Fully distributed hydrological models take into account the spatial variability of a catchment, and allow for assessing its hydrological response at virtually any location. However, these models can be time-consuming when it comes to model runtime and calibration, especially for large-scale catchments. Meanwhile, deep learning models have shown great potential in the field of hydrological modelling, but a multivariable, fully distributed hydrological deep learning model is still lacking. To address the aforementioned challenges associated with fully distributed models and deep learning models, we explore the possibility of developing a fully distributed multivariable deep learning model by using Graph Neural Networks (GNN), an extension of deep learning methods to non-Euclidean topologies. We develop a surrogate model of wflow_sbm, a fully distributed, physics-based hydrological model, by exploiting the similarities between its underlying functioning and GNNs. The GNN model uses the same input as wflow_sbm: gridded static parameters based on physical characteristics of the catchment and gridded dynamic meteorological forcings. The GNN model is trained to approximate wflow_sbm outputs, consisting of multiple gridded hydrological variables such as streamflow, actual evapotranspiration, subsurface flow, saturated and unsaturated groundwater storage, snow storage, and runoff. Our results show that the GNN model accurately predicts multiple hydrological variables in unseen catchments (median KGE=0.76), and can serve as an emulator of wflow_sbm with a shorter runtime. We furthermore demonstrate how the GNN model can function up to a prediction horizon of a full year, using physical system states to account for system memory, as well as a curriculum learning strategy combined with a multi-step ahead loss function during training. Overall, this study contributes to the field of fully distributed modelling using a deep learning approach.

Understanding the propagation of a flood is crucial for effective emergency response measures. While traditional numerical models provide reliable flood simulations, their high computational costs pose significant limitations during emergencies. Deep learning models have recently demonstrated potential in accelerating hydrological calculations while preserving high accuracy. Although various deep learning flood models have been developed, many are limited to specific case studies or neglect the dynamic propagation of flood waves, constraining their application during emergencies. To address this, Bentivoglio et al., 2023 proposes the use of a physics-based surrogate model for spatio-temporal flood modelling; the shallow water equation graph neural network (SWE-GNN). The model demonstrates promising results on small virtual landscapes, showcasing strong generalizability to unseen breach locations and domains, while achieving computational speed ups. In this research, the real-world applicability of the SWE-GNN for time-sensitive situations is analyzed. Two dike rings in the Netherlands are selected as our case study areas. The model is trained and tested within the same domain to evaluate its application during a crisis. Performance is assessed using statistical metrics and practical evaluations, including direct and indirect damage models. The SWE-GNN model is able to correctly predict the spatio-temporal evolution of floods for unseen breach locations. The mean average errors in time are of 0.027 m and 0.029 m for water depth and of 0.007 m^2/s and 0.006 m^2/s on units discharge. The resulting flood maps prove viable for practical applicability, presenting good results for both direct as indirect damage assessment. Additionally, the SWE-GNN demonstrates a speedup of roughly 5 to 6 times for the test case areas compared to a traditional numerical model. In this project, we affirm that the SWE-GNN represents a promising innovation for a new approach to time-sensitive flood modeling, providing a reliable alternative to numerical models in situations with time constraints.

Two-dimensional hydrodynamic models are computationally expensive. This drawback can limit their application to solving problems requiring real-time predictions or several simulation runs. Although the literature presented improvements in using Deep Learning as an alternative to hydrodynamic models, Artificial Neural Networks applications for flood prediction cannot satisfactorily predict floods for areas outside the training datasets with different boundary conditions. In this paper, we used a conditional generative adversarial network (cGAN) aiming to generalize flood predictions in catchments not included in the training process. The proposed method, called cGAN-Flood, uses two cGAN models to solve a rain-on-grid problem by first identifying wet cells and then estimating the water depths. The cGANs were trained using HEC-RAS outputs as ground truth. cGAN-Flood distributes a target flood volume (v_t) in a given catchment, which can be calculated via water balance from hydrological simulations. Our approach was trained on ten and tested on five urban catchments with distinct characteristics. The cGAN-Flood was compared to HEC-RAS for different rainfall magnitudes and surface roughness. We also compared our approach to the Weighted Cellular Automata 2D (WCA2D), a rapid flood model (RFM) used for rain-on-grid simulations. Our method successfully predicted water depths in the testing areas, showing that cGAN-Flood could generalize to different locations. However, cGAN-Flood tended to underestimate depths in channels in some areas for events with a small peak of precipitation intensity. cGAN-Flood was 50 and 250 times faster than WCA2D and HEC-RAS, respectively. Due to its computational efficiency and accuracy, we suggest that cGAN-Flood can be applied when fast simulations are necessary, and it can be a viable modeling solution for flood forecasts in large-scale watersheds.

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Metamodels accurately reproduce the output of physics-based hydraulic models with a significant reduction in simulation times. They are widely employed in water distribution system (WDS) analysis since they enable computationally expensive applications in the design, control, and optimisation of water networks. Recent machine-learning-based metamodels grant improved fidelity and speed; however, they are only applicable to the water network they were trained on. To address this issue, we investigate graph neural networks (GNNs) as metamodels for WDSs. GNNs leverage the networked structure of WDS by learning shared coefficients and thus offering the potential of transferability. This work evaluates the suitability of GNNs as metamodels for estimating nodal pressures in steady-state EPANET simulations. We first compare the effectiveness of GNN metamodels against multi-layer perceptrons (MLPs) on several benchmark WDSs. Then, we explore the transferability of GNNs by training them concurrently on multiple WDSs. For each configuration, we calculate model accuracy and speedups with respect to the original numerical model. GNNs perform similarly to MLPs in terms of accuracy and take longer to execute but may still provide substantial speedup. Our preliminary results indicate that GNNs can learn shared representations across networks, although assessing the feasibility of truly general metamodels requires further work.

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Numerical modelling is a reliable tool for flood simulations, but accurate solutions are computationally expensive. In recent years, researchers have explored data-driven methodologies based on neural networks to overcome this limitation. However, most models are only used for a specific case study and disregard the dynamic evolution of the flood wave. This limits their generalizability to topographies that the model was not trained on and in time-dependent applications. In this paper, we introduce shallow water equation–graph neural network (SWE–GNN), a hydraulics-inspired surrogate model based on GNNs that can be used for rapid spatio-temporal flood modelling. The model exploits the analogy between finite-volume methods used to solve SWEs and GNNs. For a computational mesh, we create a graph by considering finite-volume cells as nodes and adjacent cells as being connected by edges. The inputs are determined by the topographical properties of the domain and the initial hydraulic conditions. The GNN then determines how fluxes are exchanged between cells via a learned local function. We overcome the time-step constraints by stacking multiple GNN layers, which expand the considered space instead of increasing the time resolution. We also propose a multi-step-ahead loss function along with a curriculum learning strategy to improve the stability and performance. We validate this approach using a dataset of two-dimensional dike breach flood simulations in randomly generated digital elevation models generated with a high-fidelity numerical solver. The SWE–GNN model predicts the spatio-temporal evolution of the flood for unseen topographies with mean average errors in time of 0.04 m for water depths and 0.004 m2 s−1 for unit discharges. Moreover, it generalizes well to unseen breach locations, bigger domains, and longer periods of time compared to those of the training set, outperforming other deep-learning models. On top of this, SWE–GNN has a computational speed-up of up to 2 orders of magnitude faster than the numerical solver. Our framework opens the doors to a new approach to replace numerical solvers in time-sensitive applications with spatially dependent uncertainties.@en

Deep learning techniques have been increasingly used in flood management to overcome the limitations of accurate, yet slow, numerical models and to improve the results of traditional methods for flood mapping. In this paper, we review 58 recent publications to outline the state of the art of the field, identify knowledge gaps, and propose future research directions. The review focuses on the type of deep learning models used for various flood mapping applications, the flood types considered, the spatial scale of the studied events, and the data used for model development. The results show that models based on convolutional layers are usually more accurate, as they leverage inductive biases to better process the spatial characteristics of the flooding events. Models based on fully connected layers, instead, provide accurate results when coupled with other statistical models. Deep learning models showed increased accuracy when compared to traditional approaches and increased speed when compared to numerical methods. While there exist several applications in flood susceptibility, inundation, and hazard mapping, more work is needed to understand how deep learning can assist in real-time flood warning during an emergency and how it can be employed to estimate flood risk. A major challenge lies in developing deep learning models that can generalize to unseen case studies. Furthermore, all reviewed models and their outputs are deterministic, with limited considerations for uncertainties in outcomes and probabilistic predictions. The authors argue that these identified gaps can be addressed by exploiting recent fundamental advancements in deep learning or by taking inspiration from developments in other applied areas. Models based on graph neural networks and neural operators can work with arbitrarily structured data and thus should be capable of generalizing across different case studies and could account for complex interactions with the natural and built environment. Physics-based deep learning can be used to preserve the underlying physical equations resulting in more reliable speed-up alternatives for numerical models. Similarly, probabilistic models can be built by resorting to deep Gaussian processes or Bayesian neural networks.@en

Fluvial flooding poses a major threat to mankind and annually leads to major economic losses with many casualties worldwide. The consequences of this can be mitigated when accurate and rapid predictions are available when the water will arrive at which location. Current numerical simulations take a significant amount of time due to their computational demand, which is not affordable during a calamity where each second can make the difference between life and death. Literature has shown promising results in fluvial flood forecasting by using a deep learning model, which generally takes only a fraction of the computation time compared to conventional models. However, these models have thus far only been trained on static landscapes with changing boundary conditions, which prevents the model’s application elsewhere.

This research explores therefore the possibilities of creating and training a generic non-location bound deep learning model which can predict the spatial distribution of fluvial flood arrival times per grid cell. The architecture of the created deep learning model consists of five parallel encoder-decoders, which takes the elevation, slopes, elevated elements, land roughness, and initial water levels into consideration, depending on the dataset. The model is trained, validated and tested on four unique datasets, which consists of 30,000 flooding samples. The degree of complexity within a sample increases with each dataset number.

The average error for the four consecutive test datasets were 0.91, 1.41, 1.25, and 1.76 hours per cell. The differences in the predicted and the groundtruth are relatively small although the deviation tends to become larger at the end of the simulation, in regions with a strong gradient in arrival time, and in hilly and complex landscapes.

In addition, the model has been tested on various benchmark landscapes to examine specific flow phenomena, as well as a realistic test scenario in the Dutch dike ring 48. The model shows satisfactory performances for landscapes other than those present in the dataset, untill it encounters a feature on which the model was not trained for, such as undershots or irregularly shaped waterways.

This research has shown the potential of deep learning in predicting fluvial flood arrival times on unseen before landscapes. Recommendations for further studies include the use of an active dike breach and a variable flood location.

An advection-diffusion model is proposed to simulate large wood transport during high flows. The mathematical model is derived from the wood mass balance, taking into consideration both the wood mass concentration and the log orientation, which affects log transport and, most importantly, wood accumulation. Focusing on wood mass transport, the advection-diffusion equation is implemented in a hydrodynamic model to provide a one-way coupled solution of the flow and of the floating wood mass. The model is tested on a large series of flume experiments, involving at least 30 logs and different control parameters (flow Froude number, log length, diameter, release point). The validation through the experimental data shows that the proposed model can predict the correct displacement of the most probable position of the logs and to simulate with a sufficient accuracy the planar diffusion of the wooden mass. Transversal wood distribution is more accurate than the streamwise one, indicating that a higher control on the longitudinal diffusion needs to be implemented.

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