Floods are the most frequent natural disaster and due to climate change the frequency and intensity of these events are increasing. Therefore, it is becoming increasingly important to obtain accurate estimations of extreme discharges. Statistical modelling is widely used to estimate extreme discharges by fitting observed extreme discharges to an extreme value distribution. However, limited historical data makes it difficult to confidently model the tail behavior of extremes. Additionally, several modelling assumptions impact extreme discharge estimates including selection of the nonstationary method, extreme value distribution, parameter estimation method, and the impact of seasonality. In an effort to reduce uncertainties, a new method has been developed to derive design discharges for the Meuse in the Netherlands. This method, GRADE (Generator of Rainfall and Discharge Extremes) consists of three components: a stochastic weather generator, a hydrological model, and an extreme value analysis (EVA). However, the stochastic weather generator is not capable of producing daily rainfall that exceeds the range of historical data. Therefore, a physically based climate model, RACMO, is now being studied. RACMO is capable of generating 1,040 years of synthetic meteorological data that can be routed in a hydrological model to obtain 1,040 years of synthetic discharges. The physically based climate model makes it possible to capture the underlying physical processes of extreme events and the hydrological model can provide discharge information at locations where there are no observations. This thesis evaluates the impact various modelling assumptions have on estimated discharges using synthetic data generated by the RACMO through application of a case study in the Meuse.

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.