Daily groundwater level is an indicator of groundwater resources. Accurate and reliable groundwater level (GWL) prediction is crucial for groundwater resources management and land subsidence risk assessment. In this study, a representative deep learning model, long short-term memory (LSTM), is adopted to predict groundwater level with the selected predictors by partial mutual information (PMI), and bootstrap is employed to generate different samples combination for training many LSTM models, and the predicted values by many LSTM models are used for the uncertainty assessment of groundwater level prediction. Two wells of different climate zones in the USA were used as a case study. Different significant predictors of GWL for two wells were identified by PMI from candidate predictors incorporating teleconnection patterns information. The results show that GWL is significantly affected by antecedent GWL, AO, Niño 3.4, Niño 1 + 2, and precipitation in humid areas, and by antecedent GWL, AO, Niño 3.4, Niño 3, Niño 1 + 2, and PNA in arid areas. Predictor selection can assist in improving the prediction performance of the LSTM model. The relationship between GWL and significant predictors were modeled by the LSTM model, and it achieved higher accuracy in humid areas, while the performance in arid areas was poorer due to limited precipitation information. The performance of LSTM was improved by increasing correlation coefficient (R²) values by 10% and 25% for 2 wells compared to generalized regression neural network (GRNN). Three uncertainty evaluation metrics indicate that LSTM reduced the uncertainty compared to GRNN model. LSTM coupling with PMI and bootstrap can be a promising approach for accurate and reliable groundwater level prediction for different climate zones.

Accurate and reliable monthly streamflow prediction plays a crucial role in the scientific allocation and efficient utilization of water resources. In this paper, we proposed a prediction framework that integrates the input variable selection method and Long Short-Term Memory (LSTM). The input selection methods, including autocorrelation function (ACF), partial autocorrelation function (PACF), and time lag cross-correlation (TLCC), were used to analyze the lagged time between variables. Then, the performance of the LSTM model was compared with three other traditional methods. The framework was used to predict monthly streamflow at the Jimai, Maqu, and Tangnaihai stations in the source area of the Yellow River. The results indicated that grid search and cross-validation can improve the efficiency of determining model parameters. The models incorporating ACF, PACF, and TLCC with lagged time are evidently superior to the models using the current variable as the model inputs. Furthermore, the LSTM model, which considers the lagged time, demonstrated better performance in predicting monthly streamflow. The coefficient of determination (R²) improved by an average of 17.46%, 33.94%, and 15.29% for each station, respectively. The integrated framework shows promise in enhancing the accuracy of monthly streamflow prediction, thereby aiding in strategic decision-making for water resources management.

Long-term runoff projection and uncertainty estimates can provide both the changing trends and confidence intervals of water resources, provide basic information for decision makers, and reduce risks for water resource management. In this paper, a grid-based runoff projection and uncertainty framework was proposed through input selection and long short-term memory (LSTM) modelling coupled with uncertainty analysis. We simultaneously considered dynamic variables and static variables in the candidate input combinations. Different input combinations were compared. We employed LSTM to develop a relationship between monthly runoff and the selected variables and demonstrated the improvement in forecast accuracy through comparison with the MLR, RBFNN, and RNN models. The LSTM model achieved the highest mean Kling–Gupta Efficiency (KGE) score of 0.80, representing respective improvements of 45.45%, 33.33%, and 2.56% over the other three models. The uncertainty sources originating from the parameters of the LSTM models were considered, and the Monte Carlo approach was used to provide uncertainty estimates. The framework was applied to the Yellow River Source Area (YRSR) at the 0.25° grid scale to better show the temporal and spatial features. The results showed that extra information about static variables can improve the accuracy of runoff projections. Annual runoff tended to increase, with projection ranges of 148.44–296.16 mm under the 95% confidence level, under various climate scenarios.