A Daily Runoff Prediction Model for the Yangtze River Basin Based on an Improved Generative Adversarial Network

Abstract

Hydrological runoff prediction plays a crucial role in water resource management and sustainable development. However, it is often constrained by the nonlinearity, strong stochasticity, and high non-stationarity of hydrological data, as well as the limited accuracy of traditional forecasting methods. Although Wasserstein Generative Adversarial Networks with Gradient Penalty (WGAN-GP) have been widely used for data augmentation to enhance predictive model training, their direct application as forecasting models remains limited. Additionally, the architectures of the generator and discriminator in WGAN-GP have not been fully optimized, and their potential in hydrological forecasting has not been thoroughly explored. Meanwhile, the strategy of jointly optimizing Variational Autoencoders (VAEs) with WGAN-GP is still in its infancy in this field. To address these challenges and promote more accurate and sustainable water resource planning, this study proposes a comprehensive forecasting model, VXWGAN-GP, which integrates Variational Autoencoders (VAEs), WGAN-GP, Convolutional Neural Networks (CNN), Bidirectional Long Short-Term Memory Networks (BiLSTM), Gated Recurrent Units (GRUs), and Attention mechanisms. The VAE enhances feature representation by learning the data distribution and generating new features, which are then combined with the original features to improve predictive performance. The generator integrates GRU, BiLSTM, and Attention mechanisms: GRU captures short-term dependencies, BiLSTM captures long-term dependencies, and Attention focuses on critical time steps to generate forecasting results. The discriminator, based on CNN, evaluates the differences between the generated and real data through adversarial training, thereby optimizing the generator’s forecasting ability and achieving high-precision runoff prediction. This study conducts daily runoff prediction experiments at the Yichang, Cuntan, and Pingshan hydrological stations in the Yangtze River Basin. The results demonstrate that VXWGAN-GP significantly improves the quality of input features and enhances runoff prediction accuracy, offering a reliable tool for sustainable hydrological forecasting and water resource management. By providing more precise and robust runoff predictions, this model contributes to long-term water sustainability and resilience in hydrological systems.

1. Introduction

Forecasting hydrological runoff is essential for sustainable water resource management, significantly impacting key aspects such as power scheduling, water supply reliability, navigation effectiveness, and ecological conservation. Accurate runoff prediction supports efficient water allocation, mitigates the risks associated with extreme hydrological events, and plays a critical role in maintaining long-term water sustainability [1]. Runoff prediction is classified into short-term and medium-to-long-term forecasting based on the prediction timescale. The former provides strategic guidance for reservoir operation and water resource allocation, whereas the latter, owing to its high timeliness and reliability, serves as a crucial input for real-time dynamic scheduling [2]. Runoff prediction models are generally categorized into process-driven [3,4,5,6] and data-driven models [7,8,9,10]. The former employs mathematical equations to simulate hydrological processes, yet their accuracy depends on a thorough understanding of watershed dynamics. These models also suffer from complex parameterization and high computational costs, making them less suitable for regions with data scarcity or significant heterogeneity [11,12]. In contrast, data-driven models establish predictive mapping relationships by extracting statistical patterns from historical data, making them more suitable for the highly nonlinear and non-stationary runoff series. With the growing need for sustainable water management, data-driven models offer a promising solution by improving predictive accuracy and enabling more efficient decision making in hydrological forecasting.

In recent years, data-driven models have achieved significant advancements in runoff prediction. Traditional machine learning methods, such as backpropagation neural networks (BPs) [13], support vector machines (SVMs) [14], random forests (RFs) [15], artificial neural networks (ANNs) [16], and gradient boosting machines (GBMs) [17,18], have demonstrated some ability to capture nonlinear characteristics. However, these models are susceptible to local optima and exhibit high sensitivity to hyperparameters. With advances in deep learning, LSTM and GRU networks have gained widespread use in runoff prediction and have become widely adopted for runoff prediction, owing to their strong ability to capture temporal dependencies. For instance, Han et al. [19] proposed the AT-LSTM model, incorporating attention mechanisms at both the input and hidden states. This approach was utilized for extended-period runoff prediction at Yichang and Pingshan stations in China, demonstrating improved forecasting accuracy. Sheng et al. [20] proposed ResGRU Plus, an innovative GRU-based framework for short-term runoff forecasting, utilizing hourly runoff data from the Columbia River. Their findings indicated an 18% increase in predictive accuracy compared to conventional GRU models. Wu et al. [21] constructed an ensemble deep learning model incorporating BiLSTM, which was implemented at the Wushan and Weijiabao stations in the Weihe River Basin. Their findings indicated that the proposed model exhibited strong adaptability and flood peak prediction capabilities across different hydrological environments. However, most existing studies have focused on optimizing model architectures while overlooking a critical constraint: inadequate data quality and quantity can severely degrade model performance [22,23]. The stochasticity, non-stationarity, and high monitoring costs of runoff data often lead to data scarcity, making models susceptible to overfitting and limiting their generalization ability [24].

To address data limitations, data augmentation techniques have been employed to generate synthetic samples or enhance feature representations, thereby improving model robustness. Traditional methods, such as random oversampling [25,26] and the synthetic minority oversampling technique (SMOTE) [27,28,29], increase sample size through interpolation or repetition but struggle to generate realistically distributed new data and are prone to introducing noise. In contrast, generative models, including variational autoencoders (VAEs) [30], diffusion models [31,32], and generative adversarial networks (GANs) [33,34,35], implicitly learn data distributions to generate high-dimensional nonlinear samples, offering a novel paradigm for data augmentation. Among these generative models, VAE stands out as a powerful generative model that excels not only in data augmentation but also in feature enhancement tasks. By incorporating probabilistic distributions, VAEs encode input data into a continuous latent space, enabling the model to learn the underlying structure of the data. This continuous latent space design allows VAEs to generate high-quality new samples and enhance model robustness and performance through optimized latent features.

Additionally, among the aforementioned generative models, GANs stand out due to their adversarial training mechanism, which enables the generation of high-quality data [36]. The core concept of GANs is to optimize a generator and discriminator through adversarial learning, allowing the generator to approximate the real data distribution and produce realistic samples that align with statistical properties. In hydrological runoff prediction, GANs not only facilitate data augmentation to alleviate sample scarcity but also enhance the modeling of complex nonlinear relationships by learning from historical data distributions [37]. However, conventional GANs face challenges such as gradient vanishing and mode collapse when handling time-series data, limiting their direct application in runoff forecasting [38]. Therefore, improving the stability of GAN training, optimizing data generation quality, and integrating deep temporal models for prediction are key to enhancing hydrological runoff forecasting performance. To this end, WGAN [39] proposed utilizing the Wasserstein metric to replace the traditional Kullback–Leibler divergence, effectively addressing the issue of training instability. Gulrajani et al. [40] developed an enhanced version termed WGAN-GP, which integrates a gradient penalty mechanism to ensure Lipschitz continuity within the discriminator network, thereby substantially enhancing the fidelity of synthesized outputs.

Additionally, while traditional deep learning models such as LSTM and GRU have demonstrated remarkable capabilities in handling time-series data and capturing temporal dependencies, their predictive accuracy may be constrained when confronted with complex nonlinear relationships and data scarcity issues. In contrast, WGAN-GP, through its refined adversarial training process and high-quality synthetic data generation, has the potential to significantly enhance predictive accuracy, especially in the context of complex nonlinear relationships and data scarcity. However, the training process of WGAN-GP is relatively intricate, necessitating meticulous hyperparameter tuning and extended training durations.

Recent studies have increasingly focused on applying WGAN-GP to forecasting tasks. For example, Hu et al. [41] employed WGAN-GP for spectral enhancement and starch content analysis, combining hyperspectral imaging (HSI) with advanced deep learning (DL) methodologies to estimate starch levels in Pueraria lobata. Their comprehensive evaluation framework compared the effectiveness of Partial Least Squares Regression (PLSR), Support Vector Regression (SVR), and one-dimensional Convolutional Neural Network (1D-CNN) models both with and without augmented data, revealing substantial gains in prediction reliability. Huang et al. [42] introduced a novel hybrid architecture termed BiLSTM-CNN-WGAN-GP (LCWGAN-GP) for short-term wind energy prediction, specifically designed to overcome the challenges of prediction volatility and precision limitations. Through empirical validation using operational data from a Jiuquan-based wind facility in Gansu Province, their proposed framework exhibited superior forecasting capabilities when benchmarked against conventional prediction approaches. Despite the demonstrated efficacy of WGAN-GP in data augmentation, its potential in predictive tasks remains underexplored, particularly in the realm of runoff forecasting, where relevant studies are still scarce. Moreover, the strategy of leveraging variational autoencoders (VAEs) for feature enhancement and jointly optimizing VAE with WGAN-GP has scarcely been investigated in the field of hydrological prediction, with related research virtually in its infancy. Given this context, to further enhance the accuracy and stability of runoff prediction, it is imperative to optimize and refine the existing WGAN-GP model architecture and fully unleash its potential in runoff forecasting.

To address the aforementioned challenges, this study proposes a runoff forecasting model that integrates variational autoencoders (VAEs) with an improved WGAN-GP (VXWGAN-GP). We first use the variational autoencoder (VAE) to perform feature learning on the original data and generate new features. These enhanced features are then combined with the original data features and input into the subsequent model to achieve feature enhancement. Unlike traditional WGAN-GP, we construct the generator by combining GRU, BiLSTM, and attention mechanisms to learn the distribution characteristics of time-series data and generate predictions for future time steps. Additionally, the discriminator is constructed using a four-layer one-dimensional convolutional network, which evaluates the differences between generated data and real data through adversarial training, thereby optimizing the forecasting ability of the generator. The generator and discriminator alternate training, gradually improving prediction accuracy, and ultimately forming the VXWGAN-GP runoff forecasting model. This framework not only optimizes the WGAN-GP model architecture but also innovatively couples feature enhancement with prediction tasks, aiming to further improve the accuracy, robustness, and sustainability of runoff forecasting. The main contributions of this study are as follows:

(1)

This research presents an innovative generative adversarial network framework (VXWGAN-GP) that integrates VAE and WGAN-GP, constructing a daily runoff prediction model that synergistically combines VAE, WGAN-GP, CNN, BiLSTM, GRU, and attention mechanisms.

(2)

The encoder of the VAE transforms the input features into a lower-dimensional latent space, whereas the decoder works to restore and merge the data back with the original input data. This process enhances the feature representation and boosts the model’s capacity to grasp complex data structures. Meanwhile, the model employs a CNN-based discriminator to assess the quality of generated data, and the generator integrates the temporal modeling strengths of BiLSTM and GRU, supplemented by an attention mechanism to optimize hydrological feature learning, further improving predictive performance.

(3)

The developed framework is implemented for daily streamflow prediction across three key hydrological monitoring sites—Yichang, Cuntan, and Pingshan—located in the upper and middle sections of the Yangtze River basin. Experimental results demonstrate that VXWGAN-GP significantly outperforms LSTM, BiLSTM, GRU, and WGAN-GP in terms of RMSE, MAE, and R² metrics. Moreover, the model attains the optimal overall performance across representative wet, normal, and dry years, thereby highlighting its reliability and outstanding predictive capabilities.

The rest of this paper is organized as follows: Section 2 outlines the research methodology. Section 3 details the structure of the VXWGAN-GP daily runoff prediction model. Section 4 clarifies the performance evaluation metrics. Section 5 describes the case study approach and comparative analysis, assessing the proposed model against benchmark models using data from the Yichang, Cuntan, and Pingshan hydrological stations in the upstream and midstream sections of the Yangtze River. Section 6 offers an in-depth analysis and discussion of the results. Finally, Section 7 concludes the study.

2. Theoretical Introduction to Prediction Methods

2.1. Improved Generative Adversarial Network (WGAN-GP)

Generative adversarial networks (GANs) produce data through the concurrent training of a generator and a discriminator. The generator synthesizes data from random noise, whereas the discriminator assesses whether the data are derived from the genuine distribution. These networks are trained in an alternating fashion until the generator yields data that cannot be distinguished from real data, thereby reaching a Nash equilibrium.

To overcome the gradient vanishing and unstable optimization issues inherent in traditional GAN models, Arjovsky et al. [39] introduced the Wasserstein GAN (WGAN), which employs the Wasserstein distance to quantify the discrepancy between the distributions of real and generated data. In contrast to the traditional Kullback–Leibler (KL) divergence and Jensen–Shannon (JS) divergence, the Wasserstein distance significantly mitigates the gradient vanishing issue, thus improving the stability of the training process. The Wasserstein distance is defined as follows:

$$W\left(P_r,P_g\right)=\underset{{\parallel f\parallel }_L\le 1}{\mathrm{s}\mathrm{u}\mathrm{p}}({\mathrm{E}}_{x\sim P_r}\left[f\left(x\right)\right]-{\mathrm{E}}_{x\sim P_g}\left[f\left(x\right)\right])$$

(1)

where $W\left(P_r,P_g\right)$ represents the Wasserstein distance, $P_r$ denotes the real data distribution, and $P_g$ represents the generated data distribution. The function $P_g$ is the output of the discriminator, where $f\left(x\right)$ quantifies the likelihood of sample $x$ being classified as real data. The condition ${\parallel f\parallel }_L\le 1$ ensures that f satisfies the Lipschitz continuity constraint, i.e., $\parallel \nabla f\parallel \le 1$. The term ${\mathrm{E}}_{x\sim P_r}\left[f\left(x\right)\right]$ represents the expected value of $f\left(x\right)$ under the real data distribution $P_r$, effectively serving as a weighted average score for real data, while ${\mathrm{E}}_{x\sim P_g}\left[f\left(x\right)\right]$ represents the expected value under the generated data distribution $P_g$.

WGAN enforces Lipschitz continuity in the discriminator through weight clipping. However, this constraint interacts unfavorably with the loss function, leading to difficulties in convergence and potential gradient explosion issues. To address these limitations, Gulrajani et al. [40] introduced WGAN-GP, which incorporates a gradient penalty term to enforce Lipschitz continuity. The generator loss function in WGAN-GP is formulated as:

$${\mathcal{L}}_G=-{\mathrm{E}}_{x\sim P_g}\left[D\left(x\right)\right]$$

(2)

where ${\mathcal{L}}_G$ represents the generator loss, $P_g$ denotes the distribution of generated samples, and $D\left(x\right)$ is the score assigned by the discriminator to the input sample.

The loss function of the discriminator is expressed as:

$${\mathcal{L}}_D=-{\mathrm{E}}_{x\sim P_r}\left[D\left(x\right)\right]+{\mathrm{E}}_{x\sim P_g}\left[D\left(x\right)\right]+\lambda {\mathcal{L}}_{\mathrm{G}\mathrm{P}}$$

(3)

where ${\mathcal{L}}_D$ is the discriminator loss, $P_r$ denotes the real data distribution, $D\left(x\right)$ is the discriminator’s score for sample $x$, and $\lambda$ is the coefficient for the gradient penalty term ${\mathcal{L}}_{\mathrm{G}\mathrm{P}}$. The first term $-{\mathrm{E}}_{x\sim P_r}\left[D\left(x\right)\right]$ aims to maximize the discriminator’s score for real data, while the second term ${\mathrm{E}}_{x\sim P_g}\left[D\left(x\right)\right]$ minimizes the discriminator’s score for generated data.

The gradient penalty term ${\mathcal{L}}_{\mathrm{G}\mathrm{P}}$ is defined as:

$${\mathcal{L}}_{\mathrm{G}\mathrm{P}}={\mathrm{E}}_{\widehat{x}\sim P_{\widehat{x}}}\left[{\left({\parallel {\nabla }_{\widehat{x}}D\left(\widehat{x}\right)\parallel }_2-1\right)}^2\right]$$

(4)

where $\widehat{x}$ represents an interpolated sample between real and generated data, serving as a random interpolation between the two distributions. The term $\parallel {\nabla }_{\widehat{x}}D\left(\widehat{x}\right){\parallel }_2$ represents the gradient norm of the discriminator relative to the interpolated samples, and $P_{\widehat{x}}$ is the distribution of the interpolated samples.

By incorporating the gradient penalty into the training process, WGAN-GP not only accelerates network convergence but also boosts the quality of generated data and stabilizes the entire training process. Therefore, this study employs the WGAN-GP framework to mitigate the limitations of traditional GANs, including poor convergence, gradient explosion, and low-quality generated data.

2.2. Bidirectional Long Short-Term Memory Network (BiLSTM)

The Long Short-Term Memory (LSTM) network is an enhanced variant of the Recurrent Neural Network (RNN), specifically developed to efficiently model sequential data. Although LSTM can handle variable-length time-series data, its conventional unidirectional structure processes information only in a single temporal direction, potentially neglecting critical information from future time steps. To address this limitation, the bidirectional LSTM (BiLSTM) utilizes a bidirectional RNN architecture, enabling the model to capture both past and future information at the same time.

BiLSTM comprises two LSTM layers functioning in opposing directions. The forward LSTM handles input data in a sequential manner following chronological order, whereas the backward LSTM processes data starting from the end of the sequence and moving backward to the start. By combining the outputs from both directions, BiLSTM strengthens the model’s capacity to grasp sequential dependencies, thus enhancing predictive accuracy.

2.3. Gated Recurrent Unit (GRU)

The Gated Recurrent Unit (GRU) is a simplified variant of the LSTM, which reduces complexity by merging the forget, input, and output gates into two functions: the update and reset mechanisms. This simplification not only preserves LSTM’s capability of handling long-term dependencies but also decreases computational complexity, leading to faster training times. As a result, GRU is particularly advantageous for tasks requiring efficient training and real-time prediction.

2.4. Attention Mechanism

The attention mechanism is developed to mimic the human brain’s capability to concentrate on crucial information by allocating varying weights to distinct segments of the input data. By selectively emphasizing important features while minimizing the influence of irrelevant information, the attention mechanism enhances the model’s feature extraction capability, thereby improving prediction accuracy.

In this study, we incorporate an attention-based approach into the WGAN-GP generator to refine feature weighting and improve its predictive capability. The framework consists of three key components: an input layer, an adaptive weighting module, and a final output layer. Within this module, importance scores are computed through linear transformations and activation functions. These scores are then assigned to the input features to produce the final prediction results.

2.5. Variational Autoencoder (VAE)

The Variational Autoencoder (VAE) is a generative model designed to capture a latent representation of data. It comprises two essential components: an encoder that transforms the input into a compact latent space and a decoder that restores the original data from this encoded form. Unlike conventional autoencoders, VAE assumes that the latent variables follow a standard normal distribution, allowing for more flexible data synthesis. The overall loss function of VAE consists of two primary elements: the reconstruction error and the Kullback–Leibler (KL) divergence term.

The KL divergence loss measures the difference between the encoder’s output distribution and the standard normal distribution. For each sample, it is computed as follows:

$${\mathcal{L}}_{\mathrm{K}\mathrm{L}}={\displaystyle \frac{1}{2}}\sum _{i=1}^D\left(\mathrm{e}\mathrm{x}\mathrm{p}\left(\mathrm{l}\mathrm{o}\mathrm{g}\left({\sigma }_i^2\right)\right)+{\mu }_i^2-1-\mathrm{l}\mathrm{o}\mathrm{g}\left({\sigma }_i^2\right)\right)$$

(5)

where ${\mu }_i$ represents the mean of the $i$-th latent variable, ${\sigma }_i^2$ represents the variance of the $i$-th latent variable, and $D$ is the dimensionality of the latent space.

In the VAE model, each initial input sample is depicted as a feature vector $x_i=[x_{i1},x_{i2},\dots ,x_{iL}]$, indicating the count of features in the original sample. After encoding and decoding, the reconstructed output is obtained as ${\widehat{x}}_i=\left[{\widehat{x}}_{i1},{\widehat{x}}_{i2},\dots ,{\widehat{x}}_{iN}\right]$. VAE employs binary cross-entropy (BCE) as the reconstruction loss, which is computed as follows:

$${\mathcal{L}}_{\mathrm{recon}}=\sum _{i=1}^M\mathrm{}\sum _{j=1}^N(x_{ij}\mathrm{l}\mathrm{o}\mathrm{g}\left({\widehat{x}}_{ij}\right)+\left(1-x_{ij}\right)\mathrm{l}\mathrm{o}\mathrm{g}\left(1-{\widehat{x}}_{ij}\right))$$

(6)

where $M$ represents the number of original samples, $N$ denotes the number of reconstructed features, $x_{ij}$ is the $j$-th feature value of the $i$-th sample in the original dataset, and ${\widehat{x}}_{ij}$ is the corresponding reconstructed feature value.

The overall VAE loss function integrates the reconstruction loss and KL divergence in the following manner:

$${\mathcal{L}}_{\mathrm{VAE}}={{\mathcal{L}}_{\mathrm{recon}}+\mathcal{L}}_{\mathrm{K}\mathrm{L}}$$

(7)

This formulation ensures that the learned latent representations maintain meaningful structures while allowing the generation of high-quality synthetic data.

3. Proposed Model (VXWGAN-GP)

In hydrological runoff forecasting, traditional methods often struggle to handle the complex characteristics of nonlinear and non-stationary data. To address these challenges, this study proposes a comprehensive forecasting model, VXWGAN-GP, which integrates Variational Autoencoders (VAEs), Wasserstein Generative Adversarial Networks with Gradient Penalty (WGAN-GP), Convolutional Neural Networks (CNNs), Bidirectional Long Short-Term Memory Networks (BiLSTMs), Gated Recurrent Units (GRUs), and Attention mechanisms. The VAE enhances feature representation by capturing the underlying distribution of the data and generating new features. These generated features are then combined with the original features and fed into the subsequent model to enhance predictive performance. The generator incorporates GRU, BiLSTM, and Attention mechanisms: GRU captures short-term dependencies, BiLSTM captures long-term dependencies, and Attention focuses on key time steps to produce forecasting results. The discriminator, constructed based on CNN, assesses the discrepancies between generated and real data through adversarial training, thereby refining the generator’s forecasting capability.

3.1. Primary Structure of the Improved WGAN-GP-Based Daily Runoff Prediction Model

(1)

Generator Structure

In the VXWGAN-GP model, the generator plays a crucial role in the architecture, with its primary task being to learn the distribution characteristics of the input data and generate predicted data that conforms to this distribution. To improve the accuracy of runoff prediction and effectively capture the intrinsic relationships and key information within time-series data, this study proposes a generator structure that integrates GRU, BiLSTM, and an attention mechanism.

The rationale behind this choice is that GRU, with its streamlined gating mechanism, reduces the number of model parameters, enhances training efficiency, and effectively captures short-term dependencies. BiLSTM, leveraging its bidirectional architecture, simultaneously utilizes past and future contextual information, excelling in handling long-term dependencies and thereby augmenting the model’s comprehension of time-series data. The Attention mechanism further elevates the model’s performance by dynamically weighting the information, enabling the model to focus on the most valuable data points for prediction, thus improving the accuracy and robustness of the forecasts.

Specifically, the generator initially processes the input data through a GRU layer. The GRU is capable of effectively extracting local information and temporal dependencies from sequential data, particularly excelling in capturing short-term dependencies. The output of the GRU layer is then passed to a BiLSTM layer, which processes the data in both forward and backward directions simultaneously, enabling the model to capture long-term dependencies in the sequence, thereby enhancing its ability to model time-series data. To further improve the model’s performance, an attention mechanism is introduced based on the output of the BiLSTM layer. This attention mechanism first applies a linear transformation to the hidden representations output by the bidirectional LSTM and computes attention scores for each time step using a tanh activation function. Subsequently, these scores are normalized using a Softmax function to obtain attention weights. By performing a weighted summation of the BiLSTM outputs, the model generates a context vector, which helps the model focus on the time steps that have a greater impact on the prediction results.

In the implementation, both the GRU layer and the bidirectional LSTM layer have 512 hidden units, and a Dropout layer is used for regularization to prevent overfitting and enhance the model’s robustness. The attention mechanism consists of a linear layer and a context vector computation layer, which are responsible for optimizing the weighted representation of the hidden layer outputs. Finally, the processed hidden representations are progressively mapped through three fully connected layers, with the output dimensions reduced from 512 to 128, then to 64, and ultimately to a single output dimension to generate the prediction results.

This integrated data processing pipeline, which combines the GRU’s ability to extract short-term information, the BiLSTM’s capability to model long-term dependencies, and the attention mechanism’s ability to weight key information, effectively enhances the model’s adaptability to the nonlinearity and non-stationarity of runoff time-series data, thereby significantly improving prediction performance.

(2)

Discriminator Structure

In the VXWGAN model, the discriminator plays a crucial role in evaluating the match between the predicted data generated by the generator and the real data. While traditional WGAN-GP models feature a discriminator composed of three convolutional layers, this study designs a discriminator architecture that integrates a multi-layer convolutional network and fully connected layers to enhance its ability to distinguish whether the input data originates from the real dataset or is generated by the generator.

The choice of Convolutional Neural Network (CNN) as the foundational architecture for the discriminator is due to its effectiveness in extracting local features and temporal dependencies when processing sequential data. The convolutional layers capture local patterns in the data through sliding window operations, thereby enhancing the model’s generalization capability. The rationale for increasing the number of convolutional layers to four is that additional layers enable the extraction of more abstract and higher-level features, allowing for a more comprehensive capture of complex patterns and structures within the data, thus improving the discriminator’s distinguishing ability. The discriminator’s network structure in the VXWGAN-GP model consists of four one-dimensional convolutional layers and three fully connected layers to enhance its discriminative capability.

Specifically, the discriminator’s structure comprises four one-dimensional convolutional layers, with the number of convolutional kernels set to 32, 64, 128, and 256, respectively. Each convolutional layer is followed by a LeakyReLU activation function with a leak coefficient of 0.01 to introduce nonlinearity and prevent the vanishing gradient problem. The output of the convolutional layers is then flattened and converted into a one-dimensional tensor suitable for processing by the fully connected layers. The fully connected layers include three levels, containing 220, 220, and 1 neuron(s), respectively. In the first two fully connected layers, LeakyReLU and ReLU activation functions are employed to increase the network’s nonlinear expressive power. Finally, a real-valued score is generated through the third fully connected layer, which measures whether the input data is from the real dataset or generated by the generator. This structure effectively enhances the discriminator’s role in the generator’s optimization process, aiding the generator in producing more accurate prediction data. The structural designs of both the generator and the discriminator are illustrated in Figure 1.

3.2. Specific Steps of the Daily Runoff Prediction Model Based on the Improved Generative Adversarial Network

The VXWGAN-GP model consists of five main stages, as illustrated in Figure 2.

The detailed procedures for daily runoff prediction using the VXWGAN-GP model are outlined as follows:

(1)

Step 1: Data Loading and Preprocessing. First, daily-scale runoff data and its associated features are acquired, with missing values and outliers removed to ensure data completeness and accuracy. All data are normalized to the range [0, 1] to eliminate the influence of different scales on the model. Subsequently, the dataset is divided into a calibration period (80% of the total data) and a validation period (20% of the total data).

(2)

Step 2: Feature Enhancement Using Variational Autoencoder (VAE). In this step, a VAE is employed for feature enhancement. The encoder part of the VAE maps the input to a multi-dimensional latent space through a multi-layer fully connected network, with each dimension representing a latent variable. The decoder part maps the representations from the latent space back to the input space. The model utilizes the reparameterization trick to approximate a Gaussian distribution, enabling sampling from the latent space. The training objective is to minimize the sum of the reconstruction loss and the KL divergence loss, where the KL divergence term ensures that the distribution of the latent space approximates a standard normal distribution. In each training epoch, the reconstruction loss and KL divergence are computed, and the model parameters are updated through backpropagation. The trained VAE model is then used to enhance the features, generating reconstructed features that are combined with the original features and fed into the forecasting model.

(3)

Step 3: Transforming Time-Series Data Using a Sliding Window Method. A sliding window method is adopted to transform the time-series data into a format suitable for model training. The sliding window size is set to 3, where each input sample includes data from the previous three time steps, and the output corresponds to the target value of the fourth time step.

(4)

Step 4: Constructing the Generator and Discriminator with Adversarial Training. The generator, which integrates GRU, BiLSTM, and an attention mechanism, learns the distribution characteristics of the time-series data and generates predictions for future time steps. The discriminator evaluates the discrepancy between the generated data and the real data through adversarial training, thereby optimizing the generator’s predictive capability. The generator and discriminator are trained alternately, continuously improving prediction accuracy.

(5)

Step 5: Model Prediction and Performance Evaluation. Finally, the trained generator is used to make predictions, and the predicted results are compared with the actual data. By evaluating various performance metrics, the effectiveness and accuracy of the model are validated.

4. Model Evaluation Metrics

To thoroughly evaluate the predictive capability of the proposed model, three metrics are utilized: Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and the Coefficient of Determination (R²). RMSE quantifies the standard deviation of the residuals, indicating how far predictions deviate from actual values. MAE calculates the average absolute difference between predicted and observed data, reflecting the mean prediction error. R² assesses the model’s goodness of fit, illustrating the proportion of variance explained by the predictions.

The formulas for RMSE, MAE, and R² are as follows:

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}$$

(8)

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{n}}\sum _{i=1}^n|y_i-{\widehat{y}}_i|$$

(9)

$${\mathrm{R}}^2=1-{\displaystyle \frac{\sum {\left(y_i-{\widehat{y}}_i\right)}^2}{\sum {\left(y_i-\overline{y}\right)}^2}}$$

(10)

where $y_i$ and ${\widehat{y}}_i$ represent the observed and predicted values, respectively; $\overline{y}$ denotes the mean of observed values; and $n$ is the length of the test set.

5. Case Study

5.1. Study Area and Feature Selection

The Yichang Hydrological Station, located in Yichang City, Hubei Province, is a key hydrological monitoring station in the middle reaches of the Yangtze River. It is responsible for monitoring various hydrological parameters, including water level, discharge, water quality, and riverbed changes. This station integrates data from multiple substations, including Cuntan and Wulong stations. The Cuntan Hydrological Station, situated in Cuntan Subdistrict, Jiangbei District, Chongqing, serves as a crucial observation point in the upper reaches of the Yangtze River. It primarily conducts hydrological measurements, forecasting, and intelligence reporting for the main stream of the Yangtze River above Wushan and its major tributaries. The station collects data from multiple substations, such as Zhutuo and Beibei. The Pingshan Hydrological Station, located in Jinping Town, Pingshan County, Sichuan Province, belongs to the upper Yangtze River basin, specifically, the Jinsha River system. In this study, hydrological data from the Yichang, Cuntan, and Pingshan stations were utilized to evaluate the effectiveness of the proposed integrated framework and predictive methodology. Figure 3 illustrates the basin map of the study area, providing a comprehensive overview of the hydrological and geographical characteristics of the region. The map highlights key features, such as river networks, watershed boundaries, and the locations of hydrological stations.

The dataset for model input was divided into three subsets:

Dataset 1: Runoff data from Yichang Station and its two associated hydrological stations (Cuntan and Wulong), along with meteorological data from Yichang Station. The dataset spans from 1 January 1976 to 31 December 2015 at a daily scale. The training set includes data from 1 January 1976 to 31 December 2007, while the test set covers 1 January 2008 to 31 December 2015.

Dataset 2: Runoff data from Cuntan Station and its two associated hydrological stations (Zhutuo and Beibei), along with meteorological data from Cuntan Station. This dataset also spans from 1 January 1976 to 31 December 2010 at a daily scale. The training set includes data from 1 January 1976 to 31 December 2003, while the test set covers 1 January 2004 to 31 December 2010.

Dataset 3: Runoff data from Pingshan Station and its corresponding meteorological data. The dataset spans from 1 January 1976 to 31 December 2010 at a daily scale. The training set covers 1 January 1976 to 31 December 2003, while the test set spans from 1 January 2004 to 31 December 2010.

For all datasets, the input sequence length was set to 3 days, while the output step was 1 day.

During data preprocessing, anomalies were removed, and missing values were interpolated using a linear method to ensure data integrity and accuracy. A summary table of historical data feature factors is presented in

Table 1. Abbreviations of feature factors.

Symbol	Description	Symbol	Description
YC	Observed runoff at Yichang Station (current day)	YC-DEWP	Dew point temperature at Yichang Station
YC(t − 1)	Observed runoff at Yichang Station (1-day lag)	YC-MXTEMP	Maximum temperature at Yichang Station
YC(t − 2)	Observed runoff at Yichang Station (2-day lag)	YC-MINTEMP	Minimum temperature at Yichang Station
YC(t − 3)	Observed runoff at Yichang Station (3-day lag)	YC-TEMP	Average temperature at Yichang Station
CT	Observed runoff at Cuntan Station (current day)	YC-MXSPD	Maximum wind speed at Yichang Station
CT(t − 1)	Observed runoff at Cuntan Station (1-day lag)	YC-WDSP	Average wind speed at Yichang Station
CT(t − 2)	Observed runoff at Cuntan Station (2-day lag)	YC-PRCP	Precipitation at Yichang Station
CT(t − 3)	Observed runoff at Cuntan Station (3-day lag)	YC-VISIB	Visibility at Yichang Station
WL	Observed runoff at Wulong Station (current day)	CT-DEWP	Dew point temperature at Cuntan Station
WL(t − 1)	Observed runoff at Wulong Station (1-day lag)	CT-MXTEMP	Maximum temperature at Cuntan Station
WL(t − 2)	Observed runoff at Wulong Station (2-day lag)	CT-MINTEMP	Minimum temperature at Cuntan Station
WL(t − 3)	Observed runoff at Wulong Station (3-day lag)	CT-TEMP	Average temperature at Cuntan Station
BB	Observed runoff at Beibei Station (current day)	CT-MXSPD	Maximum wind speed at Cuntan Station
BB(t − 1)	Observed runoff at Beibei Station (1-day lag)	CT-WDSP	Average wind speed at Cuntan Station
BB(t − 2)	Observed runoff at Beibei Station (2-day lag)	CT-PRCP	Precipitation at Cuntan Station
BB(t − 3)	Observed runoff at Beibei Station (3-day lag)	CT-VISIB	Visibility at Cuntan Station
ZT	Observed runoff at Zhutuo Station (current day)	PS-DEWP	Dew point temperature at Pingshan Station
ZT(t − 1)	Observed runoff at Zhutuo Station (1-day lag)	PS-MXTEMP	Maximum temperature at Pingshan Station
ZT(t − 2)	Observed runoff at Zhutuo Station (2-day lag)	PS-MINTEMP	Minimum temperature at Pingshan Station
ZT(t − 3)	Observed runoff at Zhutuo Station (3-day lag)	PS-TEMP	Average temperature at Pingshan Station
PS	Observed runoff at Pingshan Station (current day)	PS-MXSPD	Maximum wind speed at Pingshan Station
PS(t − 1)	Observed runoff at Pingshan Station (1-day lag)	PS-WDSP	Average wind speed at Pingshan Station
PS(t − 2)	Observed runoff at Pingshan Station (2-day lag)	PS-PRCP	Precipitation at Pingshan Station
PS(t − 3)	Observed runoff at Pingshan Station (3-day lag)	PS-VISIB	Visibility at Pingshan Station

. Feature selection was then performed using the Spearman correlation coefficient and mutual information methods. A correlation threshold of 0.40 was applied, retaining only features with a correlation coefficient greater than 0.40 with runoff data. The final optimal feature set was determined, with the mutual information values and Spearman correlation coefficients of each feature illustrated in Figure 4.

For Yichang Station, 15 forecasting factors were selected as inputs, categorized into runoff-related factors and meteorological factors:

• Runoff-related factors: Measured runoff at Yichang Station for the previous 1, 2, and 3 days (YC(t − 1), YC(t − 2), YC(t − 3)); real-time and previous 1-, 2-, and 3-day runoff at Cuntan Station (CT, CT(t − 1), CT(t − 2), CT(t − 3)); and real-time and previous 1-, 2-, and 3-day runoff at Wulong Station (WL, WL(t − 1), WL(t − 2), WL(t − 3)).
• Meteorological factors: Dew point temperature (YC-DEWP), maximum temperature (YC-MXTEMP), minimum temperature (YC-MINTEMP), and average temperature (YC-TEMP) at Yichang Station.

For Cuntan Station, 15 forecasting factors were selected as inputs, also divided into runoff-related factors and meteorological factors:

• Runoff-related factors: Measured runoff at Cuntan Station for the previous 1, 2, and 3 days (CT(t − 1), CT(t − 2), CT(t − 3)); real-time and previous 1-, 2-, and 3-day runoff at Beibei Station (BB, BB(t − 1), BB(t − 2), BB(t − 3)); and real-time and previous 1-, 2-, and 3-day runoff at Zhutuo Station (ZT, ZT(t − 1), ZT(t − 2), ZT(t − 3)).
• Meteorological factors: Dew point temperature (CT-DEWP), maximum temperature (CT-MXTEMP), minimum temperature (CT-MINTEMP), and average temperature (CT-TEMP) at Cuntan Station.

For Pingshan Station, six forecasting factors were selected as inputs, categorized into runoff-related factors and meteorological factors:

• Runoff-related factors: Measured runoff at Pingshan Station for the previous 1, 2, and 3 days (PS(t − 1), PS(t − 2), PS(t − 3)).
• Meteorological factors: Dew point temperature (PS-DEWP), minimum temperature (PS-MINTEMP), and average temperature (PS-TEMP) at Pingshan Station.

These selected factors were used as model inputs to enhance the accuracy of runoff prediction, with their correlation coefficients with runoff at each hydrological station illustrated in the heatmap presented in Figure 5.

5.2. Comparative Experiments and Parameter Settings

To evaluate the effectiveness of the proposed VXWGAN-GP prediction model, this study chooses LSTM, BiLSTM, GRU, WGAN-GP, and XWGAN-GP as benchmark models for comparative analysis. Among them, BiLSTM, GRU, and WGAN-GP serve as fundamental components of VXWGAN-GP and are also designated as baseline models for predictive evaluation.

Specifically, for Yichang and Cuntan stations, VXWGAN-GP employs a VAE encoder to generate 10 additional feature factors, which are then integrated with the original dataset’s 15 predictors to form the final input for forecasting. For Pingshan Station, VXWGAN-GP applies the same approach, generating three additional features and combining them with the original six predictors. To ensure the integrity of the data augmentation process and prevent potential information leakage, the VAE model is exclusively trained on the feature data from the training set. In this study, to maintain the fairness of the experiments, all models are subjected to identical hyperparameter configurations. Additionally, given that LSTM, BiLSTM, GRU, WGAN-GP, XWGAN-GP, and VXWGAN-GP are deep learning models, whose predictive performance can be significantly influenced by weights, leading to potential variability in results across different runs, each of these models is executed 10 times. The average of these runs is then taken as the final prediction result to more accurately reflect the model’s average performance. The specific hyperparameter settings for each model are detailed in

Table 2. Parameter settings of benchmark models.

Model	Symbol	Description	Value
LSTM	h	Number of hidden neurons	512
	η	Fixed learning rate	0.0001
	T	Batch size	128
	Ep	Number of training epochs	100
	O	Optimizer	Adam
BiLSTM	h	Number of hidden neurons	512
	η	Fixed learning rate	0.0001
	T	Batch size	128
	Ep	Number of training epochs	100
	O	Optimizer	Adam
GRU	h (GRU)	Number of hidden neurons (GRU)	512
	h (BiLSTM)	Number of hidden neurons (BiLSTM)	512
	η	Fixed learning rate	0.0001
	T	Batch size	128
	Ep	Number of training epochs	100
	O	Optimizer	Adam
WGAN-GP	h (GRU)	Number of hidden neurons (GRU)	512
	h (BiLSTM)	Number of hidden neurons (BiLSTM)	512
	η	Fixed learning rate	0.0001
	T	Batch size	128
	Ep	Number of training epochs	100
	O	Optimizer	Adam
XWGAN-GP	h (GRU)	Number of hidden neurons (GRU)	512
	h (BiLSTM)	Number of hidden neurons (BiLSTM)	512
	η	Fixed learning rate	0.0001
	T	Batch size	128
	Ep	Number of training epochs	100
	O	Optimizer	Adam
VXWGAN-GP	h (GRU)	Number of hidden neurons (GRU)	512
	h (BiLSTM)	Number of hidden neurons (BiLSTM)	512
	η (VAE)	Fixed learning rate (VAE)	0.0001
	Ep (VAE)	Number of training epochs (VAE)	300
	η	Fixed learning rate	0.0001
	T	Batch size	128
	Ep	Number of training epochs	100
	O	Optimizer	Adam

.

6. Results Analysis and Discussion

6.1. Analysis of Model Evaluation Metrics Calculation Results

Table 3. Comprehensive calculation results of six models on the training sets of each hydrological station.

Model	Hydrological Station	RMSE (m³/s)			MAE (m³/s)			R2
		Max	Mean	Min	Max	Mean	Min	Max	Mean	Min
LSTM	Yichang	1423.124	1398.324	1370.567	836.123	816.128	794.345	0.9806	0.9787	0.9743
BiLSTM		1406.789	1386.712	1362.456	793.234	773.245	755.678	0.9812	0.9798	0.9765
WGAN-GP		1357.345	1337.845	1312.89	759.456	739.562	715.901	0.9823	0.9811	0.9798
GRU		1334.234	1314.239	1289.123	751.987	735.891	718.234	0.9831	0.9817	0.9802
XWGAN-GP		1239.567	1219.567	1196.345	730.234	710.234	698.765	0.983	0.9833	0.9819
VXWGAN-GP		1212.456	1200.123	1188.678	710.987	704.892	692.432	0.9852	0.9846	0.9844
LSTM	Cuntan	1646.789	1606.782	1592.456	768.123	708.123	686.543	0.9681	0.9666	0.9608
BiLSTM		1621.456	1601.456	1578.234	741.567	701.567	679.345	0.9693	0.9679	0.9642
WGAN-GP		1609.234	1589.234	1563.789	707.345	687.345	665.123	0.9702	0.9686	0.9679
GRU		1563.789	1543.789	1518.456	703.678	683.789	661.89	0.9705	0.9689	0.9681
XWGAN-GP		1536.345	1526.345	1501.234	679.234	659.234	636.567	0.9746	0.9731	0.9729
VXWGAN-GP		1518.678	1501.678	1489.901	650.567	640.567	629.345	0.9758	0.9753	0.9746
LSTM	Pingshan	463.234	438.567	421.89	256.123	230.123	218.456	0.9884	0.9859	0.9839
BiLSTM		451.567	431.234	417.678	244.678	224.567	212.345	0.9886	0.9863	0.9842
WGAN-GP		438.789	428.789	415.234	230.89	220.891	208.567	0.9898	0.9876	0.9848
GRU		432.456	422.456	408.901	232.456	218.456	206.123	0.9887	0.9881	0.9867
XWGAN-GP		419.123	414.123	400.567	224.345	214.345	198.89	0.9902	0.9887	0.9882
VXWGAN-GP		408.678	403.678	396.234	206.234	200.123	192.678	0.9907	0.9895	0.989

and

Table 4. Comprehensive calculation results of six models on the test sets of each hydrological station.

Model	Hydrological Station	RMSE (m³/s)			MAE (m³/s)			R2
		Max	Mean	Min	Max	Mean	Min	Max	Mean	Min
LSTM	Yichang	1455.789	1425.123	1395.456	980.567	953.124	925.432	0.9722	0.9698	0.9654
BiLSTM		1447.123	1417.345	1387.789	947.234	908.567	892.345	0.9725	0.9708	0.9676
WGAN-GP		1430.789	1400.567	1370.456	917.345	884.123	859.789	0.9735	0.9715	0.9703
GRU		1398.234	1367.891	1337.456	900.123	878.567	848.234	0.9747	0.9728	0.9719
XWGAN-GP		1312.345	1284.123	1256.789	844.567	824.123	803.456	0.9785	0.9767	0.9762
VXWGAN-GP		1243.789	1226.567	1210.456	813.234	810.567	789.456	0.9804	0.9798	0.9791
LSTM	Cuntan	1675.678	1641.234	1608.345	790.456	732.123	695.789	0.9621	0.9608	0.9544
BiLSTM		1668.123	1633.456	1598.789	748.234	710.567	678.901	0.9624	0.9612	0.9572
WGAN-GP		1650.345	1614.789	1580.234	742.567	724.123	685.432	0.9632	0.9621	0.9609
GRU		1605.789	1573.345	1541.234	722.345	694.567	659.876	0.964	0.9632	0.9625
XWGAN-GP		1575.678	1563.123	1530.456	704.789	682.123	652.234	0.9662	0.9655	0.9648
VXWGAN-GP		1558.234	1546.567	1524.789	679.123	676.567	649.567	0.9674	0.9668	0.9629
LSTM	Pingshan	470.567	455.123	439.789	285.432	251.123	237.901	0.9851	0.9833	0.9805
BiLSTM		461.234	446.567	432.345	270.789	246.567	232.678	0.9853	0.9839	0.9808
WGAN-GP		445.123	431.789	416.456	263.567	247.567	236.345	0.9871	0.9845	0.9825
GRU		444.567	429.345	414.789	258.234	241.567	225.789	0.9865	0.9849	0.9843
XWGAN-GP		428.123	422.567	408.789	245.678	230.567	218.456	0.988	0.9872	0.9855
VXWGAN-GP		412.345	407.891	393.456	226.89	222.567	209.345	0.9894	0.9889	0.9873

present the evaluation metrics for the six models on the training and test sets at Yichang, Cuntan, and Pingshan stations. Figure 6 provides radar charts visualizing these evaluation metrics across both datasets for each station.

Based on Table 3 and Table 4 and Figure 6, the predictive capabilities of different models can be more accurately and quantitatively evaluated.

At Yichang Station, the VXWGAN-GP model exhibited the best performance in the training set, achieving a coefficient of determination (R²) of 0.9846, with RMSE and MAE values of 1200.123 and 704.892, respectively, the lowest among all compared models. In contrast, the LSTM model demonstrated weaker performance, with an R² of 0.9787 and RMSE and MAE values of 1398.324 and 816.128, respectively, indicating higher prediction errors. Compared to the LSTM model, VXWGAN-GP improved RMSE, MAE, and R² by 14.18%, 13.63%, and 0.59%, respectively, demonstrating its strong applicability. In the test set, VXWGAN-GP continued to exhibit outstanding predictive and generalization capabilities, achieving an R² of 0.9798 and RMSE and MAE values of 1226.567 and 810.567, respectively, maintaining the lowest errors among all models. Compared to LSTM, VXWGAN-GP improved RMSE, MAE, and R² by 13.96%, 14.96%, and 1.00%, respectively. These results further validate the model’s advantages in enhancing forecasting accuracy and generalization ability.

At Cuntan Station, VXWGAN-GP also demonstrated superior performance. In the training set, it achieved an R² of 0.9753, with RMSE and MAE values of 1501.678 and 640.567, respectively, significantly outperforming the compared models. In contrast, the LSTM model had an R² of 0.9666, with RMSE and MAE values of 1606.782 and 708.123, respectively, indicating larger prediction errors. Compared to LSTM, VXWGAN-GP improved RMSE, MAE, and R² by 6.54%, 9.54%, and 0.87%, respectively. In the test set, VXWGAN-GP achieved an R² of 0.9668, with RMSE and MAE values of 1546.567 and 676.567, maintaining the lowest prediction errors. Compared to LSTM, VXWGAN-GP improved RMSE, MAE, and R² by 5.76%, 7.58%, and 0.60%, respectively, further confirming the model’s stability and robustness in predicting complex hydrological time series.

At Pingshan Station, VXWGAN-GP again outperformed all other models. In the training set, it achieved an R² of 0.9895, with RMSE and MAE values of 403.678 and 200.123, respectively, while the LSTM model had an R² of 0.9859, with RMSE and MAE values of 438.567 and 230.123, respectively, indicating significantly higher errors. Compared to LSTM, VXWGAN-GP improved RMSE, MAE, and R² by 7.94%, 13.04%, and 0.36%, respectively. In the test set, VXWGAN-GP maintained its superior performance, achieving an R² of 0.9889, with RMSE and MAE values of 407.891 and 222.567, respectively. Compared to LSTM, these three metrics improved by 10.38%, 11.37%, and 0.56%, respectively. These results further confirm the effectiveness of VXWGAN-GP in improving prediction accuracy and generalization ability.

Furthermore, to validate the impact of using VAE for feature enhancement on prediction results, a comparative analysis was conducted between VXWGAN-GP and XWGAN-GP in terms of predictive performance. At Yichang Station, compared to XWGAN-GP, VXWGAN-GP increased R² by 0.0013, reduced MAE by 5.342, and decreased RMSE by 19.444. At Cuntan Station, R² increased by 0.0022, while MAE and RMSE decreased by 18.667 and 24.667, respectively. At Pingshan Station, R² increased by 0.0008, with reductions in MAE and RMSE of 14.222 and 10.445, respectively. In the test set, VXWGAN-GP continued to outperform XWGAN-GP. At Yichang Station, R² increased by 0.0031, while MAE and RMSE decreased by 13.556 and 57.556, respectively. At Cuntan Station, R² increased by 0.0013, with reductions in MAE and RMSE of 5.556 and 16.556, respectively. At Pingshan Station, R² increased by 0.0017, while MAE and RMSE decreased by 8.000 and 14.676, respectively. These findings further substantiate the efficacy of feature enhancement using VAE.

6.2. Analysis of Model Reliability and Applicability

This study conducts a detailed analysis and discussion of the prediction outcomes obtained from six models: LSTM, BiLSTM, GRU, WGAN-GP, XWGAN-GP, and VXWGAN-GP. Each model is trained using historical runoff data and then employed to predict daily runoff for three hydrological stations: Yichang (from 1 January 2008 to 31 December 2015), Cuntan (from 1 January 2004 to 31 December 2010), and Pingshan (from 1 January 2004 to 31 December 2010).

Figure 7 illustrates the point-line plots of the forecast results for both the training and testing sets across the six models at Yichang, Cuntan, and Pingshan hydrological stations.

To provide a clearer comparison of model performance in runoff forecasting, this study selects representative years for analysis. Specifically, for Yichang Station, the selected years include a wet year (2012), a normal year (2010), and a dry year (2011); for Cuntan Station, a wet year (2004), a normal year (2006), and a dry year (2005); and for Pingshan Station, a wet year (2005), a normal year (2009), and a dry year (2006). The forecast results for these representative years at the three stations are presented in Figure 8, offering a more comprehensive evaluation of the models’ predictive performance.

As shown in the point-line plots depicted in Figure 7, the predictive performance of various models exhibits substantial differences. The LSTM and BiLSTM models exhibit substantial deviations between predicted and actual values, particularly in capturing peak and valley runoff values. Among all individual models, WGAN-GP demonstrates improved predictive accuracy compared to LSTM and BiLSTM but still underperforms relative to GRU.

As depicted in Figure 8, under three different hydrological scenarios, the prediction curves generated by the proposed model closely match the observed runoff curves at Yichang, Cuntan, and Pingshan stations. The VXWGAN-GP model outperforms all other models, demonstrating superior predictive capability. By integrating a Variational Autoencoder (VAE) for feature augmentation, VXWGAN-GP demonstrates a notable enhancement in prediction accuracy over XWGAN-GP.

Notably, all models achieve higher performance on the training set than on the test set. This disparity may result from shifts in data distribution between the two sets, potentially affected by extreme climate events and human activities. Under such evolving conditions, model stability and reliability become particularly critical.

Figure 9a, Figure 9b, and Figure 9c, respectively, display the scatter plots of daily runoff forecasting results for each model at Yichang, Cuntan, and Pingshan Hydrological Stations, intuitively reflecting the degree of fit between the model predictions and the measured values. Ideally, if the model predictions were perfectly accurate, all the scatter points would strictly distribute along the 45° reference line of the measured values. Therefore, the degree of scatter, the magnitude of deviation, and the distribution trend of the points can be used to measure the prediction accuracy and stability of the models.

From the scatter plots, it can be seen that the prediction results of VXWGAN-GP are closest to the 45° reference line, indicating the highest overall fit and the best match between predicted and measured values. Moreover, the scatter points of this model are the most concentrated, suggesting good stability across different flow ranges, with the ability to accurately predict runoff changes whether the flow is large or small. The prediction performance of XWGAN-GP ranks second, with most of its scatter points distributed near the 45° reference line. However, compared with VXWGAN-GP, there is a slight dispersion, especially under high-flow conditions, where some deviations still exist. Nevertheless, overall, XWGAN-GP exhibits better fitting effects than traditional LSTM and BiLSTM models. For the traditional LSTM and BiLSTM models, the scatter points are more dispersed, particularly under high-flow conditions, where their prediction capabilities are relatively weaker. The prediction results of GRU and WGAN-GP show improvements compared to LSTM and BiLSTM, with scatter points closer to the 45° reference line, although some deviations remain, especially under high-flow conditions, where prediction errors are still relatively noticeable.

Overall, VXWGAN-GP demonstrates the best performance in the scatter plots across all stations, indicating not only superior overall trend fitting compared to other models but also stronger adaptability under extreme flow conditions. XWGAN-GP has the second-best fitting effect but still shows some errors under high-flow conditions. The scatter points of traditional LSTM, BiLSTM, and GRU models are more dispersed, indicating insufficient adaptability to highly nonlinear and highly fluctuating hydrological time series. This further validates the effectiveness of VXWGAN-GP, which integrates VAE feature generation and WGAN-GP optimization strategies to more accurately describe the runoff process and improve the accuracy and stability of runoff forecasting.

In summary, the VXWGAN-GP model achieved excellent results in runoff forecasting at the Yichang, Cuntan, and Pingshan Hydrological Stations, demonstrating both precision and robustness. The analysis above confirms that the proposed model surpasses other approaches in runoff prediction tasks across these stations, highlighting its effectiveness in diverse hydrological conditions. By integrating WGAN-GP, CNN, BiLSTM, GRU, VAE, and attention mechanisms, this daily runoff forecasting model effectively enhances the predictive capability of complex hydrological time series, significantly improving both the accuracy and reliability of runoff forecasts. These advancements contribute to more precise and reliable predictions for practical applications, thereby supporting sustainable water resource management, flood mitigation, and ecological conservation efforts.

However, several potential sources of error and uncertainty remain in the experimental setup, which could influence the model’s predictive performance. Firstly, the quality of input data plays a crucial role in model training. Despite the preprocessing steps applied, such as outlier removal and normalization, measurement errors, data imputation methods, and inherent data randomness may still affect the final prediction results. Secondly, the choice of hyperparameters significantly impacts prediction accuracy. Different combinations of hyperparameters can lead to variations in outcomes. Moreover, hydrological processes are highly nonlinear and uncertain, and the input features utilized in this study may not fully encompass all the critical influencing factors, thereby introducing some level of prediction error. Future research could focus on incorporating additional environmental features, optimizing data preprocessing methods, and adjusting model structures to further enhance the robustness and predictive accuracy of the model, and the effectiveness in long-term sustainable water management.

7. Conclusions

This research introduces a daily runoff prediction approach utilizing the VXWGAN-GP model. By preprocessing data and integrating a Variational Autoencoder (VAE) for feature enhancement, the model effectively captures complex data structures. The WGAN-GP framework boosts the model’s adaptability to runoff data and enhances predictive accuracy via refined adversarial training. The CNN further stabilizes the adversarial training process, enhancing predictive performance. The BiLSTM and GRU effectively capture both long- and short-term dependencies in runoff data, strengthening the model’s ability to represent dynamic time-series patterns and improving overall prediction accuracy. Additionally, the attention mechanism enhances the model’s focus on crucial time steps by assigning higher weights to key input sequences, further improving its performance in handling complex temporal dependencies.

To evaluate the performance of the proposed model, several benchmark models—including LSTM, BiLSTM, GRU, WGAN-GP, and XWGAN-GP—were selected for comparison. The key findings of this study are summarized as follows:

(1)

Superior predictive performance: Through comparative analysis with benchmark models, the VXWGAN-GP model demonstrated superior performance across all evaluation metrics at the Yichang, Cuntan, and Pingshan stations. Its scatter plots exhibited a better overall trend fit than other models. Under three distinct hydrological conditions, the predicted runoff curves closely aligned with observed values, further confirming that the proposed model, based on an improved generative adversarial network, effectively enhances the accuracy and stability of hydrological runoff forecasting.

(2)

Effectiveness of VAE-based feature enhancement: This study validates the effectiveness and reliability of the VXWGAN-GP model, which integrates VAE for feature enhancement in daily-scale runoff forecasting. Experimental results indicate that, compared to XWGAN-GP, the proposed model achieves an R² improvement of 0.0031 at the Yichang station, with MAE and RMSE reductions of 13.556 and 57.556, respectively. At the Cuntan station, R² increases by 0.0013, with MAE and RMSE reductions of 5.556 and 16.556, respectively. Similarly, at the Pingshan station, R² improves by 0.0017, while MAE and RMSE decrease by 8.000 and 14.676, respectively.

(3)

Future research directions: Although the VXWGAN-GP model demonstrates strong accuracy and generalization ability in runoff forecasting, its complex architecture increases the computational cost. Future research could explore lightweight deep learning models or leverage techniques such as knowledge distillation to reduce the model complexity. By optimizing the model structure while maintaining predictive accuracy, computational efficiency can be further improved.