Multi-step regional rainfall-runoff modeling using pyramidal transformer

Rainfall-runoff modeling is the key to water resources management and thus is an important task in hydrology. Compared with individual rainfall-runoff modeling, regional rainfall-runoff modeling is more difficult, especially for the traditional models. With the fast development of the deep-learning based data-driven models (e.g, the Long Short-Term Memory (LSTM)-based ones and the Transformer-based ones), such a task has a certain amount of progress. In this paper, we focus on multi-step regional rainfall-runoff modeling and propose a novel pyramidal Transformer (PT) rainfall-runoff model, which can explore information from different time resolutions with a pyramidal attention architecture considering dynamic and static attributes. Its structure is more advanced than the original Transformer-based model RR-Former, which is shown by testing the performance in 448 basins of the Catchment Attributes and Meteorology for Large-sample Studies in the United States (CAMELS-US) dataset. Besides, we show that the catchment static attributes and historical runoff observations are important for regional rainfall-runoff modeling. Moreover, we pointed out that the mean-absolute-error (MAE) is a better choice than the mean-square-error (MSE) as a loss function for such a task.