Flood prediction based on feature selection and a hybrid deep learning network

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.

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 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 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, 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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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 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

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.

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.

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.

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.

All relevant data are available from http://113.57.190.228:8001/#!/web/Report/RiverReporthttp://data.cma.cn/

The authors declare there is no conflict.