Predicting runoff with precision holds immense importance for flood control, water resource management, and basin ecological dispatch. Deep learning, especially long short-term memory (LSTM) neural networks, has excelled in runoff prediction, often outperforming traditional hydrological models. Recent studies suggest that deep learning models employing the self-attention mechanism, such as Transformer and Informer, can achieve even better results than LSTM. However, research exploring the multi-step runoff prediction capabilities of these novel models across diverse scenarios remains scarce. In this investigation, we introduce a relative location coding-enhanced Informer model, termed Rel-Informer, and compare its performance in rainfall-runoff prediction against the standard Informer, Transformer, and LSTM models. The publicly available CAMELS dataset is utilized for training and validating the models, and four experiments are designed: (1) Individual rainfall-runoff modeling (one model per catchment); (2) Regional rainfall-runoff modeling (one model per region); (3) Fine-tuned regional rainfall-runoff modeling (fine-tuned from Experiment 2); (4) Large-scale rainfall-runoff modeling for ungauged catchments (one model for all catchments). The findings reveal that Rel-Informer consistently performs better than the other models, particularly in short-term runoff predictions (1–3 days ahead). Although regional modeling is less precise than individual modeling, it significantly benefits from fine-tuning. The large-scale regional Rel-Informer model effectively predicts runoff in ungauged catchments, showcasing its potential for widespread runoff prediction. This study underscores the influence of hydrological characteristics, such as snowmelt and baseflow indices, on prediction accuracy. In conclusion, the Rel-Informer model, enhanced with improved relative position encoding, emerges as a promising tool for runoff forecasting, especially in data-rich catchments.

To improve the precision of water quality forecasting, the variational mode decomposition (VMD) method was used to denoise the total nitrogen (TN) and total phosphorus (TP) time series and obtained several high- and low-frequency components at four online surface water quality monitoring stations in Poyang Lake. For each of the aforementioned high-frequency components, a long short-term memory (LSTM) network was introduced to achieve excellent prediction results. Meanwhile, a novel metaheuristic optimization algorithm, called the chaos sparrow search algorithm (CSSA), was implemented to compute the optimal hyperparameters for the LSTM model. For each low-frequency component with periodic changes, the multiple linear regression model (MLR) was adopted for rapid and effective prediction. Finally, a novel combined water quality prediction model based on VMD-CSSA-LSTM-MLR (VCLM) was proposed and compared with nine prediction models. Results indicated that (1), for the three standalone models, LSTM performed best in terms of mean absolute error (MAE), mean absolute percentage error (MAPE), and the root mean square error (RMSE), as well as the Nash–Sutcliffe efficiency coefficient (NSE) and Kling–Gupta efficiency (KGE). (2) Compared with the standalone model, the decomposition and prediction of TN and TP into relatively stable sub-sequences can evidently improve the performance of the model. (3) Compared with CEEMDAN, VMD can extract the multiscale period and nonlinear information of the time series better. The experimental results proved that the averages of MAE, MAPE, RMSE, NSE, and KGE predicted by the VCLM model for TN are 0.1272, 8.09%, 0.1541, 0.9194, and 0.8862, respectively; those predicted by the VCLM model for TP are 0.0048, 10.83%, 0.0062, 0.9238, and 0.8914, respectively. The comprehensive performance of the model shows that the proposed hybrid VCLM model can be recommended as a promising model for online water quality prediction and comprehensive water environment management in lake systems.

The development of sequence decomposition techniques in recent years has facilitated the wide use of decomposition-based prediction models in hydrological forecasting. However, decomposition-based prediction models usually use the overall decomposition (OD) sampling technique to extract samples. Some studies have shown that the OD sampling technique causes abnormally “high” performance of models owing to the utilization of future information, and this technique cannot be applied in practice. Several researchers have also proposed novel sampling techniques, such as semi-stepwise decomposition (SSD), fully stepwise decomposition (FSD), and single-model SSD (SMSSD). Moreover, an improved single-model FSD (SMFSD) sampling technique is proposed in this study. Four decomposition methods, namely discrete wavelet transform (DWT), empirical mode decomposition (EMD), complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), and variational mode decomposition (VMD), are introduced in this study. A systematic investigation of the models developed using OD sampling techniques is conducted, and the applicability of SSD, FSD, SMSSD, and SMFSD sampling techniques is reasonably evaluated. The application of monthly runoff prediction using the five sampling techniques and four decomposition methods at five representative hydrological stations in Poyang Lake, China, shows that (1) EMD and CEEMDAN (including the improved EMD-based adaptive decomposition method) cannot be used to construct stepwise decomposition prediction models because the implementation of the stepwise decomposition strategy leads to a variable number of sub-series. (2) OD sampling techniques cannot develop convincing models for practical prediction because future information is introduced into the samples for model training. (3) Models developed based on SSD and SMSSD sampling techniques do not use future information in the training process, but suffer from severe overfitting and inferior prediction performance. (4) Models developed based on FSD and SMFSD sampling techniques can produce convincing prediction results, and the combination of the proposed SMFSD sampling technique and VMD develops prediction models with superior performance and significantly enhances the efficiency of the models.

Reliability and vulnerability (RV) are two very important performance measures but, due to their stage-inseparable nature, they cannot be explicitly incorporated in stochastic dynamic programming (SDP), which is extensively used in reservoir operation. With inflows described as a Markov chain, a stochastic linear programming (SLP) model is formulated in this paper to explicitly incorporate the RV constraints in the reservoir operation, aimed at maximizing the expected power generation by determining the optimal scheduling decisions and their probabilities. Simulation results of the SLP and SDP models indicate the equivalence of the proposed SLP and SDP models without considering the RV constraints, as well as the strength of the SLP in explicitly incorporating the RV constraints. A simulated scheduling solution also reveals a reduction of power generation fluctuation, with the reservoir capacity emptied in advance to meet given reliability and vulnerability.

The scheduling and optimization of short-term hydrothermal operation utilize the water resources efficiently and magnify the benefits of hydro energy while reducing the fuel and operation cost of thermal power plants. Short-term hydrothermal operation is a complex non-linear and non-convex optimization problem, which reflects thermal valve point effects, load balances, generation bounds and water transport delay. It is highly important and significant to figure out these problems to maximize the benefits of hydrothermal joint operation for energy saving, emission reduction and efficient resources management. This article presents a 1D linearization technique to deal with the non-linear function of two variables, a combined mixed-integer linear programming (MILP) and non-linear programming (NLP) method to solve this problem. The applied method introduces integer variables to linearize the original model into a MILP one; the solution by MILP is then corrected and re-optimized to formulate a feasible solution to warm start NLP. The 1D linearization method is efficient for MILP as it avoids the coupled relationships of integer variables, and the NLP local search is used to correct the influence of linearization errors and search further. The case studies show that the result derived by the 1D linearization–based MILP–NLP method is superior to that of previous works. The method is tested with different linearization accuracy, and the results demonstrate that the method is stable. The presented technique is promising for real-world hydrothermal operation and related problems.