Abstract. Long Short-Term Memory (LSTM) networks have been applied to daily discharge prediction with remarkable success. Many practical applications, however, require predictions at more granular timescales. For instance, accurate prediction of short but extreme flood peaks can make a lifesaving difference, yet such peaks may escape the coarse temporal resolution of daily predictions. Naively training an LSTM on hourly data, however, entails very long input sequences that make learning difficult and computationally expensive. In this study, we propose two multi-timescale LSTM (MTS-LSTM) architectures that jointly predict multiple timescales within one model, as they process long-past inputs at a different temporal resolution than more recent inputs. In a benchmark on 516 basins across the continental United States, these models achieved significantly higher Nash–Sutcliffe efficiency (NSE) values than the US National Water Model. Compared to naive prediction with distinct LSTMs per timescale, the multi-timescale architectures are computationally more efficient with no loss in accuracy. Beyond prediction quality, the multi-timescale LSTM can process different input variables at different timescales, which is especially relevant to operational applications where the lead time of meteorological forcings depends on their temporal resolution.

Abstract. Long Short-Term Memory Networks (LSTMs) have been applied to daily discharge prediction with remarkable success. Many practical scenarios, however, require predictions at more granular timescales. For instance, accurate prediction of short but extreme flood peaks can make a life-saving difference, yet such peaks may escape the coarse temporal resolution of daily predictions. Naively training an LSTM on hourly data, however, entails very long input sequences that make learning hard and computationally expensive. In this study, we propose two Multi-Timescale LSTM (MTS-LSTM) architectures that jointly predict multiple timescales within one model, as they process long-past inputs at a single temporal resolution and branch out into each individual timescale for more recent input steps. We test these models on 516 basins across the continental United States and benchmark against the US National Water Model. Compared to naive prediction with a distinct LSTM per timescale, the multi-timescale architectures are computationally more efficient with no loss in accuracy. Beyond prediction quality, the multi-timescale LSTM can process different input variables at different timescales, which is especially relevant to operational applications where the lead time of meteorological forcings depends on their temporal resolution.

Quantifying the behavior and performance of hydrologic models is an important aspect of understanding the underlying hydrologic systems. We argue that classical error measures do not offer a complete picture for building this understanding. This study demonstrates how the information theoretic measure known as transfer entropy can be used to quantify the active transfer of information between hydrologic processes at various timescales and facilitate further understanding of the behavior of these systems. To build a better understanding of the differences in dynamics, we compare model instances of the Structure for Unifying Multiple Modeling Alternatives (SUMMA), the Variable Infiltration Capacity (VIC) model, and the Precipitation Runoff Modeling System (PRMS) across a variety of hydrologic regimes in the Columbia River Basin in the Pacific Northwest of North America. Our results show differences in the runoff of the SUMMA instance compared to the other two models in several of our study locations. In the Snake River region, SUMMA runoff was primarily snowmelt driven, while VIC and PRMS runoff was primarily influenced by precipitation and evapotranspiration. In the Olympic mountains, evapotranspiration interacted with the other water balance variables much differently in PRMS than in VIC and SUMMA. In the Willamette River, all three models had similar process networks at the daily time scale but showed differences in information transfer at the monthly timescale. Additionally, we find that all three models have similar connectivity between evapotranspiration and soil moisture. Analyzing information transfers to runoff at daily and monthly time steps shows how processes can operate on different timescales. By comparing information transfer with correlations, we show how transfer entropy provides a complementary picture of model behavior.