As climates change globally, water-related disasters increase, causing substantial economic losses and safety risks. During floods, river water levels show unpredictable fluctuations, introducing substantial noise that complicates accurate prediction. A hybrid model that uses eight-dimensional input data from hydrological and meteorological stations is proposed to address these challenges. Initially, the Variational Mode Decomposition preprocesses and denoises water level data, resulting in decomposed Intrinsic Mode Functions (IMFs). Then, the Pearson correlation coefficient between each IMF and input characteristics is computed, and the fluctuation factor for each IMF is defined. IMFs are categorized based on a threshold, leading to a hybrid prediction model. This model integrates convolutional neural networks (CNNs) for spatial information and bidirectional long short-term memory (BiLSTM) networks with an attention mechanism for learning from past and future data points. Comparative evaluations of mean absolute percentage error, root mean square error, mean absolute error, and goodness of fit (R2) show that the proposed model outperforms existing LSTM and CNN–BiLSTM frameworks, reducing RMSE by at least 20% and increasing R2 by approximately 10% on average. The model's practical significance lies in improving the accuracy and efficiency of meteorological forecasting and flood warning systems, contributing substantially to global disaster preparedness and response strategies.

  • A hybrid model is constructed using eight-dimensional input data from hydrological and meteorological stations. Variational mode decomposition is used for data preprocessing and denoising.

  • The fluctuation factor proposed can categorize the IMFs using mode classification and feature selection.

  • The hybrid model proposed can strengthen the grasp of the essential input characteristics and has better flood prediction accuracy.

The world is currently experiencing the impact of climate change, manifesting in ongoing floods that pose substantial threats to lives and property. Forecasts suggest that by 2050, both the frequency and intensity of floods will escalate, potentially leading to substantial financial losses estimated at USD 1 trillion (Huang et al. 2019; Rahman et al. 2021). Floods commonly arise from factors such as intense rainfall and increased water levels in rivers and reservoirs. Therefore, precise prediction of water levels is crucial for optimizing water resource utilization and enhancing water resource management, which is conducive to promoting sustainable resource management development.

During the flood period, water level fluctuations become more random, and frequency changes become more complex, introducing noise that complicates flood prediction. Therefore, scholars frequently employ data denoising techniques to preprocess the input water level data, normalizing it to enhance prediction accuracy. Variational mode decomposition (VMD) (Dragomiretskiy & Zosso 2014; Jiang et al. 2023) is a recent preprocessing method commonly used in flood prediction that effectively reduces signal noise. VMD, a nonrecursive time–frequency analysis technique, decomposes time series data into modal components, resulting in smooth amplitude-modulated frequency signals known as intrinsic mode functions (IMFs). VMD has been applied to preprocess water level data (Xu et al. 2021; Yan et al. 2021a; Zhang et al. 2023a), enhancing the signal-to-noise ratio and improving prediction accuracy. With deep learning neural networks (Xu et al. 2021), VMD preprocessing substantially improves water level forecasting accuracy. The most popular deep learning method is based on long- and short-term memory (LSTM) networks, a type of recurrent neural network (RNN) capable of avoiding the problem of gradient vanishing during long-term RNN training. Garg et al. (2023) conducted daily runoff prediction of the Godavari River in India, collecting meteorological, hydrological, land, and other data combined with feature selection. The study demonstrated that the predictive ability of LSTM is superior to that of the ARIMA model. To further enhance the flood prediction speed, Hu et al. (2019) developed an integrated LSTM and reduced-order model framework that combined two data decomposition methods. Moreover, Chen et al. (2022) constructed a ConvLSTM network integrated with a convolutional neural network (CNN) and LSTM, demonstrating that CNN can extract spatiotemporal features of hydraulic information, improving the prediction accuracy of flood arrival time and peak discharge. Furthermore, Yang et al. (2021) constructed a CNN–LSTM network with attention to predict water quality variables, and experimental results showed that the CNN–LSTM with attention model outperforms other models and is more stable. In addition, Nguyen et al. (2023) constructed a CNN–LSTM model to predict daily streamflow in three river basins using daily average temperature and precipitation data, demonstrating that the hybrid model has features conducive to improving predictions. Moreover, Guo et al. (2023) created a VMD–LSTM transformer model to predict the monthly runoff from the Miyun Reservoir in Beijing, China, combining rainfall and air temperature; the prediction model with VMD preprocessing performed better.

The LSTM-based water level prediction method enhances accuracy; however, LSTM processes information in only one direction, lacking the ability to capture information bi-directionally. Zhang et al. (2023b) introduced a coupled VMD–bidirectional long short-term memory (BiLSTM) model optimized by the sparrow search algorithm, demonstrating its superior performance over both the BiLSTM and VMD–BiLSTM models. Floods result from rising water levels and meteorological factors, particularly large-scale continuous rainfall. Concurrently, temperature and humidity strongly influence rainfall (Mann & Gupta 2022), heightening the challenges in flood prevention. Also, Nie et al. (2021) proposed a CNN–BiLSTM–attention model for water level prediction, showcasing its exceptional ability to extract local information effectively. In addition, Wu et al. (2023) introduced a VMD–CNN–BiLSTM model for predicting daily runoff data, enhancing performance through parameter optimization and VMD preprocessing. However, the realignment of component signals to features post-VMD decomposition was overlooked.

VMD is a potent technique for simultaneously decomposing a signal into its constituent intrinsic modes. Integrating VMD preprocessing with deep learning networks improves model prediction accuracy. However, parameter selection for VMD is challenging, and post-decomposition, each IMF displays a distinct probability distribution and varying correlations with input variables. When making flood predictions, it is crucial to simultaneously consider natural context properties, including rainfall, topography, and hydrometeorology, to harness the context's full natural capacity in flood risk mitigation (Kuriqi & Hysa 2021). Directly inputting all comprehensive features into the model for prediction increases model complexity, potentially leading to inaccurate feature matching, and the model may not effectively prioritize important features, resulting in potential deviations. Few studies have explored categorizing VMD components and matching different features to enhance subsequent prediction performance. LSTM and BiLSTM exhibit superior capacity in regulating long-term stationary signals, whereas CNN excels in extracting short-term features. CNN is susceptible to overfitting because of the overemphasizing of features for relatively stable signals. The low-frequency part of the VMD flood level decomposition is relatively smooth and contains essential information. In contrast, the high-frequency component fluctuates substantially. It may contain noise and other detailed information that is challenging to predict accurately with a unified model, especially with multiple feature variables. Hence, constructing a comprehensive model utilizing the advantages of BiLSTM and CNN may enhance the flood prediction capacity.

Building upon the preceding discussion, we posit the following inquiries: (1) Different parameter selections may yield diverse VMD components even with the same dataset. How can we classify and match features of VMD IMFs and input variables? (2) How do we appropriately select features to align with VMD IMFs after integrating meteorological and other variables? (3) Given the continuity of water flow and the impact of terrain characteristics, the current flood water level exhibits a distinct relationship with the water levels before and after this particular time. How can a hybrid model be constructed to consider hydrological and meteorological information, thereby enhancing flood prediction performance through multi-climate feature screening?

To address these questions, a hybrid prediction framework named the VMD-F hybrid model to refine water level prediction is proposed. The primary innovations and contributions include the following:

  • (1)

    Utilizing inverse distance weighting, meteorological data from three nearby hydrological stations were collected, and eight-dimensional input data were constructed. VMD is employed for data preprocessing and denoising, thereby improving the prediction model's performance.

  • (2)

    The fluctuation factor is introduced to aid in classifying VMD's decomposition modes, and Pearson's correlation is employed to screen characteristic variables.

  • (3)

    A hybrid prediction model is developed that amalgamates the strengths of the CNN–BiLSTM–attention network for spatial information capture and BiLSTM networks for learning from historical and future data points.

The proposed study has practical implications for flood prediction and management. It integrates advanced data processing techniques and a robust hybrid modeling approach to enhance the accuracy and reliability of flood forecasts, contributing to better preparedness and response strategies in the face of natural disasters.

The article is structured as follows: the Instruction section introduces the research background and literature review. The Methodology section introduces the research theory and the proposed algorithm framework. The Experiment section introduces the research area, research innovation, and comparative experiments on four datasets and compares the prediction error with traditional algorithms. The fourth part is the Discussion section, which further discusses the advantages of the model, its limitations, predictive sensitivity, and potential applications. The last is the Conclusion section, which provides conclusions and future research directions.

VMD theory

VMD was introduced by Dragomiretskiy & Zosso (2014) to formulate and address the following variational constraint problem:
formula
(1)
where represents the number of modes; and are the mode after decomposition and its corresponding center frequency, respectively; and denote the Dirac delta function and the partial derivative, respectively. is an imaginary number, denotes the original data, and is converted into a simple harmonic through the Euler transform, which is utilized to adjust the spectrum of each mode component to its corresponding baseband.
The quadratic penalty factor ensures signal reconstruction accuracy and mitigates noise interference. The Lagrange multiplier operator is utilized to transform the constrained variational problem (Equation (1)) into an unconstrained variational problem, as depicted in Equation (2).
formula
(2)

The iterative alternating direction multiplication algorithm is then applied to determine the saddle point of the extended Lagrangian function. This involves a combination of Fourier transform to optimize the modal components and the center frequency. The optimal solution is identified through alternating optimization search iterations, which decompose the final initial signal into K-modal components. A comprehensive description of the VMD algorithm can be found in Dragomiretskiy & Zosso (2014).

CNN network

CNN is utilized for feature extraction from input datasets to establish diverse connections between neurons and their internal layers. Introduced by LeCun et al. (2015) and LeCun et al. (1989), CNNs were initially proposed as a solution to computer vision problems. Since then, CNNs have gained widespread adoption in machine vision, feature extraction, and variable prediction tasks. CNNs are remarkably effective at capturing local patterns within input data through convolutional operations. This method leverages weight sharing, where the same set of weights is applied to different locations in the input data. Such weight sharing substantially reduces the number of network parameters, thereby enhancing computational efficiency.

A standard CNN model consists of five fundamental components: the input, convolutional, pooling, fully connected, and output layers. The convolutional layers extract spatial features using convolutional filters. In 2D input data, the convolution operation can be expressed as follows (Yang & Zhang 2021):
formula
(3)
where represents a specific position in the feature map after convolution, and I and denote the size of the input array and the convolution kernel, respectively (Yang & Zhang 2021). For 1D convolutions, represents a specific position along the sequence, where I is the input sequence length and K is the kernel length.

A one-dimensional CNN is well suited for processing time series data with multiple features. When the input data have N columns and aim to predict a single time series column, the ‘Conv1D’ function treats these N columns as distinct feature channels. The input data are represented as a matrix of sequence length multiplied by N, where each column signifies a different characteristic or feature. The CNN operation involves sliding the convolutional kernel over the input sequence, conducting a weighted sum of the data within the window. At each sliding position, the kernel undergoes element-wise multiplication with the corresponding portion of the input sequence, and the results are summed to yield a single value in the output sequence. This operation effectively captures local features and patterns within the input sequence.

BiLSTM theory

BiLSTM, or bidirectional LSTM network, excels in capturing long-term dependencies and temporal correlations in historical data because of its bidirectional learning capability. This feature positions it as superior to LSTM for comprehending both forward and backward dependencies in sequences.

The LSTM network consists of multiple LSTM cells, and Figure 1 illustrates the operational state of one cell (Hochreiter & Schmidhuber 1997).
Figure 1

Structure of one LSTM cell.

Figure 1

Structure of one LSTM cell.

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Let be the activation function that transforms any value to the interval [0, 1]. The output double tangent activation function () is employed to adjust the value flowing through the network, ensuring that it remains within the range of −1 to 1. t and represent the current and previous moments, respectively. Three data inputs are accessible: , the output value , and the cell state . The LSTM produces two data outputs: the short-time output value and the long-term cell state . The LSTM cell is governed by three control switches: the forgetting gate , the input gate , and the output gate . The update process of a cell is outlined as follows (Yan et al. 2021b; Chen et al. 2022):
formula
(4)
where are the weight matrices and denote the bias vectors of the forget, input, and output gates, respectively. is the bias vector of the candidate cell state , and represents the new memory cell state. denotes the matrix product. The forget gate determines how much of the cell state at the previous time remains at the current time , (Zhao et al. 2020), and the input gate determines how many network inputs are saved to the cell state ; controls how much of the status outputs to the current output value .
BiLSTM integrates forward and backward LSTMs to augment data comprehension and improve prediction accuracy. In the structure of a single-layer BiLSTM, two LSTMs operate in opposite directions: one processes input sequentially, while the other processes it in reverse order. After completing this dual processing, the outputs are combined through concatenation to yield the final BiLSTM output. The operational formula for BiLSTM at a specific time t denoted as is articulated as follows (Lin et al. 2022):
formula
(5)
where and represent the forward and backward transfers of the LSTM network, respectively, denotes the forward hidden layer state, signifies the backward hidden layer state, represents the output weight of the hidden layer in the forward propagation unit, is the output weight of the hidden layer in the backward propagation unit, and denotes the optimization parameter of the hidden layer offset at the current time.

Attention mechanism

The attention mechanism was initially implemented in image processing (Zhang et al. 2022). Upon integrating the attention mechanism, the visual system identifies a focal point within an image, intensifying attention while mitigating the acquisition of extraneous information. This refinement contributes to heightened computational efficiency and improved prediction performance. In deep learning prediction, the weighted attention mechanism assigns varying importance to data, accentuating substantial factors and enhancing the model's prediction accuracy (Dyer et al. 2016; Yan et al. 2021b). Figure 2 illustrates the weighted attention mechanism.
Figure 2

Structure of weighted attention.

Figure 2

Structure of weighted attention.

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According to Bahdanau et al. (2014), the attention mechanism formulated in this study is expressed as follows:
formula
(6)
where denote the hidden layer state corresponding to the input sequence , is the weight value of the hidden layer output corresponding to the current time t, represents the hidden layer state, denotes the weight matrix obtained through the training parameters and continuously adjusted during the model training process, and is a bias term that adjusts the results of linear combinations to better fit the data.

In the subsequent experiments, we incorporated a fully connected layer with the ReLU activation function into the CNN–BiLSTM–attention model. This addition aims to augment the model's representation capability and elevate its capacity to capture intricate patterns and relationships inherent in the data.

VMD-F hybrid model

The flow chart of the proposed VMD hybrid model is illustrated in Figure 3.
Figure 3

The research flow chart.

Figure 3

The research flow chart.

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As Figure 3 shows, the specific implementation steps are as follows:

  • (1)

    Data collection and preprocessing:

Initially, hydrological and meteorological data are collected. Inverse distance interpolation is performed on the data from three neighboring meteorological stations, following the method described in Section 3.1. This process yields meteorological data for the hydrological station, creating eight dimensions of input data. Missing values are filled using the sequential neighborhood averaging method. The dataset is then divided into training and test sets in a ratio of 0.75:0.25.

  • (2)

    VMD-based water level decomposition:

VMD is applied to perform water level decomposition and noise reduction, resulting in IMF components. Component division is executed according to Equation (8) in Section 3.2. Feature matching is further performed based on Pearson's correlation.

  • (3)

    Normalization and prediction:

The input data are normalized using Equation (7). Either BiLSTM or CNN–BiLSTM–attention is employed to predict each IMF. The individual predictions are integrated to generate the final output.

  • (4)

    Experimental analysis:

Predictive experiments are conducted on multiple datasets. Subjective and objective comparisons are made with other deep learning algorithms to showcase the predictive advantages of the proposed model.

This comprehensive approach combines data preprocessing, VMD-based decomposition, normalization, and deep learning techniques to enhance the model's predictive capabilities, as demonstrated through rigorous experimentation and comparative analysis.

Study area

The research area is around Hankou Station in Wuhan, Hubei Province, China, as depicted in Figure 4. Wuhan, a city within the Yangtze River basin, is particularly vulnerable to flood threats because of its location. Positioned in the middle reaches of the Yangtze River, Wuhan faces substantial flood risks, primarily due to the convergence of the Yangtze and Hanjiang Rivers. The geographical coordinates of the area are approximately 29°58′–31°22′N latitude and 113°41′–115°05′ E longitude. The flood season in Wuhan typically spans from May to September each year, with substantial flood events often occurring in July, as illustrated in Figure 5.
Figure 4

The research area.

Figure 4

The research area.

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Figure 5

Water level and flow volume visualization in the Hankou station. (a) Water level and flow volume from 2012 to 2020. (b) 2016, 2017, and 2020 water level.

Figure 5

Water level and flow volume visualization in the Hankou station. (a) Water level and flow volume from 2012 to 2020. (b) 2016, 2017, and 2020 water level.

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The upper reaches of the Yangtze River are located at elevations between 3,500 and 5,000 meters, where ice and snow are slowly melting due to global warming. Yangtze River flooding is primarily attributed to heavy basin rainfall, upper reaches snowmelt, constrained river channels, and sediment accumulation. The interplay of these elements contributes to elevated water levels and subsequent flooding. Researchers have undertaken substantial efforts in flood prediction and water control preparations (Xia & Chen 2021; Sun et al. 2022). In a study by Yuan et al. (2022), dynamic time warping and clustering were employed to group monitoring stations, creating a multi-station daily water level prediction model that combines LSTM and seasonal models. Another approach by Wang et al. (2022) introduced the attention–LSTM model for water level prediction. This model enhances spatiotemporal information extraction through an attention module based on the Softmax function. While most studies focus on training and predicting multiyear data, the Yangtze River exhibits distinct flood season characteristics, with megafloods notably occurring in July. Our research is centered on short-term flood prediction, specifically during July. This emphasis allows us to tailor our approach to the unique flood patterns observed during this critical period.

Data analysis and preparation

Figure 5(a) presents a visualization of 39,528 data points representing the Hankou station's water level and flow volume. The data span from 1 April 2012 to 30 September 2020. Additional statistical details are shown in Table 1.

Table 1

Water level data description from 2012 to 2020 (/m)

Average value95% confidence interval of the mean valueMedian valueVarianceStandard deviationMinimum valueMaximum valueFull rangeInterquartile distance
21.7592 21.7307–21.7879 22.01 8.379 2.8946 15.38 28.77 13.39 4.13 
Average value95% confidence interval of the mean valueMedian valueVarianceStandard deviationMinimum valueMaximum valueFull rangeInterquartile distance
21.7592 21.7307–21.7879 22.01 8.379 2.8946 15.38 28.77 13.39 4.13 

According to government records, the Yangtze River's Hankou station has established defense and warning water levels at 25 and 27.3 m, respectively. Throughout the past decade, water levels have consistently peaked above the warning level in July each year. Noteworthy instances occurred in 2016, 2017, and 2020, where substantially high water levels were observed, leading to casualties and property losses. This is particularly evident in the water level comparison of 2016, 2017, and 2020 provided in Figure 5(b). Specifically, 2016 and 2020 stand out as periods marked by elevated water levels resulting in adverse consequences.

For training and testing, two datasets, each containing 2,928 records from April to June in both 2020 and 2016 at the Hankou station, were utilized (see Figure 5(b)). Hourly data on rainfall, temperature, relative humidity, and wind speed were collected from the three nearest meteorological stations to Hankou: Jiangtan (1.48 km away), Huda (2.56 km away), and No. 14 Middle School (3.03 km away), as shown in Figure 4. Luoshan, an upstream station of Hankou on the Yangtze River, plays a pivotal role in early warning downstream. By analyzing Pearson's correlation coefficient, we identified that the water level at Luoshan 24 h in advance holds a more robust correlation with the water level at the Hankou station. Consequently, our prediction model incorporates the water level data from Luoshan 24 h in advance as a control variable. This results in eight dimensions, outlined in Table 2, comprising three hydrological station variables, four meteorological variables, and one upstream water level control variable. These dimensions are crucial for subsequent flood prediction and analysis.

Table 2

Symbolic explanation

Variableswv1v2v3v4v5v6v7
Interpretations Water level The water level difference between today and yesterday at the same time Water volume Rainfall Temperature Humidity Wind speed Water level of Luoshan 
Variableswv1v2v3v4v5v6v7
Interpretations Water level The water level difference between today and yesterday at the same time Water volume Rainfall Temperature Humidity Wind speed Water level of Luoshan 

After dividing the data, normalization is performed using the following equation:
formula
(7)
where is the input data after standardization, is the mean value, and is the Standard Deviation.

Water level decomposition using VMD

The experiment utilized Python 3.6 on hardware with a 12th Generation Intel Core i7 processor, 16 GB memory, and Windows 11. Missing data were addressed using the sequential neighborhood averaging method. The dual ascent time increment was set to 0 in the VMD algorithm, and the convergence tolerance criterion was . VMD involves two essential parameters affecting decomposition results: the modulus number K and the penalization factor. Obtaining suitable parameters often involves time-consuming optimization algorithms with somewhat random results. For comparison, VMD decomposition was performed on the 2016 dataset using and on the 2020 dataset using . Separate decompositions were carried out for flood-prone months in both datasets, integrated with hybrid model predictions to evaluate stability. Figure 6 illustrates VMD decompositions of the 2020 dataset and data for the period of 10 June to 10 July 2016.
Figure 6

VMD decomposition curve and signal spectrum of Hankou station. (a) VMD curves for April–July 2020 data (). (b) VMD curves for 10 June to 10 July 2016 ().

Figure 6

VMD decomposition curve and signal spectrum of Hankou station. (a) VMD curves for April–July 2020 data (). (b) VMD curves for 10 June to 10 July 2016 ().

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As depicted in Figure 6, VMD decomposition yields varying volatilities for each IMF, concentrating low-frequency information in the initial components and high-frequency information, including noise, in subsequent components. Pearson correlation calculations with the original water level that IMF1 exhibits the strongest correlation with the original data (exceeding 0.9), encapsulating the primary information of the original variable. Correlations with the original signal for other components are less stable; nevertheless, they encompass substantial information about the original data and are pivotal for signal reconstruction.

Classification and feature matching of VMD components

By statistical principles, a higher coefficient of variation (CV) indicates greater data volatility, while a lower value suggests lower relative data volatility. Unlike variance, which can be influenced by scale, the CV is more adept at distinguishing between multiple variables. Furthermore, the Fourier frequency value of a signal serves as an indicator of signal volatility, where higher signal power spectra correspond to more substantial signal fluctuations. Both the CV and Fourier frequency value f (as per Equation (9)) are introduced to assess the volatility of IMFs and to classify them. The fluctuation factor Cf is defined by Equation (8).
formula
(8)

To avoid a denominator of 0, a perturbation of 0.01 is added to each column element. In analyzing the decomposition features of the Yangtze River water level, IMF1 exhibits relative smoothness; thus, BiLSTM, adept at capturing long-term contextual information, is employed for predicting IMF1. For the remaining IMFs, a threshold of 0.5 is set when , indicating relatively smooth data with long-term characteristics; these IMFs are predicted using BiLSTM. Conversely, when , signifying sharp data fluctuations, CNN–BiLSTM–attention, skilled at capturing short-term localized features, is utilized for prediction analysis. Table 3 details the Cf values for IMFs in the 2020 and 2016 water level data.

Table 3

IMF's Cf values of the 2020 and 2016 water level data

VMD IMFsIMF1IMF2IMF3IMF4IMF5
2020 Cf 0.34 33.71 8.28   
July 2020 Cf 0.56 50.91 8.94   
2016 Cf 0.2411 34.4131 7.4811 0.4287 0.4733 
10 June to 10 July 2016 Cf 0.1888 51.911 13.4878 0.7638 0.9573 
VMD IMFsIMF1IMF2IMF3IMF4IMF5
2020 Cf 0.34 33.71 8.28   
July 2020 Cf 0.56 50.91 8.94   
2016 Cf 0.2411 34.4131 7.4811 0.4287 0.4733 
10 June to 10 July 2016 Cf 0.1888 51.911 13.4878 0.7638 0.9573 

For seven feature variables, a Pearson correlation test was conducted at a two-tailed significance level of 0.01. The top 70% of variables based on correlation coefficients were selected as input features. For the 2020 dataset, the input features for IMF1 are v1, v2, v4, v5, and v7; for IMF2, they are v2, v4, v5, v6, and v7; and for IMF3, they are v1, v2, v3, v5, and v7. In the case of the 2016 dataset, the input features for IMF1 are v1, v2, v4, v6, and v7; for IMF2, they are v1, v2, v4, v5, and v7; for IMF3, they are v1, v2, v3, v4, and v5; and for IMF4 and IMF5, they are v1, v2, v3, v4, and v6. The same calculation process is applied to select relevant variables for the month of flooding.

Experiment

The MSE is employed as the loss function. Objective evaluation indices include root mean square error (RMSE), mean absolute percentage error (MAPE), mean absolute error (MAE), and the goodness of fit (R2), as expressed in Equation (9). In addition, the comparison curve serves as the subjective evaluation index.
formula
(9)
where denotes the ith actual input value, represents the predicted value, is the number of training data, and is the average value of . Smaller values of , , , and close to 1 signify the superiority of the prediction model.

The CNN employs the Conv1D model with parameters set to filters = 128, kernel_size = 1, and the Sigmoid function as the activation function. LSTM, BiLSTM, BiLSTM–attention, and CNN–BiLSTM–attention use two-layer neural networks. To ensure a fair comparison, uniform parameters are set as (learning rate, training times, batch sizes, number of nodes in the first hidden layer, number of nodes in the second hidden layer, number of output nodes of the fully connected layer) = (0.002, 60, 55, 98, 49, 10). A total of 2,928 data points from April to July 2020 and for 2016, along with 744 data points in the flood month, are divided into the training set and test set at a ratio of 0.75:0.25. Data normalization is performed using Equation (7), and an experimental comparison of prediction models is conducted.

  • (1)

    Prediction step selection

We analyzed the hydrological and meteorological data's partial autocorrelation function (PACF) to determine the prediction step size. In Figure 7, PACF plots for water level and rainfall are presented, depicting partial autocorrelation coefficients and 95% confidence intervals for lag orders ranging from 1 to 100. Based on the experiments and the information provided in Figure 7, the number of lag points for meteorological data is determined to be 4, while for hydrological data, it is 2, both of which fall outside the 95% confidence interval. Therefore, in our subsequent experiments, we opt for a prediction step size of 3, which is the average of the two.
  • (2)

    Prediction for the April–July 2020 dataset

Figure 7

PACF hysteresis diagram.

Figure 7

PACF hysteresis diagram.

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Based on the data in Table 3 and the feature selection in Section 3.2, the model and input features are selected for each IMF, and a comparison of the prediction results is presented in Table 4 and Figure 8. Here, Md3 represents the CNN–BiLSTM–attention algorithm (Nie et al. 2021), Md4 and Md5 correspond to the algorithms mentioned in Zhang et al. (2023b) and Wu et al. (2023), respectively, and Md6 is the proposed algorithm, the hybrid prediction model of IMFs classified by their fluctuation factor, with input feature selection.
Table 4

Experimental predictive results of the July water level at Hankou station for the April–July 2020 dataset

NumberModelRMSE (m)MAPE (%)MAE (m)R2
Md1 LSTM 0.1156 0.3076 0.0837 0.9849 
Md2 BiLSTM 0.0848 0.2468 0.0677 0.9919 
Md3 CNN–BiLSTM––attention 0.1941 0.5509 0.1504 0.9574 
Md4 VMD–BiLSTM 0.1071 0.2121 0.0566 0.9871 
Md5 VMD–CNN–BiLSTM–attention 0.1709 0.3119 0.0823 0.9670 
Md6 VMD-F hybrid Model 0.0627 0.1389 0.0375 0.9956 
NumberModelRMSE (m)MAPE (%)MAE (m)R2
Md1 LSTM 0.1156 0.3076 0.0837 0.9849 
Md2 BiLSTM 0.0848 0.2468 0.0677 0.9919 
Md3 CNN–BiLSTM––attention 0.1941 0.5509 0.1504 0.9574 
Md4 VMD–BiLSTM 0.1071 0.2121 0.0566 0.9871 
Md5 VMD–CNN–BiLSTM–attention 0.1709 0.3119 0.0823 0.9670 
Md6 VMD-F hybrid Model 0.0627 0.1389 0.0375 0.9956 
Figure 8

Comparing forecast curves for Hankou 2020 data.

Figure 8

Comparing forecast curves for Hankou 2020 data.

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Table 4 indicates that the prediction accuracy of BiLSTM and CNN–BiLSTM–attention did not improve after incorporating VMD. This can be attributed to the critical parameters K and in VMD; improper selection of these parameters may lead to a decrease in the accuracy of subsequent processing. However, following model classification and feature selection, the proposed VMD-F Hybrid model exhibits a 26.06% reduction in RMSE, a 43.71% reduction in MAPE, and a 44.61% reduction in MAE compared to M2—the best model among the previous five. This showcases excellent predictive ability and stability. Combined with the prediction curve shown in Figure 8, the proposed model Md6 performs best in the initial and final tracking of real data, demonstrating the most stable prediction performance.

  • (3)

    July 2020 dataset

Referring to Table 3, the VMD hybrid uses BiLSTM for IMF1, while CNN–BiLSTM–attention is applied to IMF2 and IMF3. The prediction comparison is presented in Table 5 and Figure 9.
Table 5

Comparative experimental results for the July 2020 dataset

NumberModelRMSE (m)MAPE (%)MAE (m)R2
Md1 LSTM 0.0261 0.0812 0.0230 0.8510 
Md2 BiLSTM 0.0254 0.0795 0.0226 0.8583 
Md3 CNN–BiLSTM–attention 0.0300 0.0956 0.0271 0.8027 
Md4 VMD–BiLSTM 0.0305 0.0891 0.0253 0.7959 
Md5 VMD–CNN–BiLSTM–attention 0.0311 0.1006 0.0285 0.7872 
Md6 VMD-F hybrid model 0.0135 0.0386 0.0103 0.9596 
NumberModelRMSE (m)MAPE (%)MAE (m)R2
Md1 LSTM 0.0261 0.0812 0.0230 0.8510 
Md2 BiLSTM 0.0254 0.0795 0.0226 0.8583 
Md3 CNN–BiLSTM–attention 0.0300 0.0956 0.0271 0.8027 
Md4 VMD–BiLSTM 0.0305 0.0891 0.0253 0.7959 
Md5 VMD–CNN–BiLSTM–attention 0.0311 0.1006 0.0285 0.7872 
Md6 VMD-F hybrid model 0.0135 0.0386 0.0103 0.9596 
Figure 9

Comparing forecast curves for Hankou July 2020 data.

Figure 9

Comparing forecast curves for Hankou July 2020 data.

Close modal

Table 5 reveals that the proposed Md6 method demonstrates substantial predictive advantages on monthly datasets characterized by severe short-term flood fluctuations. Md4 and Md5, with VMD preprocessing, do not effectively enhance the model's prediction performance. However, Md6 effectively improves the prediction accuracy under the same VMD decomposition. It shows a 46.85% reduction in RMSE, a 51.44% reduction in MAPE, a 54.4% reduction in MAE, and an 11.8% increase in R2 compared with BiLSTM, showcasing excellent performance. In Figure 9, the similarity between the predicted and actual curves is high, with a prediction error of less than 1.5 cm, indicating high short-term prediction accuracy.

  • (4)

    April to July 2016 dataset

The prediction results are presented in Table 6.

Table 6

Comparative experimental results for the 2016 dataset

NumberModelRMSE (m)MAPE (%)MAE (m)R2
Md1 LSTM 0.0745 0.1837 0.0497 0.9807 
Md2 BiLSTM 0.0869 0.2101 0.0568 0.9737 
Md3 CNN–BiLSTM–attention 0.0870 0.2511 0.0684 0.9736 
Md4 VMD–BiLSTM 0.0278 0.7300 0.0199 0.9973 
Md5 VMD–CNN–BiLSTM–attention 0.0461 0.1241 0.0338 0.9926 
Md6 VMD-F hybrid model 0.0382 0.0974 0.0265 0.9949 
NumberModelRMSE (m)MAPE (%)MAE (m)R2
Md1 LSTM 0.0745 0.1837 0.0497 0.9807 
Md2 BiLSTM 0.0869 0.2101 0.0568 0.9737 
Md3 CNN–BiLSTM–attention 0.0870 0.2511 0.0684 0.9736 
Md4 VMD–BiLSTM 0.0278 0.7300 0.0199 0.9973 
Md5 VMD–CNN–BiLSTM–attention 0.0461 0.1241 0.0338 0.9926 
Md6 VMD-F hybrid model 0.0382 0.0974 0.0265 0.9949 

Table 6 indicates that VMD–BiLSTM exhibits the best prediction performance in the 2016 dataset, likely because of the parameter settings of VMD being more suitable for BiLSTM, which is proficient at predicting water level frequencies with less variation. Our hybrid prediction algorithm demonstrates a substantial advantage for more volatile data points, and Md6 also shows good prediction ability, ranking second only to VMD–BiLSTM.

  • (5)

    Dataset from 10 June to 10 July 2016

Another test experiment on the dataset from 10 June to 10 July 2016 is conducted to further assess the prediction model's performance for flood peaks. The prediction results are presented in Table 7 and Figure 10.
Table 7

Comparative experimental results for the June to July 2016 dataset

NumberModelRMSE (m)MAPE (%)MAE (m)R2
Md1 LSTM 0.0757 0.2229 0.0617 0.9727 
Md2 BiLSTM 0.0693 0.2079 0.0577 0.9771 
Md3 CNN–BiLSTM–attention 0.1026 0.2853 0.0789 0.9497 
Md4 VMD–BiLSTM 0.0735 0.1885 0.0519 0.9742 
Md5 VMD–CNN–BiLSTM–attention 0.0912 0.1803 0.0493 0.9604 
Md6 VMD-F hybrid model 0.0632 0.1338 0.0368 0.9809 
NumberModelRMSE (m)MAPE (%)MAE (m)R2
Md1 LSTM 0.0757 0.2229 0.0617 0.9727 
Md2 BiLSTM 0.0693 0.2079 0.0577 0.9771 
Md3 CNN–BiLSTM–attention 0.1026 0.2853 0.0789 0.9497 
Md4 VMD–BiLSTM 0.0735 0.1885 0.0519 0.9742 
Md5 VMD–CNN–BiLSTM–attention 0.0912 0.1803 0.0493 0.9604 
Md6 VMD-F hybrid model 0.0632 0.1338 0.0368 0.9809 
Figure 10

Comparison of forecast curves for the June to July 2016 dataset.

Figure 10

Comparison of forecast curves for the June to July 2016 dataset.

Close modal

Table 7 and Figure 10 illustrate that the proposed hybrid model exhibits superior prediction accuracy when forecasting flood peak values. The prediction metrics, including RMSE, MAPE, and MAE, show the smallest values, while R2 is the largest. Despite an error of less than 0.7 cm, indicating slightly lower prediction accuracy than the 2020 data, Md5 with VMD outperforms Md3, while Md4 performs marginally less effectively than Md2. This discrepancy may be attributed to the challenges associated with VMD decomposition parameters and subsequent hyperparameters in the prediction model. Identical prediction parameters were employed to ensure a consistent comparison. Adjusting these parameters could potentially yield improved prediction results. Nevertheless, the proposed VMD-F hybrid prediction model still attains commendable outcomes, affirming its stability in flood peak predictions.

Effectiveness of method analysis

The study aims to enhance flood prediction models, particularly when using VMD to handle preprocessed and denoised multidimensional input data. Initially, input data undergoes VMD-based decomposition into IMFs as a crucial preprocessing step to mitigate noise impact on predictions. However, the unique characteristics of VMD-processed data and variable correlations among components introduce complexities in developing subsequent prediction models, especially for multidimensional input data. Pearson correlations are computed between each IMF and input feature to create a comprehensive set of predictive feature components. The introduction of the fluctuation factor helps distinguish IMFs, and thresholds are applied to classify IMFs into two categories.

In our hybrid learning model proposal, CNN captures spatial information, and BiLSTM is utilized to learn information concerning past and future data points. To prioritize features during the prediction process, we also incorporate an attention mechanism to augment the flood warning capability of the model. We have demonstrated that our prediction model exhibits clear advantages through experimental subjective and objective comparisons.

Model sensitivity and error analysis

To verify the model's sensitivity, set the prediction step size to be 5 and 10 h ahead, then use the April–July 2020 dataset to compare the performance of different models. Table 8 shows the comparison results matrix, and Figure 11 compares the prediction curves.
Table 8

Comparative experimental results for different prediction steps

ModelRMSE (m)MAPE (%)MAE (m)R2RMSE (m)MAPE (%)MAE (m)R2
Prediction step is 5 hPrediction step is 10 h
LSTM 0.1403 0.3301 0.0890 0.9773 0.1963 0.4925 0.1336 0.9533 
BiLSTM 0.1218 0.3074 0.0833 0.9829 0.1640 0.4744 0.1302 0.9674 
CNN–BiLSTM–attention 0.2561 0.6864 0.1868 0.9245 0.3238 0.8833 0.2412 0.8731 
VMD–BiLSTM 0.1392 0.2845 0.0759 0.9777 0.1636 0.3460 0.0927 0.9676 
VMD–CNN–BiLSTM–attention 0.2315 0.4105 0.1082 0.9383 0.3040 0.6357 0.1700 0.8881 
VMD-F hybrid model 0.1331 0.2479 0.0658 0.9796 0.1425 0.2845 0.0759 0.9754 
ModelRMSE (m)MAPE (%)MAE (m)R2RMSE (m)MAPE (%)MAE (m)R2
Prediction step is 5 hPrediction step is 10 h
LSTM 0.1403 0.3301 0.0890 0.9773 0.1963 0.4925 0.1336 0.9533 
BiLSTM 0.1218 0.3074 0.0833 0.9829 0.1640 0.4744 0.1302 0.9674 
CNN–BiLSTM–attention 0.2561 0.6864 0.1868 0.9245 0.3238 0.8833 0.2412 0.8731 
VMD–BiLSTM 0.1392 0.2845 0.0759 0.9777 0.1636 0.3460 0.0927 0.9676 
VMD–CNN–BiLSTM–attention 0.2315 0.4105 0.1082 0.9383 0.3040 0.6357 0.1700 0.8881 
VMD-F hybrid model 0.1331 0.2479 0.0658 0.9796 0.1425 0.2845 0.0759 0.9754 
Figure 11

Prediction comparison under different prediction step sizes. (a) Prediction step is 5 h and (b) prediction step is 10 h.

Figure 11

Prediction comparison under different prediction step sizes. (a) Prediction step is 5 h and (b) prediction step is 10 h.

Close modal

By comparing Tables 4 and 8 the step size selection affects the prediction accuracy. When the prediction step size is 3 h, selected through PACF, all models achieve the best prediction accuracy. So, choosing an appropriate prediction step size can reduce prediction errors. Although the RMSE of BiLSTM is smaller than that of the VMD-F hybrid model in Table 8, the prediction curve of the proposed algorithm is closer to the actual water level value, achieving better predictive visual effects, as shown in Figure 11(a). BiLSTM and VMD BiLSTM also show good predictive stability, but the stability and accuracy of the VMD-F hybrid model are better. Different parameter choices may affect the prediction accuracy, while effective feature selection and classification can improve the model's accuracy and reduce errors under the same parameter selection.

Model improvement and potential applications

Although our model has demonstrated effectiveness in flood prediction, some limitations still warrant further improvement. Optimizing the parameters of VMD and the hybrid neural network, especially when set uniformly, could enhance the prediction accuracy. Incorporating additional techniques for feature engineering selection and data augmentation can further improve the model's predictive capabilities. In specific applications, it can be used in VMD decomposition-based prediction models to assist in optimizing the matching problem between VMD components and input features, further improving prediction accuracy and reducing human resource waste caused by large prediction errors. However, special attention should be paid to selecting features and step sizes for different datasets and optimizing the model's hyperparameters can further improve predictive performance. The priority for future research should include integrating the model into real-time flood warning systems.

By integrating BiLSTM and CNN–BiLSTM–attention, a sophisticated flood prediction model is developed. This model effectively captures fluctuations in water levels, enabling precise short-term predictions. The experimental outcomes indicate the model's proficiency in short-term flood prediction, showcasing minimal prediction errors. Moreover, when combined with VMD preprocessing, the model proposed solves the error problem of direct matching between VMD components and input features in traditional prediction methods, which can assist in applying flood warning systems.

Furthermore, introducing the fluctuation factor for IMF classification and feature selection enhances the predictive performance of subsequent models. In addition, our exploration into the time lag relationship between meteorological and hydrological data highlights the superior informativeness of inverse distance interpolation of meteorological data over data from a single station. These findings are vital references for advancing meteorological and hydrological research.

The introduced VMD-F hybrid model for flood prediction contributes to a more nuanced comprehension of the intricate relationship between meteorological and hydrological data. This model holds the potential for predicting climate, rainfall, and Environmental, Social and Governance (ESG) indicators, particularly in scenarios with complex issues and numerous influencing variables. Researchers can further advance this field by optimizing parameters, integrating diverse prediction models to enhance accuracy, and applying these insights into practical applications.

NC and MFM contributed to the conceptualization and methodology. NC contributed to software, validation, formal analysis, data curation, writing the original draft, and visualization. MFM and NC contributed to the investigation; MFM contributed to resources; FPS and MFM contributed to reviewing and editing the writing and supervision. FPS contributed to project administration. All authors have read and agreed to the published version of the manuscript.

This work was supported by a Universiti Sains Malaysia, Short-Term Grant with Project No: 304/PMATHS.6315641.

The authors declare there is no conflict.

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