Improving stage-discharge relationship modeling accuracy using a hybrid ViT-CNN framework

Predicting river flow is one of the key issues in hydrological modeling, which is particularly important in applications such as managing and controlling floods. Water resource engineers use historical observational data of river flow to establish a relationship between discharge and water level, referred to as the stage-discharge relationship or rating curve (RC). In this study, deep learning methods, including the Vision Transformer (ViT) and Convolutional Neural Network (CNN), were used to model the stage-discharge relationship in the Nahand River. The results from these models were compared with a novel hybrid method known as ViT-CNN. To optimize the input of these models, the Vector AutoRegression (VAR) method was used in which a one-time step delay for discharge and stage was selected as the model inputs. This selection of inputs was based on time-series analysis which enable the models to simulate the complexity of the flow as accurately as possible. The results showed that among the evaluated methods, the ViT-CNN hybrid method achieved the best performance in predicting flow discharge, with evaluation criteria of CC = 0.983, NSE = 0.962, RMSE = 0.178, and MAE = 0.071. The results of this study demonstrate the utility of deep learning to further enhance the predictability of stage-discharge relationships in rivers worldwide.