This paper innovatively proposes the Black Kite Algorithm (BKA), a meta-heuristic optimization algorithm inspired by the migratory and predatory behavior of the black kite. The BKA integrates the Cauchy mutation strategy and the Leader strategy to enhance the global search capability and the convergence speed of the algorithm. This novel combination achieves a good balance between exploring global solutions and utilizing local information. Against the standard test function sets of CEC-2022 and CEC-2017, as well as other complex functions, BKA attained the best performance in 66.7, 72.4 and 77.8% of the cases, respectively. The effectiveness of the algorithm is validated through detailed convergence analysis and statistical comparisons. Moreover, its application in solving five practical engineering design problems demonstrates its practical potential in addressing constrained challenges in the real world and indicates that it has significant competitive strength in comparison with existing optimization techniques. In summary, the BKA has proven its practical value and advantages in solving a variety of complex optimization problems due to its excellent performance. The source code of BKA is publicly available at https://www.mathworks.com/matlabcentral/fileexchange/161401-black-winged-kite-algorithm-bka.

To address the prominent problem of declining runoff in many rivers around the world, studying the law of runoff change and attribution analysis is very important for the planning and management of watershed water resources and has practical significance for solving the imbalance between supply and demand of watershed water resources and maintaining the healthy development of rivers. Three commonly used coupled water-energy balance equations based on Budyko hypothesis are selected to estimate the elasticity coefficient of runoff change to each driving factor, and the contribution rate of different factors to runoff change in the study area is quantified by the total differential method and the complementary method, respectively. The results show that the runoff of Huangfuchuan River basin showed a significant decreasing trend from 1954 to 2015, and the runoff mutation points were 1979 and 1996; in the alteration period I (1979–1996), precipitation was the main factor leading to the runoff reduction in Huangfuchuan River basin, followed by the influence of underlying surface; the contribution rate of underlying surface to runoff alterations ranged from 63.7% to 65.46%; the impact of potential evapotranspiration was slightly smaller. In the alteration period II (1997–2015), the underlying surface played a dominant role in runoff reduction of Huangfuchuan River basin. The contribution rate of the underlying surface to runoff change ranged from 80.21% to 86.34%, followed by precipitation, and the potential evapotranspiration had the least impact. The impact of human activities on the whole watershed increased with the passage of time. The land use change, the overall increase of NDVI (vegetation cover) and the construction of water conservation projects are important reasons for the reduction of runoff in Huangfuchuan River basin.

Studying the response of runoff to climate change and land use/cover change has guiding significance for watershed land planning, water resource planning, and ecological environment protection. Especially in the Yellow River Basin, which has a variable climate and fragile ecology, such research is more important. This article takes the Huangfuchuan River Basin (HFCRB) in the middle reaches of the Yellow River as the research area, and analyzes the impact of climate change scenarios and land use/cover change scenarios on runoff by constructing a SWAT model. Using CMIP6 GCMs to obtain future climate data and the CA–Markov model to predict future land use data, the two are coupled to estimate the future runoff process in the HFCRB, and the uncertainty of the estimated runoff is decomposed and quantified. The results were as follows: ① The SWAT model has good adaptability in the HFCRB. During the calibrated period and the validation period, R² ≥ 0.84, NSE ≥ 0.8, and |PBIAS| ≤ 17.5%, all of which meet the model evaluation criteria. ② There is a negative correlation between temperature and runoff, and a positive correlation between precipitation and runoff. Runoff is more sensitive to temperature rise and precipitation increase. ③ The impact of land use types on runoff is in the order of cultivated land > grassland > forest land. ④ The variation range of runoff under the combined effects of future climate change and LUCC is between that of single climate change or LUCC scenarios. The increase in runoff under SSP126, SSP245, and SSP585 scenarios is 10.57%, 25.55%, and 31.28%, respectively. Precipitation is the main factor affecting the future runoff changes in the HFCRB. Model uncertainty is the main source of uncertainty in runoff prediction.