The Lugeon Test: Methodology, Interpretation, and Applications in Geotechnical Engineering

Urban flooding presents a critical natural hazard globally, intensified by factors such as climate change, rapid urbanization, and aging infrastructure. Traditional flood prediction systems, primarily relying on physically-based one-dimensional (1D) and two-dimensional (2D) hydrodynamic models, are valuable for design and planning but often struggle with the demands of real-time forecasting in dynamic urban environments. Recent advances in machine learning (ML) and data-driven modeling have paved the way for hybrid modeling systems, which integrate ML with traditional hydrodynamic models to enhance urban flood risk prediction with increased speed, accuracy, and adaptability.

Limitations of Traditional Hydrodynamic Models

Conventional hydrodynamic models simulate water movement across urban surfaces and drainage systems using physical laws, such as the Saint-Venant equations. These models are instrumental in predicting flood wave propagation, estimating water levels and velocities, and assessing infrastructure impacts. However, their application in time-sensitive scenarios faces several notable limitations:

• Computational Cost: High-resolution simulations across complex urban grids are computationally intensive, often requiring hours to days, making them unsuitable for real-time operations.
• Calibration Challenges: Achieving accurate model calibration necessitates extensive field data, which is frequently unavailable or inconsistent in many urban areas.
• Simplified Assumptions: Models often rely on simplifying assumptions regarding boundary conditions, roughness coefficients, or pipe network interactions, which can introduce significant uncertainties and limit their ability to capture complex, small-scale urban features.

The Rise of Machine Learning in Flood Forecasting

Machine learning models offer a data-driven approach by learning patterns from historical datasets, sensor data, and remote sensing inputs. Models such as Artificial Neural Networks (ANNs), Support Vector Machines (SVMs), and Random Forests (RFs) are highly advantageous due to their speed, adaptability, and capacity to handle nonlinear relationships within data. For instance, ANNs are often favored for their ability to work with large datasets, while SVMs are adept at handling small samples and nonlinear problems.

However, ML models alone have their own limitations:

• They often lack physical interpretability.
• They may fail when extrapolating beyond their trained data range.
• Their performance is highly dependent on the quality and quantity of training data.

This is precisely where hybrid models emerge as a powerful solution, leveraging the strengths of both physics-based and data-driven approaches.

The Hybrid Approach: Integrating Physics with Data

Hybrid hydrodynamic-ML models are integrated systems where a physical model and a machine learning model are coupled to enhance urban flood prediction. The core idea is to combine the physical realism of hydrodynamic models with the computational efficiency and pattern recognition capabilities of ML. This integration can take several forms:

• Pre-Processing Hybridization: ML models can improve input data by, for example, predicting rainfall-runoff transformations or adjusting roughness parameters for the hydrodynamic model.
• Parallel Modeling: Both ML and hydrodynamic models can operate simultaneously, with ML refining or complementing the outputs of the physical model.
• Post-Processing Hybridization: ML models are used to correct or downscale the outputs of hydrodynamic models, particularly to achieve finer spatial or temporal resolutions.
• Surrogate Modeling: ML models can replace computationally intensive parts of hydrodynamic simulations, significantly reducing processing times while maintaining reasonable accuracy. This often involves simulating multiple flood scenarios with a hydrodynamic model and then using these outputs as training data for ML algorithms to learn the relationship between inputs and flood outcomes.

Key Benefits of Hybrid Hydrodynamic-ML Models

Hybrid models have consistently demonstrated superior performance compared to standalone hydrodynamic or ML models.

1. Faster Computation: Once trained, ML models can generate predictions in seconds, making them ideal for real-time flood forecasting and early warning systems, a significant improvement over the hours or days required for traditional hydrodynamic simulations.
2. Improved Accuracy: Hybrid models effectively correct biases and structural errors found in physical models, especially in complex urban environments with intricate drainage patterns. Studies show that they can predict flood hazards with lower root mean square error (RMSE) and accurately forecast a higher proportion of flood events.
3. Adaptability and Robustness in Data-Scarce Environments: ML models can adapt more easily to changing urban landscapes and weather patterns than static physical models. Furthermore, they can be trained using synthetic data generated by hydrodynamic simulations, reducing reliance on extensive historical flood observations, which are often scarce. This makes them particularly valuable in regions with limited monitoring infrastructure.
4. Enhanced Spatial and Temporal Resolution: Hybrid models can be trained to predict flood depth and extent at fine spatial and temporal scales, capturing localized variations in urban flood risk and assimilating a wide range of real-time input data.
5. Handling Compound Flooding Events: Urban floods frequently result from multiple interacting drivers, such as heavy rainfall, riverine flooding, storm surges, and tidal effects. Hybrid models can integrate these diverse inputs, effectively capturing the complexities of compound flooding scenarios that traditional models may struggle with.
6. Enhanced Visualization: Outputs from ML-enhanced models support real-time 3D flood mapping and augmented reality overlays, providing critical information for city planners and emergency responders.

Technical Innovations in Hybrid Modeling

Advancements in hybrid modeling also involve sophisticated technical innovations:

• Feature Selection and Data Preprocessing: Techniques like variational mode decomposition (VMD) and wavelet analysis are used to preprocess and denoise hydrological time series, improving the ML model’s ability to learn from noisy and non-stationary data.
• Model Fusion: Some hybrid frameworks use ML-generated forecasts as synthetic observations, which are then assimilated into hydrodynamic models, maintaining physical consistency while leveraging ML’s predictive power.
• Metaheuristic Optimization: Algorithms such as the Grey Wolf Optimizer (GWO) and Bat Optimizer are employed to tune ML model parameters, further enhancing flood prediction performance.

Real-World Applications and Case Studies

Numerous studies and urban implementations have demonstrated the effectiveness of hybrid models:

• In Jakarta, integrating hybrid models reduced simulation times by 70% and improved flood extent predictions by 20% compared to standalone hydrodynamic models.
• Cities like Seoul and Rotterdam utilize ML models trained on historical flood events for rapid flood extent predictions, which are then refined by hydrodynamic simulations.
• In Pontianak, Indonesia, a Random Forest-based hybrid approach successfully predicted 10 out of 17 compound flooding events with an RMSE of 0.11 m, outperforming other ML models.
• For Amol, Iran, hybrid models achieved high accuracy (AUC > 0.97) in mapping urban flood susceptibility, aiding emergency response and resilience planning.
• Hybrid data assimilation in tidal estuary modeling has reduced prediction errors by over 40% compared to baseline numerical models for short-term flood forecasting.

Challenges and Future Directions

Despite their significant promise, hybrid models face ongoing challenges:

• Data Quality and Availability: The performance of ML components is inherently limited by the quality and quantity of training data, with inaccuracies in input forecasts potentially propagating through the model.
• Model Interpretability: Many ML techniques operate as "black boxes," making it challenging for engineers and policymakers to fully trust their outputs or understand the underlying physical reasons for predictions.
• Integration Complexity: Coupling ML with existing or legacy hydrodynamic models requires interdisciplinary expertise and robust computational frameworks.

Future research is focused on addressing these challenges and further advancing the field:

• Physics-Informed Neural Networks (PINNs) that directly integrate physical laws into ML architectures.
• Edge Computing and IoT sensor networks for decentralized, real-time flood prediction capabilities.
• Explainable AI (XAI) methods to enhance model transparency and promote regulatory acceptance.
• Incorporating diverse indicators like land use changes and social vulnerability, adapting to climate change impacts such as sea-level rise, and reducing uncertainty through ensemble modeling and probabilistic forecasting.

Conclusion

The integration of hydrodynamic and machine learning models represents a transformative leap in flood risk prediction. Hybrid approaches effectively overcome the limitations of standalone systems by leveraging the structural integrity of physics-based simulations and the adaptability and speed of data-driven machine learning. As urban areas continue to expand and face escalating climate risks, these models provide the predictive power and operational speed essential for resilient city planning and effective real-time disaster response, becoming a critical tool in the ongoing effort to combat urban flooding.