Optimal reservoir operation is an important measure for ensuring flood-control safety and reducing disaster losses. The standard particle swarm optimization (PSO) algorithm can find the optimal solution of the problem by updating its position and speed, but it is easy to fall into a local optimum. In order to prevent the problem of precocious convergence, a novel simulated annealing particle swarm optimization (SAPSO) algorithm was proposed in this study, in which the Boltzmann equation from the simulated annealing algorithm was incorporated into the iterative process of the PSO algorithm. Within the maximum flood peak reduction criterion, the SAPSO algorithm was used into two floods in the Tianzhuang–Bashan cascade reservoir system. The results shown that: (1) There are lower maximum outflows. The maximum outflows of Tianzhuang reservoir using SAPSO algorithm decreased by 9.3% and 8.6%, respectively, compared with the measured values, and those of Bashan reservoir decreased by 18.5% and 13.5%, respectively; (2) there are also lower maximum water levels. The maximum water levels of Tianzhuang reservoir were 0.39 m and 0.45 m lower than the measured values, respectively, and those of Bashan reservoir were 0.06 m and 0.46 m lower, respectively; and (3) from the convergence processes, the SAPSO algorithm reduced the convergence speed in the early stage of convergence and provided a superior objective function value than PSO algorithm. At the same time, by comparing with GA algorithm, the performance and applicability of SAPSO algorithm in flood operation are discussed further. Thus, the optimal operation model and SAPSO algorithm proposed in this study provide a new approach to realizing the optimal flood-control operation of cascade reservoir systems.

The performance evaluation of a city’s flood control system is essentially based on accurate storm designs, where a particular challenge is the development of the joint distributions of dependent rainfall variables. When it comes to the research design for consecutive rainfall, the analytical investigation is only focused on the maximum of consecutive rainfalls, and it does not consider the probabilistic relations between the first day of rainfall and the overall rainfall included in consecutive rainfall events. In this study, the copula method is used to separate the dependence structure of multi-day rainfall from its marginal distribution and analyse the different impacts of the dependence structure and marginal distribution on system performance. Three one-parameter Archimedean copulas, including the Clayton, Gumbel, and Frank families, are fitted and compared for different combinations of marginal distributions that cannot be rejected by statistical tests. The fitted copulas are used to generate rainfall events for a system performance analysis, including the conditional probability and design values for different return periods. The results obtained in this study highlight the importance of taking into account the dependence structure of one-day and multi-day rainfall in the context of storm design evaluations and reveal the different impacts of the dependence structure and the marginal distributions on the probability.

Radar-rain gauge merging methods have been widely used to produce high-quality precipitation with fine spatial resolution by combing the advantages of the rain gauge observation and the radar quantitative precipitation estimation (QPE). Different merging methods imply a specific choice on the treatment of radar and rain gauge data. In order to improve their applicability, significant studies have focused on evaluating the performances of the merging methods. In this study, a categorization of the radar-rain gauge merging methods was proposed as: (1) Radar bias adjustment category, (2) radar-rain gauge integration category, and (3) rain gauge interpolation category for a total of six commonly used merging methods, i.e., mean field bias (MFB), regression inverse distance weighting (RIDW), collocated co-kriging (CCok), fast Bayesian regression kriging (FBRK), regression kriging (RK), and kriging with external drift (KED). Eight different storm events were chosen from semi-humid and semi-arid areas of Northern China to test the performance of the six methods. Based on the leave-one-out cross validation (LOOCV), conclusions were obtained that the integration category always performs the best, the bias adjustment category performs the worst, and the interpolation category ranks between them. The quality of the merging products can be a function of the merging method that is affected by both the quality of radar QPE and the ability of the rain gauge to capture small-scale rainfall features. In order to further evaluate the applicability of the merging products, they were then used as the input to a rainfall-runoff model, the Hybrid-Hebei model, for flood forecasting. It is revealed that a higher quality of the merging products indicates a better agreement between the observed and the simulated runoff.

Water resource spatial equilibrium evaluations provide the bases for water resource utilization and allocation. To analyze the regional spatial water resource matching balance, this study constructed a water resource spatial matching model based on the Gini coefficient and Lorenz curve methods. To further reflect the influence of each subregion on the whole region, we combined the correlation number and Gini coefficient methods to propose the water resource spatial balance evaluation method. Herein, we constructed nine Lorenz curve pairs that matched the total water resources and total water use with cultivated land area, population, GDP (Gross Domestic Product) of the secondary industry, GDP (Gross Domestic Product) of the tertiary industry, and agricultural irrigation water consumption. Set pair analysis theory was applied to calculate sample correlation numbers and determine equilibrium levels, which were then compared to Gini coefficient method-based results for Tai’an city evaluation. The results showed that the total water consumption spatial equilibrium in Tai’an city from 2011 to 2020 was favorable, while the total water resource results for Tai’an city greatly differed, especially the balance between total water resources and GDPs of the secondary and tertiary industries, which should be further improved. In practice, quantitative analysis of the water resource spatial equilibrium state in Tai’an city is important for efficient water resource utilization and coordinated development of water resources and economic and social environments.

HIGHLIGHTS. A de-nonstationarity method is used to remove the nonstationary influence and transform the nonstationary annual runoff series.The climate change fa

Short-term heavy precipitation is a crucial factor that triggers urban waterlogging and flash flood disasters, which impact human production and livelihood. Traditional short-term forecasting methods have time- and scale-based limitations. To achieve timely, location-specific, and quantitative precipitation forecasting, this study applies the precipitation spectral decomposition algorithm, along with variational echo tracking and autoregressive AR2 extrapolation techniques, to forecast three cases of heavy precipitation events during the rainy season in Hebei Province. The variational optical flow extrapolation forecasting based on precipitation spectral decomposition has a forecasting lead time of up to 3 h. However, noticeable discrepancies in forecast accuracy can be observed around 2 h, and the forecasting skill gradually weakens with longer lead times. For 3 h lead time forecasts, substantial variability occurs among different performance metrics, lacking clear comparability. The effective forecast lead time for variational optical flow forecasting based on precipitation spectral decomposition is up to 1.6 h for severe convective weather systems and up to 2.2 h for stratiform cloud weather systems. Overall, the forecast effect of this method is good in the three rainfalls—the highest CSI is up to 0.74, the highest POD is up to 0.87, and the forecast accuracy and success rate are high.