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In hydrology, runoff predictions are challenging when the data is lacking (e.g., predictions in un-gauged basins (PUB) and predictions with limited data (PLD)). Here, PLD refers to the case that the data is not enough for training or fine-tuning a data-driven model well (e.g., a new-gauged basin). We also name PLD as PNB (predictions in new-gauged basins). The difference between PNB and PUB is that the new-gauged basins can provide some data (e.g., runoff observations) while the un-gauged basins cannot. The long short-term memory (LSTM)-based models have shown good performance in runoff predictions due to their advanced structures. However, those structures have low level of flexibility and two nonadjacent positions cannot communicate directly. For high level of flexibility and better performance, we propose a simple Transformer-based rainfall-runoff model named RRS-Former, and want to show its power and also the power of the previously proposed RR-Former in PNB compared with LSTM-based models. The main part of RRS-Former is attention modules in which two arbitrary positions can be connected directly. Four hydrological units including 241 basins in the Catchment Attributes and Meteorology for Large-Sample Studies (CAMELS) dataset are used to compare the performance of our Transformer-based models and that of LSTM-based models. Besides using the k-fold validation to test performance for PNB, we propose a new way named unit-fold validation, in which we train the models by using the basins in three hydrological units and then test the performance using basins in the rest one hydrological unit. The results based on both k-fold and unit-fold show that our RRS-Former and RR-Former have better performance and are more reliable compared with the LSTM-based models. • A data-driven rainfall-runoff model based on Transformer is proposed and named RRS-Former. • A Transformer-based model is more flexible than LSTM and has better transfer ability. • RRS-Former has less parameters and less training time compared with RR-Former. • A Transformer-based model is more reliable than LSTM in the case of data lacking. • Unit-fold has more advantages for testing the transfer ability compared with k-fold. [ABSTRACT FROM AUTHOR]

• A new framework named LSTM-SS is proposed to deal with rainfall-runoff modeling. • LSTM-SS improves performance significantly on the CAMELS data set. • LSTM-SS achieves good performance for multi-day-ahead runoff predictions. • LSTM-SS has good performance with short input sequence length. 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. [ABSTRACT FROM AUTHOR]

[Display omitted] • Four S2S models show their power to runoff predictions in ungauged basins (PUB). • For 1-day-ahead PUB, our model performs best and much better than benchmark models. • For multi-day-ahead PUB, S2S models can provide promising performance. • Attribute-weighting module is introduced to PUB for the first time • Multi-head-attention module is beneficial for improving performance of PUB. How to improve the performance of runoff predictions in ungauged basins (PUB) is challenging. Recently, the long short-term memory (LSTM) based models have excellent performance and receive many attentions. In this paper, to improve the performance for 1-day-ahead runoff PUB and provide good performance for multi-day-ahead runoff PUB, we propose four sequence-to-sequence (S2S) models to deal with PUB. Furthermore, we introduce two modules named attribute-weighting module and multi-head-attention module for improving the performance. To show the power of these S2S models and the advantages of those two modules, we test our four S2S models and also three benchmark models including a PUB-LSTM model and two process-driven models by using k-fold validation on 531 basins of the Catchment Attributes and Meteorology for Large-Sample Studies (CAMELS) dataset. For 1-day-ahead runoff PUB, the median and the mean of Nash–Sutcliffe efficiency for the 531 basins provided by our best model achieve 0.78 and 0.70 , respectively, while those provided by the PUB-LSTM model (the best one among those three benchmark models) are 0.69 and 0.54 , respectively. Besides, our S2S models have promising results for multi-day-ahead runoff PUB. For 7 th-day-ahead runoff PUB, the median and the mean of Nash–Sutcliffe efficiency for the 531 basins provided by our best model are 0.68 and 0.57 , respectively. Furthermore, the results also show that the two modules are beneficial for improving the performance. [ABSTRACT FROM AUTHOR]

• A new seq2seq rainfall-runoff model named LSTM-MSV-S2S is proposed. • LSTM-MSV-S2S has promising performance on the CAMELS data set. • LSTM-MSV-S2S is more appropriate for multi-day-ahead runoff predictions. Rainfall-runoff modeling is a challenging and important nonlinear time series problem in hydrological sciences. Recently, among the data-driven rainfall-runoff models, those ones based on the long short-term memory (LSTM) network show good performance. Furthermore, LSTM-based sequence-to-sequence (LSTM-S2S) models achieve promising performance for multi-step-ahead runoff predictions. In this paper, for multi-day-ahead runoff predictions, we propose a novel data-driven model named LSTM-based multi-state-vector sequence-to-sequence (LSTM-MSV-S2S) rainfall-runoff model, which contains m multiple state vectors for m -step-ahead runoff predictions. It differs from the existing LSTM-S2S rainfall-runoff models using only one state vector and is more appropriate for multi-day-ahead runoff predictions. To show its performance and advantages, we compare it with two LSTM-S2S models by testing them on 673 basins of the Catchment Attributes and Meteorology for Large-Sample Studies (CAMELS) data set. The results show that our LSTM-MSV-S2S model has better performance in general and thus using multiple state vectors is more appropriate for multi-day-ahead runoff predictions. [ABSTRACT FROM AUTHOR]