Technical note: An approach for handling multiple temporal frequencies with different input dimensions using a single LSTM cell

Abstract. Long short-term memory (LSTM) networks have demonstrated state-of-the-art performance for rainfall-runoff hydrological modelling. However, most studies focus on predictions at a daily scale, limiting the benefits of sub-daily (e.g. hourly) predictions in applications like flood forecasting. Moreover, training an LSTM network exclusively on sub-daily data is computationally expensive and may lead to model learning difficulties due to the extended sequence lengths. In this study, we introduce a new architecture, multi-frequency LSTM (MF-LSTM), designed to use input of various temporal frequencies to produce sub-daily (e.g. hourly) predictions at a moderate computational cost. Building on two existing methods previously proposed by the co-authors of this study, MF-LSTM processes older inputs at coarser temporal resolutions than more recent ones. MF-LSTM gives the possibility of handling different temporal frequencies, with different numbers of input dimensions, in a single LSTM cell, enhancing the generality and simplicity of use. Our experiments, conducted on 516 basins from the CAMELS-US dataset, demonstrate that MF-LSTM retains state-of-the-art performance while offering a simpler design. Moreover, the MF-LSTM architecture reported a 5 times reduction in processing time compared to models trained exclusively on hourly data.