Enhancing streamflow prediction in the Wujiang River basin: a two-stage decomposition approach with deep learning integration

The rapid changes in global climate and significant human interventions have profoundly impacted the geological and hydrological processes within river basins (Zhang X. Q. et al. 2023), thereby amplifying the challenges in runoff prediction (Shahid et al. 2018, 2021). The Wujiang River basin stands as one of the largest tributaries on the southern bank of the upper Yangtze River, rendering the establishment of accurate and efficient hydrological prediction models crucial for water resources management in the region. Existing runoff prediction models fall into two main categories: process-driven and data-driven (He et al. 2021, 2024; Xu et al. 2024). Compared to process-driven models, data-driven models offer strong operability, as they do not require consideration of the physical mechanisms underlying runoff occurrence (Zheng et al. 2024a, 2024b); instead, they only necessitate mathematical analysis of time series to establish the functional relationship between input and output variables (Zhao et al. 2023). In recent years, machine learning has experienced significant advancements in the hydrology field due to its powerful learning capabilities (Ghazi et al. 2022; Adera et al. 2024; Zeydalinejad et al. 2024). In contrast to traditional algorithms like support vector machine regression and random forest, the gating units within long short-term memory (LSTM) networks are capable of effectively capturing long-term dependencies and temporal correlations within data, thus finding widespread applications in hydrology (Vatanchi et al. 2023; Hu et al. 2024). Zhang et al. (2020) successfully developed a hybrid model for monthly runoff prediction at a control hydrological station in the upper reaches of the Jinjiang River, combining a multi-population genetic algorithm (MPGA) with LSTM neural networks. The MPGA–LSTM model exhibited exceptionally high accuracy. Temporal convolutional networks (TCNs) are capable of effectively capturing short-term local patterns. However, LSTM often encounters issues of vanishing or exploding gradients during training, especially with long sequence data. TCN's convolutional structure effectively alleviates this problem, enabling better gradient propagation and enhancing the model's training efficiency and stability. Based on the TCN–LSTM model, Zhao et al. (2022) successfully addressed the issue of incomplete landslide time information leading to low accuracy in rainfall threshold models, thereby improving the accuracy and efficiency of landslide meteorological warning models. Yao et al. (2023) proposed a method for predicting urban inundation depth using TCN–LSTM models based on data from inundation monitoring stations, achieving high prediction accuracy and enhancing urban inundation perception capabilities.

Long sequence runoff data exhibit complex nonlinear relationships, long-term dependencies, and temporal correlations, containing a wealth of sequential information. Ban et al. (2023) introduced a novel decomposition–integration coupled model, variational mode decomposition (VMD)–DBO–gated recurrent units (GRU), which effectively enhances prediction accuracy by coupling VMD and Dung Beetle Optimization (DBO) with GRU. Zhang, X et al. (2023) proposed a VMD–Singular Spectrum Analysis (SSA)–Bidirectional Long Short-Term Memory (BiLSTM) coupled model for monthly runoff prediction, successfully improving the accuracy and smoothness of downstream Yellow River monthly runoff prediction, and providing significant insights for water resources management. Yang et al. (2023) successfully enhanced the accuracy of runoff trend prediction in the middle reaches of the Huai River by combining the improved complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm, northern goshawk optimization algorithm, and LSTM algorithm. The aforementioned studies all indicate that the performance of decomposition–integration coupled models surpasses that of single prediction models (Choubin et al. 2019; Liu et al. 2019). The decomposition–integration approach can better capture the features of time series, thereby improving prediction accuracy. However, high-frequency components generated by single decomposition methods exhibit significant volatility and instability, increasing the difficulty of model simulation and affecting the overall accuracy of runoff sequence simulation. To further explore effective information within high-frequency components and enhance their stability, a two-stage decomposition process is employed on top of the single decomposition technique. Wang et al. (2017) employed a two-stage decomposition technique coupled with extreme learning machines optimized by the differential evolution algorithm for predicting the air quality index. The results demonstrated that the predictive accuracy of the two-stage decomposition coupled model significantly surpassed that of other considered models. Currently, the application of two-stage decomposition techniques in runoff prediction remains relatively limited.

Based on this, the present study proposes a two-stage decomposition prediction model, coupled model of adaptive noise-adaptive mode decomposition CEEMDAN–VMD–TCN–LSTM. The integration of the TCN–LSTM model effectively incorporates meteorological factors into runoff prediction, thereby enhancing the accuracy of forecasts. Building upon the traditional decomposition–integration framework, a two-stage decomposition is applied to the high-frequency modal components to reduce their nonstationary characteristics. Monthly runoff and meteorological data from the Wulong station, covering the period from 1957 to 2021, were selected to validate the performance of the CEEMDAN–VMD–TCN–LSTM coupled model in runoff simulation. This model is expected to open new research directions in the field of runoff prediction.

The Yangtze River Hydrological Network's real-time water data collection of monthly runoff measurements from 1957 to 2021 at the typical Wulong station in the Wujiang River basin was chosen for this study. This dataset was chosen for its real-time and continuous monitoring capability, which provides a wealth of information about river flow over time. The Wujiang River basin is situated between latitudes 26°07′ and 30°22′N and longitudes 104°18′ and 109°22′E. The Wujiang River is the most extensive tributary on the south bank of the upper parts of the Yangtze River, with a basin area of around 87,900 km². The basin covers 62 counties (cities and districts) in 10 prefecture-level administrative areas in China's Guizhou, Chongqing, Hubei, and Yunnan provinces (municipalities directly under the Central Government).

Based on Figure 2, it can be observed that the runoff data from the Wulong hydrological station in the Wujiang River basin between 1957 and 2021 do not exhibit any significant trends. Although the overall trend of runoff shows a slight decrease, the decrease is negligible. Moreover, the majority of monthly runoff values during this period range from 0.5 × 10⁸ to 3 × 10⁸ m³.

The basic assumptions of the CEEMDAN–VMD–TCN–LSTM model are as follows: The model assumes that (1) the fundamental statistical properties of runoff data remain stable within the considered time period, (2) the relationships between various components (intrinsic mode functions (IMF), Variational mode decomposition–Intrinsic Mode Function (VIMF), TCN, and LSTM) are linear, and (3) the available historical runoff data are sufficient to capture underlying patterns and dependencies.

The EEMD methodology has a problem with modal mixing and residual auxiliary noise in signal decomposition (Zhang & Zheng 2023). Torres et al. (2011) presented the CEEMDAN method, which is an enhanced version of the EEMD technique. The CEEMDAN algorithm has demonstrated to be effective with minimal reconstruction errors and fast processing times (Kala et al. 2019), making it a comprehensive solution for signal decomposition. Moreover, the CEEMDAN algorithm produces better modal decomposition results compared to other techniques (Zhang et al. 2021):

• 1. Gaussian white noise is added to the original monthly runoff signal

  

  (1)

  where is the amplitude of white noise.
• 2. The first modal component and the residual can be obtained by decomposing the monthly runoff signal by empirical mode decomposition (EMD) after adding Gaussian white noise

  

  (2)

  

  (3)

  where n is the amplitude of the added white noise.
• 3. After conducting EMD, add white noise to the residual to get the second modal component and the residual

  

  (4)

  

  (5)

  where E is the symbol for the EMD decomposition and is the resultant Cth order modal component.
• 4. The initial monthly runoff signal is decomposed into the following equation by repeating the previous stages for each additional white noise decomposition until the residuals produced cannot be further decomposed:

  

  (6)

CEEMDAN decomposes the runoff data from Wulong station into nine IMF components and a residual term. The sample entropy of each component is calculated, where a higher entropy value indicates a more complex component. The entropy values of IMF₁–IMF₄ range from 0.98 to 0.63, indicating high-frequency components that reflect the irregular fluctuations in the runoff sequence. The entropy values of IMF₅–IMF₉ range from 0.50 to 0.35, representing low-frequency components that reveal the trend characteristics of the runoff sequence and exhibit regularity. In Figure 6, the IMF₁–IMF₄ components are characterized as high-frequency components. VMD is employed to further decompose the high-frequency components obtained after the initial CEEMDAN processing.

After bimodal decomposition, five VIMF components and a residual term (VRes) are generated. In Figure 7, compared to the IMF₁–IMF₄ components obtained from CEEMDAN decomposition, the components after VMD decomposition exhibit reduced fluctuations and greater regularity. This makes them more conducive to capturing information within the components for subsequent use in the TCN–LSTM model and for improving runoff prediction.

After bimodal decomposition, TCN employs the rectified linear unit (ReLU) activation function, while LSTM utilizes the hyperbolic tangent (tanh) activation function. The most significant influences on predictive accuracy stem from the size of convolutional kernels, the number of convolutional layers, the number of LSTM layers, and the quantity of neurons. Consequently, determining the optimal values for these four elements becomes the focal point of building an enhanced predictive model for comparative experiments.

• 1. Determining the size and number of convolutional kernels: Based on the bimodal decomposition and dual-channel convolution, two layers of LSTM (with 100 neurons each) were employed. The convolutional kernel size and the number of convolutional layers were varied in both channels. Comparative results for various errors are presented in Table 1.

• 2. Determining the number of LSTM layers and neurons: Using bimodal decomposition and dual-channel convolution with convolutional kernels of (2,2,1) and (3,3,1), the number of LSTM layers and neurons were varied. Comparative results for different errors are presented in Table 2.

After comparison, the combination estimation model constructed with convolutional kernels (2,2,1) and (3,3,1), 2 Convolutional Neural Network (CNN) layers, 3 LSTM layers, and 100 neurons fits the experimental data in this paper better, delivering the best fitting performance.

After the bimodal decomposition with CEEMDAN–VMD, a total of 10 components and 2 residual terms are generated. These decomposition results are utilized in the TCN–LSTM prediction model. TCN can capture both long-term and short-term dependencies in the data, while LSTM is well suited for handling sequential data. The TCN–LSTM model optimizes the overall network structure, resulting in excellent predictive performance and a better fit to the measured dataset. It leverages the advantages of both TCNs and LSTM networks, enabling more effective processing of long-term data and enhanced high-order feature extraction from multisource data. The model parameters are set as follows: TCN has an expansion factor of [1, 2, 4, 8, 16] for each layer, and a convolutional kernel size of 3 × 3, with 64 convolutional kernels in each layer. LSTM uses a three-layer model with 64 hidden nodes and a tanh activation function.

In Figure 8, the prediction accuracy of IMF₅ is notably high, with minimal deviations between the predicted and observed values. The variations in the predicted values align closely with the variations in the initial 624 months of IMF₅ from the training samples (Figure 6). The fluctuation range of predicted values for IMF₆-VRes generally corresponds to the corresponding training samples in Figure 6, and the error between predicted and observed values is small. These outcomes demonstrate the CEEMDAN–VMD–TCN–LSTM model's capability to effectively extract and reliably predict the trends and features of the training samples.

However, due to the substantial fluctuations and limited regularity of VIMF₁–VIMF₃, some errors are observed in the prediction results. Nevertheless, the fluctuation range of the predicted values for VIMF₁–VIMF₃ remains consistent with the training samples.

To validate the effectiveness of bimodal decomposition, both the LSTM and TCN–LSTM prediction models were subjected to both single-mode and bimodal decomposition. Comparative analysis was performed to evaluate the prediction accuracy of these two prediction models under different decomposition modes.

As shown in Table 3, the CEEMDAN–VMD–LSTM model reduced the MAE and RMSE by 29.00% and 30.45%, respectively, compared to the CEEMDAN–LSTM model. Furthermore, the CEEMDAN–VMD–TCN–LSTM model exhibited a reduction of 47.78% in MAE and 35.26% in RMSE when compared to the CEEMDAN–TCN–LSTM model. These results indicate that bimodal decomposition significantly enhances the prediction model's accuracy (Zhang et al. 2024), further confirming the effectiveness of the CEEMDAN–VMD decomposition method.

In order to verify that the TCN-LSTM prediction model can capture more implicit features and improve the prediction accuracy of the sequences, CEEMDAN-VMD-TCN-LSTM is therefore compared with the CEEMDAN-VMD-TCN and CEEMDAN-VMD-LSTM models. The results of inter-model error metrics are shown in Table 4.

The CEEMDAN–VMD–TCN–LSTM model effectively extracts the hidden features of time series, resulting in improved prediction accuracy (Ying et al. 2023). Compared to the CEEMDAN–VMD–LSTM model, the CEEMDAN–VMD–TCN–LSTM model reduced the MAE and RMSE by 37.03 and 18.17%, respectively. When compared to the CEEMDAN–VMD–TCN model, the CEEMDAN–VMD–TCN–LSTM model also demonstrates outstanding performance in terms of prediction accuracy, with a reduction in MAE and RMSE by 43.13 and 24.57%, respectively. The sole use of TCN–LSTM for runoff prediction yields relatively average results (Guo et al. 2024). In contrast, the CEEMDAN–VMD–TCN–LSTM model exhibits remarkable performance in terms of prediction accuracy, achieving a score of 0.95.

While utilizing the CEEMDAN–VMD–TCN–LSTM model for runoff prediction, certain limitations persist. In this study, monthly runoff data from the Wulong station for the period 1957–2021 were utilized. However, due to the data being limited to a single station, the broad applicability of the model to other stations or under varying geographical conditions has not yet been verified. This limitation constrains the model's generalization capability across different basins. The study focuses primarily on runoff prediction at the monthly scale, and verification at finer temporal scales (such as daily or hourly) has not yet been conducted. Future research could explore the model's applicability using data at shorter time intervals.

This study proposes a runoff prediction model based on TCN–LSTM deep learning and CEEMDAN–VMD bimodal decomposition. Through bimodal decomposition, the prediction errors caused by high-frequency IMFs can be effectively addressed. The IMF processed by bimodal decomposition serves as input to the prediction model TCN–LSTM, resulting in MAE = 0.1022 × 10⁸ m³/month and RMSE = 0.1873 × 10⁸ m³/month. Compared to the prediction results of single-mode decomposition, the error is reduced by at least 35%. After dual modal decomposition using CEEMDAN and VMD, the MAE and RMSE of the TCN–LSTM model were reduced by 37.03 and 18.17%, respectively, compared to the standalone LSTM. The CEEMDAN–VMD–TCN–LSTM model demonstrates promising potential for application in runoff prediction.

RZ conceptualized the whole study, developed the methodology, wrote the original draft, and investigated and validated the work. ZZ supervised the process, wrote the review and edited the article, rendered support in data curation, and visualized the work.

This manuscript was supported by the Innovation Fund for Doctoral Students of North China University of Water Resources and Electric Power. The grant number is NCWUBC202303.

Rainfall data are available at https://data.cma.cn. Temperature data are available at https://www.geodata.cn.

The authors declare there is no conflict.