TreeLSTM: A spatiotemporal machine learning model for rainfall-runoff estimation

The Jinsha River (JRB) and Han River basins (HRB), China. Due to challenges in interpreting neural network algorithms in hydrological runoff processes, our research focuses on enhancing the temporal dependency and spatial correlation learning capacities. To address these issues, we proposed a multi-layer spatiotemporal model, i.e., the tree long short-term memory model (treeLSTM), for runoff estimations. Because downstream hydrological stations are affected by their own historical and current upstream rainfall and runoff, the treeLSTM’s horizontal and vertical inputs are historical and upstream rainfall-runoff for temporal and spatial features extraction, respectively. The daily rainfall-runoff from 1992 to 2016 in JRB and that from 2011 to 2020 in HRB are predicted. Results of validation periods (2012–2016 in JRB, 2019–2020 in HRB) indicate that the treeLSTM in terms of (JRB: RMSE (root mean square error) = 0.5375, MAPE (mean absolute percent error) = 8.27 %, NSE (Nash–Sutcliffe model efficiency coefficient) = 0.9621; HRB: RMSE = 3.3562, MAPE = 2.91 %, NSE = 0.9934) outperformed the backpropagation neural network (BP) and LSTM models. Therefore, the treeLSTM has considerable advantages in runoff estimation due to its integration of time dependence in historical hydrological data with the spatial correlation of meteorological and hydrological elements, which may be useful for enhancing the physical interpretability of machine learning algorithms. [Display omitted] •Downstream stations are affected by historical and current upstream runoff.•TreeLSTM model considers time dependence and the spatial correlations on runoff.•The results of treeLSTM model outperform the BP and LSTM models.