Estuarine salinity prediction using empirical mode decomposition and random forest for supporting water resource management

Abstract

Seawater intrusion during dry seasons presents significant challenges to water supply security and estuarine ecosystem management, highlighting the need for accurate salinity forecasting. However, the non-stationary nature of estuarine salinity time series complicates its prediction. This study employs Empirical Mode Decomposition (EMD) to decompose inputs (runoff, tide level, wind) and outputs (salinity) into intrinsic mode functions (IMFs) and integrates them with Random Forest (RF) for forecasting in the Pearl River Estuary. Seven hybrid models under the three EMD decomposition frameworks (X: decomposing inputs, Y: decomposing outputs, XY: decomposing both inputs and outputs) are proposed and compared against a traditional RF model. Results show that the EMD-RF hybrid model significantly improves the accuracy and stability of salinity forecasts. The XY-ANN framework, which combines decomposition of both inputs and outputs with Artificial Neural Networks (ANN) for integration, showed the highest predictive accuracy, achieving an NSE of 0.91. The proposed method could provide stable and accurate predictions over extended forecasting periods (1 ~ 30 days), without performance degradation. Upstream runoff and tidal factors were identified as key predictors for salinity forecasting. This study also highlights the significant role of low-frequency components in improving prediction accuracy, especially for long-term forecasts. Overall, the introduction of the decomposition framework enables a more efficient analysis of complex hydrological patterns, offering a simple and effective method for estuarine salinity prediction.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-48012-5.

Introduction

In recent decades, saltwater intrusion has become increasingly severe due to global climate change, especially during the dry season, which has greatly affected the water supply security of estuarine areas^1–3. Saltwater intrusion reduce agricultural production and industrial water quality, which can lead to economic losses, affect social stability and increase government emergency pressure^4,5. Therefore, salinity prediction is significant for the rational allocation of water resources, ensuring water supply security, and managing estuarine ecosystems⁶.

In general, the methods for salinity prediction could be classified into two types, including the physical models based on hydrodynamics and salt transport, and the data-driven models based on machine learning models^7–10. The hydrodynamic models are complex and require extensive field data, significant effort for parameter calibration, and involve uncertainties that can accumulate errors during the modeling process¹¹. In contrast, machine learning models have the inherent property of processing nonlinear data without prior knowledge of the entire physical process, so machine learning techniques have been successfully used in modeling nonlinear hydrological processes in recent years^12–15. Lu¹³; Saccotelli et al.¹⁶ applied Bayesian Model Averaging (BMA) to integrate RF, SVM, and Elman Neural Networks (ENN) for predicting monthly saltwater intrusion in the Pearl River Delta, offering robust forecasts. Pham et al.¹⁷ compared several machine learning algorithms, including Multiple Linear Regression (MLR), Random Forest Regression (RFR), and Artificial Neural Networks (ANN), and found that ANN provided superior predictive performance for saltwater intrusion in the Mekong Delta. Saccotelli et al.¹⁶ used various machine learning models, including Random Forest (RF) and Least-Squares Boosting, to predict salinity levels in the Po River estuary, achieving a substantial reduction in error metrics and improvement in R². Bui et al.¹⁸ proposed a novel approach for surface water salinity prediction in the Mekong Delta by integrating hourly in-situ salinity data, remote sensing, and machine learning models, with the Particle Swarm Optimization-Random Forest model demonstrating superior accuracy in generating salinity maps for real-time assessment and decision-making. Al-Sulttani¹⁹ integrated a kernel extreme learning machine (KELM) with a boosted salp swarm algorithm based on differential evolution (BSSADE) to predict potential salinity in river water for irrigation in arid and semi‑arid regions, offering enhanced estimation performance for water quality management.

It is found that the process of saltwater intrusion is affected by various factors such as river flow, wind, precipitation, topography and human activities, and the correlation between different variables is highly complex and nonlinear^20,21,14. Despite the advantages of machine learning models, machine learning models face challenges when dealing with non-stationary data due to the different frequency components in the time series, such as periodicity and noise due to meteorological factors, human activities, and other external influences^15,22,23. To overcome these challenges, various hybrid frameworks—ranging from algorithmic optimization to data preprocessing—have been developed to enhance the predictive performance of machine learning models in estuarine salinity forecasting. Tian²⁴, Wu²⁵, Zhou²⁶. Nguyen et al.²⁷ used a hybrid GRU model enhanced by Grey Wolf and Sailfish Optimizers, showing better short-term forecasting performance than standalone GRU models. Zheng et al.²⁸ proposed an improved LSTM model combined with grey relational analysis to improve accuracy, especially for non-stationary data with complex behaviors. Zhou et al.²⁶ demonstrated that a wavelet transform combined with an artificial neural network (ANN) significantly improved salinity prediction by addressing non-stationary data.

Despite the wide application of machine learning, most current studies still rely on a “direct forecasting” mode, where raw variables are used for modeling without pre-processing. This “black-box” approach often overlooks the multi-scale physical features embedded in salinity signals, such as seasonal trends, tidal cycles, and stochastic noise. Due to the high non-stationarity of raw data, direct forecasting struggles to capture local fluctuations, leading to limited accuracy²⁴. Empirical Mode Decomposition (EMD) is a data-driven signal processing method that decomposes complex, non-linear, and non-stationary signals into a series of intrinsic mode functions (IMFs) without requiring a predefined basis function²⁹. Unlike traditional Fourier or wavelet transform techniques, EMD is adaptive and entirely data-driven, making it particularly effective for handling non-linear and non-stationary time series data, such as improving forecasting accuracy of annual runoff and drought forecasting^30–34. These IMFs represent the inherent oscillatory modes embedded within the data, which can capture periodicity, trends, and noise components with remarkable precision³⁵.

Therefore, in order to solve the non-stationary components in estuarine salinity time series, the empirical mode decomposition coupled random forest (RF) models for estuarine salinity prediction may also be an interesting attempt. RF is specifically chosen for this hybrid approach due to its robustness against noise and its capacity to model non-linear relationships across multiple feature scales. However, the applications in this field are still few^36,37. Existing studies typically focus on decomposing either input or output variables alone, without exploring the combined effects of simultaneously decomposing both. Moreover, the influence of different decomposed components on improving the predictive performance of machine learning models has not been fully investigated³⁸. This study aims to assess the effectiveness of a hybrid model that combines EMD with RF for daily estuarine salinity prediction in the Pearl River Estuary. EMD decomposing non-linear and non-stationary salinity time series into IMFs is utilized alongside RF’s capacity to describe the complex relationships. Three distinct frameworks were developed: the X-framework, which applies EMD to decompose only the input variables; the Y-framework, which decomposes only the output variable; and the XY-framework, which applies EMD to both input and output variables. These frameworks were systematically compared against a standalone machine learning model to evaluate their predictive performance. The best-performing model was further analyzed to assess its accuracy under different hydrological and seasonal conditions, demonstrating its robustness and potential for improving salinity forecasting in estuarine systems.

Methods

General framework

To provide a comprehensive overview of the methodologies employed in this study, a systematic modeling procedure was established to evaluate the performance of different salinity forecasting approaches. Figure 1 illustrates the integrated flowchart, which encompasses data preprocessing, model construction across three EMD-RF frameworks, and the subsequent performance evaluation (the pseudo-code is provided in Table S1). The detailed steps of this procedure are described as follows.

Fig. 1.

The flowchart of three forecast frameworks coupled with EMD in this study.

Firstly, the lag times of different input variables were determined by calculating the mutual information (MI) between the input variables (e.g., runoff, tide level, wind) and the target variable of salinity content with different lag time. Based on the MI results, the lag times were adjusted to optimize the temporal alignment between the input variables and the target variable, as detailed in Sect.  Mutual information.

Secondly, the preprocessed data were used to train and test two types of models: the baseline traditional RF model (referred to as No-EMD), and the Empirical Mode Decomposition (EMD) coupled with Random Forest (RF) model (called EMD-RF). The prediction performance of the traditional RF model was compared with that of the EMD-RF model to evaluate the impact of EMD on salinity forecasting.

The EMD-RF model was constructed using three frameworks: X, Y, and XY frameworks. Under the Y and XY frameworks, three ensemble methods—direct addition (DA), multiple linear regression (MLR), and artificial neural networks (ANN)—were employed to integrate predictions. Details of the frameworks and ensemble strategies are provided in Sect.  Empirical mode decomposition.

Finally, the performances of the salinity forecasting models were assessed and compared using statistical indices, as shown in Sect.  Model evaluation indexes.

Mutual information

Due to the geographical differences between the stations with the collected inputs and the target station with the salinity content, it is crucial to account for the potential lag time between the influence of each station’s impact factors and the salinity content in the river systems. To address this challenge, it is necessary to employ methods that can accurately quantify the relationships between the input variable and the target variable, even when these relationships involve nonlinear dependencies or time lags. Mutual Information (MI), a key concept in information theory proposed by Claude Shannon³⁹, provides a robust framework for such analyses. MI measures the dependency between two random variables by quantifying the reduction in uncertainty of one variable given the knowledge of the other. Unlike traditional correlation coefficients that capture only linear relationships, MI is capable of detecting both linear and nonlinear dependencies, making it a versatile tool for analyzing complex systems⁴⁰. The MI for two continuous random variables X and Y is expressed in Eq. (1):

1

whererepresents the joint probability density function of and , while andare their marginal probability density functions. The logarithmic term reflects the divergence between the observed joint distribution and the product of the marginal distributions, indicating the degree to which the variables deviate from independence. MI equals zero if and only if the two variables are completely independent, while larger MI values indicate stronger dependency between variables⁴¹. In this study, this property of MI is used to calculate the lag time by identifying the time shift that maximizes the mutual information between the input variables and the salinity content. Mutual information (MI) is estimated using a k-nearest-neighbor (kNN) approach suitable for continuous variables. To minimize scale effects in the distance-based kNN search arising from differences in physical units and magnitudes, the lag-aligned samples of both the impact factors and the salinity content series are z-score standardized (zero mean and unit variance) at each candidate lag prior to MI computation.

To determine the optimal lag time between the impact factors and the salinity content, the following steps are carried out using continuous daily data:

1. Within a candidate lag range of 0–7 days, the time series of each impact factor is shifted by the corresponding lag and paired with the salinity content series, and MI is computed for each lag to evaluate the dependency between variables.

2. The lag associated with the maximum MI value is selected as the optimal lag, indicating the strongest statistical dependency between the impact factor and the salinity content.

3. Based on the identified optimal lag, each impact-factor time series is shifted accordingly and aligned with the salinity content series to ensure that the inferred temporal relationships are accurately represented in subsequent analyses.

Empirical mode decomposition

Empirical Mode Decomposition (EMD) is a data-driven technique first proposed by Huang et al.⁴². It is used to decompose complex signals into simple oscillatory components, known as Intrinsic Mode Functions (IMFs), along with a residual trend. Unlike traditional signal processing methods, EMD does not require predefined basis functions, making it particularly suitable for analyzing nonlinear and non-stationary signals that are common in real-world scenarios⁴³. IMFs are the fundamental components derived through the EMD process⁴⁴. These IMFs are extracted iteratively and represent oscillatory modes at different frequency scales. Each IMF satisfies two conditions: (1) the number of extrema and zero crossings in the data must differ by at most one; and (2) the mean value of the upper and lower envelopes, defined by local maxima and minima, must be zero. After extracting all IMFs, the remaining residual typically represents the long-term trend of the signal.

The IMFs obtained through EMD exhibit distinct frequency characteristics, making the method highly interpretable. The high-frequency IMFs often capture noise or fine details in the signal. The mid-frequency IMFs reflect cyclic or periodic trends, such as those observed on monthly or quarterly time scales. The low-frequency IMFs, extracted in the later stages, represent the long-term or slowly varying trends within the data. EMD has been applied across a variety of fields, including environmental monitoring, biomedical signal processing, geophysics, and engineering^45,46. Its ability to isolate signal components at different frequency scales makes it a powerful tool for tasks such as noise reduction, trend analysis, feature extraction, and time-series decomposition.

To effectively leverage the decomposition capabilities of EMD in predictive modeling, it is necessary to explore different strategies for handling input and target variables during the modeling process. Depending on the characteristics of the variables and the modeling objectives, various decomposition combinations may yield different insights or predictive performance. Therefore, we designed three distinct EMD-based frameworks—X, Y, and XY—to investigate how the decomposition of input variables, target variables, or both can influence the model training and forecasting process.

Figure 2 illustrates the specific processes of three EMD-RF frameworks. The X framework only decomposes the input variables, and the resulting IMFs are merged into a new input dataset for model training and calibration (called X-Only EMD), as shown in Fig. 2a. The Y framework decomposes only the target variables, breaking them into multiple components. For each component, the separate RF model is trained using the original input variables as predictors (called Y-Only EMD). Subsequently, the prediction results of these components are integrated using three different methods: DA, (called Y-Only DA), MLR (called Y-Only MLR), or ANN (called Y-Only ANN), as shown in Fig. 2b. The XY framework simultaneously decomposes both input variables and target variables. The IMFs of the input variables are merged into a new input dataset, while the target variables are decomposed into multiple components. The separate RF model is trained for each target component, using the corresponding decomposed input variables as predictors (called XY EMD). The results are then integrated using DA, MLR, or ANN methods (referred to as XY-DA, XY-MLR, XY-ANN), as shown in Fig. 2c.

Fig. 2.

Schematic diagrams of three EMD-RF frameworks: (a) X framework: decompose input variables; (b) Y framework: decompose target variable, and (c) XY framework: decompose both input variables and target variable.

In the Y and XY frameworks, three types of ensemble methods are used to combine the prediction components into the forecast results. In the DA method, the forecast results are obtained by directly summing all prediction components. In the MLR or ANN methods, an MLR or ANN model is trained to capture the relationship between the prediction components and the original target variables in the training set, and the resulting model is applied to generate predictions in the testing set. These frameworks provide different approaches for decomposing and modeling input and target variables, and the ensemble methods are used to complete the prediction tasks.

Model evaluation indexes

The Random Forest (RF) model is a widely used ensemble learning technique for regression and classification tasks, known for its robustness and adaptability in handling complex, nonlinear data^47,48. By constructing multiple decision trees during training and aggregating their outputs, RF improves model stability and reduces the risk of overfitting compared to individual decision trees³¹. RF was specifically selected over other machine learning models due to its robustness in handling the high-dimensional feature space resulting from EMD decomposition, its strong resistance to overfitting, and its capability to provide interpretable measures of feature importance. The model incorporates randomness through bootstrap sampling and random feature selection at each split, enhancing its generalization capability to unseen data⁴⁹. These attributes make RF particularly suitable for capturing the complex, nonlinear, and non-stationary relationships often present in complex estuarine salinity data.

In this study, the RF model was employed to process non-stationary time series data influenced by dynamic factors such as tidal forces, wind conditions, and upstream runoff. RF was selected as the core prediction model due to its ability to model complex nonlinear interactions without requiring prior assumptions about the underlying relationships.

Performance evaluation of the models was conducted using two key metrics: the Nash-Sutcliffe Efficiency (NSE) and the Root Mean Square Error (RMSE). The NSE statistic measures the relative magnitude of the residual variance compared to the measured data variance. NSE values range from -∞ to 1, with values closer to 1 representing a superior model fit⁵⁰. It is defined as Eq. (2):

2

where represents the observed value, represents the predicted value, and is the mean of the observed values.

The RMSE quantifies the average deviation between the predicted and observed values, with smaller values indicating higher prediction accuracy⁵¹. RMSE is particularly useful for understanding the absolute error magnitude and is defined as Eq. (3):

3

To further interpret the models, SHAP (SHapley Additive exPlanations) analysis was employed as a post-hoc interpretability method to unravel the “black box” nature of machine learning predictions^52,53. SHAP calculates the marginal contribution of each feature to the model’s output, offering insights at both global and local levels. Globally, SHAP identifies the most influential features across the dataset, revealing their overall importance to the predictions⁵⁴. Locally, it explains how individual features contribute to specific predictions and whether their impact is positive or negative on the output variable, providing a detailed understanding of feature interactions and their directional influence⁵⁵. By applying SHAP to the models, this study identified the key input features influencing salinity predictions and quantified their positive and negative contributions, offering valuable insights into the role of dynamic environmental factors.

Case study

Study area

The Pearl River Delta (PRD), located in southern China, is one of the most densely populated and economically developed regions around the world, with complex river network and estuarine systems (Fig. 3)^56,57. Among its key channels, the Modaomen Waterway plays a crucial role, contributing 92.3 billion cubic meters of annual runoff and 23.14 million tons of sediment transport⁵⁸. However, this region faces significant challenges of saltwater intrusion, particularly during the dry season when the reduced upstream flow exacerbates saltwater intrusion, leading to salinity levels exceeding the acceptable limits (i.e. chloride concentrations of 250 mg/L)⁵⁹. This has large impacts on the freshwater supply for domestic, agricultural, and industrial use⁶⁰.

Fig. 3.

(a) The location of the Pearl River; (b) The location of the Modaomen Waterway and the study sites. Map created using ArcGIS software version 10.8.2 by Esri (www.esri.com).

Datasets

The dataset employed in this study encompasses continuous daily observations spanning from January 1, 2006, to May 28, 2023. This comprehensive dataset focuses on the primary hydro-meteorological factors driving salinity dynamics in the Pearl River Delta, with detailed metadata provided in Table 1. Tidal factor data (T), including daily average, maximum, and minimum tide level and tidal range, were obtained from the Denglongshan hydrological station. Wind data (W), including average wind speed, maximum wind speed, and extreme wind speed, were sourced from the Zhongshan meteorological station. Upstream runoff data (R) were collected from the Makou hydrological station, providing critical information about freshwater upstream flows. Finally, salinity data (S) were measured in terms of salinity content at the pumping stations in Guangchang.

Table 1.

List of the datasets used in this study.

Category	Variables	abbreviation	Source (Coordinates)	Time series
Tidal factor	Daily average tide level (m)		Denglongshan hydrological station (22.23°N,113.39°E)	Daily scale data from 2006.1.1 to 2023.5.28
	Daily maximum tide level (m)
	Daily minimum tide level (m)
	Tidal range (m)
Wind	Average wind speed (m/s)		Zhongshan meteorological station (22.51°N, 113.41°E)
	Maximum wind speed (m/s)
	Extreme wind speed (m/s)
Runoff	Upstream Runoff (Makou) (m3/s)		Makou hydrological station (23.11°N, 112.81°E)
Salinity	Salinity content (mg/L)		Guangchang pumping station (22.19°N, 113.43°E)

The datasets were officially provided by relevant water conservancy and meteorological authorities, ensuring rigorous quality control and calibration. Consequently, the time series data are continuous and free of missing values. All variables were compiled at a daily scale. Daily data is commonly used in hydrological and meteorological monitoring, making it more readily available and ensuring comparability for analysis and forecasting. While hourly data tends to have larger fluctuations and more noise, daily aggregation smooths out these short-term variations, allowing the model to focus on long-term trends in salinity. Moreover, daily data aligns with practical needs in water resource management, particularly for monitoring long-term trends like saltwater intrusion and guiding broader decisions such as reservoir management and pumping station scheduling.

To quantify the temporal variability and distributional properties of the dataset during the dry season (spanning from October 1 to March 31 of the following year), key descriptive statistics—including the minimum (Min), maximum (Max), mean, and standard deviation (Std.)—were computed for all candidate variables. Table 2 showed these statistical characteristics for the input variables and the target salinity specifically for this critical dry season period to ensure the reliability of these datasets.

Table 2.

Statistical characteristics of the input variables and target salinity during the dry seasons.

Variables	Min	Max	Mean	Std	Sample size
	−0.92	0.88	0.08	0.18	3098
	−0.86	1.69	0.84	0.27
	−1.23	0.5	−0.65	0.23
	0	2.55	1.49	0.35
	0	5.2	1.76	0.67
	1.5	9.2	3.81	1
	2.3	19.6	6.85	2.02
	553	23,100	3710.73	2406.09
	4.62	8279.17	1716.49	1690.16

Note that EMD was applied to the entire continuous datasets from 2006 to 2023 to ensure the physical consistency of the Intrinsic Mode Functions (IMFs). After that, the decomposed dry season datasets were extracted from the continuous IMFs time series after EMD decomposition, and these datasets were partitioned into a training set (80%, 2,478 samples) and a testing set (20%, 620 samples) for salinity forecasting models. This study employed a randomized partitioning strategy, as the temporal dependencies of the estuarine system were already explicitly internalized into the feature space through the MI-based lagging operation. By transforming sequential dependencies into multi-scale lag-embedded feature vectors, the model can learn fundamental physical relationships across the 17-year record without overfitting to specific chronological trends.

Result

Correlation-based lag time calculation

Results of lag-time analysis are summarized in Table 3, which reveals that different variables exhibit varying lag times in their effect on salinity content. For example, upstream runoff (Makou) exhibits the highest MI value of 0.41 with an optimal lag of 1 day, indicating that changes in upstream runoff significantly influence salinity content with a one-day delay. Similarly, the tidal factors, such as daily minimum tide level and tidal range, show lag times of 1 and 2 days, respectively, suggesting that these variables also have strong delayed effects on salinity. These findings reveal that there are different lag effects between different influencing factors and the salinity content. Tidal factors generally exhibit short lag times (0–3 days), with the daily minimum tide level showing the strongest correlation. Wind-related variables, including average, maximum, and extreme wind speeds, consistently have a lag of 2 days, suggesting that wind-driven salinity changes require some time to propagate through the system. Upstream runoff demonstrates the highest MI value among all variables, highlighting its dominant role in influencing salinity.

Table 3.

Lagged effects of influencing factors at guangchang pump stations.

Variable	Abbreviation	Max MI	Optimal Lag (d)
Daily Average Tide Level (m)		0.0723	0
Daily Maximum Tide Level (m)		0.0527	3
Daily Minimum Tide Level (m)		0.0832	1
Tidal Range (m)		0.0755	2
Average Wind Speed (m/s)		0.0339	2
Maximum Wind Speed (m/s)		0.0328	2
Extreme Wind Speed (m/s)		0.0338	2
Upstream Runoff (Makou) (m3/s)		0.41	1

Model comparison

The comparison between the baseline model without EMD (No-EMD) and the X-Only EMD model, as shown in Fig. 4, demonstrates the significant improvement in model performance when EMD is applied. The scatter plots in panels (a) and (b) illustrate the relationship between the forecasted and observed salinity for the No-EMD and the X-only EMD models, respectively. It is evident that the model fit, as indicated by NSE, improved significantly when EMD was applied, increasing from 0.64 of the No-EMD model to 0.85 of the X-Only model. Similarly, the RMSE decreased from 1008.84 mg/L to 651.49 mg/L, highlighting the improved predictive accuracy achieved by incorporating EMD. Additionally, the fitted regression line in the X-Only EMD model (slope = 0.75) is closer to the ideal 1:1 line compared to the No-EMD model (slope = 0.65), further demonstrating the enhanced alignment of predictions with observed values after applying EMD.

Fig. 4.

The scatter plots of the observations and forecasts of salinity content without EMD (a) and the X-only EMD (b), and the panel below shows a summary plot of the SHAP values for the eight most important of the input features for the corresponding model.

The application of EMD also redistributed the feature importance (Fig. 4). In the No-EMD model, original features such as runoff (R), tidal range (T), and wind-related variables were treated as separate aggregated signals, limiting the model’s ability to isolate frequency-dependent contributions. After decomposition, the separate signals were split into multiple IMFs, allowing the model to capture distinct temporal components. Note that some features that were originally less influential became more prominent after EMD. For example, T_min_IMF_3, a high-frequency component of the minimum tide level, emerged as a key predictor in the X-Only model. In the X-Only model, specific IMFs such as R_IMF_10, T_range_IMF_7, T_min_IMF_3 played the significant roles in predictions. These IMFs reflect the decomposed components of the original features, providing more detailed representation of the relationships between the input variables and salinity. Furthermore, runoff (R) remained a highly important feature in both the No-EMD and X-Only models, demonstrating that it is a crucial variable for salinity predictions regardless of whether it was decomposed.

Combining the SHAP value plots in Fig. 4, we can observe the positive and negative effects of each feature on the output variable. As shown in Fig. 4c for the No-EMD model, features, such as runoff (R), tidal range (T_range), and maximum wind speed (W_max), primarily exhibit negative effects on salinity, while daily average tide level (T_mean) shows the positive effect. In Fig. 4d for the X-Only model, the positive and negative effects of the decomposed IMFs are also clearly displayed. For instance, R_IMF_10, T_mean_IMF_6, W_max_IMF_7 and R_IMF_8 exhibit negative impacts on the predictions, whereas T_range_IMF_7 and T_min_IMF_3 primarily shows positive contributions. These visualized positive and negative effects further elucidate the complex relationships between features and the output variable.

To characterize the decomposed salinity components, three statistical indices were calculated as shown in Table 4. The variance contribution rate represents the relative importance of each IMF in explaining the total variability of the original salinity signal, while the Pearson correlation coefficient (r) quantifies the linear relationship between each individual IMF and the raw salinity series. Furthermore, the dominant period of each IMF was identified using Fast Fourier Transform (FFT) to link these statistical components to specific physical processes. As summarized in Table 4, the derived components represent distinct physical processes ranging from high-frequency noise (S_IMF_1) to low-frequency seasonal cycles. Specifically, S_IMF_3 and S_IMF_4, with dominant periods of approximately 14.77 days, correspond to Spring-Neap tide cycles. S_IMF_8 and S_IMF_9 contribute the highest variance (totaling 47.29%) and represent annual and seasonal variations. The presence of S_IMF_12 and S_RES (S_IMF_13) further captures decadal oscillations and long-term trends, highlighting the non-stationary nature of the salinity time series.

Table 4.

Statistical characteristics and physical interpretations of salinity components derived from EMD.

Component	Variance contribution (%)	Pearson correlation (r)	Dominant period (Days)	Physical implication (Reference)
S_IMF_1	4.76	0.0794	31.39	Noise
S_IMF_2	3.84	0.1472	7.53	Weather/Storm surge
S_IMF_3	6.93	0.2613	14.77	Spring-Neap Tide
S_IMF_4	6.44	0.2619	14.77	Spring-Neap Tide
S_IMF_5	3.49	0.1632	25.64	Monthly variation
S_IMF_6	4.8	0.1819	62.12	Intra-seasonal
S_IMF_7	7.3	0.2669	98.79	Seasonal transition
S_IMF_8	18.39	0.3756	334.78	Annual / Seasonal
S_IMF_9	28.9	0.5833	376.62	Annual / Seasonal
S_IMF_10	8.68	0.2139	860.86	Inter-annual
S_IMF_11	2.83	0.2302	2008.67	Long-term cycle
S_IMF_12	3.07	0.2489	6026	Decadal oscillation
S_IMF_13/RES	0.56	0.1664	Trend	Long-term Trend
Total	100	–	–	–

Figure 5 clearly demonstrates that, under the XY-EMD framework, the NSE for each component is consistently higher than that of the Y-Only EMD framework. Additionally, within the XY-EMD framework, the prediction performance for low-frequency (e.g., IMF_8 to IMF_13) components is much higher than for high-frequency components (e.g., IMF_1, IMF_2, IMF_3). The NSE values for low-frequency components in the XY framework approach or exceed 0.9, whereas high-frequency components have relatively lower NSE values. This pattern highlights that low-frequency components are more predictable, likely due to their more stable and structured characteristics, while high-frequency components are more difficult to be predicted due to their greater variability.

Fig. 5.

The performance for all the EMD component of target variable in the Y framework and XY framework.

The predictive performance of eight models is summarized in Table 5 and visualized in Fig. 6. Overall, the results exhibit a progressive improvement in accuracy as the modeling strategy transitions from the basic No-EMD baseline to the more sophisticated XY-EMD hybrid frameworks. The No-EMD baseline model yielded an NSE of 0.64 and an RMSE of 1008.84. In comparison, the Y-Only frameworks (including DA, MLR, and ANN) showed limited variations in performance, with NSE values averaging 0.66 and RMSE remaining above 970. This pattern suggests that decomposing the target salinity (Y) alone has a marginal impact on enhancing the model’s predictive capability. A more distinct improvement was observed in the X-Only EMD framework, which achieved an NSE of 0.85 and an RMSE of 651.49. This result highlights the critical role of input feature decomposition in unmasking the multi-scale driving factors of salinity intrusion. The XY-framework—which decomposes both input and output variables—provided the highest performance across all metrics. Within this framework, the XY-ANN model emerged as the most accurate configuration, achieving a peak NSE of 0.91 and the lowest RMSE of 512.22. The improvement from X-Only to XY-EMD indicates that the simultaneous decomposition of inputs and output allows the model to capture more refined physical interactions.

Table 5.

Summary of salinity prediction performance metrics for different models.

Models	NSE	Total RMSE	STD	Corr
No-EMD	0.64	1008.84	1357.46	0.802
Y-Only DA	0.66	973.59	1321.52	0.815
Y-Only MLR	0.66	981.5	1499.36	0.815
Y-Only ANN	0.66	976.03	1487.81	0.816
X-Only EMD	0.85	651.49	1356.58	0.929
XY-DA	0.88	574.73	1450.4	0.942
XY-MLR	0.89	543.78	1533.32	0.946
XY-ANN	0.91	512.22	1555.29	0.952

Fig. 6.

(a) Comparison of NSE and RMSE Across Different Models, (b) Taylor Diagram Comparison of Salinity Prediction Performance (8 Models).

The Taylor Diagram in Fig. 6b provides additional multi-dimensional verification of these results. The XY-ANN model (represented by the brown cross) is positioned closest to the “Observed” reference point, indicating its superior performance in both correlation and phase consistency. Specifically, the XY-ANN model attained the highest Pearson correlation (0.952) among all candidates. Furthermore, its standard deviation (1555.29) is more aligned with the variability of the observed data (1690.16) compared to the No-EMD and Y-Only models, which tend to underestimate or deviate from the natural variance. These findings confirm that integrating EMD-based multi-scale decomposition with the non-linear ANN ensemble provides a reliable framework for forecasting complex salinity dynamics.

The salinity prediction performance of all three EMD-RF models is superior to that of the baseline model (Figs. 7 and S2). The prediction curves from four models during the dry season in 2022 and 2023 are presented, including three EMD-RF models (Y-Only ANN, X-Only EMD, and XY-ANN) and the traditional model (No-EMD). These predictions are compared with the observed salinity values, represented by the black line. The results clearly demonstrate that the prediction performance of all three EMD-RF models is superior to that of the No-EMD model. Specifically, the XY-ANN model, represented by the red line, achieves the best prediction accuracy with an NSE value of 0.98. It closely tracks the observed data across both the full time series and the zoomed-in period between 60 and 75 days, indicating excellent fitting performance.

Fig. 7.

Time series of salinity content prediction of four models during the dry season from Oct. 1, 2022 to Mar. 1, 2023.

In comparison, the X-Only EMD model (blue dashed line) also performs well, achieving an NSE value of 0.94. However, the Y-Only ANN model (green dashed line) shows relatively poor fitting performance, with an NSE value of 0.89, which is only slightly better than the No-EMD model (NSE = 0.82, purple dotted line). These results highlight the effectiveness of decomposing both input and output variables (XY framework) combined with ANN integration for improving prediction accuracy, particularly in capturing the dynamic variations in salinity during the dry season.

Evaluation of EMD methods with different lead-time periods

Based on the optimal model selection, Fig. 8 shows the stability of prediction performance with the lead-time of 1 to 30 days for the XY-ANN and X-Only models compared to the baseline model. The results highlight significant differences in prediction accuracy and stability among different models. Specifically, The XY-ANN model (red dashed line) and the X-Only model (blue dashed line) both demonstrate superior performance, maintaining consistently high NSE values close to 0.85 across the entire prediction period with the lead-time of 1 to 30 days. This indicates that the EMD-based models are not only accurate but also stable in their predictions in near future. In contrast, the model without EMD (purple dotted line) shows a gradual decline in prediction performance over the prediction period from 1 day to 30 days, with NSE dropping from approximately 0.6 at the beginning to below 0.2 by the end of the 30-day period. This significant performance gap underscores the effectiveness of EMD in improving predictive accuracy and robustness with different lead-time periods.

Fig. 8.

Prediction performance using EMD (X-Only, XY-ANN) versus the baseline model at different encounter periods.

To purely reveal the physical response mechanisms between external driving factors and salinity dynamics while avoiding interference from the self-correlation components of the target variable, the X-Only EMD model was selected for feature importance analysis. Figure 9 demonstrates the dynamic adjustment of feature importance in the X-Only model over the lead-time period from 1-day to 30-day, as indicated by SHAP values. The heatmap clearly illustrates the varying importance of these features, with darker shades representing higher importance. The analysis highlights several critical insights into the varying importance of IMF components with different lead-time periods. Only five IMF components are identified as significant predictors across the entire forecast period. Importantly, as the forecast period lengthens, the most important features continually change, reflecting the dynamic nature of salinity prediction with different lead-time periods. Among these features, the low-frequency (long-term) components of runoff ((R_IMF_10) remains consistently important throughout the entire forecast period, showing a particularly strong influence in the short-to-medium term (< 15-day). Additionally, the daily maximum of tide level component (T_max_IMF_7 ) increases significantly as the forecast horizon extends, becoming the most prominent predictor in long-term forecasts (17–30 days). The tidal range components (T_range_IMF_7 and T_range_IMF_9) contribute at varying intervals. Specifically, Trange_IMF_9 emerges as a more significant factor in the medium-to-long term (18–26 days), suggesting that tidal variations play a crucial role in capturing salinity fluctuations over extended lead times.

Fig. 9.

Three most important modalities (based on SHAP value) in different lead-time periods (the darker the color indicates the more important).

Discussion

Mechanism of performance enhancement by the EMD strategy

The results of this study underscore the significant improvement in model performance when EMD is incorporated as a data preprocessing step. This demonstrates the potential of EMD to enhance predictive accuracy and model stability, particularly when dealing with complex, nonlinear, and non-stationary datasets. By decomposing input variables into IMFs, EMD enables the extraction of meaningful patterns at different frequency scales. Separating high-frequency noise from low-frequency trends allows the model to leverage both short-term fluctuations and long-term stable components of the data.

As shown in Fig. 4, the EMD-RF models achieve superior predictive accuracy compared to No-EMD model, demonstrating that the decomposed IMFs provide more structured information that enhances the model’s generalization capacity. A comparative analysis of feature importance between the No-EMD and X-Only EMD models (Fig. 4c and d) further reveals that EMD significantly redistributes feature importance. The decomposed IMFs, such as R_IMF_10, T_range_IMF_7, and T_min_IMF_3, offer a more detailed representation of the relationships between features and the target variable. This redistribution enables the model to better utilize specific frequency-based information, ultimately reducing noise interference and improving prediction stability. By focusing on these decomposed components, the EMD-RF model effectively addresses the inherent complexities of the data.

From the perspective of signal physical properties, the statistical analysis in Table 4 provides the intrinsic rationale for this performance enhancement. The results indicate that the salinity components exhibit distinct physical meanings; specifically, the low-frequency components (e.g., S_IMF_8 to S_IMF_12), which account for the bulk of the variance, correspond to inter-annual, seasonal, and long-term oscillations. These components possess strong regularity and temporal continuity, providing the model with more deterministic target signals. Consequently, a key finding of this study is that low-frequency components are inherently more predictable. As shown in Fig. 5, the NSE values for low-frequency components in the XY framework are significantly higher, often approaching or exceeding 0.9, whereas high-frequency components associated with “noise” or “weather-driven disturbances” (e.g., S_IMF_1, S_IMF_2) exhibit relatively lower NSE values. This demonstrates that EMD, by isolating these stable long-term components, effectively reduces stochastic noise interference and shifts the model’s focus to the most representative features, ultimately improving overall predictive performance.

Performance superiority of the XY-ANN framework

Building on the mechanistic understanding of EMD, this study further evaluates the configuration of decomposition strategies. The XY framework of EMD-RF model demonstrates superior predictive performance compared to the X-Only and Y-Only frameworks, as illustrated in Fig. 6; Table 5. This is attributable to its ability of simultaneously decomposing both input and output variables based on EMD. By incorporating the frequency components of both variable types, the XY framework allows the model to better capture the hidden features and intricate patterns of the input variables, while also making more precise predictions for the low-frequency components (long-term trends) of the output variables. This dual decomposition approach enhances the model’s capability to leverage the structured and meaningful information derived from the input signals, as well as to effectively address the variability of the target outputs over time.

In contrast, decomposing only the output variable (Y-Only framework) does not significantly improve the model performance, as consistently evidenced by the holistic visualization of the Taylor diagram (Fig. 6). In this framework, the target variable is broken into different frequency components (IMFs), and separate models are trained for each component. However, since the input variables are not decomposed, the original input data may lack the frequency-specific information needed to accurately predict each target IMF. In other words, each target IMF requires corresponding frequency-range features from the input data, but the undecomposed input variables fail to provide such detailed frequency characteristics to support the model. This mismatch limits the predictive accuracy for individual IMFs and introduces errors during the subsequent integration phase, ultimately restricting the overall prediction accuracy.

In terms of integration methods, the ANN-based ensemble stands out due to its nonlinear modeling capabilities. Unlike DA and MLR, which assume linear relationships between the prediction components and the target variables, the ANN could capture the nonlinear dependencies and interactions that exist among these components. As a result, the XY-ANN model achieves the highest predictive accuracy among all tested models. The NSE value of 0.91 underscores the model’s ability to reconcile the complexity of the system while maintaining robustness and reliability.

Robustness of the EMD-RF model across varied lead times

The EMD-RF model’s ability to maintain a high degree of fit across different prediction periods is primarily attributed to its adaptive decomposition and feature utilization mechanisms. By decomposing input variables into IMFs, the model can dynamically adjust its reliance on key features based on the specific requirements of each prediction period. This adaptability is evident in Fig. 8, where the XY-ANN and X-Only models exhibit consistently high NSE values (close to 0.85) across a 30-day prediction period, in contrast to the model without EMD, which shows a significant decline in performance.

Figure 9 further reveals that the feature importance of IMFs varies over time, with low-frequency components like R_IMF_10 playing a dominant role across all prediction periods. These components provide stable and predictable information, supporting the model’s performance in long-term predictions. Meanwhile, as the forecast period extends, low-frequency IMFs of the maximum of tide level level (e.g., T_max_IMF_7) gain prominence, indicating their increasing relevance for capturing long-term trends. For medium- to long-term predictions, variables like tidal range (T_range_IMF_7 and T_range_IMF_9) become more important, reflecting the dynamic adjustment of the model’s feature priorities. This ability to leverage the most relevant IMFs across different lead-time periods underscores the EMD-RF model’s robustness and flexibility in handling complex, nonlinear time-series data.

Comparative analysis, practical implications and limitations

A comparative analysis of salinity prediction methodologies reveals the improvement from physic-based hydrodynamic models to data-driven approaches, and subsequently to complex coupled systems^20,22. However, existing data-driven approaches often utilize direct forecasting methods that treat non-stationary salinity signals as a single unit, whereas physical coupling models involve higher computational costs^61,62. In contrast, this study investigates the efficacy of a parsimonious decomposition method. Rather than relying on input selection or physical coupling, the study systematically evaluates the X, Y, and XY frameworks to determine if this approach enhances data mining capabilities. By decomposing non-stationary time series into intrinsic mode functions (IMFs), the EMD-RF model extracts multi-scale features from both driving forces and response signals. The results demonstrate that the decomposition-based strategy improves prediction accuracy compared to direct forecasting methods, offering a computationally efficient alternative for estuarine salinity management.

The proposed EMD-RF framework offers valuable practical implications for salinity monitoring and water resource management in estuarine regions. By effectively improving prediction accuracy and reducing model uncertainty, it can support the development of early-warning systems for saltwater intrusion, inform reservoir and gate operations. Furthermore, the flexible structure of the framework also makes it amenable for integration within an operational forecasting chain, provided that real-time or forecasted forcing inputs (e.g., runoff, tides, and meteorological variables) are available. The performance comparison among three decomposition frameworks (X-only, Y-only, XY) also provides methodological insights for other environmental prediction tasks involving nonlinear and non-stationary signals.

Although the proposed EMD-RF framework significantly improves estuarine salinity prediction accuracy compared to traditional models, several limitations remain that warrant further investigation. First, the reliance on daily-averaged data from a single station may reduce sensitivity to short-term tidal fluctuations and limit the spatial representativeness of the results. Future work should incorporate higher-frequency observations (e.g., hourly data) across multiple stations and longitudinal transects to better capture rapid salinity dynamics and diverse hydrodynamic settings. Second, inherent issues in EMD, such as mode mixing and boundary effects, require mitigation through more advanced decomposition techniques to enhance model robustness. Third, the current model does not explicitly incorporate complex physical processes, such as stratification, water temperature, and sediment transport, which are critical to salinity variations. Fourth, as the model was primarily developed and validated using dry-season data, its applicability to wet-season and transitional periods—as well as its long-term performance under climate change and human impacts—requires further assessment. Finally, while the framework is potentially transferable, its performance in other estuaries depends on local forcing mechanisms and the availability of continuous observational records. Future research could explore integrating remote sensing products or reanalysis datasets to alleviate data scarcity and enhance the model’s generalization and practical utility.

Conclusion

In this study, an EMD-RF hybrid model was developed to improve the accuracy of salinity forecasts in estuarine regions. Three decomposition frameworks (Y-Only, X-Only, and XY) and multiple ensemble methods were implemented and compared against a No-EMD model. The main conclusions of this study are as follows:

1. EMD significantly improves prediction accuracy and stability. By decomposing input variables, the model extracts more inherent information, while decomposing target variables enhances the accuracy of trend predictions. The XY framework achieves the best predictive performance with a fitting coefficient NSE of 0.91.

2. EMD ensures prediction stability across extended forecasting periods. The ability to adaptively adjust feature importance and emphasize low-frequency components enables the EMD-based models to deliver stable and robust predictions over time. The XY-ANN and X-Only models maintain high NSE (~ 0.85) over 30 days, while the model without EMD, which shows a significant decline.

3. Upstream runoff and tidal factors are key predictors for salinity forecasting. R_IMF_10 consistently holds significant importance across different prediction periods, while the low-frequency components of daily maximum tide level and tidal range play the critical roles in long-term predictions.

Despite these contributions, limitations remain regarding the reliance on single-station daily data, which restricts spatial representativeness and the capture of rapid tidal fluctuations. Additionally, the current model does not explicitly account for complex physical processes (e.g., stratification) or wet-season dynamics, and inherent EMD issues like mode mixing warrant further methodological refinement. Future research should therefore focus on incorporating high-frequency multi-station observations and exploring advanced decomposition techniques to enhance the model’s generalization and utility under diverse hydrological conditions.

In summary, this study proposes a systematic decomposition framework to capture complex hydrological dynamics at low computational costs. By mitigating the limitations of direct forecasting in handling non-stationary data, the approach offers a simple and effective method for estuarine salinity prediction.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Zheng Kang: Data curation, Formal analysis, Supervision. Hanliang Huang: Methodology, Writing—original draft preparation, Investigation, Visualization. Jingwen Zhang: Conceptualization, Validation, Data curation, Writing—Reviewing and Editing, Funding acquisition. Zejun Li: Formal analysis, Supervision. Yifan Chen: Investigation, Methodology. Boheng Du: Methodology, Formal analysis. Kairong Lin: Writing—Reviewing and Editing, Supervision. Xiaohong Chen: Writing—Reviewing and Editing, Supervision. All authors have read and agreed to the published version of the manuscript.

Funding

We acknowledge the support from Science and Technology Innovation Program from Water Resources of Guangdong Province (2024-04, 2025-05), the National Natural Science Foundation of China (52479034, 52309014), National Key R&D Program of China (2023YFC3209400), and the Fundamental Research Funds for the Central Universities, Sun Yat-sen University (23hytd011-2).

Data availability

The raw data that support the findings of this study are available from the corresponding author upon reasonable request. The predicted salinity series, model configuration examples, and analysis workflows (e.g., EMD decomposition and RF training) can be obtained from https://github.com/Harryhlhaha/emd-rf.git.

Declarations

Competing interests

The authors declare no competing interests.