Rainfall-runoff modeling using long short-term memory based step-sequence framework

Rainfall-runoff modeling, a nonlinear time series process, is challenging and important in hydrological sciences. Among the data-driven approaches, those ones based on the long short-term memory (LSTM) network show their promising performance. In this paper, for rainfall-runoff modeling, we propose a novel data-driven framework named long short-term memory based step-sequence (LSTM-SS) framework, which contains m specific models for m-step-ahead runoff predictions. This model uses the sequential information of runoff series and follows the causality in practice: the current runoff is not affected by the later meteorological data. To show its performance and advantages, we test it on 241 basins of the Catchment Attributes and Meteorology for Large-Sample Studies (CAMELS) data set and predict the 7-day-ahead runoff. The results show that our rainfall-runoff models outperform the benchmark (physically-based or data-driven) models significantly employing for the CAMELS data set, including the Sacramento Soil Moisture Accounting Model (SAC-SMA) coupled with the Snow-17 snow routine, a two-layer LSTM network, and a LSTM-based sequence-to-sequence network. For 1-day-ahead runoff predictions, the median of Nash–Sutcliffe model efficiency for the 241 basins provided by our model is 0.85, while that provided by the two-layer LSTM network is 0.65. Furthermore, the results also show that our proposed LSTM-SS framework not only can significantly improve the performance of a single daily runoff prediction, but also has good performance for multiple-step-ahead runoff predictions.