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.

Modeling the relationship between rainfall and runoff is a longstanding challenge in hydrology and is crucial for informed water management decisions. Recently, Deep Learning models, particularly Long short-term memory (LSTM), have shown promising results in simulating this relationship. The Transformer, a newly proposed deep learning architecture, has also demonstrated the ability to outperform LSTM in machine translation, text classification, etc. However, there has been limited research on applying Transformers for rainfall-runoff modeling. The research examined the performance of using Transformer architecture, including its time series forecasting variants, to develop rainfall-runoff models using the CAMELS (US) data set. These models were compared to the LSTM regional rainfall-runoff models, with a particular focus on snow-driven basins as the attention mechanism in Transformer is believed to allow it to attend to the earlier precipitation events in the meteorological forcing. Additionally, the Transformer's potential as a global rainfall-runoff model was also tested using the global Caravan data to determine if it could learn and generalize a wide range of rainfall-runoff behaviors, allowing it to potentially be applied in ungauged basins. The results suggest that while Transformer and its variants may not be able to fully replace LSTM for rainfall-runoff modeling, the variant called Reformer has shown promise for daily discharge forecasting in snow-driven basins, particularly in terms of peak flow and low flow prediction. However, using the global Caravan data for building a global rainfall-runoff model was not successful due to uncertainty in the forcing data, particularly precipitation. The code for Transformer-based rainfall-runoff modeling is available publicly at https://github.com/Numpy-Panda/neuralhydrology_Transformer.

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.

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.