Understanding of the spatial connections in rainfall is a challenging and essential groundwork for reliable modeling of catchment processes. Recent developments in network theory offer new avenues to understand of the spatial variability of rainfall. The Yellow River Basin (YRB) in China is spatially extensive, with pronounced environmental gradients driven primarily by precipitation and air temperature on broad scales. Therefore, it is an ideal region to examine the availability of network theory. The concepts of clustering coefficient, degree distribution and small-world network are employed to investigate the spatial connections and architecture of precipitation networks in the YRB. The results show that (1) the choice of methods has little effect on the precipitation networks, but correlation thresholds significantly affected vertex degree and clustering coefficient values of precipitation networks; (2) the spatial distribution of the clustering coefficient appears to be high–low–high from southeast to northwest and the vertex degree is the opposite; (3) the precipitation network has small-world properties in the appropriate threshold range. The findings of this paper could help researchers to understand the spatial rainfall connections of the YRB and, therefore, become a foundation for developing a hydrological model in further studies.

Ecological water replenishment (EWR) via interbasin water transfer projects has been regarded as a critical solution to reducing the risk of lake shrinkage and wetland degradation. The hydrological conditions of EWR water sources do not change synchronously, which may have an impact on the transferable water. Based on the GAMLSS model and the multivariate Copula model, this work presents a research approach for EWR via interbasin water transfer projects that can capture the non-stationarity of the runoff series and the frequency of dryness–wetness encounters, as well as speculates on various scenarios throughout the project operation phase. We present a case study on the Baiyangdian Lake, acting as the largest freshwater wetland in North China, which has suffered from severe degradation during the past decades and deserves thorough ecological restoration. The GAMLSS model was used to examine the non-stationarity characteristics of EWR water sources including the Danjiangkou Reservoir (DJK), the Huayuankou reach of the Yellow River (HYK), and upstream reservoirs (UR). The multivariate Copula model was implemented to evaluate the synchronous–asynchronous characteristics for hydrological probabilities for the multiple water sources. Results show that 1) significant non-stationarity has been detected for all water sources. Particularly, a significant decreasing trend has been found in UR and HYK. 2) The non-stationary model with time as the explanatory variable is more suitable for the runoff series of DJK, HYK, and UR. Under the non-stationary framework, the wet–dry classification of runoff series is completely changed. 3) Whether the bivariate or trivariate combination types, the asynchronous probability among the three water resources is over 0.6 except DJK-HYK, which indicates the complementary relationship. Multiple water resources are necessary for EWR. What is more, during a dry year of UR, the conditional probability that both DJK and HYK are in a dry year is 0.234. To alleviate the problem of not having enough water, some additional water resources and an acceptable EWR plan are required.

Reservoirs in the Daqing River mountainous area have always been an important source of replenishment for Baiyangdian Lake. With the development of water source economy and society, the reservoir’s ecological water replenishment potential for Baiyangdian Lake will undergo great changes. This article first analyzes the current situation of ecological water replenishment in Baiyangdian Lake. On this basis, the ecological water supply potential of the upstream reservoir to Baiyangdian Lake in the future was calculated. The results of the study show that from 2001 to 2018, the amount of water entering the upper reaches of the reservoir showed an overall upward trend, and the upward trend of runoff from the Xidayang Reservoir was the most obvious. Under different incoming water conditions, the ecological water supply potential of the upstream reservoir to Baiyangdian varies greatly. It can reach 320 million m3 in a wet year and only 50 million m3 in a dry year. In the continuous dry years, the average multi-year water supply potential of the reservoirs to the river and Baiyangdian Lake is about 146 million m3. The results of this paper can be used as a reference for Baiyangdian Lake’s ecological water replenishment scheduling

Understanding of the spatio-temporal propagation of drought is a challenging issue as the hydro-climatic processes are inter-connected. Recent developments in network theory offer new avenues to study the propagation of drought. Three metrics that quantify the strength, dominant orientation and distance of droughts are employed to investigate the spatio-temporal propagation. The results show that (1) the network approach based on the event synchronization is a useful tool to study the propagation of drought; (2) The drought events occurring in the south of the study area are more likely to spread outward, and the drought events occurring in the midwestern regions are more likely to be affected by drought events in other regions; (3) The dominant position of drought transmission in the study area has obvious regional characteristics. The midwestern regions are more susceptible to the influence of drought events in the western regions, while other regions are more likely to spread drought events to the inside world. The findings of this paper could help researchers to initially understand the propagation of spatio-temporal droughts over Eastern China.