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Abstract Traditional decomposition integration models decompose the original sequence into subsequences, which are then proportionally divided into training and testing periods for modeling. Decomposition may cause data aliasing, then the decomposed training period may contain part of the test period data. A more effective method of sample construction is sought in order to accurately validate the model prediction accuracy. Semi-stepwise decomposition (SSD), full stepwise decomposition (FSD), single model semi-stepwise decomposition (SMSSD), and single model full stepwise decomposition (SMFSD) techniques were used to create the samples. This study integrates Variational Mode Decomposition (VMD), African Vulture Optimization Algorithm (AVOA), and Least Squares Support Vector Machine (LSSVM) to construct a coupled rainfall prediction model. The influence of different VMD parameters α is examined, and the most suitable stepwise decomposition machine learning coupled model algorithm for various stations in the North China Plain is selected. The results reveal that SMFSD is relatively the most suitable tool for monthly precipitation forecasting in the North China Plain. Among the predictions for the five stations, the best overall performance is observed at Huairou Station (RMSE of 18.37 mm, NSE of 0.86, MRE of 107.2%) and Jingxian Station (RMSE of 24.74 mm, NSE of 0.86, MRE of 51.71%), while Hekou Station exhibits the poorest performance (RMSE of 25.11 mm, NSE of 0.75, MRE of 173.75%).

Abstract Temperature as an important indicator of climate change, accurate temperature prediction has important guidance and application value for agricultural production, energy management and disaster warning. Based on the advantages of CEEMDAN model in effectively extracting the time–frequency characteristics of nonlinear and nonsmooth signals, BO algorithm in optimizing the objective function within a limited number of iterations, and BiLSTM model in revealing the connection between the current data, the previous data and the future data, a monthly average temperature prediction model based on CEEMDAN–BO–BiLSTM is established. A CEEMDAN–BO–BiLSTM-based monthly average temperature prediction model is developed and applied to the prediction of monthly average temperature in Jinan City, Shandong Province. The results show that the constructed monthly mean temperature prediction model based on CEEMDAN–BO–BiLSTM is feasible; the constructed CEEMDAN–BO–BiLSTM model has an average absolute error of 1.17, a root mean square error of 1.43, an average absolute percentage error of 0.31%, which is better than CEEMDAN–BiLSTM, EMD–BiLSTM, and BiLSTM models in terms of prediction accuracy and shows better adaptability; the constructed CEEMDAN–BO–BiLSTM model illustrates that the model is not over-modeled and adds complexity using Friedman’s test and performance comparisons between model run speeds. The model provides insights for effective forecasting of monthly mean temperatures.

Abstract Enhancing flood forecasting accuracy, promoting rational water resource utilization and management, and mitigating river disasters all hinge on the crucial role of improving the accuracy of daily flow prediction. The coupled model of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), Sample Entropy (SE), and Bidirectional Long Short-Term Memory (BiLSTM) demonstrates higher stability when faced with nonlinear and non-stationary data, stronger adaptability to various types and lengths of time series data by utilizing sample entropy, and significant advantages in processing sequential data through the BiLSTM network. In this study, in the context of predicting daily flow at the Huayuankou Hydrological Station in the lower reaches of the Yellow River, a coupled CEEMDAN–SE–BiLSTM model was developed and utilized. The results showed that the CEEMDAN–SE–BiLSTM coupled model achieved the utmost accuracy in prediction and optimal fitting performance. Compared with the CEEMDAN–SE–LSTM, CEEMDAN–BiLSTM, and BiLSTM coupled models, the root mean square error (RMSE) of this model is reduced by 42.77, 182.02, and 193.71, respectively; the mean absolute error (MAE) is reduced by 37.62, 118.60, and 126.67, respectively; and the coefficient of determination (R2) is increased by 0.0208, 0.1265, 0.1381.

Abstract To improve the accuracy of runoff forecasting, a combined forecasting model is established by using the kernel extreme learning machine (KELM) algorithm optimised by the butterfly optimisation algorithm (BOA), combined with the variational modal decomposition method (VMD) and the complementary ensemble empirical modal decomposition method (CEEMD), for the measured daily runoff sequences at Jiehetan and Huayuankou stations and Gaochun and Lijin stations. The results show that the combined model VMD-CEEMD-BOA-KELM predicts the best. The average absolute errors are 30.02, 23.72, 25.75, 29.37, and the root mean square errors are 20.53 m3/s, 18.79 m3/s, 18.66 m3/s, and 21.87 m3/s, the decision coefficients are all above 90 percent, respectively, and the Nash efficiency coefficients are all more than 90%, from the above it can be seen that the method has better results in runoff time series prediction.

Abstract Rainfall forecasting is an important means for macro-control of water resources and prevention of future disasters. In order to achieve a more accurate prediction effect, this paper analyzes the applicability of the "full decomposition" and "stepwise decomposition" of the VMD (Variational mode decomposition) algorithm to the actual prediction service; The MAVOA (Modified African Vultures Optimization Algorithm) improved by Tent chaotic mapping is selected; and the DNC (Differentiable Neural Computer), which combines the advantages of recurrent neural networks and computational processing, is applied to the forecasting. The different VMD decompositions of the MAVOA-DNC combination together with other comparative models are applied to example predictions at four sites in the Huaihe River Basin. The results show that SMFSD (Single-model Fully stepwise decomposition) is the most effective, and the average Root Mean Square Error (RMSE) of the forecasts for the four sites of SMFSD-MAVOA-DNC is 9.02, the average Mean Absolute Error (MAE) of 7.13, and the average Nash-Sutcliffe Efficiency (NSE) of 0.94. Compared with the traditional VMD full decomposition, the RMSE is reduced by 7.42, the MAE is reduced by 4.83, and the NSE is increased by 0.05; the best forecasting results are obtained compared with other coupled models.

Abstract In order to enhance the simulation of BMPs (Best Management Practices) reduction effects in unmonitored watersheds, in this study, we combined the physically-based hydrological model Soil & Water Assessment Tool (SWAT) and the data-driven model Bi-directional Long Short-Term Memory (Bi-LSTM), using the very-high-resolution (VHR) Land Use and Land Cover (LULC) dataset SinoLC-1 as data input, to evaluate the feasibility of constructing a water environment model for the Ba-River Basin (BRB) in central China and improving streamflow prediction performance. In the SWAT-BiLSTM model, we calibrated the top five SWAT parameters sorted by P-Value, allowing SWAT to act as a transfer function to convert meteorological data into base flow and storm flow, serving as the data input for the Bi-LSTM model. This optimization improved the Bi-LSTM's learning process for the relationship between the target and explanatory variables. The daily streamflow prediction results showed that the hybrid model had 9 regions rated as "Very good," 2 as "Good," 2 as "Satisfactory," and 1 as "Unsatisfactory" among the 14 regions. The model achieved an NSE of 0.86, R2 of 0.85, and PBIAS of −2.71% for the overall daily streamflow prediction performance during the verification period of the BRB. This indicates that the hybrid model has high predictive accuracy and no significant systematic bias, providing a sound hydrodynamic environment for water quality simulation. The simulation results of different BMPs scenarios showed that in the scenarios with only one BMP measure, stubble mulch had the best reduction effect, with average reductions of 17.83% for TN and 36.17% for TP. In the scenarios with a combination of multiple BMP measures, the combination of stubble mulch, soil testing and formula fertilization, and vegetative filter strip performed the best, achieving average reductions of 42.71% for TN and 50.40% for TP. The hybrid model provides a novel approach to simulate BMPs' reduction effects in regions without measured hydrological data and has the potential for wide application in BMP-related decision-making.

Abstract Against the backdrop of accelerated global climate change and urbanization, the frequency and severity of flood disasters have been increasing. In recent years, influenced by climate change, the Hai-River Basin (HRB) has experienced multiple large-scale flood disasters. During the widespread extraordinary flood event from July 28th to August 1st, 2023, eight rivers witnessed their largest floods on record. These events caused significant damage and impact on economic and social development. The development of hydrological models with better performance can help researchers understand the impacts of climate change, provide risk information on different disaster events within watersheds, support decision-makers in formulating adaptive measures, urban planning, and improve flood defense mechanisms to address the ever-changing climate environment. This study examines the potential for enhancing streamflow simulation accuracy in the HRB located in Northeast China by combining the physically-based hydrological model with the data-driven model. Three hybrid models, SWAT-D-BiLSTM, SWAT-C-BiLSTM and SWAT-C-BiLSTM with SinoLC-1, were constructed in this study, in which SWAT was used as a transfer function to simulate the base flow and quick flow generation process based on weather data and spatial features, and BiLSTM was used to directly predict the streamflow according to the base flow and quick flow. In the SWAT-C-BiLSTM model, SWAT parameters with P values less than 0.4 in each hydrological station-controlled watershed were calibrated, while the SWAT-D-BiLSTM model did not undergo calibration. Additionally, this study utilizes both 30 m resolution land use and land cover (LULC) map and the first 1 m resolution LULC map SinoLC-1 as input data for the models to explore the impact on streamflow simulation performance. Among five models, the NSE of SWAT-C-BiLSTM with SinoLC-1 reached 0.93 and the R2 reached 0.95 during the calibration period, and both of them stayed at 0.92 even in the validation period, while the NSE and R2 of the other four models were all below 0.90 in the validation period. The potential impact of climate change on streamflow in the HRB was evaluated by using predicted data from five global climate models from CMIP6 as input for the best-performing SWAT-C-BiLSTM with SinoLC-1. The results indicate that climate change exacerbates the uneven distribution of streamflow in the HRB, particularly during the concentrated heavy rainfall months of July and August. It is projected that the monthly streamflow in these two months will increase by 34% and 49% respectively in the middle of this century. Furthermore, it is expected that the annual streamflow will increase by 5.6% to 9.1% during the mid-century and by 6.7% to 9.3% by the end of the century. Both average streamflow and peak streamflow are likely to significantly increase, raising concerns about more frequent urban flooding in the capital economic region within the HRB.

Abstract The accurate prediction of monthly runoff in the lower reaches of the Yellow River is crucial for the rational utilization of regional water resources, optimal allocation, and flood prevention. This study proposes a VMD-SSA-BiLSTM coupled model for monthly runoff volume prediction, which combines the advantages of Variational Modal Decomposition (VMD) for signal decomposition and preprocessing, Sparrow Search Algorithm (SSA) for BiLSTM model parameter optimization, and Bi-directional Long and Short-Term Memory Neural Network (BiLSTM) for exploiting the bi-directional linkage and advanced characteristics of the runoff process. The proposed model was applied to predict monthly runoff at GaoCun hydrological station in the lower Yellow River. The results demonstrate that the VMD-SSA-BiLSTM model outperforms both the BiLSTM model and the VMD-BiLSTM model in terms of prediction accuracy during both the training and validation periods. The Root-mean-square deviation of VMD-SSA-BiLSTM model is 30.6601, which is 242.5124 and 39.9835 lower compared to the BiLSTM model and the VMD-BiLSTM model respectively; the mean absolute percentage error is 5.6832%, which is 35.5937% and 6.3856% lower compared to the other two models, respectively; the mean absolute error was 19.8992, which decreased by 136.7288 and 25.7274 respectively; the square of the correlation coefficient (R 2 ) is 0.93775, which increases by 0.53059 and 0.14739 respectively; the Nash–Sutcliffe efficiency coefficient was 0.9886, which increased by 0.4994 and 0.1122 respectively. In conclusion, the proposed VMD-SSA-BiLSTM model, utilizing the sparrow search algorithm and bidirectional long and short-term memory neural network, enhances the smoothness of the monthly runoff series and improves the accuracy of point predictions. This model holds promise for the effective prediction of monthly runoff in the lower Yellow River.

Abstract Accurate medium and long-term runoff forecasts play a vital role in guiding the rational exploitation of water resources and improving the overall efficiency of water resources use. Machine learning is becoming a common trend in time series forecasting research. Least squares support vector machine (LSSVM) and grey model (GM(1,1)) have received much attention in predicting rainfall and runoff in the last two years. “Decomposition-forecasting” has become one of the most important methods for forecasting time series data. Complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) decomposition method has powerful advantages in dealing with nonlinear data. Least squares support vector machine (LSSVM) has strong nonlinear fitting ability and good robustness. Gray model (GM(1,1)) can solve the problems of little historical data and low serial integrity and reliability. Based on their respective advantages, a combined CEEMDAN–LSSVM–GM(1,1) model was developed and applied to the runoff prediction of the lower Yellow River. To verify the reliability of the model, the prediction results were compared with the single LSSVM model, the CEEMDAN–LSSVM model and the CEEMDAN–support vector machines (SVM)–GM(1,1). The results show that the combined CEEMDAN–LSSVM–GM(1,1) model has a high accuracy and the prediction results are better than other models, which provides an effective prediction method for regional medium and long-term runoff prediction and has good application prospects.