Predicting saltwater intrusion in Modaomen waterway based on an integrated deep learning model Open Access

In the past decade, the phenomenon of saltwater intrusion during the dry season in the Pearl River Delta has become increasingly severe (Hu et al. 2024a). Saltwater intrusion is the process by which saline water from the sea encroaches into freshwater estuaries and rivers, primarily due to the reduction in freshwater inflows (Hoitink & Jay 2016). This escalating issue has led to significant implications for industrial layout, domestic water consumption, and agricultural irrigation in coastal areas (Tran et al. 2024). The intrusion of saltwater into freshwater systems not only disrupts the availability and quality of water resources but also poses a serious challenge to the sustainable development of regional economies (Hu et al. 2024b). Consequently, saltwater intrusion disasters have emerged as a critical factor restricting the development of water resources and impeding economic sustainability in affected regions. Effective simulation and accurate prediction of saltwater intrusion processes are key technical issues for saltwater intrusion prevention and water safety assurance in coastal estuarine areas (Tang et al. 2020; Tong et al. 2024).

Saltwater intrusion prediction models can be broadly classified into two main categories (Weng et al. 2024): numerical hydrodynamic models (Ji et al. 2007; Veerapaga et al. 2019; Binh et al. 2020) and data-driven models (Rohmer & Brisset 2017; Lu et al. 2021; Yin et al. 2022). Each type of model offers distinct advantages and faces unique challenges, making them suitable for different applications and scenarios. Numerical hydrodynamic models have long been utilized for the prediction of saltwater intrusion due to their ability to simulate complex physical processes governing estuarine dynamics. Since 1960s, one-dimensional models (Krvavica et al. 2017; Martínez-Aranda et al. 2020) have been proposed for saltwater intrusion modeling. With the continuous rising demand of model accuracy, the one-dimensional model is gradually replaced by the two-dimensional model (Abarca & Clement 2009; Yan et al. 2024) and the three-dimensional model (Banks et al. 2024; Kihm et al. 2024). These models, which are based on the principles of fluid mechanics and hydrodynamics, such as Navier–Stokes equations, can provide detailed spatial and temporal distributions of salinity. The primary advantage of numerical hydrodynamic models lies in their robustness and accuracy in representing physical phenomena, given sufficient input data and calibration. They allow for the incorporation of various factors such as tidal movements, river discharges, and meteorological conditions. However, these models require detailed input data, such as riverbed topography data and meteorological data, which may not always be available. Furthermore, one-dimensional hydraulic models struggle to represent the three-dimensional nature of the salt intrusion processes, while two- and three-dimensional models are too computationally demanding to run on operational timescales (Wullems et al. 2023). Additionally, the process of model calibration and validation is time-consuming and requires significant expertise, which can limit their practical application in regions with limited data availability and technical capacity (Wang & Ge 2025).

Due to these limitations of numerical hydrodynamic models, data-driven models (Yin et al. 2022, 2024; Deleersnyder et al. 2024) have gained popularity in recent years as an alternative approach, primarily relying on machine learning techniques such as tree-based methods and kernel algorithms, with deep learning architectures remaining comparatively underutilized except for isolated long short-term memory (LSTM) networks applications. Tran et al. (2022) tested the performances of five algorithms (simple linear, K-nearest neighbors, random forest, support vector machine, and LSTM) for predicting saltwater intrusion in the Vietnamese Mekong Delta. Nguyen et al. (2021) establish a novel framework for monitoring salinity intrusion using remote sensing and machine learning. Leveraging advancements in machine learning and data science, these models rely on historical data to identify patterns and make predictions about future salinity levels (Zhou et al. 2020; Lal & Datta 2021). In general, the historical data utilized in these models is not only the salinity data, but also the salinity related various (Tian et al. 2024), including river flow, tide, wind, and temperature. The primary advantage of data-driven models is their ability to process large datasets and provide rapid predictions without the need for detailed physical input parameters. Once trained, data-driven models have been reported to be successful in capturing non-linear systems, and have a runtime of milliseconds to seconds per time step (Hauswirth et al. 2021). They are often more flexible and can be updated easily with new data, making them suitable for real-time monitoring and forecasting (Weng et al. 2024). However, the accuracy of these models heavily depends on the quality and quantity of available data, and they may not perform well in scenarios with limited historical records. Furthermore, previous studies (He et al. 2019; Sun et al. 2020) generally focused on daily predictions of saltwater intrusion, which do not provide the detailed information necessary for effective water resource management. Some researchers (Xu et al. 2024; Li et al. 2025) have used data-driven model to predict the maximum salinity value of the next day, but the data are daily scale and the time span is short, which may ignore the dynamic changes of higher frequency and the trend of longer period. Some researchers also used LSTM, gated recurrent units (GRUs), convolutional neural networks (CNNs) and other models to study the rule of saltwater intrusion at Modaomen Estuary, and found that runoff had the greatest impact (Tian et al. 2024), but saltwater intrusion was affected by the half-daily cycle of the tide, and the daily data may smooth out the diurnal fluctuations driven by the tide, which is not suitable for hour-level early warning. The performance of different deep learning methods also varies significantly. Therefore, it is crucial to develop and utilize algorithms that can deliver stable and reliable prediction results. Ensuring stability in simulations is essential not only for accurate predictions but also for real-time decision-making and risk management in dynamic and complex environments.

Regarding the above defects, this study aims to contribute to the field by providing a robust and efficient tool for predicting saltwater intrusion, which can support water safety management and decision-making in coastal areas. The objectives of this paper are threefold: (1) to develop an hourly saltwater intrusion prediction model with a deep learning method and limited dataset; (2) to propose an innovative deep learning algorithm to provide stable predictions; and (3) to analyze the model's performance over different forecast periods. The remainder of this paper is organized as follows: Section 2 provides an overview of the study area and details the methodology for constructing the deep learning model. Section 3 presents the results of the model's application. Section 4 offers a discussion of the findings. Finally, Section 5 concludes the paper.

As the crucial source for supplying fresh water to the surrounding cities, lots of water intakes are distributed along both sides of the Modaomen waterway. Due to its decisive role in freshwater supply, salinity data are monitored at each water intake. In this research, salinity data from Guangchang station (GC), Pinggang station (PG), and Zhuzhoutou (ZZT) station is collected. Previous literature indicates that saltwater intrusion is influenced by the coupling effects of external sea tides, upstream flows, and estuary morphology, which serve as indicators for saltwater intrusion prediction. The flows at the upstream Shijiao station (SJ) and Gaoyao station are highly correlated with the Modaomen waterway, making them suitable indicators for upstream flow. Additionally, sea tide data from Denglongshan station is collected. All data spans from October 2020 to June 2022, with a time step of one hour. In this study, 70% of the dataset was used for training and the remaining 30% for validation. The locations of all stations are depicted in Figure 1.

The main framework of the deep learning model is designed to predict the salinity at water intakes several hours into the future by utilizing relevant factors. The input to the model includes upstream river flow data, downstream tide data, and salinity monitoring data from three stations in the Modaomen Waterway collected between 2020 and 2022. The output is the predicted salinity data for the three water intakes during the prediction period. Following this framework, several deep learning models are utilized, and an integrated deep learning model is proposed in Figure 2.

LSTM networks (Gers et al. 2000) are a special kind of recurrent neural network (RNN), which are widely used in water-related prediction (Deng et al. 2022; Yin et al. 2023). They use gate units to control the logic of data updates or discards, overcoming the drawbacks of RNNs such as excessive influence of weights and the tendency for gradient vanishing or explosion. LSTM networks can converge better and faster, effectively improving prediction accuracy. LSTM has three gates: forget gate, input gate, and output gate, determining the information to be remembered or forgotten at each time step. The input gate decides how much new information is added to the cell, the forget gate controls whether the information at each time step will be forgotten, and the output gate decides whether there is any information output at each time step. The saltwater intrusion prediction model can fully utilize its memory units to capture and learn long-term dependencies in sequence data. In this study, the LSTM model is defined as part of a Sequential model. The input layer is an LSTM layer with 100 neurons and uses the ReLU activation function. A fully connected layer is added after the LSTM layer, with the number of output features the same as the number of input features.

CNN is a type of feedforward neural network mainly used for processing images and sequence data (Afrin et al. 2024; Lin & Wang 2024). They consist of convolutional layers and subsampling layers, significantly reducing the parameters needed to train the neural network. They can sample images and use the principle of local correlation to reduce the data volume while retaining useful information, effectively capturing some significant peaks. In this study, the construction method of the CNN model is similar to that of the LSTM model, also being part of a sequential model. The input layer is a one-dimensional convolutional layer (Conv1D) with 64 filters and a kernel size of 2, using the ReLU activation function. After the Conv1D layer, a pooling layer (MaxPooling1D) is added to reduce the dimensionality of the features, then the features are flattened into a one-dimensional vector. Finally, a fully connected layer is added.

GRU is another type of RNN (Zhang et al. 2021; Yuan & Chen 2022), similar to LSTM, used for processing time series data. GRU has an input gate and a forget gate but no output gate, making it more efficient at handling long-term dependencies and avoiding overfitting more easily than LSTM, with faster computation speed. In this study, the construction method of the GRU model is similar to that of the LSTM model, also being part of a sequential model. The input layer is a GRU layer with 100 neurons and uses the ReLU activation function. A fully connected layer is added after the GRU layer.

The goal of model integration is to enhance prediction performance by integrating the outputs of multiple independently trained models. This study uses the concatenate function in Keras to achieve model integration, as it effectively connects model outputs along the specified axis, fully utilizing the unique information of each model. First, an input layer is created to receive data, and the output of the input layer is connected to the input layers of the LSTM, GRU, and CNN models, respectively. Then, the outputs of these three models are concatenated using the concatenate layer, integrating the features extracted by each model. After connecting the model outputs, a dense layer with a number of features equal to the output time steps is added, resulting in the final stacked output. This indicates that the prediction at each time step is a vector determined by the number of features, and the repetition of this vector across the entire time series equals the output time steps. The dense layer uses the ReLU activation function. The model class in the Keras library is used to construct the integrated model. The initially created input layer serves as the input for the integrated model, and the stacked output obtained from the above steps serves as the output for the model. The hyperparameters of the LSTM, GRU, and CNN models remain unchanged. Finally, the integrated model is compiled using a weighted loss function to achieve the best prediction results.

While n is the training sample size; represents the actual values; represents the predicted values.

Besides the MSLE, various metrics (such as Nash–Sutcliffe efficiency (NSE) coefficient, root mean squared error, accuracy, precision, and recall) are calculated to evaluate the model's performance during the validating process.

While is the observed value at time i; is the model predicted value at time i; is the average of all observed values; n represents the total number of observations.

While n is the number of training samples; is the measured true values; are the measured and predicted values.

While TP is the number of correctly predicted positive samples; TN represents the number of correctly predicted negative samples; FP is the number of false positives; FN is the number of false negatives.

Based on the evaluation results, the hyperparameters of the model are tuned. This includes adjusting model structure, learning rate, batch size, and other hyperparameters. To maintain high accuracy, the hyperparameter range is determined to keep accuracy above 0.90, ensuring that the model performs well across various conditions. The hyperparameter tuning scale is shown in Table 1.

In the current research, models with different prediction periods are established and trained. The prediction period refers to the range of the target variable or output of the model, such as the 6-h lead time, 12-h lead time, and 24-h lead time. The following results focus on the prediction effects of the model with prediction periods of 6, 12, and 24 h.

For further analysis of model accuracy, RMSE and NSE are listed in Table 2. As shown in Table 2, RMSE and NSE indicate that the model performs well with the 6-h prediction period, while the prediction performance decreases for the 12- and 24-h periods.

Predicting salinity values is crucial for the current model. However, prediction of the occurrence of saltwater intrusion events is equally important for risk prevention. A saltwater intrusion event is determined by whether the salinity at the estuary exceeds 250. Using the observed and predicted values, the number of instances where salinity at the three stations exceeded 250 was counted, and the predicted number of saltwater intrusion events was compared to the observed number. Based on the prediction results, precision, accuracy, and recall are calculated and shown in Table 3. The closer the precision, accuracy, and recall are to 1, the better the prediction performance. As shown in Table 3, the model's prediction results for salinity events are relatively high, especially for the 6-hour prediction period, with precision values of 0.96, 0.97, and 0.98 for the three stations. The prediction accuracy remains consistent as the prediction period increases.

To illustrate the performance improvement, results from LSTM, GRU, and CNN, are also proposed in Table 4. Compared with Tables 2 and 3, it can be found that the integrated model demonstrates superior performance in salinity prediction across almost all metrics and periods compared to the individual LSTM, GRU, and CNN models.

By integrating the temporal memory of LSTM networks, the dynamic gating mechanisms of GRU, and the local feature extraction capabilities of CNN, the integrated model achieves prediction advantages tailored to the operational characteristics of different pumping stations. Compared to standalone LSTM architectures, the most significant optimization was observed, with an average NSE improvement of 25.2%, coupled with short-to-medium-term error reductions exceeding 18% at GC Station and 65% at PG Station. For GRU implementations, enhancements predominantly focused on short-to-medium horizons, exemplified by a 51% error reduction in 12-h forecasts. Regarding CNN, the integrated model exhibited limited NSE improvements (<20%) at most stations except PG, primarily due to CNN's inherently higher baseline accuracy. Comparative analysis consistently shows that the optimization effect of the integrated model on LSTM and GRU (performance gain range: 15–65%) is better than that on CNN. While station-specific data variations influenced improvement magnitudes across metrics, all results validate the integrated model's ability to enhance prediction accuracy through synergistic architectural complementarity, thereby confirming its practical utility in operational prediction tasks.

The integrated model demonstrates superior performance in medium-to-long-term forecasting (12–24 h). Specifically, it achieves 65% higher accuracy than LSTM for the 24-h forecast at PG station and 29% greater improvement over GRU for the 12-h forecast at ZZT station, showing significant advantages compared to standalone models. However, the improvement was limited (generally <20%) in the short-time (6-h) forecast. Different models show obvious differences at different sites: LSTM has the largest improvement space, GRU has the most unstable performance at the medium time scale, and CNN is relatively stable. Overall, the integrated model consistently achieves the highest scores in precision, accuracy, recall, and NSE across all three sites and periods, highlighting its robustness and effectiveness in predicting salinity levels compared to the individual LSTM, GRU, and CNN models.

Taking the Modaomen Waterway as the research area, this study proposes an integrated deep-learning model for salinity prediction according to the basic algorithms of LSTM, CNN, and GRU. Upstream flow data, downstream tide data, and salinity data from the GC, PG, and ZZT stations during 2020–2022 are utilized as model input for model training and validation. The model performance is evaluated with indicators such as RMSE, NSE, precision, accuracy, and recall. Results show the performance of the LSTM–GRU–CNN integrated model with different prediction periods. And the comparison among the integrated model, LSTM, GRU, and CNN is also analyzed. However, there are still some problems needed to be discussed.

In the domain of saltwater intrusion prediction with a deep learning model, many studies incorporate a wide range of input factors to enhance prediction accuracy. Tian et al. (2024) employed LSTM and CNN to predict the severity of saltwater intrusion with runoff, maximum tidal range, and wind as input variables. Weng et al. (2024) chose various environmental components, including antecedent chlorinity, upstream discharge, tidal level, and wind vector, to drive the clustering method for salinity prediction. More input factors can provide more learning features for the deep learning model, but they also input noise interference. Therefore, the more inputs, the better the model effect is not necessarily the case. Our research demonstrates that by selecting a more focused subset of input variables – specifically upstream runoff, downstream tide, and antecedent salinity – we can still achieve robust prediction results. Our results are also consistent with Tian et al. (2024) that the largest contributor to saltwater intrusion was runoff (40%), followed by maximum tidal range, wind speed, and wind direction, contributing 25, 20, and 15%, respectively. In other words, limited data with upstream runoff, downstream tide, and antecedent salinity can also produce acceptable prediction results.

Besides the proper selection of input variables, the proposed integrated deep learning model effectively captures the essential dynamics of saltwater intrusion, showcasing its capability to perform well despite the reduced input complexity. In the current research, the precision of the model with 24 h-ahead ranges from 0.85 to 0.91, while Weng et al. (2024) is 0.75 with their proposed model. From their results, the performance of Extreme Gradient Boosting and time-series K-means is also tested. Combined with the results of LSTM, GRU, and CNN in the current research, it can be concluded that a single or traditional algorithm is hard to produce satisfactory results for salinity prediction. The proposed model in this research not only simplifies the data acquisition process but also reduces computational costs and enhances the model's efficiency. The success of the proposed model with limited data inputs underscores the potential for deep learning techniques to extract meaningful patterns and relationships from smaller datasets. By leveraging the inherent feature extraction capabilities of deep learning, the proposed model can identify and learn from the critical interactions among the selected variables. This finding is particularly significant for regions where extensive environmental monitoring data are scarce or challenging to obtain.

The prediction period, or the forecast horizon, is a critical factor in the performance of the predictive model. Our integrated deep-learning model demonstrates that as the prediction period extends, the accuracy of the predictions diminishes. This phenomenon is consistent with the inherent challenge of long-term forecasting, where uncertainties accumulate over time, and the model's ability to capture and extrapolate underlying patterns diminishes. A clear tradeoff between the length of the prediction period and the accuracy of the predictions is illustrated. For shorter prediction periods (e.g., up to 6 h), the model maintains high accuracy, with RMSE of 51.56–604.14 mg/L, NSE of 0.91–0.94, and accuracy of 0.96–0.98. As the prediction period extends to 24 h, the model's performance exhibits a decline trend with RMSE of 73.49–625.33 mg/L, NSE of 0.86–0.90 and accuracy of 0.91–0.98. Although models with prediction periods exceeding 24 h are not included in the current study, previous research (Tian et al. 2024) shows that the RMSE doubles and accuracy declines sharply when the prediction period increases from 24 to 48 h.

In practical applications, the reliability of predictions is paramount. For decision-making purposes, especially in managing water resources and mitigating the impacts of saltwater intrusion, stakeholders must weigh the tradeoffs between prediction period and accuracy. Short-term predictions, while more accurate, may offer limited foresight, whereas longer-term predictions, despite lower accuracy, provide a broader temporal outlook. To address this, it is crucial to implement a robust validation framework that continuously assesses model performance and updates predictions based on the latest available data. Additionally, integrating ensemble forecasting techniques, where multiple models with varying strengths are combined, can enhance the overall reliability of predictions.

Furthermore, additional research should focus on refining the model to improve its long-term prediction capabilities. This could involve: (1) Incorporating real-time data and leveraging advanced data assimilation techniques to continuously update the model. (2) Combining deep learning models with traditional physical models to better capture the underlying physical processes governing saltwater intrusion. (3) Developing methods to quantify and communicate the uncertainty in predictions, providing stakeholders with a clearer understanding of the confidence levels associated with different prediction periods.

This study proposes an ensemble of deep learning models – LSTM, CNN, and GRU – for predicting saltwater intrusion. The proposed model is used for salinity prediction at the GC, PG, and ZZT stations in the Modaomen waterway. The performance of the proposed model is analyzed and discussed, leading to the following main conclusions:

By using upstream flow, downstream tide, and antecedent salinity as input data, an hourly saltwater intrusion prediction model is developed using deep learning methods. This model provides salinity predictions for the next 6, 12, and 24 h. An integrated deep-learning model based on LSTM, GRU, and CNN is proposed. Comparisons among the four models demonstrate that the integrated model performs better in saltwater intrusion prediction, particularly in terms of precision, accuracy, NSE, and stability. The integrated model has the most outstanding performance in the medium and long-term forecast (12–24 h). It achieves 65% higher accuracy than LSTM for the 24-h forecast at PG station and 29% greater improvement over GRU for the 12-h forecast at ZZT station, showing significant advantages compared to standalone models. However, the improvement was limited (generally <20%) in the short-time (6-h) forecast. Different models show obvious differences at different sites: LSTM has the largest improvement space, GRU has the most unstable performance at the medium time scale, and CNN is relatively stable. The prediction period is a critical factor in saltwater intrusion prediction. There is a clear tradeoff between the length of the prediction period and the accuracy of the predictions. As the prediction period extends, the accuracy of the predictions decreases.

This research was funded by the National Natural Science Foundation of China (52109018, 12202150).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.