Accurate flood forecasting is crucial for disaster preparedness, but traditional models often struggle with the complexity and variability of extreme flood events, particularly due to a lack of sufficient data on these rare occurrences. This research addresses this data scarcity challenge by proposing a novel method that leverages the power of Generative Adversarial Networks (GANs) to generate synthetic flood event data. While numerical and hydrological models offer a physically-based approach, they are computationally expensive and require complex calibration. GANs, on the other hand, offer a data-driven alternative, capable of learning the underlying data distribution and generating synthetic time series that capture temporal dynamics and patterns. Existing GAN architectures like SINGAN, TSGAN, TimeGAN, and RTSGAN have shown promise in generating various time-series data, but this paper focuses on enhancing TimeGAN by incorporating physical constraints to improve the realism and physical consistency of the generated synthetic data for flood forecasting applications. The aim is to improve the accuracy and reliability of flood forecasting and risk assessment by augmenting real-world datasets with physically plausible synthetic data, thereby enhancing model robustness in predicting extreme flood events.

The paper reviews existing approaches to synthetic flood event generation, contrasting the strengths and weaknesses of numerical/hydrological models and GAN-based methods. Numerical/hydrological models, while physically interpretable, are computationally intensive and require complex calibration. GANs offer a data-driven approach that learns the temporal dependencies and patterns in historical data. The authors discuss various GAN architectures relevant to time-series data generation, such as SINGAN, TSGAN, TimeGAN, and RTSGAN, highlighting their applications in different domains. They note the particular suitability of TimeGAN and RTSGAN for flood forecasting due to their ability to generate realistic synthetic time series that closely mimic real flood events. The review also touches upon existing research using GANs for flood forecasting, specifically mentioning studies that have explored the application of TimeGAN and its impact on improving prediction models in different river basins. Finally, the authors emphasize the need for incorporating domain-specific knowledge and constraints into GAN models to further enhance the quality and realism of the generated synthetic data, particularly for extreme flood events.

The study utilizes a modified TimeGAN, termed MC-TSGAN (Mass Conservative Time-Series GAN), to generate synthetic extreme flood events. The key innovation lies in incorporating mass conservation, energy balance, and hydraulic principles into the GAN model through regularization terms within the loss function and by modifying the LSTM architecture used in the generator and discriminator. This ensures that the synthetic data adhere to fundamental hydrological principles. The methodology includes: 1. **Data Collection and Spatial Data Integration:** Historical flood data (river flow rates, precipitation, water levels) from multiple monitoring sites in the Ahrtal region of Germany, along with precipitation forecasts from ECMWF, soil type information, and water level measurements, are collected and integrated. Preprocessing involves normalization and segmentation of the time-series data. 2. **MC-TSGAN Training:** The MC-TSGAN model is trained on the preprocessed data. The model architecture comprises a generator (using modified mass conservative LSTMs), a discriminator, and an embedding network. The mass conservation constraint is enforced in two ways: (1) by modifying the LSTM architecture to normalize activation functions in the input and forget gates, and to account for the output mass in the output gate; and (2) adding a regularization term to the loss function penalizing deviations from mass conservation. Similarly, energy balance and hydraulic principles (e.g., Manning's equation) are also incorporated through additional regularization terms. 3. **Data Augmentation:** Synthetic flood events generated by MC-TSGAN are combined with the original historical data to create an augmented dataset. 4. **Flood Forecast Model Training:** An encoder-decoder LSTM-based model (previously detailed in [18]) is trained on both the original and augmented datasets. The model uses historical flood events, rainfall data, soil moisture levels, catchment characteristics, and future rainfall forecasts as input to generate probabilistic flood forecasts. 5. **Evaluation:** The evaluation comprises two parts: (1) evaluation of the MC-TSGAN's data generation process, using PCA, t-SNE, and t-statistics to analyze the generated data's distribution and compare it to the original data; and (2) evaluation of the forecasting model's performance using NSE, KGE, CRPS, MPIW, and PICP metrics. Bayesian optimization is used to tune the hyperparameters of the MC-TSGAN model.

The MC-TSGAN model generated synthetic flood events that closely resembled real flood data, as evidenced by the PCA and t-SNE visualizations showing high alignment between real and synthetic data points. The t-statistic test, while not showing a statistically significant difference between the means of the generated and original data at the 0.05 level, did reveal a lower discriminative score for MC-TSGAN (0.0490) compared to TimeGAN (0.102) and RTSGAN (0.054), indicating better diversity in generated sequences. The flood forecasting model trained on the augmented dataset (original data + MC-TSGAN generated data) significantly outperformed the model trained on the original data alone, achieving higher NSE and KGE scores (NSE = 0.838 and KGE = 0.908 versus NSE = 0.829 and KGE = 0.90 for the 6th-hour-ahead prediction). This improvement in accuracy (9.8% increase in NSE) is especially notable for longer forecast horizons. The probabilistic forecasting model trained on the augmented dataset also showed a reduced MPIW, indicating narrower prediction intervals, although this came at the cost of a slightly lower PICP. The results suggest that MC-TSGAN effectively captures the temporal and spatial dependencies in the data, leading to improved flood forecasting accuracy, especially for multi-step ahead predictions. The comparison between MC-TSGAN, TimeGAN, and RTSGAN demonstrated the superiority of the MC-TSGAN model in terms of both discriminative and predictive scores.

The findings demonstrate the effectiveness of MC-TSGAN in generating realistic and diverse synthetic flood events, which significantly enhance the accuracy and reliability of probabilistic flood forecasting models, especially for multi-step ahead predictions. The incorporation of physical constraints (mass conservation, energy balance, hydraulic principles) is crucial in improving the quality and physical plausibility of the synthetic data, leading to better model performance. The improved performance metrics (NSE, KGE, CRPS, MPIW) suggest that augmenting real-world data with synthetic data generated by MC-TSGAN can lead to more accurate and reliable flood forecasts. The lower discriminative scores of MC-TSGAN indicate greater diversity in the generated sequences compared to baseline models, suggesting its ability to produce a wider range of realistic flood scenarios. However, it is crucial to acknowledge the limitations of relying solely on data-driven methods, which may struggle to represent extreme or unforeseen events that deviate significantly from past patterns. The study's success in the Ahrtal region might not generalize to all regions with different hydro-climatic characteristics. Further research should explore advanced techniques for capturing spatial-temporal correlations and expanding the model's ability to address a wider range of flood conditions.

This study successfully demonstrates the effectiveness of using MC-TSGAN, a modified TimeGAN incorporating physical constraints, for generating synthetic flood data to improve flood forecasting models. The augmented model showed significantly improved prediction accuracy (higher NSE and KGE scores) and more precise prediction intervals (lower MPIW), although with a slight decrease in PICP. Future research should focus on improving the model's ability to handle unprecedented events, exploring advanced techniques to capture spatial-temporal correlations and conducting more extensive validation studies across diverse hydro-climatic regions. The integration of MC-TSGAN generated data into operational flood forecasting systems offers promising potential for enhancing flood risk management and disaster preparedness.

The study acknowledges limitations associated with data-based models. The synthetic data generated by MC-TSGAN, while effective, may not fully capture the true variability and complexity of extreme flood events, particularly those that significantly deviate from historical patterns. The interpretability of the synthetic data is limited, making it challenging to understand the underlying physical processes. The quality and generalizability of the model depend on the size and representativeness of the training dataset. Finally, the observed improvement in prediction accuracy might be specific to the Ahrtal region and may not generalize to other regions with different hydro-climatic characteristics.