Pan evaporation (E_pan) is an important indicator of regional evaporation intensity and degree of drought. However, although more evaporation is expected under rising temperatures, the reverse trend has been observed in many parts of the world, known as the “pan evaporation paradox”. In this paper, the Haihe River Basin (HRB) is divided into six sub-regions using the Canopy and k-means (The process for partitioning an N-dimensional population into k sets on the basis of a sample is called “k-means”) to cluster 44 meteorological stations in the area. The interannual and seasonal trends and the significance of eight meteorological indicators, including average temperature, maximum temperature, minimum temperature, precipitation, relative humidity, sunshine duration, wind speed, and E_pan, were analyzed for 1961 to 2010 using the trend-free pre-whitening Mann-Kendall (TFPW-MK) test. Then, the correlation between meteorological elements and E_pan was analyzed using the Spearman correlation coefficient. Results show that the average temperature, maximum temperature, and minimum temperature of the HRB increased, while precipitation, relative humidity, sunshine duration, wind speed and E_pan exhibited a downward trend. The minimum temperature rose 2 and 1.5 times faster than the maximum temperature and average temperature, respectively. A significant reduction in sunshine duration was found to be the primary factor in the E_pan decrease, while declining wind speed was the secondary factor.

Droughts often have a substantial impact on normal socio-economic activities and agricultural production. The Haihe River Basin, one of the primary food production areas in China, has become increasingly sensitive to alternating droughts and floods, and the sharp transitions between them, due to rapid economic development and population growth combined with climate change. In this study, we employ the self-organizing map (SOM) neural network method to perform a cluster analysis on 43 meteorological stations in the study area, dividing the basin into five sub-regions. Then daily precipitation data (1960–2015) are collected, and the number of continuous dry days is used as a drought index to investigate drought evolution trends. Lastly, the Pearson-III curve is used to analyze the first daily precipitation after different drought duration, and the relationships between precipitation intensity, drought duration, and interdecadal drought frequency are observed. The results demonstrate that under the climate warming of the Haihe River Basin, the frequency of droughts increases throughout the whole basin, while the droughts are of shorter duration, the probability of more intense first daily precipitation after droughts increases during the dry–wet transition. The research provides a useful reference for the planning and management of water resources in the Haihe River Basin.

The impact of global climate change on the temporal and spatial variations of precipitation is significant. In this study, daily temperature and precipitation data from 258 meteorological stations in the Haihe River Basin, for the period 1960–2020, were used to determine the trend and significance of temperature and precipitation changes at interannual and interseasonal scales. The Mann–Kendall test and Spearman’s correlation analysis were employed, and significant change trends and correlations were determined. At more than 90% of the selected stations, the results showed a significant increase in temperature, at both interannual and interseasonal scales, and the increasing trend was more significant in spring than in other seasons. Precipitation predominantly showed a decreasing trend at an interannual scale; however, the change trend was not significant. In terms of the interseasonal scale, the precipitation changes in spring and autumn showed an overall increasing trend, those in summer showed a 1:1 distribution ratio of increasing and decreasing trends, and those in winter showed an overall decreasing trend. Furthermore, the Spearman’s correlation analysis showed a negative correlation between temperature and precipitation in the entire Haihe River Basin, at both interannual and interseasonal scales; however, most of the correlations were weak.

The spatio-temporal variation of precipitation under global warming had been a research hotspot. Snowfall is an important part of precipitation, and its variabilities and trends in different regions have received great attention. In this paper, the Haihe River Basin is used as a case, and we employ the K-means clustering method to divide the basin into four sub-regions. The double temperature threshold method in the form of the exponential equation is used in this study to identify precipitation phase states, based on daily temperature, snowfall, and precipitation data from 43 meteorological stations in and around the Haihe River Basin from 1960 to 1979. Then, daily snowfall data from 1960 to 2016 are established, and the spatial and temporal variation of snowfall in the Haihe River Basin are analyzed according to the snowfall levels as determined by the national meteorological department. The results evalueted in four different zones show that (1) the snowfall at each meteorological station can be effectively estimated at an annual scale through the exponential equation, for which the correlation coefficient of each division is above 0.95, and the relative error is within 5%. (2) Except for the average snowfall and light snowfall, the snowfall and snowfall days of moderate snow, heavy snow, and snowstorm in each division are in the order of Zones III > IV > I > II. (3) The snowfall and the number of snowfall days at different levels both show a decreasing trend, except for the increasing trend of snowfall in Zone I. (4) The interannual variation trend in the snowfall at the different levels are not obvious, except for Zone III, which shows a significant decreasing trend.

The reasonable allocation of water resources using different optimization technologies has received extensive attention. However, not all optimization algorithms are suitable for solving this problem because of its complexity. In this study, we applied an ameliorative multi-objective gray wolf optimizer (AMOGWO) to the problem. For AMOGWO, which is based on the multi-objective gray wolf optimizer, we improved the distance control parameter calculation method, added crowding degree for the archive, and optimized the selection mechanism for leader wolves. Subsequently, AMOGWO was used to solve the multi-objective optimal allocation of water resources in Handan, China, for 2035, with the maximum economic benefit and minimum social water shortage used as objective functions. The optimal results obtained indicate a total water demand in Handan of 2740.43 × 10⁶ m³, total water distribution of 2442.23 × 10⁶ m³, and water shortage of 298.20 × 10⁶ m³, which is consistent with the principles of water resource utilization in Handan. Furthermore, comparison results indicate that AMOGWO has substantially enhanced convergence rates and precision compared to the non-dominated sorting genetic algorithm II and the multi-objective particle swarm optimization algorithm, demonstrating relatively high reliability and applicability. This study thus provides a new method for solving the multi-objective optimal allocation of water resources.