1. Introduction
The Nakdong River estuary is a brackish water region where freshwater meets seawater, possessing both ecological diversity and economic importance (
Fig. 1). This area is recognized for its ecological value as a habitat for diverse species and a major stopover for internationally protected migratory birds. For residents of Busan and surrounding areas, it is also a source of domestic, agricultural, and industrial water, closely linked to the local economy. However, since the construction of the Nakdong River estuary bank in 1987, the circulation of seawater and freshwater was blocked, mitigating flood damage and saltwater intrusion, but resulting in new ecological challenges such as decline in migratory bird population and diversity in fish species (
Kim et al., 2016).
The ecological changes caused by the construction of the estuary bank have posed as a major threat to the sustainability of Nakdong River estuary. To address this problem, the government and local communities have been exploring the possibility of restoring the brackish water region by conducting trial gate openings of the estuary bank since 2017. Ecosystem restoration and water quality improvement were confirmed through this process, and since 2022, the gates have always been open during spring tides. While these measures have positively contributed to restoring biodiversity and improving water quality through reclamation of brackish water region, the changes in salinity levels have posed new challenges to managing freshwater ecosystems and water resources for domestic and agricultural use. In particular, changes in salinity concentration directly impact agricultural land and drinking water sources upstream of the estuary bank, highlighting the need for a rapid and accurate prediction system to prevent salinity intrusion.
Until now, various physics-based and data-driven models have been applied to predict salinity concentrations in estuaries. Physics-based models excel in accurately reproducing the physical processes of river and marine environments, simulating salinity intrusion by considering hydrological variables and changes in such as tides, freshwater discharge, and tidal level.
Blumberg and Mellor (1987) simulated seawater flow by combining fluid dynamics equations and transport equations.
Han et al. (2011) used ECOMSED (a three-dimensional hydrodynamic and sediment transport model) to analyze in detail the phenomenon of salinity intrusion based on tidal level change and discharge amount. They quantitatively evaluated the impact of tidal and freshwater inflow interactions on salinity levels, contributing to understanding the physical characteristics of Nakdong River.
Kim et al. (2018) applied an environmental fluid dynamics code (EFDC) to analyze the impact of discharge and tidal level changes during estuary bank openings on the distance and concentration of salinity intrusion. They predicted the spatiotemporal distribution of salinity concentration according to discharge variations and estuary bank opening levels, providing important scientific evidence for establishing management policies of the Nakdong River estuary.
These physics-based models provide high reliability and precision, making them essential tools for salinity prediction. However, these models have limitations in that the initial input value setting is complicated, a large amount of computational resource is required, and computation time is long. These characteristics can pose as constraints in real-time operations or situations requiring urgent decision-making.
Recently, the use of data-driven approaches to predict salinity concentrations in Nakdong River has been attracting interest.
Woo et al. (2022) successfully predicted salinity concentration up to 5 km upstream of the Nakdong River estuary bank using a long short-term memory (LSTM) algorithm, demonstrating that data-driven models can achieve high performance while simplifying physical complexity.
Lee et al. (2022) applied various data-driven model techniques such as light gradient boosting machine (LGBM) and extreme gradient boosting (XGBoost) to predict salinity of the Nakdong River estuary. They exhibited faster learning speeds than physics-based models. This suggests that machine learning techniques, with their low computational demands and fast learning speeds, are suitable alternatives for real-time decision-making.
Yang et al. (2025) performed exploratory data analysis on Nakdong River estuary datasets and optimized variables for salinity concentration prediction performance, demonstrating the importance of data preprocessing and variable optimization in hydrological data analysis.
However, most existing studies on salinity concentrations of Nakdong River have been limited to simply applying models. These studies relied solely on data-driven modeling, without analyzing relationships between variables or optimizing variables through additional data preprocessing. While
Yang et al. (2025) attempted to overcome some of these limitations, studies on the unique environmental conditions of the Nakdong River estuary remains scarce. In particular, Nakdong River estuary is the only area in Korea aiming to introduce seawater to create brackish owing environment, making related studies extremely limited. Furthermore, long-term data acquisition in the Nakdong River region is challenging due to sensor failures and environmental changes following recent policy shifts in estuary bank operations.
Given these circumstances, this study aimed to identify the hydro-environmental characteristics of the Nakdong River estuary region using data analysis, and based on this analysis, to develop a salinity concentration prediction data analysis model that reflects spatiotemporal lag specifically tailored to the region.
Therefore, in this study, characteristics of the Nakdong River estuary region were identified using data analysis to analyze the hydro-environment complexity of the region and utilize the findings to build a regionally specialized salinity concentration prediction data analysis model.
2. Research Data
Table 1 shows the 2021 data of Nakdong River estuary region used in this study, and
Fig. 2 illustrates the locations where each datapoint was measured. Major characteristics of the Nakdong River estuary region were examined based on the collected data.
Fig. 3 shows the salinity at Nakdong River Bridge, which was the target for prediction, along with the key influencing variables over time: rainfall at Changnyeong-Hamanbo, freshwater discharge from Changnyeong-Hamanbo, and discharge from Nakdong River estuary bank.
3. Research Method
Exploratory data analysis was performed to select key variables needed in setting up salinity prediction model based on observation data. Correlation between the statistical characteristics of each variable and salinity was analyzed, and EDA is largely composed of three stages.
(1) Seasonal pattern analysis: Fig. 4 is a visualization of the seasonal pattern changes using the principal component analysis (PCA) method on the given data; the data were found to be largely divided into two clusters. This suggests that the data characteristics clearly change according to seasonal changes, which implies that data patterns fluctuate significantly over time (Lee et al., 2024). These clustering and seasonal patterns can result in reduced prediction accuracy if the prediction model processes the entire data under the same method. This result clearly demonstrates difference in seasonal characteristics of the data. Therefore, these clustering and seasonal patterns can impact the accuracy of the prediction model. Thus, in the modeling process, structural changes must be effectively reflected in the data by separating data by time interval or adding variables that reflect seasonality.
(2) Spatial distribution and lag effect: Fig. 2 shows the spatialdistribution of various environmental variables (e.g., freshwater inflow, tidal level, and rainfall) that impact salinity concentration at key points (Changnyeong-Hamanbo, Gupo Bridge, Nakdong Bridge, etc.) in the Nakdong River estuary. In the estuary, these variables are distributed differently at each location, and changes in these variables have been observed to impact multiple locations within the estuary with a time delay (Ralston and Geyer, 2019). For example, freshwater discharged upstream takes a certain amount of time to reach downstream locations (such as the Nakdong River Bridge or the estuary bank), and this time varies depending on discharge amount and flow rate. Conversely, inflow of seawater at the estuary bank also takes time to spread upstream due to factors such as tidal cycles, degree of sluice gate opening, and upstream discharge. Such spatial distribution of environmental variables within the estuary and lag effect resulting from interaction are among the main causes of changes in salinity concentration, and not considering this in the modeling process can significantly reduce the accuracy of the prediction. Therefore, accounting for the lag effect between variables in modeling is crucial to accurately predict the complex salinity structure of Nakdong River estuary.
(3) Relationship between seawater inflow and salinity: Fig. 5 shows the relationship between salinity measured at Nakdong River Bridge and seawater inflow. Salinity is clearly observed to increase along with seawater inflow volume increase, suggesting that seawater penetration directly impacts upstream salinity concentrations. In particular, since a lag effect exists between seawater inflow volume and salinity concentration according to changes in discharge, reflecting this in the prediction model is essential to improve accuracy (Tian et al., 2024).
4. Nakdong River Salinity Concentration Prediction Experiment
Experiments were conducted using the random forest model, applying variable selection method and time-lag method that reflect data characteristics identified through exploratory data analysis. The efficiency of the salinity concentration prediction modeling for the Nakdong River was analyzed by comparing the salinity concentration prediction performance across different experimental cases.
4.1 Model Used
The random forest model is a machine learning algorithm that ensembles multiple decision trees to improve prediction performance. It was selected for this study to effectively model the zero-inflated distribution of salinity concentration and the segmented heteroscedasticity of salinity concentration caused by sluice gate operations. The salinity data of Nakdong River estuary in 2021 converged to zero when the gates were closed but rapidly changed to a range of 0.5–10 psu when opened, exhibiting nonlinear characteristics (
Fig. 5). In such a data structure, simultaneously accounting for zero-value and post-gate salinity groups in a traditional regression model is difficult. However, the random forest model can hierarchically process the two groups through tree-based conditional partitioning (
Saboori and Doostparast, 2023). In addition, the random forest calculates variable importance during the modeling process (
Breiman, 2001). This quantifies how effectively each variable reduces the variance of the target variable, which can provide insights into estuary management policies.
4.2 Prediction Period
Fig. 6 shows the discharge from Nakdong River estuary bank and salinity at Nakdong River Bridge from January to December 2022. The gray areas in the figure indicate periods when salinity measurements were not taken at Nakdong River Bridge. During periods of high discharge from the estuary bank, numerous intervals with missing data occurred owing to sensor malfunctions, making it difficult to obtain large amounts of continuous salinity data. Thus, to ensure data has no missing values, we set the salinity prediction period from January to June 2021.
4.3 Experimental Procedure
4.3.1 Sliding window method
In this study, as the estuary data exhibited a distinct seasonality pattern, sliding window method was applied to ensure that seasonal data characteristics were fully reflected in model training. The sliding window method divides time-series data into fixed intervals and repeatedly performs training and testing. It is widely used in engineering problems that require processing seasonality, non-stationarity, and real-time data (
Hota et al., 2017). Therefore, the sliding window method was designed such that each window segment fully reflects seasonal characteristics, enabling the model to effectively learn variations in seasonal data pattern.
In the experiment, the model was iteratively trained by shifting the window with 90 days of training data and three days of testing data. In this process, the impact of seasonal patterns on prediction performance of the model was systematically assessed. By simultaneously considering the seasonal variability and data non-stationarity, this approach prevents overfitting caused by historical data bias and contributes to building a predictive model capable of flexibly responding to actual environmental changes.
Fig. 7 shows the process of constructing the training and testing datasets using the sliding window method.
4.3.2 Variable optimization method reflecting time lag
In addition to reflecting seasonality through the sliding window method, this study used the Granger causality analysis to effectively reflect key variables and time lags in the salinity concentration prediction modeling of Nakdong River estuary. Granger causality is a method for assessing whether historical values of a specific variable have a statistically significant impact on predicting future values of a target variable (salinity concentration), making it well-suited for time-series data analysis (
Seth, 2007).
Table 2 shows the Granger causality analysis results, which identified discharge, seawater inflow, tidal level, and rainfall as independent variables with a significant impact on salinity concentration. By deriving the optimal time lag for each variable, we confirmed that time lag effect existed between upstream and downstream owing to water movement speed and environmental factors. For example, in
Fig. 8 (a), even the impact of changes in seawater inflow exhibits a time lag on the salinity at Nakdong River Bridge. Statistical significance increases after 5 h, reflecting the time required for seawater intrusion to pass through the estuary bank and reach Nakdong River Bridge. Furthermore, these results are consistent with those of
Kim et al. (2018), who identified the time lag relationship between seawater intrusion at the estuary bank and salinity changes at Nakdong River Bridge. Water level at Gupo Bridge has a longer time lag, and shown in (b), the strongest causal relationship (p-value 0.01) occurs at approximately 9 h. This is presumed to indicate the time required for changes in water level at Gupo Bridge to propagate downstream and affect salinity at Nakdong River Bridge. Through these results, the key variables preceding salinity concentration and the optimal time lag of these variables were identified, and subsequently salinity prediction modeling was conducted based on these findings.
4.4 Experimental Results
Table 3 shows the three experimental conditions (Case 1: basic variables, Case 2: initial conditions added, Case 3: variable optimization and time lag reflected) for assessing the performance of the salinity concentration prediction model for the Nakdong River estuary, whereby prediction accuracies were compared from 1 to 24 h using the time-series data from January to July 2021.
When the model was built using only basic variables derived from data learning, its prediction performance was significantly lower than in cases where initial conditions were added. This indicates that for water quality predictions in complex hydrological environments such as estuaries with installed sluice gates, the accuracy of the prediction model can significantly be improved by simply providing observation results of initial conditions. Furthermore, the Case 3 model, which applied time lag variable derived from Granger causality analysis, exhibited the best performance across all intervals.
Table 4 shows the salinity prediction performance for each experimental condition, and
Fig. 9 provides the graphical visualization of the results. For short-term predictions (1–6 h), the Case 3 model recorded a root mean square error (RMSE) of 0.838–1.037 psu and coefficient of determination (
R2) of 0.934–0.944, which was a significantly higher accuracy than Case 1 (RMSE: 2.471–2.653 psu and
R2 : 0.443–0.516). However, when compared with Case 2 (RMSE: 0.833–1.061 psu and
R2 0.910–0.945), Case 3 only had an average improvement in RMSE of 1.8 %. These findings suggest that the short-term prediction performance of this model is excellent, and that the physical travel time (approximately 5 h) required for seawater to reach Nakdong River Bridge after opening the estuary bank is well captured. However, the practical improvement over Case 2 in short-term prediction is modest despite its statistical significance.
Even in medium-term predictions (12–24 h), Case 3 model recorded the best performance, showing improvements over Cases 1 and 2. In particular, for medium-term predictions compared with short-term predictions, the performance gap between Cases 1 and 3 became slightly larger. Therefore, for a more accurate medium- to long-term salinity prediction at Nakdong River estuary, the random forest model that incorporates variable optimization and time lag should be applied.
However, with the increase in prediction time horizon, the RMSE tends to increase while decreases, reflecting the inability of the model to capture complex environmental factors (e.g., sudden rainfall, tidal changes, etc.) in medium- to long-term predictions.
Fig. 10 is the visualized results for each experimental case by future prediction time. During the rapid salinity change period, which occurs 5–7 h after opening of the sluice gates, prediction errors increased for all cases, suggesting limitations with data-driven models in capturing abrupt changes in physical conditions.
Therefore, although applying the lag variable derived from Granger causality method contributed in improving prediction performance, the complexity of environmental variability remains a limiting factor for long-term predictions. This suggests the need for future development of hybrid physical-machine learning models or integrated approaches such as combining weather forecast data.
5. Conclusions
This paper proposes a variable optimization method by combining exploratory data analysis (EDA) and Granger causality analysis to systematically model the hydro-environmental complexity of the Nakdong River estuary. The following are the main conclusions:
(1) Granger causality analysis identified discharge (lag 1), seawater inflow (lag 5), and tidal level (lag 3) as the main drivers of salinity concentration changes, and this is a result of reflecting the time lag effect associated with water movement speed and tidal cycles. Based on these results, the 1 h ahead prediction produced an accuracy of R2= 0.893. This proves that the data-driven approach can effectively capture the spatiotemporal interactions at Nakdong River estuary.
(2) Based on these findings, we confirmed that for water quality prediction in complex hydrological environments such as estuaries with installed sluice gates, simply providing observation data on initial conditions can significantly improve prediction model accuracy. In addition, the Case 3 model (variable optimization and time lag incorporated) that applied time lag variable derived from Granger causality analysis achieved the highest performance across all intervals.
(3) For short-term predictions (1–6 h), the Case 3 model produced the best prediction performance, confirming that the physical travel time (approximately 5 h) for seawater to reach Nakdong River Bridge after opening the estuary bank was well reflected in the model. However, when compared with Case 2 (initial condition added), improvement in short-term performance was modest in practical terms, despite being statistically significant.
(4) For medium-term predictions (12–24 h), Case 3 model also produced the best performance, demonstrating performance improvements over Case 1 (basic variable) and Case 2. In particular, the performance gap between Cases 3 and 1 widened somewhat in medium-term predictions compared with short-term predictions. Therefore, applying the random forest model with variable optimization and time lag reflected is essential for a more accurate medium- to long-term prediction of salinity at Nakdong River estuary.
This study was based on observational data for one year (2021); thus, it may not fully reflect annual environmental variability or extreme weather conditions. Therefore, further studies incorporating long-term observational data and various environmental conditions are required.
Furthermore, although short-term accuracy of salinity concentration prediction at Nakdong River estuary has been improved by combining Granger causality analysis and sliding window method, several limitations and future study needs remain. First, the experiments focused on short- to medium-term predictions, but prediction uncertainty had a tendency to increase as the prediction period increased. Therefore, to account for long-term impacts of climate change and sluice gate operation policies, models capable of medium-to long-term prediction of at least 2 days (48 h) are necessary. Second, prediction performance was poor during the rapid salinity increase occurring 5–7 h after opening the sluice gates, limiting the ability to respond to such situations. A hybrid physical-machine learning model for capturing rapid salinity changes is currently under development to address this.
Conflict of Interest
The authors declare that they have no conflict of interests.
Funding
This study was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (Ministry of Science and ICT) (No. 202301190002).
Fig. 1
Functions and impacts of estuary banks in the Nakdong River Estuary
Fig. 2
Locations of environmental monitoring sites in the Nakdong River Estuary.
Fig. 3
Observation data near the Nakdong River Estuary: (a) Nakdong River Bridge salinity; (b) Changnyeong-Hamanbo Reservoir rainfall; (c) Changnyeong-Hamanbo Reservoir total discharge; (d) seawater inflow volume of banks of the Nakdong River
Fig. 4
Characterization of seasonal patterns in estuarine data: Visualization of seasonal patterns
Fig. 5
Comparison of salinity at Nakdong River Bridge and seawater inflow volume
Fig. 6
Discharge from the estuary bank and salinity
Fig. 7
Fig. 8
Granger causality test: p-value by lag: (a) Seawater inflow volume; (b) Gupo Bridge eater level
Fig. 9
Comparison of RMSE by forecast horizon for three cases
Fig. 10
Visualization results by case: (a) 1-h ahead prediction; (b) 6-h ahead prediction; (c) 12-h ahead prediction; and (d) 24-h ahead prediction
Table 1
Status of observation data collection in the Nakdong River Estuary and surrounding areas
|
Observation site |
Observation parameter |
Temporal resolution |
Measurement unit |
|
Changnyeong Hamanbo Reservoir |
Discharge |
1 h |
m3/s |
|
Water level |
EL.m |
|
Rainfall |
mm |
|
|
|
Sang-dong |
Water temperature |
°C |
|
Electrical conductivity |
μS/cm |
|
Dissolved oxygen |
mg/L |
|
|
|
Gupo Birdge |
Water level |
EL.m |
|
|
|
Nakdong River Bridge |
Salinity |
psu |
|
Water temperature |
°C |
|
Electrical conductivity |
μS/cm |
|
|
|
The banks of the Nakdong River |
Outer water level |
EL.m |
|
Inner water level |
EL.m |
|
Water level difference |
EL.m |
|
Rainfall |
mm |
|
Discharge |
m3/s |
|
Seawater inflow volume |
m3
|
|
24-h accumulated seawater inflow volume |
m3
|
Table 2
Results of granger causality analysis
|
Independent variable |
Dependent variable |
Lag (h) |
p-value |
|
Changnyeong Hamanbo Reservoir discharge |
Nakdong River Bridge salinity |
1 |
0.017 |
|
Changnyeong Hamanbo Reservoir water level |
1 |
0.611 |
|
Changnyeong Hamanbo Reservoir rainfall |
1 |
0.001 |
|
Sang-dong water level |
6 |
0.352 |
|
Sang-dong electrical conductivity |
1 |
0.056 |
|
Sang-dong dissolved oxygen |
6 |
0.352 |
|
Gupo Bridge water level |
9 |
0.01 |
|
Nakdong Bridge water temperature |
12 |
0.001 |
|
Nakdong Bridge outer water level |
1 |
0.001 |
|
Nakdong Bridge inner water level |
9 |
0.06 |
|
Water level difference at the banks of Nakdong River |
1 |
0.002 |
|
Rainfall at banks of Nakdong River |
1 |
0.001 |
|
Discharge at banks of Nakdong River |
3 |
0.07 |
|
Seawater inflow volume at banks of Nakdong River |
6 |
0.001 |
Table 3
Input variables and lags by case for forecasting
|
No. of Case |
Input variables |
Lag (h) |
|
1 |
Changnyeong Hamanbo Reservoir discharge |
0 |
|
Changnyeong Hamanbo Reservoir water level |
0 |
|
Changnyeong Hamanbo Reservoir rainfall |
0 |
|
Sang-dong water temperature |
0 |
|
Sang-dong electrical conductivity |
0 |
|
Sang-dong dissolved oxygen |
0 |
|
Gupo Bridge water level |
0 |
|
Nakdong River Bridge water temperature |
0 |
|
Outer water level at the banks of Nakdong River |
0 |
|
Inner water level at the banks of Nakdong River |
0 |
|
Water level difference at the banks of Nakdong River |
0 |
|
Rainfall at the banks of Nakdong River |
0 |
|
Discharge at the banks of Nakdong River |
0 |
|
Seawater inflow volume at the banks of Nakdong River |
0 |
|
24-h accumulated seawater inflow volume at the banks of Nakdong River |
0 |
|
|
2 |
All variables in Case 1 |
0 |
|
Nakdong River Bridge salinity |
0 |
|
|
3 |
Changnyeong Hamanbo Reservoir discharge |
0 |
|
Changnyeong Hamanbo Reservoir water level |
0 |
|
Changnyeong Hamanbo Reservoir rainfall |
1 |
|
Sang-dong Water Temperature |
0 |
|
Sang-dong electrical conductivity |
1 |
|
Sang-dong dissolved oxygen |
0 |
|
Gupo Bridge water level |
9 |
|
Water temperature of Nakdong River Bridge |
12 |
|
Salinity of Nakdong River Bridge |
0 |
|
Outer water level at the banks of Nakdong River |
1 |
|
Inner water level at the banks of Nakdong River |
9 |
|
Water level difference at the banks of Nakdong River |
1 |
|
Rainfall at the banks of Nakdong River |
1 |
|
Discharge at the banks of Nakdong River |
3 |
|
Seawater inflow volume at the banks of Nakdong River |
6 |
|
24-h accumulated seawater inflow volume at the banks of Nakdong River |
1 |
Table 4
Prediction performance comparison across forecast horizons
|
Forecast horizon (h) |
RMSE |
R2
|
|
|
Case 1 |
Case 2 |
Case 3 |
Case 1 |
Case 2 |
Case 3 |
|
1 |
2.471 |
0.833 |
0.838 |
0.516 |
0.945 |
0.944 |
|
3 |
2.545 |
0.931 |
0.912 |
0.487 |
0.931 |
0.934 |
|
6 |
2.653 |
1.061 |
1.037 |
0.443 |
0.910 |
0.914 |
|
9 |
2.682 |
1.188 |
1.167 |
0.431 |
0.888 |
0.892 |
|
12 |
2.627 |
1.375 |
1.359 |
0.454 |
0.850 |
0.853 |
|
24 |
2.280 |
1.620 |
1.503 |
0.588 |
0.792 |
0.821 |
|
|
avg. |
2.543 |
1.168 |
1.136 |
0.487 |
0.886 |
0.893 |
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