The Indonesian seas have active exchanges with neighboring oceans through multiple channels and the Indonesian Throughflow (ITF) passing by these channels (Wyrtki, 1961; Gordon, 1986; Sprintall et al., 2019). As the unique oceanic passage between tropics, the ITF links the Pacific low-latitude western boundary current and the Indian Ocean circulation system and hence plays an important role in the Indo-Pacific Ocean circulation system (Wyrtki, 1987; Hu et al., 2015; Sprintall et al., 2019; Phillips et al., 2021). Under the context of global warming, ocean circulations, including the ITF, are expected to change significantly (e.g., Sen Gupta et al., 2016; Hu et al., 2020; Ma et al., 2020; Hu et al., 2021; Santoso et al., 2022; Shilimkar et al., 2022). Changes in the ITF may cause fluctuations in the Indo-Pacific exchange rate and have an impact on regional and global climates (Gordon, 1986; Sprintall et al., 2014; Feng et al., 2015; Lee et al., 2015; Liu et al., 2016; Hu and Sprintall, 2017; Feng et al., 2018; Li et al., 2018; Hu et al., 2019).

The Indonesian seas have complex topographies and ocean dynamic processes (e.g., Wijffels and Meyers, 2004; Gordon, 2005; Hu and Sprintall, 2016; Wei et al., 2019; Sun and Thompson, 2020; Xu et al., 2021). Several notable observational experiments have been conducted in this region, such as the Indonesian-US Arlindo program (Gordon et al., 1999), the International Nusantara Stratification and Transport (INSTANT) program (Sprintall et al., 2004; Sprintall et al., 2009; van Aken et al., 2009; Gordon et al., 2010), Monitoring the ITF (MITF; Susanto et al., 2012; Gordon et al., 2019), and the expendable bathythermograph (XBT) deployments along the IX1 section (Meyers et al., 1995), as well as the Northwestern Pacific Ocean Circulation and Climate Experiment (NPOCE; Hu et al., 2011). These observations are crucial for recovering the characteristics and underlying dynamics of the ITF. However, the lack of long-term and continuous ITF time series makes it difficult to gain a deeper understanding (Sprintall et al., 2019).

Previous studies suggested finding a proxy of ITF transport in addition to direct observations (e.g., Sprintall and Révelard, 2014; Susanto and Song, 2015; Hu and Sprintall, 2016). Wyrtki (1961) proposed that the large-scale pressure gradient between the Pacific Ocean and the Indian Ocean is the driver of the ITF on an annual to longer time scale, and the wind field changes in the Pacific and Indian oceans affect ITF transport. Susanto et al. (2007) suggested an ITF proxy using SSH anomalies from T/P altimeters and thermocline depth anomalies along the Lombok Strait. Using numerical simulations, Shinoda et al. (2012) found that sea-level differences between the eastern Indian Ocean and the western Pacific were highly correlated with ITF transport. Sprintall and Révelard (2014) used remotely sensed altimeter data to develop proxy time series of ITF transport, focusing on the three outflow passages of Lombok, Ombai, and Timor. Susanto and Song (2015) developed an ITF transport proxy from satellite altimetry and gravimetry ocean bottom pressure (OBP) data, which they validated with measurements in the Makassar Strait. Hu and Sprintall (2016) proposed an ITF transport proxy on the basis of steric height from hydrologic data to separate the salinity effect on ITF transport.

Previous research indicates a close connection between ITF transport and SSH in the Indo-Pacific Ocean. Nevertheless, the proxy of ITF derived from SSH using conventional methods, such as linear regression, is typically based on the difference of SSH between two regions within the Indo-Pacific Ocean and hence ignores SSH signals of certain regions, resulting in significant inconsistency between the proxy and observations and a lack of ability to predict ITF transport. By contrast, approaches based on machine learning may be more promising for developing a better ITF proxy and predicting ITF variability. Li et al. (2018) used a backpropagation (BP) neural network to create a multidecadal time series of 0–300 m Makassar Throughflow.

Deep learning is a more powerful tool for extracting critical information from large amounts of image data than machine learning, such as the simple BP neural network. Deep learning is capable of optimizing a non-linear function from a large amount of trainable data. Theoretically, deep neural networks can approximate non-linear mappings of any complexity (Cybenko, 1989; Hornik, 1991), and deep learning has been widely used in oceanography, e.g., automatic detection and prediction of mesoscale eddies (Zeng et al., 2015; Xu et al., 2019), prediction of El Niño–Southern Oscillation, studies of climate model parameter sensitivity, and parameterization of unresolved atmospheric processes (Ham et al., 2019; Esteves et al., 2019; Anderson and Lucas, 2018). Bolton and Zanna (2019) demonstrated the powerful potential of deep learning for estimating ocean currents using satellite observations. Deep learning was shown to accurately predict subsurface ocean currents by George and Manucharyan (2021) using synthetic data generated from a simplified ocean turbulence model.

The goal of this study is to create a proxy-ITF transport using deep learning and SSH data. The remainder of the paper is organized as follows: the Data and Methods section introduces the convolutional neural network (CNN) processing methods and architecture diagram, and the Results section investigates the performance of the CNN model with different data in estimating the transport of ITF through SSH. The final section contains a summary and a discussion.

The ITF transport of verification and test data was built using CNN training of CMIP6 data. CNN’s epoch was set to 100. One epoch indicates that all data have been sent to the network, completing the forward computation and backpropagation process. Figure 4 demonstrates that the predictive skill of verification data reached a high level around epoch 30. The average S showed a peak of 0.69 ( Figure 4 ), corresponding to a high correlation coefficient of 0.95 that was significant at a 99% confidence level between deep-learning transport and actual transport of CMIP6. This suggests that the CNN was very efficient at extracting the required information from the SSH to infer the ITF transport of CMIP6. Training for too many epochs does not result in better verification and test data results. The training skill was expected to improve further with the development of the CNN model. Nonetheless, the skill of verification and test data was approximately 0.69. The skill stabilized in a short epoch, indicating that excessive training may lead to overfitting.

Figures 5A, B show the distribution of inferred and actual ITF of CMIP6 qualitatively and quantitatively, and the inferred ITF corresponded well with the actual ITF. A comparison of CNN-inferred and actual ITF transports of CMIP6 revealed that the CNN is capable of producing a reasonable ITF transport time series ( Figure 5C ). Despite the fact that the CNN explained up to 90% of ITF transport variation ( Figure 5A ), it appeared that the results inferred by CNN had a systematic bias, which may be a result of the limitations of using only SSH data. The CNN consistently underestimated the peak values of ITF transportation ( Figures 5B, C ). Even when increasing the number of extreme ITF transport training examples, testing various optimizers (e.g., stochastic gradient descent [SGD], Adam), loss functions (mean absolute error and mean square error), and weight regularization (L1, L2), this underestimation is unavoidable.

The CNN showed excellent performance in inferring the ITF transport and we then directly substituted the data from SODA and AVISO into the model trained by the CMIP 6 (ITF without transfer, i.e., all the samples for training, test, and prediction were from CMIP 6 simulations). The average test skill of SODA data acquired by the CNN peaked at 0.54 ( Figure 4 ). Owing to overfitting, the skill dropped rapidly after the training epoch reaches approximately 70, so the training step size should be set between 30 and 70. When compared with the CNN model based on CMIP6, SODA’s test skills were significantly lower, and its inferring ability is less stable.

To compensate for the small sample size of the reanalysis data, we conducted transfer learning on SODA using the training model with CMIP6 data. The R of inferred SODA ITF transport with transfer learning was 0.91, while the R of inferred SODA ITF transport without transfer learning was 0.86. The correlation of inferring with transfer learning was slightly improved when compared to the model without transfer learning ( Figure 6 ). In inferring extreme transport, transfer learning was slightly inferior to that without transfer learning, but the degree of fitting was better than the model without transfer learning ( Figure 6 ).

Figure 7 shows a comparison of various statistical methods. We found that the CNN explains more than 90% of the variance and shows a better performance than other statistical methods (logistic regression, random forest, SVM, or DNN), as expected ( Figure 7 ). We also put different CNN variants to the test, such as the ResNet and convolutional LSTM. It is interesting to note that ResNet performed similarly to the CNN, despite having more parameters ( Figure 7 ). The addition of recurrent neural networks did not improve the CNN’s capability. Given that the CNN has an excellent ability to infer ITF transport with the SSH, we used the same model to further investigate the deep-learning approach of predicting long-term ITF transport with the CNN. It should be noted that these various statistical methods contain very different parameters that may potentially influence the comparison.

We then generated an updated long-term and continuous time series of ITF transport using the CNN-based deep-learning approach and updated satellite observations of SSH ( Figure 8 ). The CNN model’s inference of ITF transport was validated by comparing it with observations ( Figure 8 ). It appeared that the ITF from deep learning captures the general variability of ITF: the correlation coefficient was 0.43 between IX1-observed ITF and 13-month-running-mean time series of CNN-inferred ITF with satellite observation, 0.57 between INSTANT-observed ITF and CNN-inferred ITF with satellite observations, and 0.52 between MITF-observed ITF and CNN-predicted ITF with satellite observations, all of which were significant at the 99% confidence level ( Figure 8 ). The deep-learning ITF differed from the observations primarily in terms of peaks and valleys, which may be associated with the ability of CMIP6 models to reproduce the ITF’s extremes (figure not shown).

Figure 9 compares the predicted ITF transport of SODA with the actual ITF after transfer learning with different time leads. As shown in Figure 9 , the R decreased overall as the time lead increased, and the CNN model could make a valid prediction (R>0.5) with a lead time of up to approximately 7 months. It should be noted that a 12-month moving average is used before calculating the correlation coefficient between the actual ITF and predicted ITF transports to reduce the influence of the ITF’s strong seasonality, and it shows that including of seasonality leads to a higher correlation coefficient between the actual ITF and predicted ITF transports. Figure 10 compares the predicted ITF transport from various models with the actual ITF transport (time series are 12-month smoothed to focus on interannual variability). The CNN was more effective and produced a longer forecast than other models ( Figures 9 and 10 ).

In this study, we investigated the deep-learning approach for inferring and predicting ITF transport with SSH images using model simulations from CMIP6 and reanalysis data products. We discovered that the CNN-based deep-learning approach with SSH images can generate a reasonable time series of ITF transport that captures approximately 90% of the actual ITF variance. CNN-based deep learning with reanalysis data sets performed similarly well, reproducing approximately 80% of the variance of actual ITF transport. These findings imply that the CNN, which explicitly relies on two-dimensional pattern analysis, outperforms other traditional data-driven technologies, such as logistic regression (R² =0.56), random forest (R² =0.74), statistical vector machines (R² =0.22), and primary fully connected neural networks (R² =0.84).

Although the CNN performed admirably in predicting ITF transport, it appears that the CNN’s prediction has a systematic bias, and the peak values of ITF transport were consistently underestimated by the CNN. Even when some methods, such as increasing the number of extreme ITF transport training examples, testing various optimizers, loss functions, and weight regularization, were used, bias and underestimation remained unavoidable. The bias and underestimation indicate that the skill limitations are due to the inherent incompleteness of the information in SSH, rather than a lack of training data or weaknesses in the CNN architecture.

It is well known that the network parameters most likely influence deep-learning performance. Different network parameters were also tested in this study. We employed various sizes of convolutional filters (3×3, 4×4, 5×5, and 7×7) and pooling filters (2×2 and 4×4). Larger convolutional filters produced worse predictions than smaller convolutional filters. We discovered that a 3×3 convolutional filter predicts similarly to a 4×4 convolutional filter, but a larger convolutional filter means fewer parameters. Additionally, we tested various optimizers (SGD and Adam), loss functions (mean absolute error and mean square error), and weight regularization (L1 and L2), and the CNN was found to be the most efficient choice. We attempted to improve the performance of the CNN by increasing the number of parameters and the cyclic neural network, which can improve the performance at month 0. However, as prediction time increased, the prediction ability of the two remained inferior to that of the CNN. This means that in some cases, more complex networks do not produce better results. We also tried increasing the size of the input from t−9 months to time t (in months), and the performance of ResNet and convolutional LSTM improved slightly.

The performance of the CNN in the model and reanalysis data demonstrates that there is enough information in SSH to predict ITF transport. However, further improvement in predicting ITF transport using a deep-learning approach is required and is dependent on at least two factors. On the one hand, the amount of training data required for the CNN supervised learning is quite large, necessitating a sampling size of O(10⁴). As a result, advanced deep-learning techniques that reduce the amount of essential training data by at least one order of magnitude are required, as is the ability to forecast in the long term. On the other hand, considering that the ITF is influenced by baroclinic processes as well, the subsurface information is also important for inferring and predicting ITF transport. As a result, a better deep-learning approach should use subsurface information in training the model, even though observing the subsurface ocean is obviously very different from satellite-based sea surface observation. Furthermore, as the large-scale pressure gradient between the Pacific Ocean and the Indian Ocean is the driver of ITF and some key regions seem to determine the ITF (e.g., Susanto et al., 2007; Tillinger and Gordon, 2009), the deep-learning approach might be further improved if we additionally consider the SSH in these key regions. All of this points to a bright future for monitoring and predicting important large-scale ocean circulations, such as the ITF.

The original contributions presented in the study are included in the article/supplementary material. Further inquiries can be directed to the corresponding author.

SH designed the study. LX and SH conducted the analysis and wrote the initial draft of the paper. All authors contributed to the article and approved the submitted version.