution of the experiment, a linear interpolation algorithm is used to adjust the spatial resolution of the SSS data to 0.25 × 0.25°.

The labeling dataset is from the 1/12° day-averaged reanalysis dataset from the GLORYS12v1 ocean reanalysis. This dataset performs well relative to the 2013 World Ocean Atlas climatology and in situ data (global mean in situ temperature error below 0.1 °C) [31]. Considering the topographic factors of the target sea area, 1000 m is set as the maximum depth for inversion, and the data depth layer is interpolated to 21 pattern depths containing 21 × 69 × 101 pixel points. Following the data preprocessing means described above, the inversion model training dataset for long time series of ocean vertical temperature and salinity field is constructed.

In order to verify the factors affecting the inverted vertical structural temperature and salt fields in the satellite observations, this experiment only adjusts the number of channels of TSI-Net and keeps the other parameters stable as much as possible. We use the typical sea areas near the China Sea as the research target for retrieving the 3D temperature and salinity, including the northern part of the South China Sea, the main axis of Kuroshio and the Northwest Pacific Ocean, with different scale distribution characteristics (Figure 3). Based on the model training scheme, in order to test the performance of the inversion model, the experiment uses the real satellite observations of the SST, SSS and SLA as the model input data, and GLO12 as the training labels, and the experiment is divided into subgroups of elements to fit the temperature and salt multi-scale mapping relationship. The experimental scheme is designed as shown in

Table 1. Multi-factor sensitivity experiment scheme.

Experiment Name	Factor Selection	Data Selection	Purpose of the Experiment
ExT1	SST	Satellite observations of factors as single-channel inputs	Examining the effect of single-channel inversion of the temperature field
ExT2	SST + SLA	Satellite observations of factors as two-channel inputs	Examining the effect of two-channel inversion of the temperature field
ExT3	SST + SLA + SSS	Satellite observations of factors as three-channel inputs	Examining the effect of three-channel inversion of the temperature field
ExS1	SSS	Satellite observations of factors as single-channel inputs	Examining the effect of single-channel inversion of the salinity field
ExS2	SSS + SLA	Satellite observations of factors as two-channel inputs	Examining the effect of two-channel inversion of the salinity field
ExS3	SSS + SLA + SST	Satellite observations of factors as three-channel inputs	Examining the effect of three-channel inversion of the salinity field

.

3.2. Correlation Factor Test for Temperature Inversion

In Figure 4, the blue line is the average RMSE of the temperature field in January–March, the yellow line is the average RMSE in April–June, the green line is the average RMSE in July–September, and the red line is the average RMSE in October–December. The errors in the three sets of experiments are concentrated in the mixing layer and the thermocline, with the error range of 0.5–1 °C, and the errors in the deeper oceans are smaller, and the error range is generally less than 0.5 °C. During the training process of TSI-Net, the large-scale and stably varying vertical structural features are easier to extract, and it is easier to construct the mapping relationship with the corresponding spatial scale features at the sea surface; thus, the inversion effect is better in the depth layer less than 400 m.

The ExT2 group of experiments added the SLA as input data, and relative to the ExT1 group of experiments with single-channel SST, the RMSE was reduced in all the depth strata, with a particularly pronounced effect in the fall. The ExT3 group of experiments used the SST, SSS data, and SLA as inputs at the same time, and the addition of salinity constraints was able to result in a further reduction of the RMSE in the mixed layers, such as in the spring and summer.

All three groups of experiments can reconstruct the vertical temperature and salinity fields to some extent, and the R² can be around 0.8 in all four quarters, with better performance in the mixed layer, and the error decreases gradually with the depth while the correlation decreases gradually (Figure 5). The correlation of the single-channel inputs of the ExT1 group is worse, and it is especially obvious in the 200 m depth layer in summer. The correlations of the remaining two groups are significantly improved, and the correlation coefficients in the mixed layer reach more than 0.95 in all seasons except fall. Despite the linear relationship between the salinity field and the temperature difference, it is still difficult to invert the vertical temperature and salinity fields using only one element, temperature.

Since the ocean surface temperature is affected by the heat exchange between the atmosphere and the ocean, the SLA data can provide information on the ocean heat balance; thus, the R² increases significantly in all the depth layers when only the dual channels of the SST and SLA are used in the ExT2 group of experiments.

July is usually the warmest month for the ocean, with large amounts of warm water moving north and the upwelling of cold water lessening. As shown in Figure 6b,c, warm water occupies a large space at the depths of 50 m and 100 m, resulting in the suppression of cold-water upwelling. The two groups of multi-factor experiments perform better inversion in the high-temperature region, while the single-factor experiments have a large range of cold bias in the South China Sea (ExT1). The ExT1 group of experiments has poor inversion results for complex eddy variations due to the input of a single element and fewer constraints, e.g., the stronger temperature gradient in the Northwest Pacific region of the thermocline is not reproduced (Figure 6). The inversion fields of the three sets of experiments have different degrees of cold bias in each depth layer, and they are basically only consistent in the spatial distribution pattern.

The ExT1 group of experiments has some degree of cold bias in the temperature values on the right side of the Luzon Strait at 20 m, while the ExT2 group of experiments has a warm bias in this region, and the temperature distribution of the ExT3 group of experiments is more similar to the labeling (Figure A1). At the deep level, cold-water upwelling usually occurs about 50 m down near the continental slope. Because the winter ocean circulation and monsoon may cause more cold water to surge upward, the ExT3 group of experiments can better restore the distribution pattern and temperature value of the low-temperature zone in the offshore sea at a depth of 50 m. The overall ExT3 inversion is better in the 200 m depth layer, for example, the single-channel experiment inverts a lower temperature of the cold vortex on the left side of the Philippine Islands, while the two-channel inversion results in a larger difference in the spatial patterns.

The temperature gradient of the temperature field in each depth layer gradually increases as the ocean temperature gradually warms up from April (Figure A2). The oceanographic fronts may be more pronounced because the water mass convergence and convection are more active during the season. The inversion results of the three groups of experiments for the 20–100 m depth layer are too smooth and do not reproduce the small-scale temperature gradient changes. However, in terms of the overall temperature trend, the ExT1 group of experiments shows that the overall temperature is on the low side, while the ExT2 and ExT3 groups of experiments show better inversion results, such as the warm eddy on the right side of the Luzon Strait.

As shown in Figure A3, the ocean temperature begins to drop in autumn, the temperature gradient of the thermocline gradually increases, and the temperature field in October is lower than that in July. In addition, affected by the monsoon and ocean circulation, the upwelling of cold water is strengthened again. The three experiments perform well in the 20 m depth layer, with the ExT1 experiment showing a low-temperature bias near the Xisha Islands in the thermocline and a high-temperature bias in the Northwest Pacific Ocean in the 200 m depth layer, and the ExT3 experiment in the right side of the Luzon Strait in the 100 m depth layer showing a significant effect of the inversion, while the ExT2 experiment shows a cold bias to a certain extent.

According to the statistical results concerning the RMSE and R² in the

Table 2. The RMSE (Unit: °C) and R² results for each group of experiments.

Metrics	Experiment Name	20 m	50 m	100 m	200 m
RMSE	ExT1	0.3652	1.1008	1.1178	0.5346
	ExT2	0.3518	0.5767	0.5787	0.2680
	ExT3	0.3577	0.5557	0.5712	0.2668
R2	ExT1	0.8989	0.8576	0.8209	0.7561
	ExT2	0.9003	0.8755	0.8373	0.7859
	ExT3	0.9312	0.9102	0.8697	0.8154

, it can be seen that the advantage of the ExT3 group is obvious in that the correlation coefficients are enhanced about 0.04 relative to ExT2 and 0.06 relative to ExT1, which indicates that the three elements, as inputs, are essential for the inversion of the spatial distribution characteristics of the temperature field and the vertical structure. Meanwhile, the RMSEs of the ExT3 group of experiments are reduced to different degrees in all the depth layers except the 20 m depth layer. In summary, for the inversion of the vertical temperature field, the three-channel input data are more effective, which shows that the more effective the elements of the real observation, the stronger the constraints on the vertical structure and the better the inversion effect.

3.3. Correlation Factor Test for Salinity Inversion

Compared with the inversion of the temperature field, the RMSE of the salinity field inversion is one order of magnitude smaller, and the maximum error of the three sets of experiments is not more than 0.5 PSU. From the vertical error distribution, the error is basically less than 0.05 PSU for the layer less than 200 m deep, and similar to the temperature field, the error is mostly concentrated in the mixed layer and the thermocline.

The inversion of the surface salinity field in the ExS1 group of experiments is poor in the fall, with a difference of about 0.1 PSU from the other seasons. This is due to the influence of the monsoon in some areas in the fall, which leads to an increase in the input of freshwater to the surface, altering the temperature gradient of the salinity and making it more difficult to perform the inversion. The above situation is mitigated in the multi-channel experiments, especially after the addition of the SST data, when the RMSE of the surface salinity decreases to about 0.3 PSU in the fall (Figure 7). With the increase in the vertical depth, at 200 m, the RMSE of the ExS3 group of experiments increases suddenly in all four seasons, which is probably due to the fact that the depth layer is the junction between two different water masses, and the sudden change in the structure of the vertical water mass causes the error of the multi-factor inversion to increase. ExS3 has obvious advantages in all four seasons, and the inversion performance is more stable under the interference of different seasonal signals, which indicates that the multi-channel salinity field inversion is not only able to fit the vertical structure but also has a better inversion performance for the temporal signals.

On the basis of the RMSE metrics in the four seasons, it can be seen that all three sets of experiments are able to achieve an R² above 0.8 in the depth layer less than 300 m based on the vertical distribution plot of the R². For the inversion of the mixed layer, ExS3 has a better performance in all four seasons, especially in the summer, when the R² improves by about 0.2. Consistent with the analysis of the RMSE, the correlation gradually decreases with the fusion of multiple elements in the depth layer of 200 m, especially in the spring when the R² drops to 0.7 (Figure 8).

For the mixed layer shown in Figure 9, the salinity results of the three groups of experiments are lower than the labeled salinity field in the South China Sea and the Northwest Pacific but higher than the labeled field near the Kuroshio. The inversion results of the thermocline are better than those of the mixed layer east of the Luzon Strait, and the salinity still exists west of the Luzon Strait, in which the ExS3 group of experiments is relatively smooth, which is closer to the distribution of the labeled field. In the inversion results of the 200 m depth layer, ExS2 performs better, and ExS3 is salinity biased.

Figure A4 shows the inversion results of the three experiments on 15 January 2010 and the spatial distribution of the labeled temperature field in four depth layers, including the mixing layer and the thermocline. The inversion results of the ExS1 group of experiments in the 20 m depth layer are most similar to the salinity value of the labeled field, while the spatial distribution pattern of the ExS3 group is more similar to the ExS1 group of experiments. The salinity gradient distribution of the single-channel and dual-channel inversion results is blocky and differs from the real spatial variation pattern, and the above phenomenon is more obvious after integrating the SLA data and even appears to be salty. On the contrary, after adding the SST data, the salinity gradient is closer to the labeled field, e.g., the eddies in the west side of Luzon Strait are reproduced by half. The inversion results in the 50 m and 100 m depth layers are also smoother in the ExS3 group.

There is little variation in the salinity values and spatial distribution patterns at 20 m and 50 m in Figure A5. It is worth noting that the ExS3 performs better in terms of the general morphology and values in the lighter region near the Xisha Islands. In contrast, the salinity values of all three experiments in the 200 m depth layer are high compared to the labeled field, and the errors gradually increase with the increase in the elements.

In mid-October, only the ExS3 experiments reflect the motion patterns of the eddies near the South China Sea well, but the salinity inversion at 50 m is low by about 0.5 PSU east of the Philippine Islands. At 100 m, the ExS3 group performs better, and the other two sets of experiments are high in salinity in the South China Sea. The inversion of ExS3 is better in October, and the noise of ExS2 does not reproduce the range and pattern of the salinity gradient (Figure A6).

As shown in

Table 3. The average RMSE (Unit: PSU) and R² results for each group of experiments.

Metrics	Experiment Name	20 m	50 m	100 m	200 m
RMSE	ExS1	0.0696	0.0482	0.0158	0.0041
	ExS2	0.0679	0.0404	0.0138	0.0053
	ExS3	0.0591	0.0385	0.0155	0.0091
R2	ExS1	0.6616	0.4548	0.6955	0.7674
	ExS2	0.5979	0.4311	0.6554	0.7622
	ExS3	0.6669	0.5367	0.6571	0.7467

, from the statistical results of the 2010 annual average RMSE and R², it can be seen that in the mixed layer, the inversion performance of ExS3 group experiment is better than that of double-channel experiment where the RMSE is reduced by about 0.01 PSU and the correlation coefficient R² is improved by about 0.1. However, as the depth decreases to the thermocline layer, the inversion effect of the ExS3 deteriorates and the ExS2 is optimal, indicating that the constraints of the SLA can effectively enhance the performance of the inversion of the thermocline layer.

In summary, when combined with the temperature field inversion performance assessment, the ExS3 group has the best overall performance, with obvious advantages for the temperature field inversion, although the thermocline inversion for the salinity field is not satisfactory in terms of the numerical value but still has a certain advantage over the two-channel in the spatial distribution pattern. This suggests that it is necessary to set up a three-channel multi-element input data constraint model for the inversion of vertical structures during the projection of satellite observations to vertical temperature and salinity fields.

4. Discussion of Pseudo-Observational Assimilation Results

This section further discusses the pseudo-observation assimilation effects on the model errors of the temperature and salinity in the vertical subsurface and deeper layers. In this paper, we use the regional ocean model based on the numerical model POMgcs by Fu et al. as the background field, and its difference from the labeled field as the background error, which is set in the range of 13° N–30° N and 105.5° E–130.5° E, covering the northern part of the South China Sea, the Kuroshio Main Stream, and some parts of the Northwest Pacific Ocean.

We test the performance of the pseudo-observational assimilation using the profile EN4.2.2 from the UK Met Office Hadley Center as a control group. The main observational data for EN4 come from the World Ocean Database (WOD09), CORA (Coriolis Ocean Dataset for Reanalysis), the Global Temperature and Salinity Profile Program (GTSPP), and Argo datasets from the Argo Global Data Center since 2000. As shown in Figure 10, while the profile observations provide measured underwater information, the distribution of the stations differs considerably from the high-resolution model grid and is temporally discontinuous [32].

4.1. Analytical Field Evaluation of Temperature

Using the labeling data to evaluate the background, pseudo-observation and profile analysis fields, it is clear that the assimilation results of the pseudo-observations are significantly better than those of profile observations in all four quarters, especially in the 0–200 m mixed layer.

As shown in Figure 11, in the fall and winter seasons, the ocean temperature is greatly influenced by monsoon, ocean currents, climate system and other factors, and the depth and strength of the mixed layer usually change, making the ocean vertical temperature distribution change more drastically to facilitate the capture of vertical structural features. Therefore, the accuracy of the subsurface pseudo-observations in the fall and winter is higher, and the average advantage gradually decreases with the increase in depth to 400 m, but the error is still an error reduction of nearly 0.2 °C.

Warm water along the filaments usually appears in different depth layers, and its shape and strength can also change with the change of season and depth. Coastal filaments of warm water in summer may be narrower, longer and more pronounced because of the greater influence of warm water flowing ashore in summer. Upwelling is less intense and may be the shallowest in depth, as warm water begins to dominate in summer and cold-water upwelling is suppressed. In the mixed layer, it can be seen that the upwelling amplitude of cold water in the TSI-Net assimilation group experiment is small, and the temperature value is closer to the target field. According to Figure 12, the temperature field in July has a strong temperature gradient due to the highest temperature in summer; however, with the increase in rainfall brought by the monsoon, the river inflow into the sea increases, resulting in a decrease in salinity near the target sea area. Since the temperature and salinity fields in this month have more obvious spatial distribution characteristics, we choose the analyzed field in July for discussion.

According to the spatial distribution of the temperature field in the vertical mixed layer and the thermocline, the larger error of the model’s free run is manifested in the presence of a large cold bias in the South China Sea and the Kuroshio (Figure 12). In particular, the pseudo-observation assimilation accuracy is higher in the 50- and 100-depth layers south of the main axis of the Kuroshio and west of the Philippine Islands in the 100-m depth layer, etc. The enhancement of the temperature field by TSI-Net is mainly concentrated in the mixed layer and the thermocline, both of which are more obvious.

4.2. Analytical Field Evaluation of Salinity

The assimilated sea surface of the salinity field performs better compared to the temperature field, reducing the background error by about 0.4 PSU. Due to the small magnitude of the salinity field, the vertical characteristics of the pseudo-observed assimilation do not differ much from the background field.

According to Figure 13, it can be seen that the pseudo-observation assimilation is enough to correct the model error in the depth range of 0–100 m, and the advantage of the mixed layer is more obvious in the fall and winter seasons, considering that the thermocline error may be related to sudden changes in the marine environment, such as sudden strong winds, current changes, seasonal eddies and so on. These changes may lead to the increased mixing of seawater or destruction of vertical stratification, while the non-equilibrium factor interference of the multi-factor inputs leads to the poorer assimilation performance of the salinity inversion in the depth layer below 100 m. Overall, the pseudo-observations obtained by TSI-Net have significant advantages for the assimilation of the salinity fields in the surface and subsurface layers.

In summer, the salinity field may form a certain salinity gradient at a depth of 50 m, but the phenomenon of cold-water upwelling may be weak and the salinity gradient will not be too significant. As shown in Figure 14, TSI-Net’s pseudo-observation assimilation performance is better in terms of the salinity field error distribution characteristics and correction intensity, while the other two sets of experiments smoothed out the obvious salinity gradient near the Kuroshio by about 1 PSU. In July, using the Luzon Strait as the dividing line, the salinity in the sea area west of the Luzon Strait is lower in the range of 33–34, and the salinity in the sea area east of the Luzon Strait is higher in the range of 34.5–35 (Figure 14). The pseudo-observation assimilation performance is better in terms of the salinity field error distribution characteristics and correction strength. Especially near the main axis of the Kuroshio at 20 m and 50 m, both the background field and profile assimilation are characterized by salinity bias. The performance of the Northwest Pacific Ocean in the 100 m depth layer is relatively good. As the depth layer increases to the 200 m depth layer, the pseudo-observation assimilation is clearly dominant east of the Luzon Strait. In addition, we find that the spatial distribution of the salinity field is smoother after the pseudo-observations, and although the pseudo-observations perform better in terms of the numerical statistics, the profile observations are able to portray more details. In conclusion, the pseudo-observation assimilation greatly corrects the model error in terms of the large-scale spatial distribution characteristics.

4.3. General Discussion

According to the above analysis, the 3D temperature and salinity inversion results generated by TSI-Net can improve the background error to a great extent. On the one hand, the pseudo-observation field obtained from the inversion has higher accuracy, which ensures that more abundant information is input into the data assimilation algorithm. On the other hand, compared with the oceanic observations, the satellite observations have a significant advantage over the single-profile observations in terms of the spatial and temporal resolution. The experimental results also demonstrate the ability to fill in the gaps comprised of a large number of observations and help the multi-scale assimilation algorithm to better capture the global changes of ocean elements.

Deep-learning methods have been widely used in the field of atmosphere and ocean, and the contribution of deep-learning models can be seen almost everywhere from inversion to forecasting. Due to the data-driven characteristics, these models can often achieve better performance, but deep-learning models still have obvious limitations. First of all, deep-learning models as a “black box”, as researchers cannot obtain some atmospheric or ocean movement laws from the data and can only use deep-learning models to achieve these tasks. Secondly, after years of development, the application of deep-learning models in the field of atmosphere and ocean still uses a general image model. However, the atmosphere and ocean are constrained by physical processes. Adding physical constraints to the deep-learning model will help the model more easily capture the motion law of the ocean and improve the performance of the model. This is one of the limitations of current deep-learning models.

We believe that this is a valuable attempt, but there are still many aspects of this work that deserve further research due to the current conditions. Firstly, for the satellite observations, using deep-learning techniques to extend the observation range of the ocean can consistently adjust the model error to the vertical structure, which will help the model forecast to effectively accumulate new information from the observations. This is very useful for the model integration process, and the application of our method to the cyclic assimilation experiment will further improve the accuracy of the ocean forecasting model in the long-term forecast and correct the model error in a more timely and comprehensive manner. Meanwhile, this is also an important entry point for applying deep learning to physical oceanography; therefore, we will follow the above research direction to carry out related research in order to further enhance the accuracy of ocean forecasting.

5. Conclusions

The variational assimilation method is highly sensitive to errors as it relies on background errors and weighting configurations of the observations. While there are a large number of nonlinear mapping relations in the vertically structured temperature and salinity field, assimilating temperature and salinity profile observations will limit the performance of the assimilation algorithm, leading to its initial error assumption of linearity. In this paper, we propose the TSI-Net, which is capable of inverting the underwater temperature and salinity fields using high-precision satellite observations and realizing the extension of the vertical observation field. The network input uses four down samplings to progressively obtain a larger sensory field and enhance the model’s ability to extract information from neighboring pixels. In the decoding part, the four up samplings’ inverse convolution is used to realize the restoration of the original information, and the hopping connection is utilized to further reduce the information loss in the feature extraction process. The multi-scale spatial features of multiple elements of the sea surface are extracted by multiple sampling, which enables the model to learn the nonlinear mapping relationship between the structural features of the labeled temperature and salinity fields, and the vertical temperature and salinity fields, thus realizing the vertical inversion based on multiple elements such as the SST, SSS and SLA.

The sensitivity analysis results show that the temperature field of the multielement inversion has a good performance in all the depth layers underwater, and the correlation coefficient of the mixed layer is above 0.9. The ExT3 and ExS3 schemes achieved the best performance in temperature and salinity inversion, respectively. The correlation coefficient of the mixed layer can also reach above 0.8 in the case of using single-channel inversion, and the inversion results of the salinity field are similar to those of the temperature field. On the one hand, this shows that the inversion of TSI-Net for the vertical structure of the temperature and salinity field is closer to the real situation, and on the other hand, this shows that the balanced inversion with multiple elements helps to constrain the inversion performance. The assimilation experiments show that the integrated pseudo-observations can further improve the performance of the assimilation algorithm, and the assimilation of the vertical depth layer has a lower RMSE (around 1.57 °C/0.061 PSU) relative to the profile data.

The inverted temperature and salinity fields in the integrated pseudo-observation term are complete in three-dimensional time and space; thus, they can better assimilate the multi-scale features of the vertical structure and obtain a more reasonable analytical field. As an effective temperature and salinity field inversion technique, we hope that the assimilation method of integrating TSI-Net can be applied to operational numerical prediction to obtain more accurate ocean prediction products.