Shallow water equations (SWEs) are the backbone of most hydrodynamics models for flood prediction, river engineering, and many other water resources applications. The estimation of flow resistance, i.e., the Manning's roughness coefficient $n$, is crucial for ensuring model accuracy, and has been previously determined using empirical formulas or tables. To better account for temporal and spatial variability in channel roughness, inverse modeling of $n$ using observed flow data is more reliable and adaptable; however, it is challenging when using traditional SWE solvers. Based on the concept of universal differential equation (UDE), which combines physics-based differential equations with neural networks (NNs), we developed a universal SWEs (USWEs) solver, Hydrograd, for hybrid hydrodynamics modeling. It can do accurate forward simulations, support automatic differentiation (AD) for gradient-based sensitivity analysis and parameter inversion, and perform scientific machine learning for physics discovery. In this work, we first validated the accuracy of its forward modeling, then applied a real-world case to demonstrate the ability of USWEs to capture model sensitivity (gradients) and perform inverse modeling of Manning's $n$. Furthermore, we used a NN to learn a universal relationship between $n$, hydraulic parameters, and flow in a real river channel. Unlike inverse modeling using surrogate models, Hydrograd uses a two-dimensional SWEs solver as its physics backbone, which eliminates the need for data-intensive pretraining and resolves the generalization problem when applied to out-of-sample scenarios. This differentiable modeling approach, with seamless integration with NNs, provides a new pathway for solving complex inverse problems and discovering new physics in hydrodynamics.

Due to climate change the frequency and intensity of extreme rainfall events, which contribute to urban flooding, are expected to increase in many places. These floods can damage transport infrastructure and disrupt mobility, highlighting the need for cities to adapt to escalating risks. Reinforcement learning (RL) serves as a powerful tool for uncovering optimal adaptation strategies, determining how and where to deploy adaptation measures effectively, even under significant uncertainty. In this study, we leverage RL to identify the most effective timing and locations for implementing measures, aiming to reduce both direct and indirect impacts of flooding. Our framework integrates climate change projections of future rainfall events and floods, models city-wide motorized trips, and quantifies direct and indirect impacts on infrastructure and mobility. Preliminary results suggest that our RL-based approach can significantly enhance decision-making by prioritizing interventions in specific urban areas and identifying the optimal periods for their implementation. Our framework is publicly available: https://github.com/

Flood inundation forecast provides critical information for emergency planning before and during flood events. Real time flood inundation forecast tools are still lacking. High-resolution hydrodynamic modeling has become more accessible in recent years, however, predicting flood extents at the street and building levels in real-time is still computationally demanding. Here we present a hybrid process-based and data-driven machine learning (ML) approach for flood extent and inundation depth prediction. We used the Fourier neural operator (FNO), a highly efficient ML method, for surrogate modeling. The FNO model is demonstrated over an urban area in Houston (Texas, U.S.) by training using simulated water depths (in 15-min intervals) from six historical storm events and then tested over two holdout events. Results show FNO outperforms the baseline U-Net model. It maintains high predictability at all lead times tested (up to 3 hrs) and performs well when applying to new sites, suggesting strong generalization skill.

Low-lying coastal cities, exemplified by Norfolk, Virginia, face the challenge of street flooding caused by rainfall and tides, which strain transportation and sewer systems and can lead to property damage. While high-fidelity, physics-based simulations provide accurate predictions of urban pluvial flooding, their computational complexity renders them unsuitable for real-time applications. Using data from Norfolk rainfall events between 2016 and 2018, this study compares the performance of a previous surrogate model based on a random forest algorithm with two deep learning models: Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU). This investigation underscores the importance of using a model architecture that supports the communication of prediction uncertainty and the effective integration of relevant, multi-modal features.

Deep learning models have become increasingly popular for flood prediction due to their superior accuracy and efficiency compared to traditional methods. However, current machine learning methods often rely on separate spatial or temporal feature analysis and have limitations on the types, number, and dimensions of input data. This study presented a CNN-RNN hybrid feature fusion modelling approach for urban flood prediction, which integrated the strengths of CNNs in processing spatial features and RNNs in analyzing different dimensions of time sequences. This approach allowed for both static and dynamic flood predictions. Bayesian optimization was applied to identify the seven most influential flood-driven factors and determine the best combination strategy. By combining four CNNs (FCN, UNet, SegNet, DeepLabv3+) and three RNNs (LSTM, BiLSTM, GRU), the optimal hybrid model was identified as LSTM-DeepLabv3+. This model achieved the highest prediction accuracy (MAE, RMSE, NSE, and KGE were 0.007, 0.025, 0.973 and 0.755, respectively) under various rainfall input conditions. Additionally, the processing speed was significantly improved, with an inference time of 1.158s (approximately 1/125 of the traditional computation time) compared to the physically-based models.

In this technical report we compare different deep learning models for prediction of water depth rasters at high spatial resolution. Efficient, accurate, and fast methods for water depth prediction are nowadays important as urban floods are increasing due to higher rainfall intensity caused by climate change, expansion of cities and changes in land use. While hydrodynamic models models can provide reliable forecasts by simulating water depth at every location of a catchment, they also have a high computational burden which jeopardizes their application to real-time prediction in large urban areas at high spatial resolution. Here, we propose to address this issue by using data-driven techniques. Specifically, we evaluate deep learning models which are trained to reproduce the data simulated by the CADDIES cellular-automata flood model, providing flood forecasts that can occur at different future time horizons. The advantage of using such models is that they can learn the underlying physical phenomena a priori, preventing manual parameter setting and computational burden. We perform experiments on a dataset consisting of two catchments areas within Switzerland with 18 simpler, short rainfall patterns and 4 long, more complex ones. Our results show that the deep learning models present in general lower errors compared to the other methods, especially for water depths $>0.5m$. However, when testing on more complex rainfall events or unseen catchment areas, the deep models do not show benefits over the simpler ones.

Most of the two-dimensional (2D) hydraulic/hydrodynamic models are still computationally too demanding for real-time applications. In this paper, an innovative modelling approach based on a deep convolutional neural network (CNN) method is presented for rapid prediction of fluvial flood inundation. The CNN model is trained using outputs from a 2D hydraulic model (i.e. LISFLOOD-FP) to predict water depths. The pre-trained model is then applied to simulate the January 2005 and December 2015 floods in Carlisle, UK. The CNN predictions are compared favourably with the outputs produced by LISFLOOD-FP. The performance of the CNN model is further confirmed by benchmarking against a support vector regression (SVR) method. The results show that the CNN model outperforms SVR by a large margin. The CNN model is highly accurate in capturing flooded cells as indicated by several quantitative assessment matrices. The estimated error for reproducing maximum flood depth is 0 ~ 0.2 meters for the 2005 event and 0 ~ 0.5 meters for the 2015 event at over 99% of the cells covering the computational domain. The proposed CNN method offers great potential for real-time flood modelling/forecasting considering its simplicity, superior performance and computational efficiency.

Physically-based overland flow models are computationally demanding, hindering their use for real-time applications. Therefore, the development of fast (and reasonably accurate) overland flow models is needed if they are to be used to support flood mitigation decision making. In this study, we investigate the potential of Self-Organizing Maps to rapidly generate water depth and flood extent results. To conduct the study, we developed a flood-simulation specific SOM, using cellular automata flood model results and a synthetic DEM and inflow hydrograph. The preliminary results showed that water depth and flood extent results produced by the SOM are reasonably accurate and obtained in a very short period of time. Based on this, it seems that SOMs have the potential to provide critical flood information to support real-time flood mitigation decisions. The findings presented would however require further investigations to obtain general conclusions; these further investigations may include the consideration of real terrain representations, real water supply networks and realistic inflows from pipe bursts.