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Abstract Accurate runoff forecasting is of great significance for water resource allocation flood control and disaster reduction. However, due to the inherent strong randomness of runoff sequences, this task faces significant challenges. To address this challenge, this study proposes a new SMGformer runoff forecast model. The model integrates Seasonal and Trend decomposition using Loess (STL), Informer’s Encoder layer, Bidirectional Gated Recurrent Unit (BiGRU), and Multi-head self-attention (MHSA). Firstly, in response to the nonlinear and non-stationary characteristics of the runoff sequence, the STL decomposition is used to extract the runoff sequence’s trend, period, and residual terms, and a multi-feature set based on ‘sequence-sequence’ is constructed as the input of the model, providing a foundation for subsequent models to capture the evolution of runoff. The key features of the input set are then captured using the Informer’s Encoder layer. Next, the BiGRU layer is used to learn the temporal information of these features. To further optimize the output of the BiGRU layer, the MHSA mechanism is introduced to emphasize the impact of important information. Finally, accurate runoff forecasting is achieved by transforming the output of the MHSA layer through the Fully connected layer. To verify the effectiveness of the proposed model, monthly runoff data from two hydrological stations in China are selected, and eight models are constructed to compare the performance of the proposed model. The results show that compared with the Informer model, the 1th step MAE of the SMGformer model decreases by 42.2% and 36.6%, respectively; RMSE decreases by 37.9% and 43.6% respectively; NSE increases from 0.936 to 0.975 and from 0.487 to 0.837, respectively. In addition, the KGE of the SMGformer model at the 3th step are 0.960 and 0.805, both of which can maintain above 0.8. Therefore, the model can accurately capture key information in the monthly runoff sequence and extend the effective forecast period of the model.

This study proposes a hybrid model based on the combination of Sand Cat Swarm Optimization (SCSO), Echo State Network (ESN), Gated Recurrent Unit (GRU), Least Squares Method (LSM), and Markov Chain (MC) to improve the accuracy of annual runoff prediction. Firstly, conduct correlation analysis on multi-factor data related to runoff to determine the input of the model. Secondly, the SCSO algorithm is used to optimize the parameters of the ESN and GRU models, and the SCSO-ESN and SCSO-GRU models are established. Next, the prediction results of these two models are coupled using LSM to obtain the preliminary prediction results of the SCSO-ESN-GRU model. Finally, the initial prediction results are corrected for errors using MC to get the final prediction results. Choose Changshui Station and Lanxi Station for experiments, and evaluate the predictive performance of the model through five evaluation indicators. The results show that the combined prediction model corrected by the MC achieved the optimal prediction performance at both experimental stations. This study emphasizes that using a combination prediction model based on Markov chain correction can significantly improve the accuracy of annual runoff prediction, providing a reliable basis for predicting annual runoff in complex watersheds. HIGHLIGHTS A new hybrid sand cat swarm optimization-echo state network-gated recurrent unit-Markov chain (SCSO-ESN-GRU-MC) model is proposed for annual runoff prediction.; A new SCSO algorithm is used to optimize the parameters of the prediction model.; Least squares method is used to couple the ESN and GRU models for annual runoff prediction.; MC is used to correct errors in annual runoff prediction results.; The proposed model achieves the best prediction results at both experimental stations.;

Accurate runoff prediction is vital in efficiently managing water resources. In this paper, a hybrid prediction model combining complete ensemble empirical mode decomposition with adaptive noise, variational mode decomposition, CABES, and long short-term memory network (CEEMDAN-VMD-CABES-LSTM) is proposed. Firstly, CEEMDAN is used to decompose the original data, and the high-frequency component is decomposed using VMD. Then, each component is input into the LSTM optimized by CABES for prediction. Finally, the results of individual component predictions are combined and reconstructed to produce the monthly runoff predictions. The hybrid model is employed to predict the monthly runoff at the Xiajiang hydrological station and the Yingluoxia hydrological station. A comprehensive comparison is conducted with other models including back propagation (BP), LSTM, etc. The assessment of each model's prediction performance uses four evaluation indexes. Results reveal that the CEEMDAN-VMD-CABES-LSTM model showcased the highest forecast accuracy among all the models evaluated. Compared with the single LSTM, the root mean square error (RMSE) and mean absolute percentage error (MAPE) of the Xiajiang hydrological station decreased by 71.09 and 65.26%, respectively, and the RMSE and MAPE of the Yingluoxia hydrological station decreased by 65.13 and 40.42%, respectively. The R and NSEC of both sites are near 1. HIGHLIGHTS A novel model (CEEMDAN-VMD-CABES-LSTM) is proposed for monthly runoff prediction.; CEEMDAN-VMD effectively reduces the complexity of the original monthly runoff series.; CABES enhances the generalization ability and prediction performance of the LSTM.; The four evaluation indicators and seven benchmark models are employed to verify the superiority of the developed model.;

This article proposes a multi-head attention flood forecasting model (MHAFFM) that combines a multi-head attention mechanism (MHAM) with multiple linear regression for flood forecasting. Compared to models based on Long Short-Term Memory (LSTM) neural networks, MHAFFM enables precise and stable multi-hour flood forecasting. First, the model utilizes characteristics of full-batch stable input data in multiple linear regression to solve the problem of oscillation in the prediction results of existing models. Second, full-batch information is connected to MHAM to improve the model's ability to process and interpret high-dimensional information. Finally, the model accurately and stably predicts future flood processes through linear layers. The model is applied to Dawen River Basin, and experimental results show that the MHAFFM, compared to three benchmarking models, namely, LSTM, BOA-LSTM (LSTM with Bayesian Optimization Algorithm for Hyperparameter Tuning), and MHAM-LSTM (LSTM model with MHAM in hidden layer), significantly improves the prediction performance under different lead time scenarios while maintaining good stability and interpretability. Taking Nash–Sutcliffe efficiency index as an example, under a lead time of 3 h, the MHAFFM model exhibits improvements of 8.85, 3.71, and 10.29% compared to the three benchmarking models, respectively. This research provides a new approach for flood forecasting. HIGHLIGHTS Proposes a novel multi-head attention flood forecasting model (MHAFFM).; Multi-head attention mechanism strengthens the model's ability to handle high-dimensional data.; Linear layers effectively harness the performance of the multi-head attention mechanism.; MHAFFM significantly enhances the stability of forecasted results.; Even in longer lead time scenarios, the model maintains high accuracy and stability.;

In runoff prediction, the prediction accuracy is often affected by the non-linear and non-stationary characteristics of the runoff series. In this study, a coupled forecasting model is proposed that decomposes the original runoff series by an improved complete ensemble Empirical Mode Decomposition (EMD) (ICEEMDAN) combined with a wavelet decomposition (WD) and then forecasts the monthly runoff using a support vector machine (SVM) optimized by the seagull optimization algorithm (SOA). In this method, a series of Intrinsic Mode Function (IMF) and a Residual (Res) are obtained by decomposing the original runoff series with ICEEMDAN. The WD method is used to perform quadratic decomposition of high-frequency components decomposed by the ICEEMDAN method to make the runoff series as smooth as possible. Then the decomposed components are input into the SOA-SVM model for prediction. Finally, the prediction results of each component are superimposed and reconstructed to obtain the final monthly runoff prediction results. RMSE, Mean Absolute Percentage Error (MAPE), Nash-Sutcliffe Efficiency Coefficient (NSEC), and R are selected to evaluate the prediction results and the model is compared with SOA-SVM model, EMD-SOA-SVM model and CEEMDAN-SOA-SVM model other models. The proposed model is applied to the monthly runoff forecast of the Hongjiadu and Manwan Reservoirs. When compared with other benchmarking models, the ICEEMDAN-WD-SOA-SVM model attains the smallest Root Mean Square Error (RMSE) and MAPE and the largest NSEC and R. The ICEEMDAN-WD-SOA-SVM model has the best prediction effect, the highest prediction accuracy, and the lowest prediction error. HIGHLIGHTS The ICEEMDAN–WD model is used to decompose the original runoff series.; The proposed ICEEMDAN–WD model can effectively reduce the complexity of the runoff series.; The proposed SOA–SVM model can effectively improve the prediction accuracy of runoff series.; The proposed model can provide high prediction accuracy and consistency.;

The Palmer drought severity index (PDSI) is physically based with multivariate concepts, but requires complicated calibration and cannot easily be used for multiscale comparison. Standardized drought indices (SDIs), such as the standardized precipitation index (SPI) and standardized precipitation evapotranspiration index (SPEI), are multiscalar and convenient for spatiotemporal comparison, but they are still challenged by their lack of physical basis. In this study, a hybrid multiscalar indicator, the standardized Palmer drought index (SPDI), was used to examine drought properties of two meteorological stations (the Beijing and Guangzhou stations) in China, which have completely different drought climatologies. The results of our case study show that the SPDI is correlated with the well-established drought indices (SPI, SPEI, and PDSI) and presents generally consistent drought/wetness conditions against multiple indicators and literature records. Relative to the PDSI, the SPDI demonstrates invariable statistical characteristics and better comparable drought/wetness frequencies over time and space. Moreover, characteristics of major drought events (drought class, and onset and end times) indicated by the SPDI are generally comparable to those detected by the PDSI. As a physically-based standardized multiscalar drought indicator, the SPDI can be regarded as an effective development of the Palmer drought indices, providing additional choices and tools for practical drought monitoring and assessment. Keywords: Drought, PDSI, Multiscalar index, SPDI, Multifaceted comparison